CHAPTER 1
INTRODUCTION
Overview
This chapter deals with the general introduction of the study and sequentially presents
the background to the study, statement of the problem, purpose of the study, research
questions, rationale of the study, significance of the study, delimitation, limitation and
finally the organisation of the study
Background to the study:
To teach all students according to today’s standards, teachers need to have deeper
understanding of the subject matter (concepts) so that they can help students create
useful cognitive maps, relate one idea to another, and address misconceptions.
Teachers need to see how ideas connect across fields and to everyday life. This kind
of understanding provides a foundation for pedagogical content knowledge that
enables teachers to make ideas accessible to others (Shulman, 1987).
Shulman (1986) introduced the phrase pedagogical content knowledge and sparked a
whole new wave of scholarly articles on teachers' knowledge of their subject matter
and the importance of this knowledge for successful teaching. In Shulman's
theoretical framework, teachers need to master two types of knowledge: (a) content,
also known as "deep" knowledge of the subject itself, and (b) knowledge of the
curricular development. Content knowledge encompasses what Shulman (1992) cited
as the "structure of knowledge", (p.14) the theories, principles, and concepts of a
particular discipline. Especially important is content knowledge that deals with the
1
teaching process, including the most useful forms of representing and communicating
content and how students can best learn the specific concepts and topics of a subject.
"If beginning teachers are to be successful, they must wrestle simultaneously with
issues of pedagogical content (knowledge) as well as general pedagogy (generic
teaching principles)" (Grossman, 1989, Thomas, & Lasley, 2000).
Shulman (1986, 1987, 1992) created a Model of Pedagogical Reasoning, which
comprises a cycle of several activities that a teacher should complete for good
teaching. According to him, comprehension, transformation, instruction, evaluation,
reflection, and new comprehension are the major steps one may go through during
pedagogical reasoning.
To him, to teach is to first understand purposes, subject matter structures, and ideas
within and outside the discipline. He believes that teachers need to understand what
they teach and, when possible, to understand it in several ways. Comprehension of
purpose is very important. Shulman, 1992, reiterates the we engage in teaching to
achieve the following educational purposes to; help students gain literacy, enable
students to use and enjoy their learning experiences, enhance students’ responsibility
to become caring people, teach students to believe and respect others, contribute to
the well-being of their community, give students the opportunity to learn how to
inquire and discover new information, help students develop broader understandings
of new information and to help students develop the skills and values they will need
to function in a free and just society.
Shulman, 1992, is of the view that the key to distinguishing the knowledge base of
teaching lies in the intersection of content and pedagogy in the teacher’s capacity to
2
transform content knowledge into forms that are pedagogically powerful and yet
adaptive to the variety of student abilities and backgrounds. Comprehended ideas
must be transformed in some manner if they are to be taught. Transformations require
some combination or ordering of the following processes.
During preparation of the given text material which includes the process of critical
interpretation, representation of the ideas in the form of new analogies and metaphors
(Teachers' knowledge, including the way they speak about teaching, not only
includes references to what teachers “should” do, it also includes presenting the
material by using figurative language and metaphors [Glatthorn, 1990]), instructional
selections from among an array of teaching methods and models, adaptation of
student materials and activities to reflect the characteristics of student learning styles
and tailoring the adaptations to the specific students in the classroom are carried and
figured out by teachers.
Glatthorn (1990) described this as the process of fitting the represented material to the
characteristics of the students. The teacher must consider the relevant aspects of
students’ ability, gender, language, culture, motivations, or prior knowledge and skills
that will affect their responses to different forms of presentations and representations.
At instruction, teachers combine variety of teaching acts, including many of the most
crucial aspects of pedagogy: management, presentations, interactions, group work,
discipline, humor, questioning, and discovery and inquiry instruction. Teachers need
to think about testing and evaluation as an extension of instruction, not as separate
from the instructional process. The evaluation process includes checking for
understanding and misunderstanding during interactive teaching as well as testing
3
students’ understanding at the end of lessons or units. It also involves evaluating one’s
own performance and adjusting for different circumstances.
It is pertinent that teachers carry out reflective practice after every lesson. This
process includes reviewing, reconstructing, reenacting, and critically analyzing one’s
own teaching abilities and then grouping these reflected explanations into evidence of
changes that need to be made to become a better teacher. This is what a teacher does
when he or she looks back at the teaching and learning that has occurred–reconstructs,
reenacts, and recaptures the events, the emotions, and the accomplishments. Ornstein,
Thomas and Lasley (2000), argued that reflection is an important part of professional
development. All teachers must learn to observe outcomes and determine the reasons
for success or failure. Through reflection, teachers focus on their concerns, come to
better understand their own teaching behaviour, and help themselves or colleagues
improve as teachers. Through reflective practices in a group setting, teachers learn to
listen carefully to each other, which also give them insight into their own work
(Ornstein, Thomas & Lasley, 2000).
Shulman, 1992 further noted that at the final stage of teaching, teachers through acts
of teaching that are "reasoned" and "reasonable," achieves new comprehension of the
educational purposes, the subjects taught, the students, and the processes of pedagogy
themselves (Brodkey, 1986).
Students (the teacher’s audience) are another important element for the teacher to
consider while using a pedagogical model. A skillful teacher figures out what
students know and believe about a topic and how learners are likely to relate to new
ideas. Teaching in ways that connect with students also requires an understanding of
4
differences that may arise from culture, family experiences, developed intelligences,
and approaches to learning. Teachers need to build a foundation of pedagogical
learner knowledge (Grimmet & Mackinnon, 1992).
To help all students learn, teachers need several kinds of knowledge about learning.
They need to think about what it means to learn different kinds of material for
different purposes and how to decide which kinds of learning are most necessary in
different contexts. Teachers must be able to identify the strengths and weaknesses of
different learners and must have the knowledge to work with students who have
specific learning disabilities or needs. Teachers need to know about curriculum
resources and technologies to connect their students with sources of information and
knowledge that allow them to explore ideas, acquire and synthesize information, and
frame and solve problems. Acquiring this sophisticated knowledge and developing a
practice that is different from what teachers themselves experienced as students,
requires learning opportunities for teachers that are more powerful than simply
reading and talking about new pedagogical ideas (Ball & Cohen, 1996). This kind of
learning cannot occur in college classrooms divorced from practice or in school
classrooms divorced from knowledge about how to interpret practice. Good settings
for teacher learning in both colleges and schools provide lots of opportunities for
research and inquiry, for trying and testing, for talking about and evaluating the
results of learning and teaching.
It may be fashionable to suggest that different people's theories about how the world
works are equally valid. This means that we all construct our own mental structure of
ideas (cognitive structure) and hence everybody's cognitive structure is unique and
completely different from others. This is inevitable since each person's individual
5
cognitive structure is the total result of his or her unique life experience. But, if we
are to communicate and work with each other, we have to share common ideas.
Parts of our cognitive structures must be similar enough to the relevant parts of
other people's cognitive structures to make this possible. If we do not share common
conceptions of what a resistor is, what potential difference is, what stress and strain
are, what reflection of light mean and so on for example, we cannot make any
progress together. Indeed, a very large part of the training of engineers is learning a
whole set of man-made conventions and standards so that they can work productively
within the existing engineering community.
Teachers teach what they know is standard and acceptable to the masses. Invariably,
the aim of teaching and learning is to change peoples’ mental structures to conform to
what is thought of as the scientifically valid, hence the term 'Conceptual Change'.
What we do as teachers when we teach scientific principles is not actually teaching
students how the world really works. We rather teach them our shared conception or
model of how the world works. We cannot teach our students what the world is; only
how we see the world. This is an important distinction, because although we may not
be able to define right and wrong as regards what the world is, we can define right and
wrong as regards students' conceptions of our models of the world. We are entitled to
insist that students must come to what we consider to be a correct understanding of
our models of the world, to share our conceptions, and to describe other ways of
looking at these models as misconceptions. It also means that we do not have to think
that students should always “discover” how the world works for themselves. This is
totally unrealistic anyway, alas it has taken countless people thousands of years to
develop the models we now use in modern science (geometrical optics), and even an
6
Einstein cannot achieve even a fraction of this learning by himself. However, for
much of the time what teachers seek is not for the individual learner to develop their
own theory of how the world works, but that they come to share our existing theory
(Warren, 2004).
It is also evident that conceptions of knowledge, learning and instruction are related to
the way teachers design their learning environment, how they define their tasks and
how they interact with students (Kember, 1997; Tillema, 1994, 1995).
A number of studies have also investigated students' conceptions of learning in higher
education and their significance in the learning processes (Eklund-Myrskog, 1998;
Marra, Palmer, & Litzinger, 2000) and other studies have examined the relationships
between students' conceptions of learning and deep learning approaches (Chin &
Brown, 2000; Trigwell & Prosser, 1991). Since deep learning approaches lead to
better learning outcomes, understanding students' conceptions of learning is
important.
From the foregoing evidence it is an undisputable fact that students have some
knowledge no matter how small in many areas of science such as electricity, light,
solar system, plants, animals, cells, and energy before entering the formal classroom.
This existing knowledge in various areas has been constructed through their
experiences or through informal learning (Fetherstonhaugh & Treagust, 1992). Some
researchers have called this prior conception, alternative conception and
misconception (Al-Rubayea, 1996) among others but this researcher prefers to call
this knowledge as students’ level of understanding of these concepts. Some of these
levels of understanding need to provide exploration grounds for teachers to challenge
7
and as it were provide a better platform for better understanding of concepts by
learners.
Moreover, since these levels of understanding help the students to understand the
world in which they live, they are resistant to change and obstruct the learning process
(Klammer, 1998).
If the teachers to be (teacher trainees), lack the basic concepts to impact and as well
do not understand the concepts they teach, then, it can be equally impossible for them
to teach these concepts to their students in order to redirect their concept about the
world.
Recent observations made by the researcher during a couple of geometric optics
lessons taught by some science teacher trainees during their teaching practice have
shown that some science teacher trainees lack basic concepts in geometrical optics
and that their level of understanding in geometric optics (transmission of light energy)
is woefully inadequate. Typical examples of findings from these observations include:
light can only be reflected from shiny surfaces such as mirrors, and colour is an
intrinsic property of an object. Trainees also believe that an object cannot absorb and
reflect light at the same time; it must do one or the other. Of course, the correct
concept is that, all objects absorb and reflect light to different degrees. Our ability to
see objects depends on the reflection of light.
At least as a teacher, knowing that what teachers know and understand is what they
pass on to learners and also realizing that the performance of students is basically
dependent on what the teacher teaches, it became imperatively necessary to research
into how teachers acquire their knowledge and how they understand what they teach;
especially geometrical optics and to make some recommendations that will possibly
8
remedy the situation if there is actually a problem which the researcher believes there
is.
Statement of the problem
Recent observation made by the researcher in some selected Science Colleges of
Education during some science lessons on the concept of light energy (geometrical
optics) indicated that most science teacher trainees lack the concepts of reflection and
refraction in geometrical optics. In the various lessons observed it was evident that the
teacher trainees’ level of understanding in geometric optics was woefully inadequate.
The main problem under investigation is that ‘the science teacher trainees’
understanding of the concept of geometrical optics impart negatively on the way they
teach and as well on the performance of their prospective students.
Purpose of the study
The purpose of this study is to:
1. find out what the science teacher trainees’ know and understand about
geometric optics in the selected Special Science Colleges of Education in
Ghana.
2. offer some useful suggestions in the form of a course manual and hints that
will help remedy the situation during teaching and learning.
3. design model for the teaching of geometrical optics in the special science
colleges of education.
9
Research questions
The research was guided by the following research questions:
1. What is the extent of science teacher trainees’ understanding of geometrical
optics?
2. To what extent does the science teacher trainees’ understanding of the concept
of geometrical optics affect their teaching?
3. How significant is the science teacher trainees’ understanding of the concept
of geometrical optics affect students’ understanding of geometrical optics and
hence their performance?
Significance of the study
This study will help:
1. teachers will use the course manual and model lessons to improve upon the
teaching of geometrical optics.
2. students’ performance in geometrical optics will improve significantly.
3. curriculum developers will make further follow up upon the advice given in
the course manual and the model lessons of this study to design science
curriculum so as to reflect the needs and aspiration of the people.
4. textbook writers will address the basic concepts in geometrical optics
following the suggestions in the model lessons as well as the course manual in
order to facilitate teaching and learning.
10
Delimitation
Science is a broad subject with numerous theories from which many concepts can be
drawn. In this study, the focus is on science teacher trainees’ understanding of the
concept reflection and refraction in geometrical optics. The study seeks to involve a
sample size of hundred (100) teacher trainees drawn from the five (5) Science
Colleges of Education out of the sixteen (16) Science Colleges of Education in Ghana.
Limitation
In every human activity, there is a trace of imperfection. The limitation deals with the
problems that the researchers come face to face with during the study which in one
way or the order hinder the hundred percent success or otherwise total coverage of
problem area in the research work.
There was inadequate time for the researcher to move into other areas of the study
that will probably make the study rich. For example, finding how gender may affect
science teacher trainees’ understanding of geometric optics. It was also envisage that
the pilot testing could affect the validity of the study. This could result from what
Wilson & Putnam, 1982 termed as reactive or interaction effect of testing: a pretest
might increase or decrease a subject's sensitivity or responsiveness to the
experimental variable; hence the group used for the pilot test was not included in the
main study. The validity of the study could also be affected by Interaction effects of
selection biases and the experimental variable.
Organization of the Study
The study has been organized into five chapters and each chapter has sections and
sub-sections.
Chapter One deals with the following sections such as background to the study,
11
statement of the problem, purpose of the study, research questions, significance of the
study, delimitation, limitation, organizations of the study.
Chapter Two is made up of the review of related literature materials. It deals with how
other people perceived and expressed their thoughts about the materials used.
Chapter Three also gives account of the methods and procedures employed by the
researcher to collect data. It covers population, sampling work and administration of
instruments and data analysis.
Chapter Four discusses results of the study, showing an in-depth analysis of
observations recorded.
Chapter Five finally deals with conclusion drawn form the analysis and data collected
and also puts forward some recommendations and suggestion.
Definition of abbreviations
ITGO: Inventory Test on Geometrical Optics
BS9: Basic School Nine (JHS 3)
UCC: University of Cape Coast
12
CHAPTER TWO
LITERATURE REVIEW
Overview
Cognitive research demonstrates that people work best with and within a complex
system if they have a "mental model" of the system - that is, an idea of all of its parts,
what each does, how they work together and how changes in one part of the system
cause changes in other parts. This mental model permits flexibility in responding to
unexpected situations. One important function of schooling is to develop the
knowledge and mental skills students will need to construct appropriate mental
models of systems with which they will eventually work (Resnick, 1987)
It is an undisputable fact that students have some knowledge no matter how small in
many areas of science such as electricity, light, solar system, plants, animals, cells,
and energy before entering the formal classroom. As mentioned earlier in this
research, the researcher prefers to call this knowledge as students’ level of
understanding of these concepts. Some of these levels of understanding need to
provide exploration grounds for teachers to challenge and as it were provide a better
platform for better understanding of concepts by learners. The literature review on
this research work discusses students’ level of understanding on geometric optics
(light energy). The review explored such areas as:
1. What does it mean to understand something?
2. General knowledge about students’ understanding of concepts
3. Theoretical framework on students’ conceptions
13
4. Information about knowledge
5. Some students’ understanding of geometrical optics (transmission of
light)
6. Some methods of identifying students’ level of understanding of a
concept
7. Ways by which understanding of a concept affect teaching and
learning against students, performance.
8. Impact of teachers’ understanding of geometric optics on their
instructional practices
What does it mean to understand something?
At the heart of teaching for understanding lies a very basic question: What does it
mean to understand something? To draw a comparison, when a student knows
something, the student can bring it forth upon call to tell us the knowledge or
demonstrate the skill. But understanding something is a more subtle matter (Perkins,
1992). A student might be able to regurgitate reams of facts and demonstrate routine
skills with very little understanding. Somehow, understanding goes beyond knowing.
But how?
According to Perkins (1992) the meaning of understanding can be viewed in
contemporary research as in the practices of teachers with a knack for teaching for
understanding which they called performance perspective" on understanding. This
was based on a formulated conception of understanding consonant. This perspective
reflects the general spirit of "constructivism" prominent in contemporary theories of
14
learning (Duffy & Jonassen, 1992) and offers a specific view of what learning for
understanding involves. This perspective helps to clarify what understanding is and
how to teach for understanding by making explicit what has been implicit and making
general what has been phrased in more restricted ways (Gardner, 1991; Perkins,
1992).
In brief, this performance perspective says that understanding a topic of study is a
matter of being able to perform in a variety of thought-demanding ways with the
topic, for instance to: explain, muster evidence, find examples, generalize, apply
concepts, analogize and represent in a new way. Perkins, 1992 cited an example that
supposing a student "knows" Newtonian physics: The student can write down
equations and apply them to three or four routine types of textbook problems. In itself,
this is not convincing evidence that the student really understands the theory. The
student might simply be parroting the test and following memorized routines for stock
problems but supposing the student can make appropriate predictions about the
snowball fight in space then the student’s knowledge goes beyond just knowing.
Moreover, supposing the student can find new examples of Newton's theory at work
in everyday experience, e.g., why do assistant referees need to be so big? (Answer: So
they will have high inertia.), and is able to make other extrapolations, the more we are
convinced that the student understands. In short, the more thought-demanding
performances the student can display, the more confident we would be that the
student understands.
In summary, understanding something is a matter of being able to carry out a variety
of "performances" concerning the topic (Perkins, 1992).
15
General knowledge about students' understanding of concepts
There have been a lot of studies conducted in science education. Many of these
studies were interested in students’ ideas concerning phenomena taught in science.
These studies’ results show that students come to class with their existing knowledge
that they construct with their experiences or formal learning (Fetherstonhaugh &
Treagust, 1992). Students’ prior knowledge is called preconceptions. Some of these
preconceptions are in conflict with the scientific view. Preconceptions which are in
conflict with the scientific view are misconceptions. In this literature misconceptions
have also been called students’ level of understanding of concepts.
It is important to understand that not all preconceptions are wrong (Klammer, 1998).
If a student has an understanding of a concept, his/her understanding may not be true
even though it works for the student (Eryılmaz & Sürmeli, 2002).
In the past students were thought of as empty entities when they came to classes. The
role of the teachers was to fill these empty entities with knowledge. If the students’
minds are filled with misconceptions, where do they originate from? What are the
sources of students' knowledge in concepts? According to Klammer (1998), the
sources are experiences, language and a curriculum of “truths”
For example, students experience that feathers fall down more slowly to the ground
than do stones. However, when students in secondary schools are confronted with the
experiment that stones and feathers fall at the same rate in a vacuum, they are
confused and surprised with this situation, because, their experiences and the
experiment are in conflict. Similarly, there are many metaphors ingrained in language.
Although these metaphors help the students understand the world they do not function
in scientific fields every time.
16
Reiner, Slotta, Chi and Resnick (2000), stated that students’ understanding of
concepts can stem from their substance-based knowledge. Students try to assimilate
new physics knowledge with their substance-based knowledge. For example, they
consider force as a property of moving objects. They tend to understand abstract
physics concepts with properties of material substances such as force, heat, electricity
and light. In the absence of relevant knowledge, students explain some of these
concepts with the materialistic language that is used in everyday language as well as
in the science classroom. For example, “close the door, you are letting all the heat
out,” “throw some more light on things,” etc. These concepts seem difficult for them
to learn. Therefore, students have too many robust meanings in these concepts.
Al-Rubayea (1996) interestingly stated that the sources of students' knowledge were
teachers and textbooks. He investigated secondary school students’ physics
misconceptions in Nigeria and administered a 20 item multiple-choice test to the
students from eight schools. He also gave the test to the teachers in these schools. He
found some misconceptions among the students. The results also showed that teachers
had similar misconceptions in the same area of physics that the students had.
Researches on peoples’ misconceptions show that misconception is resistant to
change because they help students to understand the world around them. Dupin and
Johsua (1989) investigated students’ misconceptions about direct-current electricity.
They concluded that some of the misconceptions can be overcome by teaching;
however, some are resistant to change.
According to Perkins and Simmons (1988) the term “naive knowledge” refers the
misconceptions which retain after instruction. He believed that to incorporate some
new knowledge, learners must change the connections among the things they already
17
know. The alternatives to the necessary restructuring are to distort the new
information to fit their old ideas or to reject the new information entirely.
According to Perkins and Simmons (1988), students do not understand the physical
science with deep understanding. Although, they are able to pass almost any
examination through the memorization of basic problem skills, they do not understand
the principles involved in the problems.
To sum up, misconceptions have become a part of science education. Researchers
have done lots of studies to investigate students’ misconceptions. Teachers should
take them seriously in order to teach their students in a more reliable way.
Theoretical framework on students’ conception
Theories which have been presented by Ausubel (1963) and Gagne (1985) have a
commonality in that they postulate that new knowledge is acquired based on existing
knowledge. In other words, these theories share a constructivist view, maintaining that
people acquire and organize new knowledge logically consistent with existing
knowledge. According to the constructivist view, if people have incorrect knowledge
about a phenomenon, and are given incorrect information about it by any media, they
continue to hold the incorrect knowledge. If people have incorrect knowledge about a
phenomenon, and are given correct information about it, they may change their
existing knowledge and accommodate the new conflicting idea, or they may keep the
existing incorrect knowledge, not reorganizing mutual contradictions between the
existing and new given idea or ignoring the new and less familiar idea (Hewson &
Hewson, 1984).
18
Information about knowledge
The field of psychology started to influence education and was used to explain
learning process. The spectrum of learning theories consists of many approaches or
ways of explaining how humans learn. Behaviourism, cognitivism and constructivism
are three fundamental theories. Theorists of behaviourism are J. B Watson, E. L
Thorndike and B. F. Skinner (http://www.learning-theories.com). They focused on
behaviour rather than internal thought process. According to them, learning is
manifested by a change in behaviour and that the environment shapes what one learns.
Skinner, 1953) studied operant conditioning and explained that learning occurs
through positive reinforcement and that old patterns are abandoned by negative
reinforcement.
Behaviourists were unable to explain certain social behaviours. For example, children
do not imitate all behaviour that has been reinforced. Furthermore, they may model
new behaviour days or weeks after their first initial observation without having been
reinforced for the behaviour (Mergel, 1998).
One assumption of cognitivism is that an existing knowledge structure must exist to
learn. These structures are called schema (Rumelhart & Norman, 1981). In
cognitivism, human brain and nervous system and their development are very
important. Jean Piaget studied human cognitive development process. According to
him, there are four stages in cognitive development process:
1. Sensorimotor period (0-2yrs)
2. Preoperational Period (3-7yrs)
3. Concrete operational period (8-11yrs)
19
4. Formal operational period (12-15yrs)
In the sensorimotor stage, intelligence takes the form motor actions (reachinggrasping-pulling). In preoperational stage, intelligence is intuitive in nature and
partially logical thought begins. In concrete operational stage, cognitive structure is
logical but it is concrete. In formal operational stage, cognitive structure is logical and
also abstractions can be made in this stage. He stated that cognitive development is
effected by three processes. Assimilation, accommodation and equilibration.
Assimilation is integration of new information with existing schemas.
Accommodation is the adjustment of schemas to the new situation or constructing
new schemas. Equilibration is the continuing readjustment between assimilation and
accommodation according to Piaget (1972).
Piaget’s assumptions about knowledge and learning process are similar to
constructivist theory. Constructivism is a theory of knowledge that describes the
nature of knowledge and how an individual acquires it. In constructivism, knowledge
is created in the mind of the learner i.e. the student attempts to make sense of his or
her world using previously acquired knowledge through everyday experiences or
formal learning. According to Merril (2001), there are six assumptions of
constructivism among which he cited:
1. Knowledge is constructed from experience. Learning is a personal
interpretation of the world an active process in which meaning is developed on
the basis of experience.
Conceptual growth comes from the negotiation of meaning, the sharing of
multiple perspectives and changing of our internal representations through
collaborative learning.
20
2
Learning should be situated in realistic settings; testing should be integrated
with the task and not a separate activity.
Perhaps the above assumptions are in conformity with other views on the learning
theory of constructivism. Each of these perspectives shares a common premise that
individuals actively construct knowledge based on experience. Thus, knowledge
cannot be simply passed on from learner to learner, but must be constructed
individually by each learner. Boethel and Dimock (2000, p. 6-8) outline that
constructivist-learning theory emphasizes six assumptions of constructivism namely;
learning is an adaptive activity, learning is situated in the context where it occurs,
knowledge is constructed by the learner, experience and prior understanding play a
role in learning, there is resistance to change in learning and also social interaction
plays a role in learning.
Examples of constructivist learning are found in experiential learning, self-directed
learning and reflective practice. These learning strategies explicitly show that the
focus is squarely on the learner’s construction of knowledge within a social context.
The implication is that instructional designs considerations within a framework of
constructivism begin with taking into account the learner’s prior knowledge,
understandings, and interests. Boethel and Dimock (2000, p. 17) mentioned that
teachers must understand what learners bring to the learning situation and begin there
in helping students build new knowledge, therefore, like cognitivism, constructivism
begins with a thorough learner analysis and determination of appropriate tasks to
promote constructivist learning.
According to Von Glasersfeld (1996), constructivism assumes that knowledge is
actively built up by the learner through a process of construction or interpretation in a
way that fits his or her own world.
21
So students learn by trying to fit what they are taught to their own worlds; learning
from constructivist perspective is the production of self-organization.
Some students’ understanding of Geometric Optics (transmission of light)
Although, there have been great number of studies done to investigate the students’
misconceptions in mechanics, there have been few studies done to investigate the
students’ misconceptions in geometrical optics. Misconception studies in geometrical
optics show that students have difficulties in understanding vision and the nature and
propagation of light.
Langley, Ronen and Eylon (1997) investigated pre-instruction students’ conceptions
and representations of optical systems, light propagation, illumination patterns and
visual patterns. They found that students did not indicate light emanating from the
light source in any of the diagrams they drew. They showed something existing
around the light source, without an explicit connection with it. Light was not shown
emanating from the specific points of the light source. Moreover, the path of
emanation and propagation of the light was influenced by barriers around the source
or by remote optical components. The students rarely indicated directionality in their
representation of light. They used variety of graphic objects to represent light: straight
lines, dashes, curves and filled-in areas. In the study, students also showed little
understanding how to see luminous and nonluminous objects. The understanding that
there is no sight without light was shared by about 50% of the sample. The students
who involved light in the sight process showed the light emanating from the object
and being received by the eye, saw the object because it was contained within the
geometrical sector spanned by the eyes and saw the object because the observer
directs sight lines toward it, with light possibly emitted from the eyes.
22
Fetherstonhaugh and Treagust (1992) investigated the 8-10 grades students’ (age 1315 years) understanding of light and its properties. In their findings, students’
conceptions were:
1
Light travels a different distance depending upon whether it is day or
night
2
Light does not travel during the day.
3
Light does not travel at all during the night.
As given above students had some conceptions about traveling of the light.
In the interviews some students thought that light does not hit anything as it travels,
others think that light can travel a variable distance while some of the students
thought light does not travel and thus even if it travels, the distance it travels depends
on its energy. Students also had some misconceptions about sight process:
1
People see by looking, not by light being reflected to their eyes.
2
People can just see in the dark.
3
Cats can see in the dark.
In the interviews, students were asked to explain how objects are seen. For example,
what role does light play in seeing an object? Students were also quizzed on whether
one cold see without light. Students answered these questions in a variety of ways.
Several students said that something leave the eye and strike the pencil. Moreover,
they claimed that it is possible to stare at a person’s back and have that person feel the
stare. For seeing in the darkness, significant numbers of the students expressed that
eyes can get used to seeing in total darkness.
In another study about light, Bendall, Goldberg, and Galili (1993) investigated
prospective elementary teachers’ prior knowledge about light and shadow. They
23
interviewed thirty (30) prospective teachers who were all in their junior or senior year
out of which very few had taken a physics course in high school. They found that
about 20% of their subjects tended to explain the shadow phenomenon in terms of a
reified shadow (attributing the shadow to the presence of something, rather than to the
absence of light). The students also could not explain what will become of the shadow
when two light sources were used at the same time.
Most of the students reasoned that in the region of geometrical overlap there would be
either lightness (full illumination) or darkness (shadow). They did not consider semi
darkness. In the study, students had a static general illumination conceptualization in
which light only exists in space. For example, students could not explain the
brightness of a screen. They did not recognize the role of the light in that process
(light had to go from the bulb to the screen). Like, for example, in the interview
studies a student recognized that light must be present to observe mirror images, but
did not recognize any explicit role for light in that process. In the interviews most of
the students thought that presence of the light was necessary to see the nonluminous
objects in which they gave to the light a static role. Even if, the students said that for
seeing luminous objects light must enter to eyes, they did not draw ray diagrams for
this situation. Students also had difficulties in understanding of the idea that light
from each point on a source goes out in all directions. They thought of light as
emanating in only one direction from each source, like flash light beams. In their ray
diagrams, they tended to show only single lines going outward from individual points
on the bulb which is the root of many students’ difficulties in understanding image
formation. Feher and Rice (1988) investigated the middle school children’s
conceptions of shadow formation. They interviewed 40 children using a protocol that
was developed through more than fifty interviews. The children explained the shadow
24
as the presence of something that is pushed, moved or thrown to the screen i.e. as a
reified shadow. They gave a material characteristic to the shadow. In their diagrams,
there were movements of dark areas or shadows between object and screen. Most of
the children gave a role to the light in the shadow formation as initiating the shadow
by hitting to the object and pushing it to the screen. Some of these students thought
that light reflects off the object and due to this reflection shadow is formed and light
carries it to the screen. Moreover, in the study children were asked “Is there a shadow
in the dark, where there is no light?” The students thought shadow exists in the dark
but they cannot see it. They explained this situation in two different ways. One is that
either the object produces the shadow hiding within the object and cannot be
produced or cast until the light hits the object and provokes it to do so. The other one
is that their visual mechanisms are not operative in the darkness. The researchers also
found most of the children had an idea that shadow belongs only to the non-luminous
object and it always looks like the object. The students did not consider the role of the
light source in the shadow formation. Misconceptions of the students about nature and
propagation of light and shadows point out that, students have difficulties in
explaining and interpretation of image formation by mirrors and lenses.
Langley et al. (1997) investigated pre-instruction students’ conceptions about plane
mirror images. They found that the students thought that creating images was an
inherent attribute of the silvery mirror material, rather than the product of the
reflection process. The students did not show image observation without including a
representation for image formation in their diagrams. In some situations the issues
were treated separately, with the image projected holistically onto or into mirror and
the observer directing sight lines at the image.
25
Goldberg and McDermott (1986) investigated students’ difficulties in understanding
image formation by a plane mirror by using individual demonstration interviews.
They found that one-third of the students believed that the image of an object in a
plane mirror lies on the surface. In the study, students had difficulties in
understanding the position of the image depends only on the position of the object
relative to the mirror and is independent of the observer’s position. They had a
misconception that an image in a plane mirror lies behind the mirror along the line of
sight between a viewer and the object. Moreover, some of the students invoked a
parallax argument for their explanation in which they referred to their experience of
watching an object shift its position as they viewed it from different perspectives.
They had mistakenly suggested that the absolute position of the object remains the
same as an observer moves. Only change is its apparent position relative to the
background. Finally, they found that the students believed they would see more of
themselves in the plane mirror by moving back. In fact, in a plane mirror anyone can
see more of himself/herself with a minimum amount of eye movement not with
moving back.
Bendall et al. (1993) investigated prospective elementary teacher’s ideas about mirror
images. They interviewed prospective teachers and asked open-ended questions to
learn how they think a mirror works. For creation of image, only about half of the
students thought that light was necessary for image creation but they were not able to
explain the role of light in that process. In their diagrams, the lines between the light
source and its image in the mirror suggest a holistic way of thinking. They just
implied that the image somehow went to the mirror. Moreover, most of the students
thought that nothing happened between their eyes and the mirror when seeing image
of any object in a plane mirror. They said that they saw just by looking. Although,
26
most of the students thought that light is necessary for them to see the image, they
seemed to be thinking only that background light was necessary for their eyes to
function, and not that light from the mirror had to enter their eyes to see the image of
any object in the mirror. In the interviews, an interesting interpretation of how a
mirror works was interpretation of reflection term differently from a scientific view.
When the students said the mirror reflects the light, they did not mean something
actually bounding of the mirror. Instead, they meant that the mirror makes a
reproduction or duplicates. According to some of the students, the ability of the mirror
to make a reproduction of the image was due to reflective substance of the mirror.
Almost half of the students thought that a mirror could make a reproduction even if
there was no light in the medium. For example, in the interviews, one student said: “it
will be a picture of the bulb, but it will be covered with dark.” Chen, Lin and Lin
(2002) developed a two-tier diagnostic test to identify the misconceptions of high
school students about image formation by a plane mirror. They found 9
misconceptions in the study: (1) Students thought that to see an image of any object, it
should be inside the front region straight ahead of the mirror. (2) Students thought that
image of an object depends on the observer and they believed that image of any object
is located right ahead of the observer. (3) Students claimed that image of an object is
located on the surface of the mirror, not equal distance behind the mirror as the object
is in front. (4) Students thought that if a person wants to see him or herself, he or she
should illuminate the mirror rather than himself or herself. (5) Students believed that
image of an object is in the line sight of the observer. They could not explain that the
image of an object does not depend on the observer. (6) Students confused the image
with the shadow. They expressed image of an object on the mirror was its shadow. (7)
Students claimed that image of a black object on the mirror was due to black rays
27
bouncing off the black object.
They could not realize that image of the black object was due to the reflection of
surroundings around the object and there was no light reflected from the mirror due to
the black object. (8) Students confused image formation with shadow formation. They
believed that in the presence on an illuminant the position and size of the image of an
illuminated object depends on the illuminant. For example, they thought image size of
an object gets longer when the illuminant is gotten closer to the object. (9) Finally,
students thought position and size of the image of any object depend on the location
of the observer. They thought that when the observer retreats, size and position of the
observer would change.
Gee (1988) investigated a different aspect of the image in a plane mirror. According
to researcher, students believed that plane mirrors rotate the right to the left and vice
versa. School texts books mention this topic as lateral inversion when discussing the
nature of the image in a plane mirror. Some texts books state that lateral inversion
occurs but they do not explain how it occurs. The only thing that is understood is that,
the left and right of the object are reversed. According to the students, the only thing
that occurs in a plane mirror is that object points that are near to mirror have images
near to mirror and object points that are further to mirror have further images. This is
known as longitudinal inversion and thus the reality of how plane mirror works. In
reality, plane mirrors causes lateral inversion. This is caused by the laws of reflection.
Some methods for identifying students’ understanding of concepts
It is important to know what prior knowledge students bring to learning environment
in order to help them to construct new knowledge. In the past, students’ prior
knowledge was not considered seriously. When the misconception studies started to
28
appear in the literature, science educators have focused on developing valid and
reliable methods to identify them. Therefore, they proposed variety of methods to
identify students’ misconceptions such as various types of interviews, word
associations, open-ended questions, multiple-choice tests, multiple-choice tests with
explanation, and two-tiered multiple choice tests (Al- Rubayea, 1996). Interviews and
Open-ended Tests Interview methods used by Osborne and Gilbert (1980) and openended questionnaires have some advantages and disadvantages. Although, researchers
gain more information by depth of probing and flexibility of questioning by
interviews (Beichner, 1994), they require a large amount of time to interview with a
large number of students (Chen et al., 2002) to get greater generalizability (Beichner,
1994). Moreover, these methods also require additional training of researchers
(Haslam & Treagust 1987). Also, although open-ended questionnaires give students
more time to think and write about their ideas, interpretation and analyzing the results
of the open-ended questionnaires are difficult and time consuming (Al-Rubayea,
1996).
Multiple-Choice Tests and Force Concept Inventory (FCI)
Multiple-choice tests have been found as an effective way of identifying the
misconceptions of the students by researchers. Al-Rubayea, (1996) cited that
multiple-choice tests are more effective than oral or written open-ended essays in
detecting students’ misconceptions.
Force Concept Inventory (FCI) is the one of the most popular multiple- choice test in
physics education to monitor understanding of students’ conception of force and
kinematics. The first version of FCI, Mechanics Diagnostic Test (MDT), was
published in 1985 (Savinainen & Scot, 2002). It constituted 34 items designed to
29
identify students’ misconceptions.
Initially, it was implemented to the college students in written and opened- answer
form. Then, students’ difficulties were identified from their responses and multiplechoice version of the test was constructed based on these misconceptions (Savinainen
& Scot, 2002). In 1992, an improved version of MDT was published by Hestenes and
Halloun, (1995) with 29 multiple-choice items. The questions of the FCI were
categorized into six dimensions: kinematics, first law, second law, third law,
superposition principle, and kinds of force. They also provided a list of thirty (30)
misconceptions that the test probed and the questions that addressed each
misconception.
Steinberg and Sabella (1997) investigated the how student performance on the FCI
correlates with their understanding of the subject matter. They found that sometimes
students’ performances on the FCI do not correlate. They do not attribute it to the test
and claimed that it may be due to the inconsistency in student thinking about the
physics.
Steinberg and Sabella (1997) also found that items of the FCI are given from real life
experiences. However, in formal exams there are no or a few items that include real
life situations. Therefore, students find the items of the FCI very strange which can
confound the data. Finally, they found that since the students knew that the results of
the test would not be counted towards their grades, some students did not take the test
seriously.
Multiple-choice tests have many advantages. They can be scored immediately and
objectively. Teacher can administer them easily and they are applicable to large
number of students (Al-Rubayea, 1996). Moreover, Çataloğlu, (2002) expressed that
30
multiple-choice tests are better liked by the students than other measures and can give
diagnostic information. Marx (1988) has cited nine appropriate reasons for using of
multiple-choice tests: (1) they provide greater variety of questions. (2) They can be
qualitative questions regarding physics principles. (3) Choosing between alternatives
and having a general understanding are much more like real life. (4) Options act like
hints. (5) The teachers can ask subtle points with them. (6) Multiple-choice items are
next best thing to essay type questions. (7) The teachers can ask for a quick numerical
calculation and make them worth a point. (8) More material can be covered. (9) They
are good for review.
There are also some criticisms to the multiple-choice tests. According to Rollnick and
Mahooana (1999) the disadvantage of multiple-choice tests is that questions do not
provide deep enough inside into the students’ ideas on the topic and students very
often give correct answers for wrong reasons. According to Çataloğlu (2002)
multiple-choice tests direct the students’ attention on information in isolation by
testing one element at a time. Therefore, the larger context and structure of
relationships between and among the elements get lost. According to Marx (1988),
multiple-choice tests should never be used. He expressed five reasons to support his
assertion. First, multiple-choice items encourage guessing. Second, the items are not
from real life situations. Third, they are not friendly for students because students see
them in somewhat a derogatory fashion, connected with the fact that guessing is
involved.
Fourth, he stated that ‘There is no real use for them. For example, we hardly ever use
multiple-choice in the computer based quizzes’. And the last, writing good items is
too difficult. He had seen A-grade students do B-grade in the multiple- choice exams
31
and vice-versa. He attributed this to careless wording of stems and questions based on
weak examples. Marx (1988) added two more reasons for why multiple-choice tests
are not effective: First, students may have extracted the right answer by a fortuitous
combination of errors. Second, multiple-choice tests heavily depend on reading
comprehension skills. According to Al-Rubayea (1996) when researchers used them
to identify the students’ misconceptions, researchers became worried about students
who through rote learning select the correct answer.
As it is seen, multiple-choice tests are easily applicable and their results can be
analyzed quickly and easily. The problem is their effectiveness. To overcome this
problem,
Al-Rubayea (1996) cited recommendations that students should justify their answers.
As a result, researchers extended the multiple-choice tests into several tiers, two or
three tiers.
2
Two-tier Tests
Two-tier tests include, in addition to selecting correct answer among the distracters,
multiple reasons or justifications from which the students choose their reason for their
response is required in the second tiers. Haslam and Treagust (1987) described the
item format of the two-tier multiple choice tests as the first tier consisting of a content
question with two, three, or four choices. The second tier consists of four possible
reasons for the first part with three of them alternative reasons and one desired reason.
The second tier can also include a blank that students can write a reason for the first
tier when they can not see their reasons among the alternatives of the second tier
(Griffard & Wandersee, 2001).
3
Advantages of the two-tier tests
32
Tsai and Chou (2002) stated that ‘since, two-tier test is in multiple-choice format, it is
much easier for teachers to score or interpret students’ responses. In this way, even
with numerous students, a teacher can efficiently diagnose their alternative
conceptions.’ According to Zeilik (n.d.) teachers can use these diagnostic tests for
formative and summative assessments over semesters. If teachers use them as a
formative test, they will understand their students’ cognitive states, preconceptions
and misconceptions prior to instruction. Therefore, they can take some precautions for
misconceptions which can possibly obstruct the lecture.
For example, they can tutor the students in their weak areas individually or assign the
students into heterogeneous cooperative learning teams. If teachers use the diagnostic
tests for summative assessment, they will see impact of their instruction method
positive or negative which can serve feedback for later on instructions.
However, it is important to say that results of the diagnostic tests cannot be used for
assigning the grades of the students. Because, the main purpose of the tests is to
diagnose not to assess achievement of the students.
4
Development process of two-tier tests
Developing reliable and valid conceptual diagnostic tests is a struggling process and
requires great efforts (Zeilik, n.d.). The development process of a two-tier test was
defined by Haslam and Treagust (1987) in three main phases:
Phase 1:
1. The content boundaries were defined with a list of prepositional knowledge
statements.
2. Content validity of prepositional knowledge statements was determined.
33
Phase 2:
1. Students’ misconceptions were identified by interviews.
2. Multiple-choice questions with free response reasons were constructed and
administered.
Phase 3:
1. Final test questions were constructed based on multiple-choice questions with
free response reasons.
2. The final test questions were revised and a pilot study was conducted.
3. Final content and face validity of each test item were determined with the
assistance of a specification grid.
4. The final version of the test was administered.
Some two-tier diagnostic tests were developed based on this process in different fields
of science education. Most of the developments of two-tier diagnostic tests include
both interviews and open-ended questionnaires or multiple- choice tests to identify the
misconceptions of the students which will be used for distracters of the two-tier test.
Including interview method gives a chance to researcher to probe the students’ mind
deeper and ask the questions more flexibility. On the other hand, including openended or multiple-choice tests gives a chance to the researcher to deal with more
subjects to generalize the results (Beichner, 1994). In the following part, some studies
including development process of two-tier tests are told.
Odom and Barrow (1995) developed and applied a two-tier diagnostic test to identify
college students’ misconceptions in diffusion and osmosis. They followed a procedure
that is similar to the Treagust model. First, they defined the content boundaries of the
topic and listed propositional knowledge statements about the topic by using two
34
college biology texts books and a college biology laboratory manual. The content
validity of the propositional statements was established by a panel of two science
education professors and one biology professor. Second, 20 volunteer introductory
college biology students were interviewed. The interview questions were-open ended
questions. The interviews were audiotape recorded and were used to develop a list of
student misconceptions about ‘’diffusion’’ and ‘’osmosis’’ concepts. Third, 15-item
multiple-choice format test with free response was developed based on the
propositional knowledge statements and the findings of the interviews. The first tier
of this test was in multiple-choice format with two, three or four choices. In the
second tier students were asked to give their reasons for their multiple-choice
selection in the first tier. This test was administered 171 non-science major
introductory college biology students who had previously been taught diffusion and
osmosis concepts. Fourth, two-tier multiple choice test including 12 items was
constructed based on multiple-choice questions with free response reasons. Fifth, face
validity of the test was checked. Two major questions were addressed while
determining the face validity: Does the question assess the content as defined by the
validated propositional statements? And is the question at a level of sophistification
appropriate for college freshman biology students? If these criteria were not met, the
item was dropped. Finally, the test was applied to 240 students enrolled in a freshman
biology laboratory course. In analyzing the results of the test, the researchers
estimated discrimination indexes and difficulty levels for each item and they
estimated the reliability of the test by using the Spearman-Brown formula.
Tan, Goh, Chia and Treagust (2002) developed and applied a two-tier multiple-choice
diagnostic instrument to assess high school students’ understanding of inorganic
chemistry.
35
Their methodology was very similar to Odom and Barrow’s (1995) study in which
they used Treagust model (as cited in Odom & Barrow, 1995).
Chen et al. (2002) investigated the high school students’ misconceptions about image
formation by a plane mirror. They developed a two-tier diagnostic test based on
Treagust model. There are two differences in this study from the previous study
described above. First, an open-ended questionnaire, not a multiple-choice test with
free response, was used to identify students’ misconceptions which could serve as
distracters for the later construction of the multiple choice instrument. Second,
interviews were conducted after open-ended questionnaire was administered, not
before. In analyzing the results, they estimated the reliability by using Cronbach alpha
and they also calculated discrimination index and difficulty level for each item. They
gave attention to the misconceptions which existed in at least 10% of the student
sample.
Beichner (1994) developed a diagnostic multiple-choice test to identify the
misconceptions of the students in kinematics graphs. The construction process of the
test was very similar to the Treagust Model (as cited in Odom & Barrow, 1995). The
difference was that in defining content boundaries of the study, he wrote specific
objectives instead of concept map or propositional statements.
5
Critics about the two-tier tests
Although, diagnostic tests are very helpful for teachers to identify the misconceptions
of the students, some researchers criticize them. Griffard and Wandersee (2001) cited
that forced choice instruments like two-tier tests give clues to the students to select
correct answers that they would not have had in interviews and open-ended questions.
Griffard and Wandersee (2001) investigated the effectiveness of a two-tier instrument
36
developed by Haslam and Treagust in 1987 about photosynthesis. The test was given
to the students and wanted them to think aloud while they were answering the items.
They found that, using unnecessarily wording to distract students caused them to
make mistakes. It is not certain that whether these mistakes were due to
misconceptions that students had or unnecessarily wording of the test.
Moreover, these unnecessarily wording can cause create a new misconception in
students’ mind. They also stated that ‘students consider the second tier as a distinct
multiple-choice item and finalized their choice on the basis of whether it logically
follows from their response to the first tier. Therefore, two-tier test seemed to measure
the students’ test-taking skills rather than the extant knowledge’.
Moreover, the feelings of the students are very important. Students bring these types
of tests different amounts of sincerity, anxiety, persistence and meticulousness which
can confound the test results. They also criticized the two- tier test about the
estimating the proportions of the misconceptions. According to them, two-tier tests
overestimate the proportions of the misconceptions because gab in knowledge can not
be discriminated by two-tier tests. Therefore a third tier is necessary to be sure that
whether a wrong answer for the first two-tiers is a misconception or a mistake due to
lack of knowledge.
6
Three-tier Tests
Three-tier tests are very similar to the two-tier tests. In three-tier tests, an item has one
additional tier which asks students confidence about the answer of the former twotiers (Çataloğlu, 2002). Eryılmaz and Sürmeli (2002) developed a three-tier test to
assess the misconceptions of the 9th grade students about heat and temperature.
According to them, all misconceptions are errors but not all errors are misconceptions.
37
Some errors may stem from lack of knowledge. If a student explains his/her error as a
true with reasons and says his/her confidence, it is acceptable that this student has
misconception. In two-tier tests and multiple-choice tests it is not asked to the
students for their confidence about their answers. Three- tier tests are required to
remove this problem. These types of tests have one more tier in which it is asked to
the students to seek their confidence about the first two tiers. In their study, they
compared the proportions of the misconceptions that the students had with respect to
the tiers of the items. They found out that the students had misconceptions with an
average of 46 % for the first tiers of the items, 27 % for the first two tiers of the items
and an average of 18 % for all three tiers of the items. From these results, the
researchers concluded that one tier and two-tier tests overestimate the proportions of
the misconceptions. For the one tier tests it was accepted that all wrong answers are
misconceptions. However, some of the wrong answers may be false negatives which
are incorrect answers by mistake in spite of correct reasons in the second tier and
some may be due to randomly given answers by chance because related reasons of the
incorrect answers were not chosen on the second tiers. Therefore, 19 % (subtracting
27 % from 46 %) indicated incorrect answers by mistake or chance. The researchers
also found that two tiers tests also overestimate the proportions of the misconceptions.
Because as mentioned above, it is required that if a student has a misconception
he/she should say his/her confidence. In two-tier tests it is not asked to the students
whether they are confident about their responses. The researchers found that 9 % of
the students were not confident for the answers of the first two-tiers even if their
answers indicated the misconceptions. They explained that those students gave
incorrect answers due to lack of knowledge. To sum up, the researchers concluded
that three-tier tests assess the misconceptions of the students more validly than one38
tier and two tier tests.
The impacts of teachers’ understanding of science on their instructional
practices
A person’s understanding of the nature of science and mathematics predicates that
person’s view on how teaching should take place in the classroom. (Hersh, 1986).
Research has recently begun to emerge indicating that science and mathematics
teachers’ conceptions about the subject matter, teaching, and learning influence their
action in the classroom. (Madsen-Nason, A & Lanier (1986), Thompson, 1984;
Dougherty, 1990).
Thompson (1990) notes such new areas as the nature of teachers’ beliefs about
science subject matter and about its teaching and learning as well as the influence of
those beliefs on teachers’ classroom practices. In her earlier study, Thompson (1984)
also contends that there is a strong reason to believe that mathematics and for that
matter science teachers’ conception (their beliefs, views, and preferences) about the
subject matter and its teaching play an important role in affecting their effectiveness
as the primary mediators between the subject and the learners.
Furthermore, according to Ernest (1988), teachers’ conceptions on the nature and
meaning of science are crucial to teachers’ approach to science teaching. However,
Hersh (1979) points out the root of the problems in the teaching i.e. Controversies
about teaching cannot be resolved without confronting problems about the true nature
of science and mathematics. Thus Thom (1973) sees that the teachers’ perception
about the nature of science is an integral feature of a science classroom. In fact,
whether one wishes or not all science pedagogy, even if scarcely coherent, rests on a
39
philosophy of science.
Guyton and Farokhi (1987) agreed that if prospective teachers are recruited from
among the academically best candidates, if they perform well in university courses, if
they possess basic skills competency and are educated extensively in their academic
disciplines, and if they are placed in schools under the guidance of master teachers,
then highly competent teachers will emerge. Currently, subject matter knowledge of
teachers is highly emphasized. The nature of teachers' professional development
varies considerably across different nations. According to Calderhead (1995) ..."how
we prepare new teachers for the profession, how we support them in their first post as
teachers, and how we help them to develop in their future careers varies widely". He
also agreed that the training of teachers is seen as a key influence in the improvement
of education. Adler (1982) suggested that teachers should themselves be at least as
well-schooled as the graduates of the schools in which they are expected to teach.
Clark and Elmore (1981) reported that teachers adapt curricula to fit their knowledge
and Calderhead (1995) explained that studies of novice and experienced teachers
suggest that the competent teacher possesses an enormous diversity of knowledge not only about subject matter, but about children, teaching and the classroom context that enables teachers to make sense of classrooms and to monitor and shape their
classroom routines and behaviour.
Teachers’ practices are influenced by many factors. Ernest (1988) emphasizes there
are these factors (elements): teachers’ system of beliefs about science and its teaching
and learning; the social context of the teaching situation and teachers’ level of
reflection. Although it seems teachers’ beliefs about science and its teaching and
learning receives attention equal to the other element, Ernest emphasizes the
importance of science teachers’ beliefs by claiming that teachers approach to science
40
teaching depend basically on their systems of beliefs; in particular on their
conceptions of the nature, and on their mental models of teaching and learning science
and mathematics.
In spite of some literature suggesting that teachers’ conception of science and its
teaching and learning are not related in a simple cause-and-effect way to their
instructional practices (Pepin 1999), and, even though there exist some disparities
between teachers’ conception of the subject and their actual practices due to many
constraints (e.g., fixed curricula, time pressure and many other external factors)
(Raymond, 1993), many researchers and research findings indicate that there is
considerable agreement that beliefs influence action (Abelson, 1979). The teachers’
subject image in particular, affect teachers’ interpretation of content knowledge
(Kitchener, 1986) and their instructional approaches (Pope & Scott, 1984.)
The teachers who hold the absolutists’ view about science and for that matter its
teaching and learning are more likely to create teacher-centered instructional
environment, teach science as rules to be memorize, and portray science as an
infallible discipline. Such teachers who hold this view tend to present science to
students in a way that suggest science is a paper and pencil activity. Science the
teachers’ main objective is the learners’ mastery of scientific skills, the clear
presentation of step by step of any mathematical (science) and the emphasis on right
or wrong answers are likely to be practiced.
Teachers holding constructivist view of science are expected to adopt teacher-student
interaction mode of instruction by allowing students to explore and investigate while
teachers reside in their classrooms as facilitators. Problem solving is central to
teaching for constructivist science teachers where purposeful activity stems from the
41
problem situation that require reasoning and creative thinking, gathering and applying
information, discovering, inventing, communicating and testing ideas (Thompson,
1992). Consequently the classroom takes on constructivist environment.
Research studies and findings (Pepin, 1999; Teo, 1997) provide evidence that
teachers’ instructional practices especially in science and mathematics, do not reflect
the teachers’ conception of the subject matter. Pepin (1999) studied the conception
and work of science and mathematics teachers in three countries: England, France,
and Germany. The study explored the issues concerning conceptions of science and
mathematics and their teaching and learning. Pepin’s findings suggest that teachers’
conceptions are manifested in their practices and can be traced back to their
educational trends of science (mathematics) and science education as well as to
personal constructions. The findings also suggest that teachers’ pedagogical style are
a personal response to a set of assumptions about the subject (science) and its teaching
and learning, to a set of educational and philosophical traditions, and to a set of
institutional and societal constraints.
Thompson (1984) reported a study in which she researched the relationship of
teachers’ conceptions of science and science teaching to institutional practice. She
demonstrated that there was consistency between the teachers’ professed conception
of science and the manner in which they presented the content to their classes. She
also found out that, teachers posses conceptions about teaching that are general rather
than being specific to the teaching of science and mathematics.
Thompson (1984)’s reports and other research findings discussed above provide
strong evidence to suggest that teachers’ conception of science and mathematics have
effect on their teaching practice in a number of ways.
42
In conclusion, I find Hersh (1986)’s message embodied in the quotation below fitting
with my professional practices as a classroom science and mathematics tutor:
The teacher trianees’ understanding of geometric optics is affected by their
conception of how it should be presented. One’s manner of presenting it is an
indication of what one believes to be most essential in it. The issue is not, what is the
best way to teach?
I interpret this quotation to signify what teachers consider to be more effective ways
to teach science and mathematics as dependent on their beliefs and conceptions about
science. In view of this, I will present my beliefs about geometric optics, its teaching
and learning; linking it to my personal teaching experience, which reflects my
conception of science.
Cooney (1994) has stated that science and mathematics teachers’ beliefs about science
and mathematics, their teaching and learning have been shown to critically influence
what happens in the classroom. In order to position myself within the science and
mathematics education conceptual paradigm, it is necessary to present my own
conception of science (geometric optics), its teaching and learning as being aligned
within the non-traditional constructivist view about science and mathematics as well
as the teaching and learning of science and mathematics.
I believe science (geometric optics) is a man-made universe to construct and revise
our knowledge. My belief about science and mathematics teaching and learning is
centered on the adoption of teacher-student interaction mode of instruction by
allowing students to explore and investigate, while I reside as a facilitator in my
classroom. Associated with my teaching practice, problem solving discovery, group
working and creativity are central to my teaching strategies. As a teacher, I attempt to
43
enhance the conceptual and practical understanding of scientific problems through
integration of subjects, especially in non-classroom settings. For example, taking
students outside on a sunny day and asking them to estimate the height of a tall
building (without climbing it) or the width of a river (without crossing it) to show the
integration of geometry and mathematics as well as the practical side of geometric
optics. One of the strategies that I advocate and use to show my students the practical
side of science is revealing the specialized application involved in many professions
such as telescopes, binoculars, mirrors etc.
Acknowledging the existence of many flaws in constructing a constructivist
environment in my classroom, I consider the desirable way to teach geometric optics
through constructivist paradigm which rests, to large extent on my belief and
conception of science and mathematics.
Also admitting my awareness of the influence of my conception of science on my
instructional practice of the subject may be assumed as another evidence of Hersh
(1986) and Cooney (1994)’s statement on the teachers’ conception of subject matter
and its effects on teaching practices.
Summary of the Literature Review
Students come to classes with existing knowledge that they construct with their
experiences or learning (Fetherstonhaugh & Treagust, 1992). Some of these students’
prior understanding can be in conflict with the scientific view and thus the researcher
prefers to call this misunderstanding. If a student has inadequate knowledge or
misunderstands a concept, his or her conception may be wrong scientifically, but it is
true for him or her and works properly and helps him/her to understand the world
(Eryılmaz & Sürmeli, 2002).
44
Research studies show that what people know and understand resist change.
Moreover, according to Nussbaum and Novick (1982) they interfere with learning
process and inhibit students’ learning.
Teachers should take serious care of what learners know and how deep they
understand a concept in order to teach their students in a reliable way. There were
many methods used and developed to investigate students’ understanding of concepts;
interviews, word associations, open-ended questions, multiple-choice tests, multiplechoice tests with explanation, two-tier tests and three –tier tests.
Even if the interviews provide more information by depth of probing and flexibility, it
is necessary to study with the larger samples to generalize the results (Beichner,
1994). Moreover, conducting interviews require a large amount of time (Chen et al.,
2002). On the other hand, even if the open-ended tests overcome generalizability
problem, information obtained from open-ended tests are not as deep as those of
interviews’ (Beichner, 1994). For the multiple-choice tests, although they are easily
applicable to a large number of the samples and can be scored easily and objectively
(Al-Rubayea, 1996), one of the main disadvantages of multiple-choice tests is that
questions do not provide deep enough inside into the students’ ideas on the topic and
students very often give correct answers for wrong reasons (Rollnick & Mahooana,
1999).
Marx (1988) cited that multiple-choice tests should never be used. He expressed that
multiple-choice items encourage guessing. As it is understood, multiple-choice tests
are easily applicable and their results can be analyzed quickly and easily, the problem
is their effectiveness. To overcome this problem, Al-Rubayea (1996) recommended
that students should justify their answers. In two tier tests, the first tiers consist of a
45
content question with two, three, or four choices. The second tiers consist of four
possible reasons for the first part with three of them alternative reasons and one
desired reason. It requires students to justify their responses in the first tier by the
reasons in the second tier (Haslam & Treagust, 1987). However, Griffard and
Wandersee (2001) investigated the effectiveness of a two-tier instrument developed
by Haslam and Treagust in 1987 and criticized two-tier tests. One of the main
criticisms was that two-tier tests overestimate the proportions of students’
understanding because gap in knowledge can not be discriminated by two-tier tests.
Therefore, an additional tier is required to discriminate a mistake whether it stems
from inadequate understanding or lack of knowledge.
Eryılmaz and Sürmeli (2002) stated that lack of understanding do not stem from lack
of knowledge. In three-tier tests, the third tier is asked to find out if students are
confident with their answers for the first two tiers. Asking the students’ confidence
level in the third tier provides information as to whether a wrong answer to the first
two tiers was due to lack of inadequate understanding or lack of knowledge. It is
expected that if a student explains his or her false as a true with reasons and says his
confidence, it is acceptable that this student has inadequate understanding of the
concept.
It is imperative that what teachers know and understand is what they teach. These
levels of understanding are likely to influence what students will know and
understand.
Finally, some common students’ understanding in geometric optic found from the
literature review can be listed as the following:
46
1. For seeing in the darkness, students express that eyes can get used to seeing in
total darkness (Fetherstonhaugh & Treagust, 1992).
2. Students think that light travels a different distance depending upon whether it
is day or night (Fetherstonhaugh & Treagust, 1992).
3. Students think of light as emanating in only one direction from each source,
like flash light beams (Bendall et al., 1993).
4. Students have an idea that shadow belongs only to the non-luminous object
and it always looks like the object (Feher & Rice, 1988).
5. Most of the students reason that in the region of geometrical overlap there
would be either lightness (full illumination) or darkness (shadow). They do not
consider semi darkness. Students treat the shadow as the presence of
something i.e. they give material characteristics to the shadow, rather than
absence of the light (Bendall et al., 1993).
6. Students think that to see an image of any object, it should be inside the front
region straight ahead of the mirror (Chen et al., 2002)
Students have a misconception that an image in a plane mirror lies behind the mirror
along the line of sight between a viewer and the object (Goldberg & McDermott,
1986).
7. Students think that an observer see the object because the observer directs
sight lines toward it, with light possibly emitted from the eyes (Langley et al.,
1997).
8. Students confuse image formation with shadow formation. They believe that
in the presence on an illuminant the position and size of the image of an
illuminated object depends on the illuminant. For example, they think image
47
size of an object gets longer when the illuminant is gotten closer to the object
(Chen et al., 2002).
9. Students think that the position and size of the image of any object depend on
the location of the observer. They have an idea that when the observer retreats
size and position of the observer is changed (Chen et al., 2002).
10. Students claim that image of a black object on the mirror was due to black
rays bouncing off the black object (Chen et al., 2002).
11. Students think that creating images is an inherent attribute of the silvery mirror
material, rather than the product of the reflection process. The students say
that “The mirror reflects and so the person sees” (Langley et al., 1997)
12. Students have a misconception that while watching an object its position also
shifts as they view it from different perspectives. They mistake that the
absolute position of the object remains the same as an observer moves. Only
change is its apparent position relative to the background (Goldberg &
McDermott, 1986).
13. Some of the students believes that image of any object is located right ahead
of the observer (Chen et al., 2002).
14. Students think that if a person wants to see him or herself in a dark room, he or
she should illuminate the mirror rather than himself or herself (Chen et al.,
2002).
It is also clear that the teachers’ understanding of a concept in science would
definitely affect their classroom practices including the way they prepare for the
lesson and the way they present the subject matter. I am of the view that the desirable
way to teach geometrical optics is through the constructivist approach. This conforms
48
to a large extent with my belief and conception of the teaching of science and
mathematics. I strongly believe that teachers teach what they know and understand.
Finally, Calderhead (1995: 3) believes that since children's own backgrounds vary
considerably and they approach a subject with particular understanding of their own,
teachers need a wide repertoire of pedagogical content knowledge to cater for
children's individual differences. The analogy that works for one child, for example,
may be completely meaningless to another. Debate about the knowledge base for
teacher education is at the core of the move to establish professional standards for
teaching (Beaudry 1991). Grossman (1989) agreed that teachers must have a
theoretical understanding of how students learn a particular subject in addition to
knowledge of the subject matter itself. This will help them to teach effectively.
49
CHAPTER THREE
METHODOLOGY
Overview
This chapter provides and discusses the methodology used for the study. It focuses on
the following areas as Research design, Research approach, Population, Sample,
sampling techniques and participation, Instrumentation, Scoring of the instruments,
Validity and Reliability, Pilot testing, Administration of instruments, Method of data
analysis as well as designing of a course manual and hints for the teaching of the
subject under investigation (Appendix A).
Research design
The research design is that of a survey. In this survey, questionnaire inventory test on
geometric optics, observation checklist on trainees’ performance during teaching and
students’ achievement test items on geometric optics were used to obtain information
from which analysis was carried out to arrive at the various findings after some
descriptive exercises were carried out on the data collected.
Research approach
The data collection strategy for this study was a standard survey methodology within
the quantitative research tradition. The study was a fixed non-experimental
descriptive survey that went beyond the descriptive to the interpretive in order to
provide explanations of patterns and relationships of the results obtained. The
justification for the fixed non-experimental descriptive survey is that, unlike an
experimental research, the variables were not manipulated (Cooper & Schindler,
2001; McMillan & Schumacher, 1997). Also according to Best (1970), descriptive
50
research looks at beliefs, points of views, or attitudes that are held by individuals or
groups in order to describe, compare, classify, analyse and interpret findings.
Furthermore, most non-experimental fixed research projects also deal with averages
and proportions (Robson, 2002). Cronbach’s reliability tests were conducted on the
data, i.e. the student achievement test as well as the geometric inventory test for the
questionnaire. Descriptive statistics provides documentation on general attitudes,
experiences, interests, priorities and expectations. In this study, the characteristics of
descriptive statistics and the percentages of various dimensions that were measured to
examine the science teacher trainees’ understanding of geometric optics were used as
yard sticks to make some basic judgments.
Why the choice of survey approach?
A survey has several characteristics and several claimed attractions; ‘typically it is
used to scan a wide range of issues, populations and programmes in order to measure
or describe any generalized features’ as stated by Cohen, Manion and Morrison
(2000: 171). In other words, survey research is a way of collecting information from a
large and dispersed group of people rather than from the very small number, which
can be accommodated in a case study. A survey method was appropriate for this study
because the study aimed at obtaining information about a specific population and also
because of lack of logistics and the fact that the actual population involved is the
study’s true identity was not to be discussed. The information that was sought
included the trainee teachers’ opinions and understandings of the concept of
geometric optics as well as the trainees’ efficiency in impacting the knowledge they
have to their students. This was followed by a model way of going about teaching the
topic; a systematic approach.
51
Population
The target population consisted of all the final year teacher trainees in the Special
Science and Mathematics Colleges of Education in Ghana in the year 2010 totaling
seven hundred and fifty (750). Although the study was geared towards all the Special
Science and Mathematics Colleges of Education in Ghana of which they are fifteen
(15) in the country, it was not practically possible to cover the entire country due to a
number of constraints, such as, logistics, time, accessibility and human resources.
Since all the colleges in question have practically the same resources, that is, both
material and human resources (justifiable in view of the fact that all the science
colleges have science laboratories well stock with apparatus and also qualified
physics tutors per personal investigation), there was no problem in choosing five (5)
colleges from which samples were drawn.
Sample: Sampling techniques and participation
Considering such factors as finance, time and accessibility, it was practically
impossible to access information from a target population. It became appropriate
therefore, to measure from a smaller group of the population. This was done in such a
way that the information obtained was representative of the total population under
study. This smaller group from the population represented the sample. It was not
necessary to use the whole population. Five (5) special Science and Mathematics
Colleges of Education from five regions in Ghana were selected for the study at based
on proximity and accessibility to the colleges in terms of easy transportation. Each
class was made up of twenty (20) students totaling one hundred (100) students in all.
Also fifty (50) pupils were drawn from the five (5) demonstration schools where the
teacher trainees did their teaching practice. Observation and achievement test were
52
carried out on the pupils after the teacher trainees have taught the topic under
investigation.
Instrumentation
This study adopted a structured geometric optics inventory two tier questionnaire
items on some understandings that students have in transmission of light energy
(geometric optics) as well as pupils’ achievement test (multiple choice)
on
transmission of light (geometric optics) from the literature review. Also an
observation checklist based on the four point Likert scale (Appendix D) was used to
access the teacher trainees’ performance during the teaching of the topic in question
under areas or phases of teaching (introduction, presentation, closure and application
of concept). The confidence level of trainee teachers, their competence level, time of
delivery and their content knowledge were also accessed.

Questionnaire
The questionnaire (Appendix B) contains basic concepts on the transmission of light
(reflection and refraction) which form part of the teacher training college science
syllabus and also present in the basic school integrated science syllabus. The
questions set under these concepts on both items have bearing on the teacher trainees’
as well as the pupils’ daily experiences. This is because students use light in diverse
ways; such as watching their faces in the mirror and snapping photographs. Fifteen
questions consisting of questions under reflection and refraction was used on both
items. The construction of the questionnaire and the students’ achievement test items
(multiple choice tests) was guided by the nature of test items used for the DBE and
the BECE exams. The choice of these items was informed by the fact that various
studies investigating the relationship between affective and cognitive variables equate
53
learning with performance or academic achievement and also understanding of
concepts. Besides, the questionnaire was chosen in order to obtain consistency and
wide range of exploratory data from the trainee teachers who answered the
questionnaire (Robson, 1995). As indicated by Walonnick (2004), using questionnaire
in interpretive study reduces middle-man bias and minimizes verbal or visual clues.

Observation check list
Data obtained from the observations were attractive as they afforded the researcher
the opportunity to gather ‘live data’ from ‘live situations’ rather than at second hand
(Padgett, 2004) this is because the researcher is the instrument and feels the reality of
the subjects. According to Robson (1995), observation can be used to gather
exploratory data on what is going on in a situation or set in perspective data obtained
by questionnaire or interviews. Since this research sought to explore and interpret
among others, trainee teachers’ understanding of geometric optics, observation check
(Appendix D) list was used to gather information because of the following reasons:
 To give the researcher the opportunity to interact and ask the teacher trainees
some few questions on some of the issues that may crop up during the
teaching process.
 To give the researcher the opportunity to come to terms with what learners
are being taught and perhaps why this will affect their performance.

Pupils’ achievement test
An achievement test (Appendix C) is a test of developed skill or knowledge. The most
common type of achievement test is a standardized test developed to measure skills
and knowledge learned in a given grade level, usually through planned instruction,
54
such as training or classroom instruction. Achievement tests are often contrasted with
tests that measure aptitude, a more general and stable cognitive trait.
Achievement test scores are often used in an educational system to determine what
level of instruction for which a student is prepared. High achievement scores usually
indicate a mastery of grade-level material, and the readiness for advanced instruction.
Low achievement scores can indicate the need for remediation or repeating a course
grade.
Under No Child Left Behind (Center on Education Policy, From the Capital to the
Classroom: Year 2 of the No Child Left Behind Act, Washington, D.C), achievement
tests have taken on an additional role of assessing proficiency of students. Proficiency
is defined as the amount of grade-appropriate knowledge and skills a student has
acquired up to the point of testing. Better teaching practices are expected to increase
the amount learned in a school year, and therefore to increase achievement scores, and
yield more "proficient" students than before.
When writing achievement test items, writers usually begin with a list of content
standards (either written by content specialists or based on state-created content
standards) which specify exactly what students are expected to learn in a given school
year. The goal of item writers is to create test items that measure the most important
skills and knowledge attained in a given grade-level. The number and type of test
items written is determined by the grade-level content standards. Content validity is
determined by the representativeness of the items included on the final test.
My choice for this instrument was informed by the fact that what the teacher knows
and teaches would have impact on the way they teach and hence this can affect
55
students’ performance (Ernest, 1988). Thus, one means to ascertain this is to conduct
achievement test on the area under investigation. These comprised of a pretest to find
out the entry behaviour of the learners as well as a post test to assess what kind of
knowledge the teacher has imparted after instruction.
Scoring of Instruments
The questionnaire for the trainees contained 15 true or false items in which under each
item respondents were asked to state reasons for their choice. All items followed the
same basic structure: a statement was presented, and the respondents asked to give
their responses by ticking the appropriate box in a fixed scale of true or false after
which they cited their reasons for their choices. The results were analysed using
percentages. The second instrument, the trainee teachers’ observation checklist was
analysed based on a pass mark of fifty percent (50%) and above accrued from marks
on various dimensions of teaching as spelt out in the observation checklist in order to
show how the trainee teachers’ understanding of geometric optics affected their
teaching. The fifty percent mark (50%) pass mark was adopted based on the grading
system of Institute of Education, University of Cape Coast, Ghana. The third
instrument, students’ achievement test items (multiple choice tests) were also scored
in terms of percentages for students marks obtained in the pretest and the post-test.the
two tests will be compared for any significant difference.
Validity and Reliability of instrument
The quality of a research instrument or a scientific measurement is determined by
both its validity and reliability (Aikenhead & Ryan, 1992). Validity seeks to
determine whether the instrument actually measures what is intended to be measured
56
and reliability, on the other hand, it refers to the consistency of data when multiple
measurements are gathered (Gott, Duggan & Roberts, 2003).

Validity
The instruments for the study were designed for exploring the variations in cognitive
domains of science educational objectives, such as variations in knowledge, and
conceptions. However, there are no direct means for measuring cognitive dimensions
as it exists in the physical sciences for the measurement of, for example, length and
weight.
The questionnaire items as well as the test items were developed from the DBE and
BECE examination and teaching syllabuses. This improved the standards of both
teacher trainees and the basic school students. The expertise of Science Education
Lecturers from the Department of Science Education was drawn to validate the
instruments for content and face validity of the three instruments. A pilot test was
conducted to correct lapses in the instrument.

Reliability
Reliability is about the consistency in a research result. If the survey is given again,
will it yield the same or similar results? Reliability of the data can be assessed if the
items are examined to show internal consistency. A measure for this internal
consistency (or reliability) may be gauged by the use of Cronbach’s alpha which
depended on the number of samples and the maturity of the respondents. (0.6-0.7)
However, repeated measurements of the same quantity with the same instrument
seldom give exactly the same value. This is partly because of the error inherent in the
scientific instruments itself during scientific measurements (Aikenhead, 2003) or
partly because of the transient nature overtime of the quantity that is measured using a
survey instrument, for example, evaluating concepts and knowledge and perception.
57
Social interaction and influence, for instance, may be key factors of changes in
concepts and knowledge as well as their understanding of concepts as well as their
perceptions. According to Crawley and Koballa (1994), people make evaluative
judgments about a wide variety of targets and rely on these judgments in deciding
among several possible courses of action in the future. The theory of reasoned action
proposed by Ajzen Fishbein and (1977) rests on the assumptions that humans are
rational and has control over their behaviour which I presume will affect their
knowledge base. They also seek out, utilize and process all available information
about pending decision before taking action. For these reasons, cognitive dimensions
of learning are likely to change with the passage of time. Hence peoples’ knowledge
base, level of understanding and perception, for example, continue to be a subject of
research in areas of social psychology and science education.
Pilot test
A pilot test of the instrument was carried out with fifty (50) teacher trainees from two
science colleges of education and also twenty (20) students from two basic schools
where the teacher trainees practiced. The students used for the pilot did not form part
of the sample for the actual study.
Administration of instrument
The survey was conducted in March 2010. This is the normal period when all basic
schools are back from the Christmas break. Once the schools were selected by
proximity and accessibility of transportation, letters of notification of and
participation in the study were sort for schools to take part in the study from various
Education authorities including Heads of the Basic schools and Principals of the
selected Colleges. The researcher went to the schools to brief them on the nature of
58
the study and gave insight of the study to the Heads of schools. The Heads were
assured of confidentiality and the importance of the study.
Data analysis procedure
The responses to the instruments were analysed by simple percentages. An average
percentage value for each dimension (true and false) was calculated and plotted on a
pie chat for both trainee teachers and students. This was used to establish whether
trainee teachers’ understanding of the topic under investigation have impact on the
performance of students. The trainee teachers’ observation checklist was analysed
based on a pass mark of fifty percent (50%) and above accrued from marks on various
dimensions of teaching as spelt out in the observation checklist in order to show how
the trainee teachers’ understanding of geometric optics affected their teaching.
Development of a Course Manual and Hints for Teaching Geometrical Optics
The approach to the teaching of geometric optics in our schools currently, the
researcher believes is not the best. Among the problems the researcher observed is the
lack of correlation between subtopics during the teaching of the topic in question. The
researcher proposes that the course manual at appendix 1 should be used to facilitate
the smooth learning of the topic. Again a model presentation of the topic has been
provided in a form of hints to support the course manual for effective teaching and
learning.
59
CHAPTER 4
RESULTS, ANALYSIS AND DISCUSSION
In this chapter, results of the study are explained in three parts. First, the statistical
analyses for the results of the ITGO are presented. In the second part, the science
teacher trainees’ lesson observation and evaluation check list results was interpreted
based on their performance in relation to how their understanding affect the teaching
of the topics under investigation. In the third part, the students’ achievement test
results on geometric optics (true /false) questions including fill in the blank spaces
was analyzed to ascertain the impact of the trainee teachers’ understanding of
geometrical optics on the performance of the students.
The researcher prepared a questionnaire on the basis of the literature results. In the
literature review, many studies were conducted to investigate students’ understanding
in geometrical optics. In those studies different types of methods were used to collect
data; interviews, open-ended questions, multiple-choice tests and two-tier tests as well
as a three tier test were used. The researcher obtained the questions of the
questionnaire from these studies. Some of the questions were taken without making
any changes and some of the questions were modified with the help of senior science
lecturers. There were 15 true / false questions in the questionnaire. The questions
required teacher trainees to give reasons for their choice.
60
RESULTS AND ANALYSIS
Table Ia: Trainees’ responses to questionnaire
S/No
1
Items
True
Light reflects from a shiny surface in an
%
False
%
85
85
15
15
82
82
18
18
67
67
33
33
arbitrary manner
2
Light is reflected from smooth mirror
surfaces but not from non-shiny surfaces
3
The mirror image of an object is located
on the surface of the mirror. The image is
often thought of as a picture on a flat
surface.
4
Curved mirrors make everything distorted
77
77
23
23
5
The way a mirror works is as follows: the
81
81
19
19
77
77
23
23
image first goes from the object to the
mirror surface. Then the observer either
sees the image on the mirror surface and
the image reflects off the mirror and goes
into the observer’s eyes.
6
Light always passes straight through a
transparent material without changing its
direction.
61
Items
7
true
An observer can see more of his image by
%
False
%
77
77
23
23
79
79
21
21
68
68
32
32
moving further back from the mirror.
8
When an object is viewed through a
transparent solid or liquid material the
object is seen exactly where it is located.
9
When sketching a diagram to show how a
lens forms the image of an object, only
those light rays that are drawn which
leave the object in straight parallel lines
exit.
10
A mirror reverses everything.
72
72
28
28
11
The effects of light are instantaneous.
56
56
44
44
76
76
24
24
Light does not travel with a finite speed.
12
Light from a bulb only extends outwards
to a certain distance and then stops. How
far it extends depends on the brightness of
the bulb.
13
Refraction can produce images.
69
69
31
31
14
An object is seen because light shines on
16
16
84
84
11
11
89
89
it. Light is a necessary condition for
seeing an object in the eye.
15
In reflection the image produced may be
large or small depending on the surface.
62
From Table Ia, eighty five (85) students representing 85% chose the true option
indicating that they did not understand the concept under investigation in
questionnaire item one (1) which suggests that light reflects from a shinny surface in
an arbitrary manner. The most popular reason they gave was that once light hits any
surface it scatters back into the medium from which it came. On the same concept,
16% of the trainees displayed their sound knowledge by choosing false as their
option. The most popular of their reasons was that the two types of reflection (regular
and diffuse) obey the laws of reflection. This is an indication that they do understand
the concept of reflection.
On questionnaire item two (2), eighty two (82) trainees representing 82% were of the
view that the item was true. The most popular of their reasons is that only shinny
surfaces reflect light. On the other hand 18% of the trainees believe that the statement
was wrong hence chose false. Their reason was that there are two types of reflection,
diffuse reflection (occurs on rough non-shinny surfaces) and regular reflection (occurs
on shinny surfaces). It can be concluded that the latter group did understand the
concept.
Questionnaire item three (3) recorded sixty seven percent (67%) false and twenty
three percent (33%) true. Most of the trainees who chose true were of the view that
the mirror is a flat body and hence images can only be formed on the surface. This is
obviously a misunderstanding of the concept. Those who chose the true as their option
gave their reason as ‘images in the mirrors are far behind them as the objects that
form them are in front of the mirror.
On item four (4), seventy seven (77) trainees were of the view that the statement
‘curve mirrors distort images’ is true. Most of them believe that all curved mirrors are
the same. This is absolutely a misunderstanding. Moreover, twenty three (23) trainees
63
representing thirty three percent (33%) believe that there are at least three types of
curved mirrors. They named these mirrors as concave, convex and parabolic mirrors
hence chose false as their answer.
It was also recorded that eighty one (81) trainees representing 81% believe that
questionnaire item five is true. They believe that the image first goes from the object
to the mirror surface and this allows the observer to see the image on the mirror
surface. Hitherto, 19% of the trainees were of the view that images are seen in mirrors
because light travels from the object to the mirror and thence reflects into the eye.
This is an indication that the later group understands the concept.
The next statement, item six (6) recorded seventy seven (77) true(s) as against twenty
three (23) false (s). Those who subscribed to the option, ‘true’ among their reasons
was that transparent materials do not obstruct the path of light. However, the opposing
group believes that once light travels from one medium into another medium its path
will change. Hence they believe the statement is false.
Questionnaire item seven (7), registered seventy seven (77) true and twenty three (23)
false. Amongst the popular reasons auctioned by the earlier group was that the more a
person moves away from a mirror the bigger they become. Nevertheless, those who
chose false indicated that image size in a plane mirror is the same as object size but
may vary in curved mirrors. This is evidence that they do understand the concept
under investigation.
Seventy nine percent (79%) of the trainees opted for true on questionnaire item
number eight (8), assigning a reason that the object will always be at where it is
placed and hence its position will not change. Twenty one (21) trainees however
displayed their understanding of the concept by opting for false while citing their
64
reason as ‘When an object is viewed through a transparent solid or liquid material the
object is seen at different location due to refraction.
On questionnaire item number nine (9), sixty eight (68) of the trainees representing
68% chose true. They believe that when sketching a diagram to show how a lens
forms the image of an object, only those light rays that are drawn which leave the
object in straight parallel lines exit because light travels in a straight line. Twenty two
percent (22%) of them believe that there are many other rays except that few rays are
required to locate the image of an object based on some principles. This was the basis
upon which the chose the option, false.
Recording responses on item number ten (10), it was realized that seventy two (72) of
the trainees representing 72% were of the view that mirrors reverse everything.
Meanwhile, 28% of the trainees did not believe this was the case hence opted for
false. Interestingly enough both groups did not give any tangible reason for their
choices.
Questionnaire item eleven (11), recorded fifty six percent (56%) true and forty four
percent (44%) false. The item sought to find out if the effects of light are
instantaneous and whether light does not travel with a finite speed. Those who
selected true, have among other reasons that light does not travel with a finite speed
because the speed of light changes as it moves further away. However their opponents
believe that light travels with a finite speed but the speed of light in a medium
depends on the refractive index of the medium.
Further more, seventy six (76) of the trainees were of the view that item 12, was true
while twenty four (24) objected to their option hence chose false. According to the
last group, light from a bulb only extends outwards to a certain distance and then
65
stops. How far it extends depends on the brightness of the bulb because bright bulbs
give more light. This is obviously a misunderstanding.
Questionnaire item number thirteen (13) recorded 69 true with a most common reason
that we can see our faces in water when light moves from air into water. Thirty one
(31) of the trainees opted for false on the basis that it is only reflection that produce
image. They argue that the image we see in water is not due to refraction but
reflection.
The last but one statement, item 14 sought to investigate trainees understanding of the
effect of light on seeing. Sixteen (16) trainees opted for true explaining that light
travels from an object into the eye for one to see it. However eighty four (84) of the
trainees did not agree with them they however said objects can be seen whether there
is light on the object or not. This displays their misunderstanding of the concept under
discussion.
Finally, questionnaire item fifteen (15), received 11% and 89% true and false
responses respectively. The bone of contention was ‘in reflection the image produced
may be large or small depending on the surface’. The former group cited among other
reasons that nature and size of image depends on the reflecting surface and also the
position of the object in front of the reflecting surface. While the later group agrees
that the image of an object is always the same irrespective of the reflecting surface.
This is a misunderstanding. Table 1b, shows the summary of trainees responses to the
questionnaire item. It sought to highlight trainees’ understanding on the various items.
66
Table Ib: Summary of trainees’ responses of questionnaire items
Items
1
2
3
4
5
6
8
9
10
11
12
13
14
15
Average
Percentage true
85
82
67
77
81
77
79
68
72
56
76
69
16
11
62.2
MISUNDERSTANDING
66%
Percentage false
15
18
13
23
19
23
21
22
28
44
24
31
84
89
33.8
UNDERSTANDING
34%
Fig 1 : TRAINEES' UNDERSTANDING OF GEOMETRICAL OPTICS
From the chart (Fig.1), it is evident that 66% of the trainees do not understand the
questionnaire items. This means that only 34% of the trainees do understand the
questionnaire items.
The Table II presents the results of an observation and evaluation conducted on
trainees during lessons on the topic under investigation.
67
Table II: Summary for observation and evaluation of trainees during teaching
Range
percentage
frequency
31-40
52
52
41-50
18
18
51-60
17
17
61-70
13
13
71-80
1
1
total
100
100
After a careful classroom observation of teacher trainees in the course of teaching the
various lessons on the topic under investigation, it came to light that fifty two (52) of
the trainees representing 52% (table II) obtained marks between 31 and 40. This falls
below the fifty percent (50%) pass mark set by the researcher. This is an indication
that majority of the trainees could not teach properly due to their lack of
understanding of geometrical optics. The few trainees who performed satisfactorily
well however were around the 60-70 range. This represents 13% of the sample size.
Only one trainee could hit the 70-80 range mark.
In the ensuing table (i.e. Table III), a summary of students’ achievement test results is
presented and analysed to show the entry behaviour of students before the trainees
taught the topic under discussion.
68
Table III: Students’ achievement test results on entry behaviour of students
Range
(%)
frequency
percentage
1-5
28
56
6-10
16
32
11-15
6
12
Total
50
100
From the students’ achievement test results, (i.e. Table III); it is evident that the
performance of the students was not the best. Out of fifty (50) students selected,
twenty eight (28) students representing 56% had marks in the range of 1-5. Sixteen
of the pupils representing 32% had marks in the range of 6-10 while only 12% had
marks within the range of 11-15. The implication is that students’ entry behaviour
was not good. This is evident in the pie chart below, (Fig. 2)
11--15
12%
6--10
32%
1--5
56%
Fig. 2 STUDENTS' PERFORMANCE BEFORE TEACHING
69
The next table, (i.e. Table IV) represents the post teaching behaviour of students from
the achievement test conducted.
Table IV: Students’ achievement test results after teaching
Range
frequency
percentage
1-5
26
52
6-10
14
28
11-15
10
20
Total
50
100
After the trainees have taught the various lessons, the students’ achievement test was
conducted as a post test to ascertain the impact of the teaching on the students’
performance. This time round, the questions were rearranged in order not to give clue
for students to find the answers easily. It was observed that there was no significant
improvement (see Table IV). Twenty six (26) students representing fifty two percent
(52%) had marks in the range of 1-5 less two students as in the results of the entry
behaviour. Also fourteen (14) students representing twenty eight percent (28%) had
marks in the range of 6-10 less two students as in the case of the marks obtained in the
entry behaviour test. There was a little improvement though; in that, ten (10) students
representing 20% had marks in the range of 11-15. However this was not significant
enough to show that what the trainees taught had an impact on the students.
70
11--15
20%
1--5
52%
6--10
28%
Fig. 3. STUDENTS' PERFORMANCE AFTER TEACHING
In Fig. 3, 52% of the students fell in the range of 1-5 indicating that their
performances even after the trainees have taught the said topics did not improve
significantly. Only 20% of the students made it in the range of 11-15 marks,
obviously not impressive. Twenty-eight percent (28%) were able to fall in the range
of 6-10.
DISCUSSION
The study sought to answer the following research questions:
1. What is the extent of science teacher trainees’ understanding of geometrical
optics?
2. To what extent does the science teacher trainees’ understanding of the concept
of geometrical optics affect their teaching?
3. How significant does the science teacher trainees’ understanding of the
concept of geometrical optics affect students’ understanding of geometric al
optics?
71
ANSWERING OF RESEARCH QUESTIONS
RQ1
What is the extent of science teacher trainees’ understanding of geometrical
optics?
Literature reports on students’ understanding of geometrical optics in physics suggest
that students at various levels of teaching hold certain understanding (conception)
about many concepts (Bradley & Mosimege, 1998). The literature also points to the
need for pedagogies that will help avoid or change these alternative conceptions
otherwise called misunderstanding and thus improve students’ conceptual
understanding (Nakhleh & Krajcik, 1994; Sisovic & Bojovic; Demircioglu &
Demircioglu, 2005). This notion forms the basis for the present inquiry.
From the results obtained in the study, it is evident that trainees’ level of
understanding in geometrical optics is inadequate. Questionnaire item one (1) for
example revealed that eighty five percent (85%) of the trainees believe light travels on
shinny surface in an arbitrary manner, a premise to suggest that they did not
understand the concept of reflection. Similarly, questionnaire items two (2), three (3)
and all others provided evidence that most science teacher trainees do not understand
the concepts they teach under geometrical optics. In general terms however sixty six
percent (66%) of the trainees do not understand what they teach.
RQ2
To what extent does the science teacher trainees’ understanding of the concept of
geometrical optics affect their teaching?
The observation and evaluation check list has provided the basis upon which the
researcher agrees with Perkins’ (1992) that understanding something (topic) is a
72
matter of being able to carry out a variety of "performances". Besides, Guyton and
Farokhi (1987) agreed that if prospective teachers are recruited from among the
academically best candidates, if they perform well in university courses, if they
possess basic skills competency and are educated extensively in their academic
disciplines, and if they are placed in schools under the guidance of master teachers,
then highly competent teachers will emerge. Currently, subject matter knowledge of
teachers is highly emphasized. According to Calderhead (1995), "how we prepare
new teachers for the profession, how we support them in their first post as teachers,
and how we help them to develop in their future careers varies widely". He also
agreed that the training of teachers is seen as a key influence in the improvement of
education. Adler (1982) suggested that teachers should themselves be at least as wellschooled as the graduates of the schools in which they are expected to teach. Clark
and Elmore (1981) reported that teachers adapt curricula to fit their knowledge and
Calderhead (1995) explained that studies of novice and experienced teachers suggest
that the competent teacher possesses an enormous diversity of knowledge - not only
about subject matter, but about children, teaching and the classroom context - that
enables teachers to make sense of classrooms and to monitor and shape their
classroom routines and behaviour. From the observation it was evident that more than
52% of the trainees could not obtain a pass mark of 50 % that the researcher set as a
target for them to meet. Among the other things which prevented them from meeting
the demand is inadequate knowledge in the subject matter hence their incompetence.
This suggests that trainees understanding of the concept under investigation did affect
their teaching negatively.
73
RQ3
How significant does the science teacher trainees’ understanding of the concept
of geometrical optics affect students’ understanding of geometric al optics?
A person’s understanding of the nature of science and mathematics predicates that
person’s view on how teaching should take place in the classroom. (Hersh, 1986) also
Science and Mathematics teachers’ conceptions about the subject matter, teaching,
and learning influence their action in the classroom. (Madison, Nason, & Lanier,
1986; Fennema, & Peterson, 1985; Thompson, 1984; Dougherty, 1990). Students
have much trust in their respective teachers. This was revealed in results of the
students’ achievement test that was administered after the trainees have taught the
topics in the area under investigation. The result revealed that there was no significant
change in the learning behaviour of the students; whereas twenty eight (28) students
representing 56% had marks in the range of 1-5, Sixteen (16) of the students
representing 32% had marks in the range of 6-10 and12% had marks within the range
of 11-15, the post teaching result indicates that Twenty six (26) students representing
fifty two percent (52%) had marks in the range of 1-5 while fourteen (14) students
representing twenty eight percent (28%) had marks in the range of 6-10 and ten (10)
students representing 20% had marks in the range of 11-15. Thus in terms of positive
change in behaviour as a results of the teaching, there was a marginal increase in the
number of students who had marks in the range of 11-15; an eight percent (8%)
increase. To the researcher, teachers who hold the absolutists view about science and
for that matter its teaching and learning are more likely to create teacher-centered
instructional environment, teach science as rules to be memorize, and portray science
as an infallible discipline but teachers holding constructivist view of science are
expected to adopt teacher-student interaction mode of instruction by allowing students
74
to explore and investigate while teachers reside in their classrooms as facilitators.
This can be linked to the fact that what you know is what you teach. Besides,
Calderhead (1995: 3) believes that since children's own backgrounds vary
considerably and they approach a subject with particular understanding of their own,
teachers need a wide repertoire of pedagogical content knowledge to cater for
children's individual differences. The analogy that works for one child, for example,
may be completely meaningless to another. Debate about the knowledge base for
teacher education is at the core of the move to establish professional standards for
teaching (Beaudry, 1991). Grossman (1989) agreed that teachers must have a
theoretical understanding of how students learn a particular subject in addition to
knowledge of the subject matter itself.
75
CHAPTER 5
SUMMARY OF FINDINGS, CONCLUSION, SUGGESTION AND
RECOMMENDATION
This chapter consists of four sections. The first section is the summary of the findings.
The second section includes the conclusions based on the results. This is followed by
the third section which constitutes the suggestion of the study. The chapter closes with
a set of recommendations for further studies and consideration.
SUMMARY OF FINDINGS
This study employed a two-tier inventory test on geometrical optics to investigate the
science teacher trainees’ understanding of geometric optics. An observation and
evaluation check list was also designed to evaluate the impact of trainees’
understanding of geometrical optics on their teaching practices. Finally, a student
assessment test was also used to find out how the teaching of the topic by the trainees
would affect the performance of the students.
The research design was that of a survey. Firstly, related literature was reviewed to
investigate students’ conceptions or otherwise their understanding about geometrical
optics and other concept areas. Secondly, views of hundred (100) science teacher
trainees were sampled using a set of questionnaire constructed with the help of the
literature Inventory Test on Geometrical Optics (ITGO). Thirdly, a multiple choice
test was constructed based on the literature review for the basic school students who
otherwise may have benefited from what trainees know and perhaps have taught in
class. This was administered to 50 students. Fourthly, the results were analyzed and
recommendations as well a design was made in the form of a course manual and hints
to help facilitate the teaching of the topic at issue. It was found out among other
things that:
76
1. Teacher trainees do not understand what they teach and thus are unable to
teach the concepts when they go out.
2. It was found that the trainees who had answered the questionnaire right with
scientific reasons also did not understand some of the concepts they answered
right.
3. Even if the trainees were above average, they had little or no understanding of
a conceptual understanding of a physical phenomenon based on geometrical
optics.
4. Multiple-choice tests and also two-tier tests overestimate the understanding of
the trainees. Because, they do not take into account the mistakes of the
students and lack of knowledge of the students.
5. What teacher trainees understand and teach affect their way of teaching and in
turn affect the performance of the learners they teach.
CONCLUSION
 It appears most trainees do not understand the practicalities of the aspect of
geometrical optics in the Physics syllabus they use in teaching. E.g. of topics
include reflection and refraction of light.
 Teacher trainees’ understandings of the concept of geometrical optics affect
their teaching and in turn affect the performance of the students they teach.
Trainees should be given the pre-requisite concept through the constructivist approach
of learning in order that they will be able to impact positively on the learners they
teach
77
SUGGESTIONS
According to the results of the study and findings of the previous studies, the
following suggestions can be offered:
1. This study was carried out to investigate science teacher trainees’ understanding
about Geometrical optics. Other physics topics can be studied so that trainees’
understanding can be investigated by a three-tier test. It is also important to say that in
the literature’ some concepts have been studied too much, whereas some concepts
have seen little studies. Therefore, it is worth working with the concepts which have
been studied less.
2. The ITGO was administered to 100 students. However, the independent variables
such as school type, gender and socio-economic status were not taken into account.
Therefore, a study that investigates the effects of these independent variables of
trainees’ understanding in geometrical optics can be studied.
3. The ITGO was administered to 100 students. For ecological validity concerns, it
can be administered to larger population to reflect the actual situation on the ground.
4. Textbook writers and editors should look at a more constructivist approach to
writing so as to help facilitate interesting reading and learning.
5. The course manual designed by the researcher dwells on only the theoretical aspect
of geometrical optics taught in the Colleges of Education. However researchers can
equally take a look at the practical aspect as well.
78
RECOMMENDATION

Trainees be taken through the constructivist’s school of teaching and learning
in order that they would acquire concepts in geometrical optics through
investigation.
 Teacher trainees do not understand what they teach and thus are unable to
teach the concepts when they go out. Tutors should find out what trainees
know and understand in order to ascertain where to start teaching from. This
can be done through assessing the entry behaviour of trainees. The more tutors
know about what trainees’ know, the more they will be able to help them to
study and understand concepts.
 In the study, it was found that the trainees who had answered the questionnaire
right with scientific reasons also did not understand some of the concepts they
answered right. This means that even the brilliant teacher trainees have
problems of their own. Every trainee is a learner; therefore, tutors should
consider that even if the students have high scores in exams, they may still
have many of them who do not understand those concepts they get right.
Hence teaching should be done comprehensively and thoroughly.
 The manual and the model lessons (hints) on this study should be adhered to in
teaching geometrical optics (light energy) in the science and mathematics
colleges of education.
79
REFERENCES
Abelson, R. (1979). Differences between belief system and knowledge systems. Cognitive
Science, 3, pp, 355-366.
Adler, M. J. (1982). 'The Paideia Proposal. New York: MacMillan.
Aikenhead, G. S., & Ryan, A. G. (1992). ‘The development of a new instrument: “Views
on science-technology-society” (VOSTS), Science Education 76, 477-491.
Aikenhead, G. S. (2003). Research report: Concepts of evidence used in science-based
occupations: Acute-care nursing. Available at URL:
http://www.usask.ca/education/people/aikenhead/acnursing.htm.
Ajzen, I. & Fishbein, M. (1980). Understanding attitudes and predicting social behavior.
Englewood Cliffs, NJ: Prentice-Hall.
Al-Rubayea, A. A. M. (1996). An analysis of Saudi Arabian high school students’
Misconceptions about physics concepts. Kansas State University. Dissertation
Abstracts International (University Microfilms No. 9629018).
Ausubel, D. P. (1963). Cognitive structure and the facilitation of meaningful verbal
learning. Journal of Teacher Education, 14, 217-222.
Baron, J. (1990). Performance assessment: Blurring the edges among assessment,
curriculum and instruction. In A Champagne, B. Lovetts and B.
Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is--or might be--the role
of curriculum materials in teacher learning and instructional reform? Educational
Researcher, 25(9), 6-8.
Beaudry, M. L. (1991). Post Carnegie developments affecting teacher education: The
struggle for professionalism. Journal of Teacher Education 41(1), 63-70.
80
Behr, M., Lesh, R., Post, T., & Silver, E. (1983). Rational-number concepts. In R. Lesh
and M. Landau (eds.), Acquisition of mathematics concepts and processes (pp. 91126). New York: Academic Press.
Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. American
Journal of Physics, 62 (8), 750-762.
Bendall, S., Goldberg, F., & Galili, I. (1993). Prospective Elementary Teachers' Prior
Knowledge about Light. Journal of Research in Science Teaching, 30 (9), 1169-87.
Beothel, M., & Dimock, K. V. (2000). Constructing Knowledge with Technology.
Austin, TX: Southwest Educational Development Laboratory.
Bereiter, C. & Scardamalia, M. (1985). Cognitive coping strategies and the problem of
inert knowledge. In S.S. Chipman, J. W. Segal, and R. Glaser (Eds.), Thinking and
learning skills, 2: Current research and open questions (pp. 65-80). Hillsdale, N.J.:
Erlbaum.
Best, J.W. (1970). Research in education. New Jersey: Prentice-Hall Inc.
Bradley J.D., & Mosimege M.D., (1998). Misconceptions in acids and bases: a
comparative study of student teachers with different chemistry backgrounds. S.
African. Journal. Chemistry. 51(3): 137-145.
Brodkey, J. J. (1986). Learning while teaching. Unpublished doctoral dissertation,
Stanford University.
Brown, A. L. (1989). Analogical learning and transfer: What develops? In S. Vosniadou
and A. Ortony (Eds.), Similarity and analogical reasoning (pp. 369-412). New York:
Cambridge University Press.
81
Brown, A. L., Ash, D., Rutherford, M., Nakagawa, K., Gordon A. & Campione, J.C.
(1993). Distributed expertise in the classroom. In G. Salomon (Ed.), Distributed
cognitions: Psychological and educational considerations (pp. 188-228). New York:
Cambridge University Press.
Calderhead, .J. 1995. Knowledge and skills: Informing reform in teacher education. In
Proceedings of ITEC 95. pp.1-13. Department of Curriculum Studies. University of
Hong Kong.
Carretero, M., Pozo, J.I., & Asensio, M. (Eds.) (1989). La ensenanza de las Ciencias
Sociales. Madrid: Visor.
Case, R. (1985). Intellectual development: Birth to adulthood. New York: Academic
Press.
Case, R. (1992). The mind's staircase: Exploring the conceptual underpinnings of
children's thought and knowledge. Hillsdale, N.J.: Lawrence Erlbaum Associates.
Çataloglu, E. (2002). Development and Validation of an Achievement Test in Introductory
Quantum Mechanics: The Quantum Mechanics Visualization Instrument. The
Pennsylvania State University. Center on Education Policy, From the Capital to the
Classroom: Year 2 of the No Child Left Behind Act, Washington, D.C.: Center for
Education Policy, 2004.
Chen, C. C., Lin, S. H., & Lin, M. L. (2002). Developing a Two-Tier Diagnostic
Instrument to Assess High School Students’ Understanding – The Formation of
Images by a Plane Mirror. Proc. Natl. Sci. Counc. ROC(D), 12 (3),106-121.
Chin, C. & Brown, D. E. (2000). Learning in science. A comparison of deep and surface
approaches. Journal of Research in Science Teaching. 37. 109-138.
82
Clark, C. M. & Elmore, J. L. (1981). Transforming curriculum in mathematics, science
and writing: A case study of yearly planning. East Lansing. MI: Michigan State
University.
Cohen, L., Manion, L., & Morrison, K. (2000). Research Methods in Education (5th Ed).
New York: Routledge Falmer.
Cooney, T. J. (1994). Research and teacher education: In search of common ground.
Journal for Research in Mathematics education, Vol. 25, pp. 608-636.
Cooper, D. R. & Schindler, P. S. (2001). Business Research Methods. 7th Ed. Boston;
Mcgraw-Hill.
Crawley, F. E., & Koballa, T. R. (1994). Attitude research in science education:
contemporary models and methods. Science Education, 78, 35–55.
Demircioğlu, A. A. & Demircioğlu, H. (2005) Conceptual change achieved through a
new teaching program on acids and bases, Chemistry Education Research Practice 6
pp. 36–51.
Dewey, J. (1916). Democracy and Education. New York: Harper and Row.
Dougherty, B. J. (1990). Influences of Teacher Cognitive Conceptual Level on Problem –
Solving Instruction. In G. Booker et al. (Ed.), proceedings of Fourteenth
International Conference for Psychology of Mathematics Education (pp. 119- 126).
Oaxtepec, Mexico: International study group for the Psychology of mathematics
education.
Duffy, T. M., & Jonassen, D. H. (1992). Constructivism and the technology of
instruction: An Education, 76, 653-672. Erlbaum Associates.
83
Dupin, J. J., & Johsua, S. (1989). Analogies and "Modeling Analogies" in Teaching:
Some Examples in Basic Electricity. Science Education, 73(2), 207-224.
Eklund-Myrskog, G. (1998). Students' conceptions of learning in different educational
contexts. Higher Education. Vol.35. 299-316.
http://portal.acm.org/citation.cfm?id=1613552. Last accessed date February, 2010
Ernest, P. (1988). The Impact of Beliefs on the Teaching of mathematics. In P. Ernest
(Ed.), Mathematics Teaching: The State of the art, (pp. 249-254). London: Falmer.
http://www.ex.ac.uk/~PErnest/impact.htm (pp. 1-5)
Ernest, P. (1989). The Knowledge, Beliefs and Attitudes of the Mathematics Teacher: A
Model. Journal of Education for Teaching, 15 (1), 13-33.
Eryılmaz, A., & Sürmeli, E. (2002). The assessment of students’ misconceptions about
heat and temperature concepts by means of three-tier questions]. Retrieved;1;
February 2,. [2010,] from http://www.fedu.metu.edu.tr/ufbmek5/netscape/b_kitabi/PDF/Fizik/Bildiri.
Feher, E., & Rice, K. (1988). Shadows and Anti-Images : Children’s Conceptions of
Light and Vision. 2. Science Education, 72 (5), 637-649.
Fetherstonhaugh, T., & Treagust, D. F. (1992). Students’ understanding of light and its
and its properties: teaching to engender conceptual change. Science education, 76,
653-672.
Fischer, K. W. (1980). A theory of cognitive development: The control and construction
of hierarchies of skills. Psychological Review, 87(6), 477-531.
84
Fiske, E. B. (1991). Smart schools, smart kids. New York: Simon & Schuster. Foundation
of everyday knowledge. In G. Leinhardt, R. Putnam, and R.A. Hattrup (Eds.),
Francisco: Jossey-Bass.
Gardner, H. (1991). The unschooled mind: How children think and how schools should
teach. New York: Basic Books.
Gagné, R. M. (1985) The Conditions of Learning (4Ed), New York: Holt, Rinehart and
Winston.
Gee, J. K. (1988). The myth of lateral inversion. Physics Education, 28, 300-301
Gifford, B. R., & O'Connor, M. C. (Eds.) (1991). Changing assessments: Alternative
views of aptitude, achievement and instruction. Norwood, Mass.: Kluwer Publishers.
Glatthorn, A. A. (1990). Supervisory leadership. New York: Harper Collins.
Goldberg, F., & McDermott, L. C. (1986). Student difficulties in understanding image
formation by a plane mirror. The Physics Teacher, 24, 472- 480.
Gott, R., Duggan, S., & Roberts, R. (2003). Understanding scientific evidence. Available
at URL: http://www.dur.ac.uk/∼ded0rg/Evidence/cofev.htm.
Griffard, P. B., & Wandersee, J. H. (2001). The Two-Tier Instrument on Photosynthesis:
What Does It Diagnose? International Journal of Science Education, 23 (10), 10391052.
Grimmet, P., & MacKinnon, A. (1992). Craft knowledge and the education of
teachers. In G. Grant (Ed.), Review of research in education 18, (pp. 5974) Washington, DC: AERA.
Grossman, P. L. (1989). Teachers of substance: subject matter knowledge for teaching.
In Knowledge Base for the Teacher. Reynolds, M. C. (Ed). New York: Pergamon.
85
Guyton, E., & Farokhi, E. (1987). Relationship among academic performance, basic
skills, Subject matter knowledge and teaching skills of teacher education graduates.
Journal of Teacher Education 38(5): 37-41.
Haslam, F., & Treagust, D.F. (1987). Diagnosing secondary students’ misconceptions of
photosynthesis and respiration in plants using a two-tier multiple choice instrument.
Journal of Biological Education, 21(3), 203-211.
Hersh, R. (1979). Some proposals for revising the philosophy of mathematics. Advances
in Mathematics, Vol. 31. pp. 31-50.
Hersh, R. (1986). Some proposals for revising the philosophy of mathematics. In T.
TYMOCZKO (Ed.), New Directions in the Philosophy of Mathematics. Boston:
Birkhauser.
Hestenes, D., & Halloun, I. (1995). Interpreting the Force Concept Inventory. A response
to Huffman and Heller. The Physics Teacher, 33, 502-506.
Hewson, P. W., & Hewson, M. G. A. B. (1984).The role of conceptual conflict in
conceptual change and the design of instruction. Instructional Science, 13(1), 1-13.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to
adolescence. New York: Basic Books. Institute of Education, University of Cape
Coast, Chief Examiners Report on second year Physics theory (FDC 224P), 2008 &
2009.
Kember, D. (1997); Tillema, (1994, 1995) conceptions of knowledge, learning and
instruction p://www.manchesteruniversitypress.co.uk/uploads/docs/670044.pdf. Last
accessed date 8th February, 2010.
86
Kitchener, K. S. (1986). The reflective judgment model: Characteristics, evidence, and
measurement. In R. A. Mines & K. S. Kitchener (Eds.), Adult Cognitive
Development: Methods and Models, (pp. 76-91). New York: Praeger.
Klammer, J. (1998). An Overview of Techniques for Identifying, Acknowledging and
Overcoming Alternative Conceptions in Physics Education,
http://www.klingenstein.org/html/research/projects/1998/klammer.htm, Last accessed
date January 2004.
KumkporLiu, L. & Johnson, L. (2002). A technology integration model and weak areas.
Computers in the schools, 20 (2).
Langley, D., Ronen, M., & Eylon, B. (1997). Light Propagation and Visual Patterns: Preinstruction Learners' Conceptions. Journal of Research in Science Teaching, 34 (4),
399- 424.
Lochhead, J., & Mestre, J. (1988). From words to algebra: Mending misconceptions. In
A. Coxford and& A. Schulte (Eds.), The idea of algebra k-12: National Council of
Teachers of Mathematics Yearbook (pp. 127-136). Reston, Va.: National Council of
Teachers of Mathematics.
Madsen-Nason, A., & Lanier, P. E. (1986). Transforming Instructional Practice in
General Mathematics Classes. Paper presented at annual meeting of the North
American Chapter of the International Group of Psychology of mathematics
education, East Lansing, Michigan.
Marra, R. M., Palmer, B., & Litzinger, (2000). The Relationships between Students'
Conceptions of Learning: conceptions of learning in higher education and their
significance in the learning processes
87
http://www.britannica.com/bps/additionalcontent/18/39246484. Last accessed date
February, 2010.
Marx, J. D. (1988). Creation of a diagnostic exam for introductory, undergraduate
electricity and magnetism. Rensselaer Polytechnic Institute, Troy, New York.
Dissertation Abstracts International (University Microfilms No.9908686).
Mayer, R. E. (1989). Models for understanding. Review of Educational Research, 59, 4364.
McCloskey, M. (1983). Naive theories of motion. In D. Gentner and A. L. Stevens (Eds.),
Mental models (pp. 299-324). Hillsdale, N.J.: Lawrence Erlbaum Associates.
McMillan, J. H., & Schumacher, S. S. (1997). Research in Education: A Conceptual
Introduction. New York: Longman.
Mergel, B. (1998). Instructional design and learning theory. Retrieved October 11, 2006
from http://www.usask.ca/education/coursework/802papers/mergel/brenda.htm.
Merrill, M. D. (2001). Components of Instruction Toward a Theoretical Tool for
Instructional Design. Instructional Science, 29, 291-310.
Miller, L., & Silvernail, D. L. (1994). Wells Junior High School: Evolution of a
professional development school. In L. Darling-Hammond (Ed.), Professional
development schools: Schools for developing a profession (pp.56-80). New York:
Teachers College Press.
Nakhleh, M. B., & Krajcik, J. S. (1994). Influence on levels of information as presented
by different technologies on students' understanding of acid, base, and pH concepts.
Journal of Research in Science Teaching, 31(10), 1077-1096.
88
National Assessment of Educational Progress (1981). Reading, thinking, and writing.
Princeton, N. J.: Educational Testing Service.
National Council of Teachers of Mathematics (1989) Curriculum and evaluation
standards for school mathematics. Reston, Va.: National Council of Teachers of
Mathematics.
Nussbaum, J. (1985): The earth as a cosmic body, In R. Driver, E. Guesne, and A.
Tiberghien (Eds.), Children's ideas in science (pp. 170-192). Philadelphia, Pa.: Open
University Press.
Nussbaum, J., & Novick, S. (1982). Alternative frameworks, conceptual conflict and
accommodation: Toward a principled teaching strategy. Instructional Science, 11,
183–200.
Odom, A. L., & Barrow, L. H. (1995). Development and Application of a Two-Tier
Diagnostic Test Measuring College Biology Students' Understanding of Diffusion
and Osmosis after a Course of Instruction. Journal of Research in Science Teaching,
32 (1), 45-61.
Ornstein, A. C., Thomas, J., & Lasley, I. (2000). Strategies for effective teaching. New
York: McGraw-Hill.
Osborne, R., & Gilbert, J. K. (1980). Physics Education: Students’ conceptions of ideas in
mechanics – The use of everyday language. http://www.iop.org/EJ/article/0031120/17/2/309/pev17i2p62.pdf. last accessed 8th February, 2010.
Padgett, D. K. (Ed) (2004). The qualitative Research Experience. USA:
Wadworth/Thompson.
89
Palmer, J. P., & Mark S. (2003). "What Do Faculty Want?" Library Journal 128, pp. 2628.
Pepin, B. (1999). Epistemologies, beliefs and conceptions of mathematics teaching and
learning: The theory and what is manifested in mathematics teachers' work in
England, France and Germany. TNTEE Publications, 2(1), pp.127-146.
Perkins, D. N. (1986). Knowledge as design. Hillsdale, N.J.: Lawrence Erlbaum
Associates.
Perkins, D. N., & Salomon, G. (1988). Teaching for transfer. Educational Leadership,
46(1), 22-32.
Perkins, D. N., & Simmons, R. (1988). Patterns of misunderstanding: An integrative
model for science, math, and programming. Review of Educational Research, 58(3),
303-326.
Perkins, D. N. (1992). Smart schools: From training memories to educating minds: New
York: The Free Press.
Perkins, D. N., & Unger, C. (in press). A new look in representations for mathematics and
science learning. Instructional Science.
Perrone, V. (1991). A letter to teachers: Reflections on schooling and the art of teaching.
San Francisco: Jossey-Bass.
Perrone, V. (ed.) (1991b). Expanding student assessment. Alexandria, Va.: Association
for Supervision and Curriculum Development.
Peterson, L., & Fennema, E. (1985). Effective teaching, student engagement in classroom
activities, and sex-related differences in learning mathematics. American
Educational Research Journal, 22, 309-335.
90
Piaget, J. (1972). To Understand Is To Invent. New York: The Viking Press, Inc.
Pope, M. L., & Scott, E. M. (1984). Teachers' epistemology and practice. In R. Halkes, &
J. K. Olson (Eds.), Teachers thinking: A new perspective on persisting problems in
education, (pp. 112-122). Lisse: Swets & Zeitlinger.
Raymond, A. M. (1993). Understanding Relationships between Beginning Elementary
Teachers' Mathematics Beliefs and Teaching practices. Abstract from: Pro Quest File:
Dissertation Abstracts Item: 9404352
Reiner, M., Slotta, J. D., Chi, M. T. H., & Resnick, L. B. (2000). Naive physics
reasoning: A commitment to substance-based conceptions. Cognition and Instruction,
18(1), 1-35.
Resnick, L. B. (1987). Constructing knowledge in school. In L. Liben (Ed.), Development
and learning: Conflict or congruence? (pp. 19-50). Hillsdale, NJ.: Lawrence Erlbaum
Associates.
Resnick, L. B. (1992). From proto-quantities to operators: Building mathematical
competence on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam, and
R.A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 373-429).
Hillsdale, N. J.: Lawrence Erlbaum Associates.
Robson, C. (1995). Real Word Research: A resource for social scientists and
Practitioners-Researchers, Great Britain, Padstow: T.J. Press Ltd.
Robson, C. (2002). Real world research: A resource for social scientists and practitioner
researchers. Malden: Blackwell Publishing.
Rollnick, M., ＆ Mahooana, P. (1999). An Online System Using Dynamic Assessment
and Adaptive Material: Using another form of testing to diagnose students' scientific
91
conception. A two-tier assessment.
http://ieeexplore.ieee.org/iel5/4417794/4417795/04417982.pdf?arnumber=4417982.
Last accessed date February, 2010.
Royer, J. M., & Cable, G. W. (1976). Illustrations, analogies, and facilitative transfer in
Prose learning. Journal of Educational Psychology, 68(2), 205-209.
Rumelhart, D. E., & Norman, D. A. (1981). Analogical processes in learning. In J. R.
Anderson, (Ed.), Cognitive skills and their acquisition. Hillsdale, NJ: Erlbaum.
Salomon, G., & Perkins, D. N. (1989). Rocky roads to transfer: Rethinking mechanisms
of a neglected phenomenon. Educational Psychologist, 24(2), 113-142.
Savinainen, A., & Scot, P. (2002). The Force Concept Inventory: a tool for monitoring
student learning. Physics Education, 37 (1), 45-52.
Schwab, J. (1978). Science, curriculum, and liberal education: Selected essays (I.
Westbury and N.J. Wilkof, Eds.). Chicago: University of Chicago Press.
Sharon, B. (1993). Prospective elementary teachers' prior knowledge about light. Journal
of Research in Science Teaching.1993 30(9), 1169-1 187.
http://doi.wiley.com/10.1002/tea.3660300912. Last accessed date February, 2010.
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational
Researcher, 15 (2), 4-14.
Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard
Educational Review, 57 (1), 1-22.
Shulman, L. (1992). September-October).Ways of seeing, ways of knowing, ways of
teaching, ways of learning about teaching. Journal of Curriculum Studies, 28, 393396
92
Shelmit, D. (1980). History 13-16, evaluation study. Great Britain: Holmes McDougall.
Sisovic, D., & Bojovic, S. (2000D). Approaching the concepts of acids and bases by
cooperative learning, Chem. Edu:Res. Prac. in Eur 1 (2000), pp. 263–275.
Sizer, T. B. (1984). Horace's compromise: The dilemma of the American high school
today. Boston: Houghton Mifflin.
Skinner, B. F. (1953). Science and Human Behaviour. New York: Macmillan.
Steinberg, R. N., & Sabella, M. S. (1997). Performance on Multiple-Choice Diagnostics
and Complementary Exam Problems. Physics Teacher, 35, 150-155. The Free
Dictionary (2005), http://www.thefreedictionary.com/conception, Last accessed date
September, 2005
Tan, K. C. D., Goh, N. K., Chia, L. S., & Treagust, D. F. (2002). Development and
application of a two tier multiple choice diagnostic instrument to assess high school
students’ understanding of inorganic chemistry qualitative analysis, Journal of
Research in Science Teaching, 39, 283-301.
Teo, W. L. (1997). Espoused Beliefs of Singapore Teachers about Mathematics and its
Teaching and Learning. Master paper, Ontario Institute for studies in Education of the
University of Toronto.
Tsai, C. C., & Chou, C. (2002). Diagnosing students’ alternative conceptions in science.
Journal of Computer Assisted Learning, 18, 157-165. Watts, D. M. (1985). Student
Conceptions of Light: A Case Study. Physics Education, 20 (4), 183-87.
Tillema, H. H. (1994), ‘Training and professional expertise: bridging the gap between
new information and pre-existing beliefs’, Teaching and Teacher Education 10 (6),
01–15.
93
Tillema, H. H. (1995), ‘Changing the professional knowledge and beliefs of teachers: a
training study’, Learning and Instruction 5 (4), 291–381.
Thompson, A.G. (1984). The Relationship of Teachers’ Conceptions of Mathematics and
Mathematics Teaching to Instructional Practice. Educational Studies in Mathematics,
5(2), pp. 105-127.
Thompson, A G. (1992). Teachers’ Beliefs and Conceptions: A Synthesis of the Research.
In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and
Learning, (pp.127-146). New York: Macmillan Publishing Company.
Thom, R. (1973). Modern Mathematics: Does it exist? In A. G. Howson (Ed.),
Developments in Mathematics Education: Proceedings of the Second International
Congress on Mathematics Education. Cambridge University Press.
Trigwell, K., & Prosser, M., (1991). Improving the quality of student learning: the
influence of learning context and student approaches to learning on learning
outcomes. Higher Education, 22, 251-266. U.S. Department of Education, No Child
Left Behind Web site, http://www.nochildleftbehind.gov.
Von Glasersfeld, E. (1996). Introduction: Aspects of constructivism. In C. Fosnot (Ed.),
Constructivism: Theory, perspectives, and practice, (pp.3-7). New York: Teachers
College Press.
Walonnick , D. S. (2004), Survival Statistics. StatPac, Inc., 8609 Lyndale Ave. S. #209A,
Bloomington, MN 55420.
Warren, H. (2004). Engineering Subject Centre Guide: Learning and Teaching Theory
for Engineering Academics. Loughborough: HEA Engineering Subject Centre.
94
White, B. (1984). Designing computer games to help physics students understand
Newton's laws. York: Academic Press.
Zeilik, M. (n.d.). Conceptual Diagnostic Tests,
http://www.flaguide.org/extra/download/cat/diagnostic/diagnostic. PDF, Last
accessed date March 2004
95
APPENDICES
Appendix A
PROPOSED COURSE MANUAL AND HINTS FOR TEACHING
GEOMETRICAL OPTICS IN THE SCIENCE AND MATHEMATICS
COLLEGE OF EDUCATION
GEOMETRICAL OPTICS COURSE MANUAL
Introduction:
This course manual is designed to help facilitate the teaching and learning of the
theoretical aspect of geometrical optics dubbed light energy, as part of the second
year, second semester course in elective physics for the Science and Mathematics
Colleges of Education in Ghana. Though this course is not taught in isolation in the
semester, the researcher believes that a maximum of seven weeks for three credit
hours per week will be sufficient to teach and learn this concept. Currently an average
of three weeks for three credit hours per week is used to treat the course in question.
This is not helping as this has led to poor performance of teacher trainees in this area
during the second semester. Institute of Education (UCC), Chief examiners report,
Physics, 2008&2009.
Hints on the various topics of the course have been provided to give support for the
teaching and learning of this course.
Assessment: Two quizzes, two exercises and one assignment should be used to assess
trainees’ performance in the course. The two quizzes should be scored over 50 while
the two exercises and the assignment should be scored over 30 and 20 respectively.
Caution: Attendance to lectures should form the basis of writing the two quizzes.
96
Objective(s): By the end of this course trainees will be able to:
a. Classify the various sources of light into luminous and no-luminous.
b. Draw ray diagrams to illustrate the path taken by light in both reflection and
refraction.
c. Explain the formation of images in plane mirrors, curved mirrors and lenses
and also state the uses of mirrors and lenses.
d. Identify the various laws of reflection and refraction.
e.
Carry out simple calculations using the lens and mirror formula.
f. Explain the concept of dispersion of light; pure and impure spectrum using
diagrams.
g. Explain the functions of some optical instruments and their uses.
h. Identify at least three defects of the human eye (myopia, hyperrmetropia, and
presbyopia) and how they can be corrected.
i. State at least four differences and four similarities between the human eye and
the lens camera.
Outline:
1.1 Sources of light and definition of light energy.
1.2 Differences between luminous and non luminous bodies.
1.3 Transmission of light and definition of transmit light including terms like opaque
bodies, phosphorescent bodies, fluorescent bodies and incandescent bodies.
1.4 Types of beams and their uses
97
1.5 Experiment to show that light travels in a straight line (rectilinear propagation of
light) and its application
1.6 Ray diagrams to illustrate practical application of rectilinear propagation of light
e.g. formation of shadows and photography (pin-hole cameras) as well as eclipses.
1.7 Calculation involving images in pin-hole cameras; magnification and position as
well as size and distance of images
1.8 Quiz one (1) and exercise one (1)
1.9 Reflection; types, laws and the terms associated with it.
1.10
Reflection in mirrors; plane and curved mirrors and the characteristics of their
images.
1.11
Real and virtual images and their characteristics.
1.12
Formation of images in plane mirrors and the uses of plane mirrors.
1.13
Relationship between the angle between two inclined plane mirrors and the
number of images produced.
1.14
Curved mirrors and the terms associated with them.
1.15
Formation of images in curved mirrors; concave and convex mirrors
1.16
The curved mirror formula and calculation
1.17
Assignment.
1.18
Refraction, laws and the terms associated with it.
1.19
Calculations on refractive index based on Snell’s law, and real and apparent
depths.
1.20
Critical angle and total internal reflection.
1.21
Lenses and the terms associated with them
1.22
Formation of images in lenses, calculations using the lens or curved mirror
formula and the uses of lenses.
98
1.23
Dispersion of white light: pure and impure spectrum
1.24
Optical instruments; microscope, lens camera etc and their uses.
1.25
The human eye; defects of the human eye and their correction.
1.26
Differences and similarities between the lens camera and the human eye.
1.27
Quiz two (2) and exercise two (2).
BELOW ARE HINTS PROVIDED TO GUIDE TUTORS TO HELP THEM TEACH
THE CONCEPT PROPERLY
LIGHT ENERGY
Lesson 1
(Guide learners to define light energy through series of activities and questions: e.g.
Close all windows in the class and ask learners to identify what can help them to see
in the room guide them to define light energy. Give them your own definition and
then throw more light on it). Also guide learners to enumerate some properties of
light through discussion)
Definition:
Light is a form of energy that forms part of the electromagnetic spectrum which
stimulates vision or the sense of sight.
The intensity of light in a place is measure with an instrument called photometer
Light has a dual particle nature. This makes it behave as:

A particle which travels in the form of photons

A wave which can interfere and also diffract.
99
The wave nature of light makes it have the same characteristics as electromagnetic
waves.
Properties of electromagnetic waves (light waves)
1. It travels through vacuum in a straight line with a speed of 3.0 x 108m/s.
2. It can be reflected (bounce back) when obstructed.
3. It can be refracted (changes direction when changing speed)
4. It can be interfered (meeting of light waves)
5. It can be diffracted (spread out)
Lesson 2
(With the aid of examples discuss the sources of light and explain technical terms to
learners)
Sources of light
There are two main sources of light energy. These are:

Artificial source

Natural source.
The artificial sources of light include:
1. Candle light
2. Tungsten filament bulb light
3. Light from a hurricane lamp.
4. Light from a car lamp
5. Light from a stove etc.
Natural sources of light:
100
1. The sun (star)
2. Fire fly
3. Some deep sea fishes
4. Glowing worms
The natural and artificial sources of light that emit or produce light on their own are
known as luminous bodies.
Examples of luminous bodies include:

Sun

Glowing worm

Fire fly

Lighted candle

Hurricane lamps

Tungsten filament bulb

Some deep sea fishes etc.
Non-luminous bodies/illuminated bodies:
These are bodies that do not emit or produce light on their own but are seen
(illuminated) as a result of a light cast on them.
Examples of non-luminous bodies:

Mirrors

Moon

Glass

Water

Wood etc.
101
Lesson 3
(Through a number of activities; e.g. cast a source of light on a mirror, plain glass,
white board and ask learners to discuss what they see and then explain various
terms to them)
When light is cast on an object, one or two of the following may occur:

The light may be obstructed ( in the case of opaque objects)

The light may be reflected ( in the case of mirrors)

The light may be transmitted ( in the case of transparent bodies)

The light may be absorbed (in the case of phosphorescent bodies).
Opaque bodies: These are bodies that do not allow light to pass through them. They
absorb and reflect the light that fall on them. Examples of opaque bodies include
wood, human body, cement block, ceramic, the moon (satellite), and the earth
(planets).
Transparent bodies: These are bodies that allow almost all the light that fall on them
to pass through them without scattering them. Examples of transparent bodies are
plain glass, clean water, clean air etc.
Translucent bodies: These are bodies that that allow small percentage of light to pass
through them and reflect the rest. Such bodies can not be seen through clearly.
Examples of translucent bodies include: frosted glass, oiled paper, tinted glass etc.
Incandescent bodies: These are bodies that produce light because they are hot.
Examples of incandescent bodies are sun, tungsten filament bulb, wood etc.
102
Fluorescent: These are bodies that produce light without being hot. Examples of
fluorescent bodies are firefly, glowing worms, fluorescent tubes, some deep sea fishes
etc.
Phosphorescent bodies: These are bodies that absorb incident light energy, react
chemically and produce their own light of different frequency and colour later or
immediately. Examples of these bodies include road sign paints, neon etc.
Lesson 4
(Discuss with learners the path taken by light and guide learners to identify the
types of beams and their uses)
Transmission of light
The direction or path taken by single unit of light is known ray (Fig.5). A ray is
represented with a straight line carrying an arrow.
NB.
A collection of light rays are referred to as beam
Types of beams and their uses

Parallel beam
This is a collection of light rays coming from different sources and parallel to one
another (the individual light rays do not meet at any point along their travel), Fig. 6.
103
The search light used on the sea by the Navy produces parallel beam in order for
security men to see far away.

Convergent beam
This is a collection of light rays coming from different sources but meeting at a
common place (point), Fig.7. This beam of light enables us to spot tiny particles on
the ground. It is also used by surgeons during medical operations. The search light
used by helicopter search team produces convergent beam in order to locate targets.

Divergent beam
A collection of light rays coming from the same point but moving in different
directions is called divergent beam (Fig. 8). The head lamp of a vehicle diverges light
rays so as to enable the driver to see wide area.
Lesson 5
104
(Guide learners to perform experiment to show that light travels in a straight line
and discuss its application)
Light travels in a straight line in an isotropic medium (a medium of uniform optical
density). This property of light is referred to as rectilinear propagation of light.
Experiment to show that light travels in a straight line in an isotropic medium
Things needed:
1. Three identical cardboards (screens) with identical holes in their geometrical
centre.
2. A source of light (lamp)
3. 3 holders
4. A thread/string
Method/procedure:
 The three cardboards (screens) are arranged in their holders such that running
the thread (string) through their holes put them in a straight line (Fig.9a).
 The thread is carefully removed so that it does not disturb the cardboards.
 The source of light (lamp) is then placed behind the screens so that an
observer is allowed to watch through the holes at the other end of the screens
(cardboards).
 One of the cardboards (screens) is then shifted out of place so that its hole is
not in straight line with the others (fig.9b).
 The observer is allowed to watch through the holes again and his/her
observations are recorded.
105
Observation: It is observed that when the holes are in straight line the light is seen but
when one of the cardboards (screens) is removed so that the holes are not in straight
line the light is not seen.
Conclusion: This shows that light travels in a straight line in an isotropic medium (the
same medium).
Application of rectilinear propagation of light

Formation of shadows

Formation of eclipses

Photography.

Formation of images in mirrors (reflection).
Shadows
A shadow is formed when an opaque body comes between a source of light and a
screen. The opaque body prevents light from falling on the screen hence the shadow
of the object is cast on the screen.
106
Types of shadows
There are two types of shadows. These include:
1. Umbra
2. Penumbra
Formation of umbra shadow:
An umbra shadow is formed when an opaque body comes between a point source of
light and a screen (Fig.10).
Characteristics of an umbra shadow:

It is very sharp

It has a uniformly dark region.

It has a regular shape
Formation of a penumbra shadow
A penumbra shadow is formed when an opaque body comes between an extended
source of light and a screen (Fig. 11).This type of shadow has two parts; a very dark
region (umbra) and a partially dark region (penumbra).
107
Characteristics of penumbra shadows:

They are soft and have no sharp edges.

They are made up of two parts; a dark part and a partially dark part.

They usually have irregular shape.
NB. Due to their soft and not too sharp edges, penumbra shadows are preferred in
sitting and bed rooms, hence frosted lamps and lamp shades may be used to provide
this kind of shadows.
Differences between umbra and penumbra shadows
Umbra
Penumbra
It is very sharp
It is soft and has no sharp edges
It has one uniformly dark region
It is made up of two parts (umbra &
penumbra)
It has a regular shape
It has an irregular shape
108
Eclipses
An eclipse is said to occur when there is total or partial disappearance of the sun or
the moon from the earth due to movements and the relative positions of the earth and
the moon.
 Eclipse is the shadow formed as a result of the arrangement of the sun,
moon and the earth.
There re three (3) types of eclipse namely:
1. Solar eclipse (eclipse of the sun)
2. annular eclipse ( a kind of eclipse of the sun)
3. lunar eclipse (eclipse of the moon)
Solar eclipse (eclipse of the sun)
Eclipse of the sun occurs when the moon comes between the sun and the earth and all
are in a straight line so that the moon casts both total shadow and partial shadow on
the surface of the earth (Fig.12).
Here the shadow cast by the moon on the earth surface has both umbra and penumbra.
People in the umbra see total eclipse and those in penumbra see partial eclipse
109
When solar eclipse occur, certain places which are in the daytime turn into night as
the moon cast a shadow on these places. That means that solar eclipse is observed at
places which are supposed to be in the daytime.
a. The region along U is in total eclipse or total shadow. An observer in this
umbra area is in total darkness and cannot see the sun.
b. The regions along Q and P are in partial eclipse or penumbra region. An
observer in any of these two penumbra areas receives less light energy and the
sun does not appear bright but rather reddish.
Annular eclipse
This also occurs when we have the moon between the sun and the earth. Annular
eclipse is the type of solar eclipse that occurs, when the moon is positioned further
away from the earth and the umbra does not fall on the earth (Fig.13).
Here since the moon revolves round the earth in non-perfect circle it is sometimes
positioned so far away from the earth.
In such a situation the umbra does not reach the surface of the earth, hence people at
the centre of eclipse observe a halo of light (coned shape) around the disc of the
moon. This is called annular eclipse.
110
Lunar eclipse (Eclipse of the moon)
Eclipse of the moon occurs when the earth comes between the sun and the moon such
that all three are in a straight line and the earth casts total shadow on the moon
(Fig14). Here, the shadow of the earth is cast on the surface of the moon. Because the
earth is large in size, the shadow is also broad. The moon therefore takes a longer
period to cross over the shadow.
The part of the earth, which is not directly exposed to the sun, is supposed to be in
nighttime. When lunar eclipse occurs those who are in the night experience it and its’
effect on the moon.
Differences between solar eclipse and lunar eclipse
solar eclipse
lunar eclipse
1. Moon between sun and earth.
1. Earth between sun and moon
2. Takes short time to elapse.
2. Takes long time to elapse.
3. Does not happen often.
3. Happens often.
111
4. Produces both umbra and penumbra 4. Produces only an umbra region.
regions.
Students answer the following questions
Q.1 With the aid of a well labeled diagram, distinguish between eclipse of the sun and
eclipse of the moon.
Q.2 With the help of a diagram, describe annular, total and partial eclipse of the sun.
Photography
Photography is the process, activity and art of creating still or moving pictures by
recording radiation on a sensitive medium, such as a photographic film, or an
electronic sensor.
Light patterns reflected or emitted from objects activate a sensitive chemical or
electronic sensor during a timed exposure, usually through a photographic lens in a
device known as a camera that also stores the resulting information chemically or
electronically. Photography has many uses for business, science, art, and pleasure.
A camera basically is a gadget used mainly for the purpose of capturing images. The
expression camera emerged from the expression "camera obscura", meaning "dark
chamber" according to the Latin language.
Cameras work with the light of the evident spectrum or with other segments of the
electromagnetic spectrum.
A camera comprises of an enclosed void, with a gap (aperture) towards one section so
that light can enter along with a recording or screening exterior for capturing the light
112
at the other end.
Nearly all cameras have lenses fixed in façade of the cameras opening to capture the
inward light and to focus on the representation.
Because of the optical properties of photographic lenses, only articles inside a
particular range can be captured. The initially replicas of the camera were invented
by well known Muslim scientist Alhazen.
Kinds of cameras

Pinhole camera

Lens camera
Pinhole camera:
The pinhole camera is an air tight rectangular wooden or metallic box with a pinhole
located at the geometrical centre of one of its phases (Fig.15). The inside is painted
black to avoid multiple reflections when light from an object placed in front of it
enters it. It contains a photographic film (light sensitive material) placed inside at the
back of the box to capture images of objects once they are placed in front of the
camera.
113
Principle and function of the pinhole camera:
The image in the pinhole camera is created on the basis of the rectilinear propagation
of light. Each point on the surface of an illuminated object reflects rays of light in all
directions.
The hole lets through a certain number of these rays which continue on their course
until they meet the projection plane (photographic plate or film) where they produce
a reverse image of the object.
Thus the point is not reproduced as a point, but as a small disc, resulting in an image
which is slightly out of focus.
This description would suggest that the smaller the hole, the sharper the image.
However, light is essentially a wave phenomenon and so, as soon as the dimensions of
the opening are commensurable with the dimensions of the light wavelength,
diffraction occurs. In other words, if the hole is too small, the image will also be out
of focus.
Characteristics of images produced in pinhole cameras
1. Image is real and can be formed on a screen.
2. Image is smaller than object (diminished)
3. Image is inverted (turned upside down)
4. Image is closer to the pinhole as object is far from the pinhole (image distance
is smaller than object distance)
114
Magnification in the pinhole camera (m)
The magnification (m) of a pinhole camera is:
 The ratio of the image distance (v) to the object distance (u)
𝑖𝑚𝑎𝑔𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑣)
Magnification (m) = 𝑜𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑢)
 The ratio of the image height (hi) to the object height (ho)
𝑖𝑚𝑎𝑔𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 (ℎ𝑖)
Magnification (m) = 𝑜𝑏𝑗𝑒𝑐𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 (ℎ𝑜)
From the above,
𝒗
𝒉𝒊
Magnification (m) = 𝒖 = 𝒉𝒐
Sample Question
A pinhole camera is used to take the photograph of a 1.7m tree. Given that the camera
is placed 0.8m away from the tree and the image is formed 0.5m behind the pinhole
inside the camera, calculate the height of the image. What is the magnification?
Solution
From the question,
Object distance (u) = 0.8m, image distance (v) = 0.5m, height of object (ho) = 1.7m,
Height of image (hi) =? And magnification (m) =?
But,
𝒗
𝒉𝒊
(m) = 𝒖 = 𝒉𝒐
115
Therefore,
0.5
ℎ𝑖
=
0.8 1.7
0.5 x 1.7 = 0.8hi
hi = (0.5 x 1.7) / 0.8
hi = 1.0625m (the height of the image is 1.1m approximately)
Magnification (m) =
𝑖𝑚𝑎𝑔𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 (ℎ𝑖)
𝑜𝑏𝑗𝑒𝑐𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 (ℎ𝑜)
=
1.1𝑚
1.7𝑚
= 0.65
NB.
The magnification is a ratio of similar quantities hence has no unit.
Lesson 6
(Provide learners with plane mirror, curved mirrors, mica, a polished table and ask
them to cast light onto each one in turn. Let them explain what they observe and
guide them to define reflection. Guide learners to identify the types of reflection and
their characteristics. Guide learners to identify the terms associated with reflection
and the laws of reflection. Guide learners to identify the types of images; real and
virtual images and their characteristics. Learners to locate images in plane and
curved mirrors using principles and to state their uses. Learners to use the mirror
formula to solve basic problems)
116
Reflection
Definition:
This is the bouncing back of light into the medium from which it emanated after it
has hit a surface.
A light ray is a stream of light with the smallest possible cross-sectional area (path
taken by a single light). (Rays are theoretical constructs.)
Terms used in reflection (Fig.16):

The incident ray is defined as a ray approaching a surface.

The point of incidence is where the incident ray strikes a surface.

The normal is a construction line drawn perpendicular to the surface at the
point of incidence.

The reflected ray is the portion of the incident ray that leaves the surface at the
point of incidence.

The angle of incidence is the angle between the incident ray and the normal.

The angle of reflection is the angle between the normal and the reflected ray.

The glancing angle is the angle between the incident ray and the reflecting
surface or the angle between the reflected ray and the reflecting surface.
117
The Laws of reflection:
 The angle of incidence is equal to the angle of reflection (i o = r o).
 The incident ray, the normal, and the reflected ray are coplanar OR
 The incident ray, the normal and the reflected ray at the point of incidence
all lie in the same plane.
Types of reflection
 Specular reflection (regular reflection): this occurs when incident parallel
rays are also reflected parallel from a smooth surface (Fig.17a)
 If the surface is rough (on a microscopic level), parallel incident rays are no
longer parallel when reflected (Fig.17b). The rays are scattered. This results in
diffuse reflection (irregular reflection).
NB.
The laws of reflection apply to both regular (Specular) and diffuse reflections as
shown in Fig.17a & b. In the irregular reflection, the irregular surface can be
considered to be made up of a large number of small planar reflecting surfaces
118
positioned at slightly different angles. Indirect (or diffuse) lighting produces soft
shadows.
It produces less eye strain than harsher, direct lighting from regular (Specular)
reflection.
Characteristics of regular (Specular) reflection:
 It produces the exact image of the object
 It is bright and harsh
 It is strenuous to the eye
 Obeys the laws of reflection
Examples of bodies that produce regular reflection include;

Plane mirrors

Spherical mirrors

Parabolic mirrors
Characteristics of irregular reflection:
 It does not produce the exact image of the object
 It is dull and soft (less harsh)
119
 It is less strenuous to the eye
 It obeys the laws of reflection
Examples of bodies that produce irregular reflection include;

Mat surfaces

Ceramic tiles

Wood etc.
Students answer the following questions
Q1. With the aid of a diagram, distinguish between specular reflection and diffuse
reflection.
Q2. Tabulate any three differences between regular reflection and irregular reflection.
Q3. State any two characteristics each of regular reflection (specular) and irregular
(diffuse) reflection.
Calculations based on the laws of reflection
Q1. A ray of light hits a reflecting surface making an angle of 43o with the reflecting
surface. Calculate the angle of reflection.
Solution
It is advisable you draw a diagram to illustrate this.
120
From the diagram,
43o + io = 90o (angle sum of right angle)
io = 90o – 43o = 47o
But from the law of reflection; angle of incidence (io) = angle of reflection (ro) = 47o
This implies that the angle of reflection is 47o
Mirrors
Mirrors are materials whose one part are silvered so that the unsilvered part acts as
reflecting surfaces which produces images of objects that are placed in front of them.
Types of mirrors

Plane mirror

Spherical mirrors (concave and convex mirrors)

Parabolic mirrors
Images
An image is a point in space which is produced as a result of rays that intersect
(real image) or appear to intersect (virtual image). These are usually produced by
reflecting surfaces.
Types of images: there are two types of images. These include:

Real image

Virtual image
121
Real image:
This is a point in space which is produced by the actual intersection of light ray.
Characteristics of real images

They can be formed on a screen

They are usually diminished (smaller in size compared to the size of their
objects)

They are formed by actual intersection of light rays

They are usually inverted (turned upside down)
Bodies that produce real images include; pinhole camera, lens camera, parabolic
mirrors and concave mirror (converging mirrors).
Virtual image:
This is a point in space which is produced by apparent intersection of light rays when
produced backwards.
Characteristics of virtual images

They can not be formed on a screen

They are usually enlarged or of the same size as the objects that produced
them.

They are formed by apparent intersection of light rays

They are usually upright and erect.

They are usually laterally inverted (left side of object becomes the right part of
the image and vice-versa).
122
Bodies that produce virtual image include; plane mirrors, convex mirrors (diverging
mirrors), concave lens (diverging lens) etc.
Students answer the questions below
Q1. Distinguish between a real image and a virtual image. Give any two
characteristics of each type of image.
Reflection in plane mirrors and formation of images
A plane mirror is a plane material whose outside is silvered so that the unsilvered
surface will act as a reflecting surface. This type of mirror produces a regular
(specular) reflection and hence forms a virtual image (Fig.18).
Hint.
Measure the object and image distances as the same
Q2. With the aid of a diagram show how the image of an object is located in a plane
mirror.
123
Characteristics of images produced in plane mirrors

Image is erect

Image is virtual (can not be formed on a screen)

Image is of the same size as object

Image is laterally inverted

The image is at the back of the mirror as the object is in front of the mirror
(image distance is equal to object distance.
Number of images (N) produced in two plane mirrors inclined at an angle θ
The number of images (N) produced in two plane mirrors inclined at an angle; θ is
given by the relation;
N=
360
𝜃
− 1 , where θ is the angle between the two plane mirrors.
Sample question
How many images are produced in two plane mirrors inclined at 45o if an object is
placed between them?
Solution
Angle between the two mirrors (θ) = 45o
But,
N=
360
𝜃
−1
Therefore,
N=
360
45
− 1 = 8 – 1; N = 7 images.
124
Trial question
Calculate the angle between two inclined plane mirrors if they produce approximately
10 images when an object is place in between them. [ans. 34o].
Two plane mirrors inclined at right angle
Two plane mirrors inclined at right angle (90o) will produce three images. This can be
illustrated diagrammatically as shown in Fig.19.
Uses of plane mirrors
1. They are used in salons for barbering.
2.
They are used in meters to eliminate parallax.
3. They are used in shops to detect thieves
4. They are used by interior designers to create an illusion of depth
5. They are used to fold light as in a periscope and other optical instruments
6. They are used to make kaleidoscope, an interesting toy (A kaleidoscope is a
tube of mirrors containing loose coloured beads, pebbles, or other small
coloured objects. The viewer looks in one end and light enters the other end,
reflecting off the mirrors).
125
7. It is also used in making the sextant (A sextant is a navigational instrument
used to measure the angle of elevation of celestial bodies, usually the sun or
moon, in order to determine one's location and direction. More generally, a
sextant can be used to measure the angle between any two objects.)
Curved mirrors (spherical mirrors)
Definition:
 A curved mirror is a mirror with a curved reflective surface, which may be
either convex (bulging outward) or concave (bulging inward) - (Fig.20a & b).
 It is a part of a transparent hollow sphere whose one surface is polished.
Fig.20a
Fig.20b
Most curved mirrors have surfaces that are shaped like part of a sphere.
Types of curved mirrors

Concave (converging) mirror

Convex (diverging) mirror

Parabolic mirror
A convex mirror, fish eye mirror or diverging mirror is a curved mirror in which the
reflective surface bulges toward the light source.
Convex mirrors reflect light outwards; therefore they are not used to focus light.
126
Convex mirrors always form virtual images, since the focus (principal focus) F and
the centre of curvature 2F are both imaginary points "inside" the mirror, which cannot
be reached.
Therefore images formed by convex mirrors cannot be taken on screen, as they are
inside the mirror.
Uses of convex mirrors
 Convex mirrors are used in some automated teller machines as a simple and
handy security feature, allowing the users to see what is happening behind
them.
 They are sold to be attached to ordinary computer monitors.
 Some camera phones use convex mirrors to allow the user correctly aim the
camera while taking a self-portrait.
 They are used as car driving mirrors.
A concave mirror, or converging mirror, has a reflecting surface that bulges inward
(away from the incident light). Concave mirrors reflect light inward to one focal
point; therefore they are used to focus light.
Unlike convex mirrors, concave mirrors show different image types depending on the
distance between the object and the mirror.
 These mirrors are called "converging" because they tend to collect light that
falls on them, refocusing parallel incoming rays toward a focus.
This is because the light is reflected at different angles, since the normal to the
surface differs with each spot on the mirror.
127
Uses of concave mirrors
 They are used in microscopes to focus light onto the stage
 They are used for constructing optical cavity
 They are used for producing laser lights.
 Concave mirrors are commonly found and used as reflectors in flashlights and
some telescopes.
 They are used in solar ovens,
 and though one cannot see the reflected electromagnetic rays, a satellite dish
is essentially a concave mirror.
 Principal axis: If a curved mirror is thought of as being a slice of a sphere,
then there would be a line passing through the center of the sphere and
attaching to the mirror in the exact center of the mirror. This line is known as
the principal axis (Fig.21)
 Radius of curvature(r): This is the distance between the vertex (pole) and the
centre of curvature forming the radius of the sphere from which the mirror was
cut (Fig.21)
 Focal length (f): This is the distance between the mirror and the focal point
(principal focus). - Fig.21.
128
NB
Since the focal point is the midpoint of the line segment adjoining the vertex and the
centre of curvature, the focal length would be one-half the radius of curvature.
𝑟
i.e. f = 2
Sample question
Q1. The surface of a concave mirror is pointed towards the sun. Light from the sun
hits the mirror and converges to a point. How far is this converging point from the
mirror's surface if the radius of curvature (r) of the mirror is 150 cm?
Solution
Answer: 75 cm
If the radius of curvature is 150 cm. then the focal length is 75 cm. The light will
converge at the focal point, which is a distance of 75 cm from the mirror surface.
 Pole of mirror (vertex): The point on the mirror's surface where the principal
axis meets the mirror is known as the vertex (pole) and is denoted by the letter
p. It is the geometrical centre of the mirror (Fig.21).
 Centre of curvature: The point in the centre of the sphere from which the
mirror was sliced is known as the centre of curvature and is denoted by the
letter C (Fig.21).
 Principal focus (focal point): This is the point, F on the principal axis at
which the rays of light parallel to the axis converge or diverge after being
reflected (Fig.21).
129
Sample question
Q2. Describe a simple experiment you will conduct to determine the focal point of a
concave mirror.
Solution
To determine the focal point of the mirror, the mirror is used in focusing light from a
distant source (the sun is ideal) upon a sheet of paper.
The distance between the mirror (vertex) and the paper (image) is measured with the
help of a metre rule.
This gives the focal length of the mirror. Where the image is located on the paper
from the vertex of the mirror is the focal point.
 Aperture: This is the effective diameter of light reflecting area of the mirror.
NB.
 Power : this is the converging or diverging ability of a mirror given by:
1
Power = 𝑓 (reciprocal of the focal length)
where f, is the focal length of the mirror. The power of the mirror is measured in
dioptres [per metre (m-1)].
For example, if the focal length of a curved mirror is 5cm, then the power of the
mirror is 0.2dioptres
130
Principles of locating images in curved mirrors

Rays close and parallel to the principal axis after reflection will pass through
the principal focus (F). (Fig.22a & b)

Rays through the principal focus (F) will after reflection travel parallel to the
principal axis (Fig.22c & d)

Rays hitting the mirror at the centre (pole) will reflect according to the laws of
reflection (Fig.22e & f)

A ray through the centre of curvature is reflected back along the same path.
Formation of images in curved mirrors
There are two types of images formed in curved mirrors. These are real image and
virtual image;
131
 For convex (diverging) mirrors no matter where an object is placed in front of
it, the resulting image is a virtual one.
Characteristics of images produced in convex (diverging) mirrors
 Image is virtual
 Image is erect
 Image is diminished
NB.
 Convex (diverging) mirrors have wide view hence their use as driving
mirrors.
 Convex (diverging) mirrors have a disadvantage of distorting distances.
Thus objects seen in these mirrors are closer than they appear.
On the other hand, images produced in concave (converging) mirrors may have
different characteristics depending on where the object is placed in front of the
mirror (Fig.23).
NB. At all positions of the object in front of the mirror:
 The image produced in a concave (converging) mirror will be a real image.
132
 Except when the object is placed between the principal focus and the pole of
the mirror in which case a virtual image will be formed.
Illustration of positions of objects in front of a concave (converging) mirror and
their resulting images
 Object beyond centre of curvature (Fig. 24)
When an object is placed beyond the centre of curvature, per the principles
mentioned in Fig.22, the image is formed between the centre of curvature and the
focal point.
 Object at centre of curvature (C), Fig.25.
When the object is placed at the centre of curvature, using similar principles (Fig.23),
the image will be formed at the centre of curvature (same place as object).
133
 Object between centre of curvature (C) and principal focus (F), Fig 26.
The image of an object placed between centre of curvature and principal focus is
located beyond the centre of curvature.
 Object at principal focus (F), Fig.27.
When the object is placed at the principal focus, the image is formed at infinity.
 Object between principal focus (F) and pole of mirror (p), Fig.28.
When the object is placed between the principal focus and the pole, the image is
formed behind the mirror and it is virtual.
134
 Object at infinity (Fig. 29)
The image of an object at infinity is formed at the principal focus. This makes it
possible for a converging lens to start a fire as a result of the sun falling on it.
The mirror formula:
The focal length, f the object distance, u and the image distance v from the curved
mirror are related by:
𝟏
𝟏 𝟏
= +
𝒇
𝒖 𝒗
Sign conversions
 Real is positive
 Virtual is negative
NB.1
For concave mirrors, f, u and v are all positive except for when the object is placed
between the principal focus and the pole (vertex) of the mirror in which case the
image formed, v will be negative.
NB.2
135
In convex mirrors only the object distance is positive for any position it is place in
front of the mirror.

The focal length (f) is always negative

The image distance is always negative except for when you are to calculate
for it, in which case you will obtain a negative value (when it is given, assign
negative, if not given your calculated answer should be negative but do not
assign negative to the v in the formula before computing).
Sample question
Q1. An object is placed 30cm in front of a concave mirror whose focal length is
15cm. Calculate the image distance.
Solution
Object distance (u) = 30cm
Focal length (f) = +15cm (concave mirror)
Image distance (v) =?
From the mirror formula;
𝟏
𝟏 𝟏
= +
𝒇
𝒖 𝒗
Then,
𝟏
𝟏
𝟏
=
+
𝟏𝟓
𝟑𝟎 𝒗
→
𝟏
𝟏
𝟏
−
=
𝟏𝟓 𝟑𝟎
𝒗
→
𝟏
𝟐−𝟏
𝟏
=
=
𝒗
𝟑𝟎
𝟑𝟎
V = 30cm (the image distance is 30cm, the same as the object distance)
136
Q2.The object distance of an elephant standing in front of a concave (converging)
mirror is twice the focal length plus five. Calculate the focal length if the image
distance is 10m hence what is the object distance.
Q3. An object is placed 22cm in front of a concave mirror of focal length 25cm.
Calculate the image distance and hence describe the image.
Description

The image is virtual because it is negative

Image is erect

Image is enlarged

Image is at the back of the mirror.
Q4. The focal length of a convex mirror is 20cm. What is the image distance if the
object is placed 50cm in front of the mirror? Hence describe the image.
Description
 Image is virtual
 Image is erect
 Image is at the back of the mirror
 Image is closer to the mirror
Trial question
Q1. Calculate the focal length of a convex mirror assuming an object placed 12m in
front of the mirror produces an image 18m at the back of the mirror. Describe the
image produced.
137
Q2. With the help of a ray diagram, locate the image of an object placed 20cm in front
of a concave mirror of focal length of 15. Describe the nature and orientation of the
image.
Q3. How far will the image of an object placed 45cm in front of concave mirror given
that the focal length of the mirror is 30cm. describe the image formed if any.
Linear magnification:
This the ratio of the image distance to the object distance in the mirror
i.e.
Magnification (m) =
𝒊𝒎𝒂𝒈𝒆 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 (𝒗)
𝒐𝒃𝒋𝒆𝒄𝒕 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 (𝒖)
It seeks to find out how large or small the object has been increased (magnified) by
the mirror. It has no unit since it is a ratio of two similar quantities, length.
 A magnification value less than one (1) means the image is smaller than the
object.
 A magnification of one (1) means the image of the same size as the object.
 A magnification value greater than one (1) means the image is greater than
the object.
Lesson 7
(Let learners look through a plain glass, frosted glass and a bucket of water. Also
let learners observe a coin under a rectangular glass prism. Discuss with learners
what they observe. Guide them to define refraction and the terms associated with it
138
as well as the laws of refraction. Learners to use diagrams to explain refraction in
lenses, and a pool of water with the help of principles. Learners to use the lens
formula to solve basic problems associated with lenses. Learners to identify the uses
of various types of lenses. Guide learners to identify the application of refraction;
e.g. total internal reflection)
Refraction: Refraction is the bending of light as it travels through the boundary of
two mediums as shown in Fig.30.
NB.
1. When light moves from a denser medium (thick) into a less dense
(light) medium, the refracted ray bends away from the normal showing
an increase in speed of the light ray.
2. When light moves from a less dense (light) medium into a denser
(thick) medium, the refracted ray bends towards the normal showing a
decrease in speed of the light ray.
How much the light bends depends on the refraction indices of the two mediums.
 The refraction index is simply the ratio between the speed of light in a
vacuum and the speed of light in the medium.
139
Mathematically,
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚
Refractive index = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚
Consequently, the refraction index is also
 The ratio of the wavelength of light in a vacuum and the wavelength of light
in the medium.
𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚
Refractive index = 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚
When light travels from one medium into another medium, then the refractive index
may be given as:
 The ratio of the speed of light in medium one to the speed of light in
medium two
Refractive index =
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 𝑜𝑛𝑒
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 𝑡𝑤𝑜
NB. Light travels slower in denser materials, this slowdown as the light crosses the
boundary is what causes the bending.
140
Laws of refraction
From the diagram above (Fig.30)
 The ratio of the sine of the angle of incidence to the sine of the angle of
refraction for any two media is a constant. This is known as Snell’s law.
 The incident ray, the normal and the refracted ray at point of incidence
(interface) all lie in the same plane.
Consider a ray of travelling from medium ‘A’ to medium ‘B’ then from Snell’s law;
𝑠𝑖𝑛 (𝑖)
sin(𝑟)
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. (𝑏𝑢𝑡 𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑑𝑖𝑢𝑚)
It therefore implies that;
sin(𝑖)
Refractive index (𝜇) = sin(𝑟)
Sample question
Q1. A ray of light travelling from air into water makes an angle of incidence of 45o.
Calculate the refractive index of the water if the angle of refraction is 30o.
141
NB. When light travels from vacuum into another medium (e.g. from vacuum into
glass) then, the ratio of the sine of the angle of incidence to the sine of the angle of
refraction is known as the absolute refractive index.
Thus, 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥(𝜂) =
sin(𝑖 𝑜 )𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚
𝑠𝑖𝑛(𝑟 𝑜 )𝑖𝑛 𝑔𝑙𝑎𝑠𝑠
Every substance (material) has its unique absolute refractive index which indicates the
refraction that would occur if light travels from vacuum into it.
The speed of light in air is approximately equal to the speed of light in vacuum. For
this reason when light travels from air into another medium, then the ratio of the sine
of the angle of incidence to the sine of the angle of refraction may be called refractive
index hence dropping the word absolute.
Thus, we can simply write;
𝑅𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥(𝜂) =
sin(𝑖 𝑜 ) 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 𝑜𝑛𝑒
𝑠𝑖𝑛(𝑟 𝑜 ) 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 𝑡𝑤𝑜
Principle of reversibility of light
The principle of reversibility of light states that, the path taken by a light ray or rays
is/are reversible.
Explanation: This means that if light is sent in exact opposite direction as it is
travelling, it will follow the same path.
142
From the principle of reversibility of light, if a ray of light is travelling from medium
one (1) into medium two (2), then we can write that 1η2. So that the refractive index
can be written as;
sin(𝑖 𝑜 )
1𝜂2 =
sin(𝑟 𝑜 )
Where io is the angle of incidence in medium one and ro is the angle of refraction in
medium two.
NB. We can use letters representing the mediums to write a similar relation for the
refractive index. Thus, for a ray of light travelling from air into glass, then we can
write;
sin(𝑖 𝑜 )
𝑎𝜂𝑔 =
sin(𝑟 𝑜 )
The by the principle of reversibility of light, we can write the reciprocal;
1
1
sin(𝑟 𝑜 )
= 𝑔𝜂𝑎 =
=
sin(𝑖 𝑜 )
𝑎𝜂𝑔
sin(𝑖 𝑜 )
𝑜
sin(𝑟 )
Note that sin (ro) for the reverse direction of the light is the angle of incidence (so that
the second medium, glass becomes the first medium).
Sample question
The refractive index of an air-glass interface is 1.5. Calculate the angle of incidence in
air that will result in an angle of refraction of 35o in the glass medium.
Solution: Refractive index for air-glass interface (aηg) = 1.5
143
Angle of refraction in glass (ro) = 35o, angle of incidence in air (io) =?
sin(𝑖 𝑜 )
By Snell’s law; 𝑎𝜂𝑔 = sin(𝑟 𝑜 )
sin(𝑖)
→ 1.5 = sin(35)
→ 0.86 = sin(𝑖)
𝑖 = 𝑠𝑖𝑛−1 0.86 = 59.32𝑜 (Hence the angle of incidence is 59.32o)
Students answer the following questions
Q1. Explain the following terms:
a) Principle of reversibility of light
b) Absolute refractive index of a material or medium
c) Snell’s law.
The relationship between the ratio of speed (velocity) of light in vacuum to that in a
second medium and the refractive index according to Snell’s law is given by;
sin(𝑖 𝑜 ) 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚 1(𝐶1 )
=
= 𝑎𝜂𝑔
sin(𝑟 𝑜 ) 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛 𝑚𝑒𝑑𝑖𝑢𝑚2(𝐶2 )
Q2. The refractive index of air-water interface is 1.3. Calculate the speed of the light
in water if the speed of light in water is 3 x 1010m/s. (answer 2.31 x 108m/s)

If η is greater than one (1) then for ray entering an optically denser medium, it
will bend towards the normal.(i.e. η>1)

If η is equal to one (1) then for either direction, there is no bending of the
ray.(i.e η =1)

If η is less than one (1) then for ray entering an optically less dense medium,
ray bends away from the normal. (i.e. η<1)
144
Total internal reflection and critical angle
When light ray travels from an optically denser medium into a less dense medium, the
refracted ray bends away from the normal.
As the angle of incidence is increased in the optically denser medium, the refracted
ray moves further away from the normal towards the interface of the two media.
At a critical angle of incidence in the optically denser medium, the refracted ray
makes an angle of 90o with the interface of the two media.
A further increase in the angle of incidence beyond this critical angle results in the
total internal reflection of the incident ray (into the optically denser medium from
which it emanated). This phenomenon is called total internal reflection (Fig. 31).
In Fig.31, a ray of light is moving from water (an optically denser medium) into air (a
less dense medium). As the angle of incidence in the water is increased, the refracted
ray moves away from the normal. At θi = θc, the refracted ray makes an angle of 90o
with the normal. When the angle of incidence is further increased in the water so that
θi > θc, there is total internal reflection in the water.
145
Critical angle: This is the angle of incidence in an optically denser medium which
produces an angle of refraction of 90o in a less dense medium when light travels from
one medium to another.
Sample question
Q1. With the aid of a diagram explain what is meant by total internal reflection.
Hence define the critical angle.
Relationship between critical angle and refractive index
At critical angle (θc), the angle of refraction is 90o. For light travelling from air into
water, Snell’s law states that;
sin(𝑖 𝑜 )
= 𝑎𝜂𝑤
sin(𝑟 𝑜 )
Then for light travelling from water into air (by the principle of reversibility of light);
sin(𝑖 𝑜 )
1
= 𝑤𝜂𝑎 =
𝑜
sin(𝑟 )
𝑎𝜂𝑤
Where io is the angle of incidence in water (denser medium)
ro is angle of refraction in the less dense medium (air).
For io = co = critical angle, ro =90o
sin(𝑐 𝑜 )
sin(90𝑜 )
1
= 𝑤𝜂𝑎 = 𝑎𝜂
𝑤
(Note that sin 90o = 1)
1
Sin (co) = 𝑤𝜂𝑎 = 𝑎𝜂
𝑤
146
1
Therefore, 𝑎𝜂𝑤 = sin(𝑐 𝑜 ) . Where η is the refractive index of water
Examples of refraction of light in life and their effects

When light hits the surface of water at an angle, the beam of light will bend,
its speed as well as its wavelength will also decrease hence the water will
appear shallower than it really is as in the case of the swimming pool.

A stick placed in a bucket of water at an angle appears bent at the interface
between the air and the water because of refraction of light rays as it enters
the air from the water.

A mirage is formed due to the bending of light rays from a warmer air into a
colder air

A coin placed in a bowl of water seems shallower because of refraction of
light rays as it leaves the bowl of water into the air.

A glass block placed on a news print makes the letters appear closer to the top
of the glass than they really are.
Lenses
A lens is an optical device which is made up of a transparent piece of glass or
plastic with at least one curved surface.
Convex lenses bulge out in the middle like lentils, while concave lenses "cave in" in
the middle and bulge out at the edges.
How do lenses work?
A lens works by refraction: it bends light rays as they pass through it so they change
direction. That means the rays seem to come from a point that's closer or further away
147
from where they actually originate and that's what makes objects seen through a lens
seem either bigger or smaller than they really are.
Types of lenses
There are two main types of lenses, known as convex (or converging) and concave
(or diverging) but these can be modified into other types as presented in
Fig.32a,b,c,d,e & f..
Convex lenses: In a convex lens (sometimes called a positive lens), the glass (or
plastic) surfaces bulge outwards in the center giving the classic lentil-like shape. A
convex lens is also called a converging lens because it makes parallel light rays
passing through it bend inward and meet (converge) at a spot just beyond the lens
known as the focal point.
Convex lenses are used in things like telescopes, and binoculars to bring distant light
rays to a focus in your eyes and also in cameras to focus image on a photographic
films. The human eye contains convex lens which enables it to focus distance and
near objects onto the retina.
148
Concave lenses: A concave lens is exactly the opposite with the outer surfaces
curving inward, so it makes parallel light rays curve outward or diverge. That's why
concave lenses are sometimes called diverging lenses.
NB: One easy way to remember the difference between concave and convex lenses is
to think of concave lenses caving inwards.
Concave lenses are used in things like car headlamps, TV projectors to make light
rays spread out into the distance. In a flashlight, it's easier to do this job with a
mirror, which usually weighs much less than a lens.
NB: A combination of convex and concave lenses form a compound lens
Definitions:
 Radius of curvature (r): This is the distance from the optical centre of the lens
to the centre of curvature (Fig.33).
 Centre of curvature (c): This is the centre of the sphere of which the surface
of the lens is a part (Fig.33).
 Principal axis: This is line that passes through the center of curvature of a lens
so that light is neither reflected nor refracted (Fig.33).
149
 Principal focus (F): This is a point towards which incident rays parallel to the
principal axis of a lens converge, or from which they diverge, after refraction
(Fig.33).
NB
The principal focus of a converging (convex) lens or of a parabolic concave mirror
is the point at which parallel incident rays will converge when refracted or
reflected. It is a real focus.
and
The principal focus of a diverging (concave) lens is the point from which incident
rays parallel to the principal axis appear to diverge after refraction. It is a virtual or
imaginary focus at which no light rays actually meet.
Optical centre (P): This is the point within a lens on the optical axis through which
any rays entering the lens pass without deviation (Fig.33).
Focal length (f): The distance between the optical centre and the principal focus of a
lens is called the focal length (f), Fig.33.
The bigger the focal length, the more powerful the lens
Optical axis: The optical axis is the line joining the two centres of curvature of a lens
or, in the case of a lens with one plane surface, the line through one centre of
curvature that is normal to the plane surface (Fig.33).
150
Formation of image in lenses
 Diverging lens (concave lens)
An object placed in front of a concave mirror will yield a virtual image no matter
where the object is placed (Fig. 34). The rays after refracting through the lens, is seen
to becoming from the side of the lens where the object is placed.
 Converging lens (convex lens)
Converging lens has a positive focal point and hence positive focal length. When
objects are placed any where before the principal focus including the focal point, a
real image is produced (Fig. 35). However when the object is placed between the
focal point and the pole of the lens, an enlarged virtual image is produced (Fig. 36).
151
NB. The principles used in locating images in curved mirrors (Fig. 22) apply to
the lenses. The only difference lies in the fact that in the mirrors, the principles follow
from reflection while in the lenses the principles follow from refraction. For example,
when an object is placed beyond the centre of curvature (2F) of the convex lens (Fig.
37), the image produced is real, inverted, diminished and found between the principal
focus and the centre of curvature (2F).
Lens formula (same for curved mirror):
The lens formula:
152
The focal length, f the object distance, u and the image distance v from the lens are
related by:
𝟏 𝟏 𝟏
= +
𝒇 𝒖 𝒗
Sign conversions
 Real is positive
 Virtual is negative
NB.1
For convex lens, f, u and v are all positive except for when the object is placed
between the principal focus and the pole (vertex) of the lens in which case the
image formed, v will be negative.
NB.2: In concave lens only the object distance is positive for any position it is place
in front of the lens.

The focal length (f) is always negative

The image distance is always negative when given except for when you are to
calculate for it, in which case you will obtain a negative value (when it is
given, assign negative, if not given your calculated answer should be negative
but do not assign negative to the v in the formula before computing).
Students answer the following questions
Q1. An object is placed 30cm in front of a convex lens whose focal length is 15cm.
Calculate the image distance.
153
Q2.The object distance of an elephant standing in front of a convex (converging) lens
is twice the focal length plus five. Calculate the focal length if the image distance is
10m, hence, what is the object distance?
Solution: The object distance (u) = (2f + 5) m = 2 (14.5) + 5 = 34m.
Q3. An object is placed 22cm in front of a convex lens of focal length 25cm.
Calculate the image distance and hence describe the image.
Description

The image is virtual because it is negative

Image is erect

Image is enlarged
Magnification: This the ratio of the image distance to the object distance of the lens
i.e.
𝒊𝒎𝒂𝒈𝒆 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒗
Magnification (m) = 𝒐𝒃𝒋𝒆𝒄𝒕 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 = 𝒖
It seeks to find out how large or small the object has been increased (magnified) by
the lens. It has no unit since it is a ratio of two similar quantities, length.
 A magnification value less than one (1) means the image is smaller than the
object.
 A magnification of one (1) means the image of the same size as the object.
 A magnification value greater than one (1) means the image is greater than
the object.
154
Trial questions
Q1. An object is placed 8.5cm in front of a convex lens of focal length, 4.0cm.
Calculate the magnification of the lens.
Q2. Calculate the focal length and the magnification of a concave lens assuming an
object placed 12m in front of the mirror produces an image 18m at the back of the
lens. Describe the image produced.
Q3. With the help of a ray diagram, locate the image of an object placed 20cm in front
of a concave lens of focal length of 15. Describe the nature and orientation of the
image.
Real and apparent depths: When an object, say a stick or a coin is dropped into a
pond of water or a bucket of water or under a rectangular prism, the object appears to
be shallower than it really is (Fig. 38).This is the action of refraction. In the diagram
below, a coin placed under a rectangular prism is shown.
From Fig. 38, the real depth is represented with the letter H, while the apparent depth
(not real depth) is represented with the letter h. The refractive index will be given by:
𝑹𝒆𝒂𝒍 𝒅𝒆𝒑𝒕𝒉
Refractive index = 𝑨𝒑𝒑𝒂𝒓𝒆𝒏𝒕 𝒅𝒆𝒑𝒕𝒉 =
𝑯
𝒉
155
The displacement (d) = real depth (H) – apparent depth (h)
i.e.: d = H – h
Lesson 8
(Use colour wheels to explain the composition of white light to learners. Through
experiment guide learners to disperse white light using a triangular prism and a
converging lens. Guide learners to differentiate between pure and impure spectrum
with the aid of diagrams)
Dispersion of light
Definition:
This is the separation of white light into the colours of the visible spectrum.
A beam of white light incident at an angle to a triangular prism is separated into seven
different colours in the following order:
Red, Orange, Yellow, Green, Blue, Indigo and Violet (ROYGBIV) on emergence at
the other side of the prism.
Explanation: The refractive index for glass is different for different colours. While
red is deviated the least, violet is deviated the most hence the two colours at the
extreme end of the spectrum.
156
Impure Spectrum:
The spectrum in the diagram above is known as an impure spectrum, since the
colours overlap (Fig.39).
Definition: An impure spectrum is a spectrum of the seven colours of white light
which have overlapped after a white light has passed (refracted) through a triangular
prism.
Pure Spectrum: This is produced when a white light is allowed to pass through a
converging (convex) lens from a narrow slit before refracting through a triangular
prism and thence through a second converging lens onto a screen in order to produce
the seven colours with little overlap or no overlap (Fig.40).
157
Solved questions
Q1. What is referred to as the visible spectrum?
Solution
The visible spectrum is the part of the electromagnetic spectrum which consists of
seven colours namely; red, orange, yellow, green, blue, indigo and violet contained in
white light and are dispersed as a result of a white light passing through a triangular
glass prism.
Q.2 With the aid of a diagram show how an impure spectrum is produced. (Answer:
Fig. 39)
Lesson 9
(Learners to identify optical instruments and their functions. Learners to use ray
diagrams to explain how the camera and the microscope works. Learners to identify
some defects of the human eye and how they can be corrected)
Optical instruments
These are instruments that make use of lenses and mirrors to aid vision. They
include;

Microscopes, Telescopes, Binoculars, Periscopes, Cameras and Projectors
Lens Cameras
The lens camera consists of a light tight box with a lens at one end and a photographic
film at the other end (Fig. 41). A diaphragm having a circular shutter forms a circular
158
hole of variable size which alters the aperture of the lens and hence allowing in light
when a photograph is to be taken.
The lens, a converging one is used to focus a real and diminished image onto the
photographic film at the back of the camera.
Simple microscope or hand lens
This microscope uses a converging (convex) lens to view an object placed within the
focal length of a lens. The image formed is erect, enlarged and virtual as shown in
Fig.42.
The compound microscope
This consists of a combination of objective and eye-piece lenses or a system of
lenses and mirrors (Fig. 43). An object placed on an illuminated stage yields a real
159
image by the objective lens which has a short focal length. This image becomes an
object for the eye-piece lens with a long focal length which in turn forms an enlarged
virtual image either in front or at the back of the objective lens. The positions of the
two lenses are adjusted by both the coarse and fine adjustment knobs.
NB. The human eye is a biological optical instrument.
The human eye
The eye is a biological organ which helps the brain to receive and interpret images.
160
It is an organ for sight and consists of the following parts (Fig. 44):
1. Cornea: This is a transparent layer in front of the lens which helps the eye to
refract light rays from objects.
2. Iris: Coloured opaque disc of muscles which regulate the amount of light that
enters the eye.
3. Lens: A refracting material which focuses rays of light from objects onto the
retina
4. Retina: A light sensitive material on which the image is formed.
5. Optic nerves: A nerve optic fibre connecting the eye to the brain. It transmits
impulses to the brain for interpretation.
6. Aqueous humour: A fluid between the cornea and the lens which lubricates
the lens and refracts rays that enter the eye.
7. Vitreous humour: A fluid between the lens and the retina which helps in
further refraction of light rays onto the retina.
8. Ciliary muscles: Muscles which help in the contraction and relaxation of the
lens
9. Blind sport: A region on the retina which is not sensitive to light.
10. Fovea (macula): This is the most sensitive part of the retina where image is
produced.
Human beings have a binocular vision. This vision enables the eye to form two
images on the retina for the brain to combine and interpret depth and distinction
between the two images.
Accommodation of the eye
161
This is the ability of the eye to change shape and to focus distant and near objects
onto the retina of the eye for correct vision.
The nearest and far points that can be focused by the eye are referred to as:
Near point (about 25cm) and Far point.
Defects of the eye
These refer to abnormal functioning of the eye which may arise as a result of old age,
over use and misuse of the eye and accidents. These do not include diseases of the eye
such as river blindness, night blindness, cancer of the eye, glaucoma etc.
Types of defects of the eye

Myopia (short sightedness): The defect eye can see near objects but can not
see objects that are far away (Fig. 46a). Some of the reasons for this defect
are;
1. The eye ball is too long
2. The focal length of the lens is too short
3. Inelastic Ciliary muscles
The defect is corrected using contact lenses made of concave (diverging) lens which
diverge rays from distant object so that they are brought to focus on the retina by
the eye lens (Fig.46b).
162

Hyperrmetropia (long sightedness): The defect eye can see far or distant
objects but can not see objects that are close to the eye (Fig.47a). Some of the
reasons for this defect include:
1. Eye lens too relaxed
2. The eyeball being too short
3. Eye lens having long focal length.
The defect eye can be corrected using contact lenses made of converging lens
(Fig.47b).
163

Astigmatism: the defect eye has distorted cornea or a non-spherical eye lens
which can not focus light from different part of an object in one plane on the
retina hence a distorted image.
This can be corrected by using spectacles with asymmetrical lenses (nonspherical lenses) with their curvature designed to correct the fault in the eye.

Presbyopia (after 40 years vision): this is the condition of the eye which makes
it difficult to maintain clear focus of near objects but can see clearly far
objects.
This is caused by lessening in the flexibility of the eye crystalline lens and the
weakening of the ciliary muscles which control lens focusing due to old age.
Presbyopia can be corrected by using contact lenses.
Differences between the lens camera and the human eye
No.
Lens camera
Human eye
1.
Has a view finder
Has no view finder
2.
Has only air inside
Has eye fluid for refraction of rays
3.
The light sensitive material is the film
The light sensitive material is the
retina
4.
Light is refracted by the lens only
Light is refracted by the cornea, lens
and fluids
5.
The diaphragm controls the aperture.
The aperture is the pupil which is
controlled by the iris.
6.
Focusing is done by adjusting the lens
position relative to the film.
Focusing is done by changing the
shape of the lens
7.
Exposure is controlled by the shutter
and is brief. (0.02seconds)
Exposure is continuous
8.
It is not a biological organ
It is a biological organ
164
Students solve the following questions
Q1. Explain how the lens camera works.
Q2. With the aid of a ray diagram, explain how the compound light microscope forms
an image of an object placed on its stage.
Q3. State any three optical instruments and what they are used for.
Q4. What do you understand by the term total internal reflection?
165
Appendix B
Questionnaire for science teacher trainees
This questionnaire is for academic purpose and all responses will be treated with
confidentiality. Counting on your co-operation
Bio-data
Sex …………..
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Name of school …………………………….
Statement about the concept
Light reflects from a shiny surface in an arbitrary
manner
Light is reflected from smooth mirror surfaces but
not from a non-shiny surface
The mirror image of an object is located on the
surface the mirror. The image is often taught of as
a picture on a flat surface.
Curved mirrors make everything distorted.
The way a mirror works is as follows: the image
first goes from the object to the mirror surface.
Then the observer either sees the image on the
mirror surface and the image reflects off the
mirror and goes into the observer’s eyes.
Light always passes straight through a transparent
material without changing its direction.
An observer can see more of his image by moving
further back from the mirror.
When an object is viewed through a transparent
solid or liquid material the object is seen exactly
where it is located.
When sketching a diagram to show how a lens
forms the image of an object, only those light rays
that are drawn which leave the object in straight
parallel lines exit.
A mirror reverses everything
The effects of light are instantaneous. Light does
not travel with a finite speed.
Light from a bulb only extends outwards to a
certain distance and then stops. How far it extends
depends on the brightness of the bulb.
Refraction can produce images.
An object is seen because light shines on it. Light
is a necessary condition for seeing an object in the
eye.
In reflection the image produced may be large or
small depending on the surface.
166
TRUE
FALSE
REASON
Appendix C
Student achievement test sheet
This test item is for academic purpose and all responses will be treated with confidentiality. I
should be very grateful if you could answer the questions honestly and independently as
possible. Thank you for your co-operation.
Bio-data
Sex ……
Class/Form ……………………….
School
…………………............
Answer all the questions below
1. Light is a form of energy that stimulates vision. TRUE/FALSE
2. Reflection is the bouncing (throwing) back of light from a surface into the
medium from which it came from when the light hits the surface.
TRUE/FALSE
3. Name the types of reflection. (……………………………….,
……………………)
4. Which material will produce each type of reflection?
5. In reflection the image produced may be large or small depending on the
surface. TRUE/FALSE
6. All reflections produce images. TRUE/FALSE
7. Objects are seen when light falling on them move into our eyes.
TRUE/FALSE
8. The path taken by light is called
…………………………………………………
9. What is refraction? ………………………………………………
10. The speed of light is the same in all media. TRUE/FALSE
11. When light moves from air into water the speed increases. TRUE/FALSE
12. The ratio of the sine of the angle of incidence to the sine of the angle of
refraction is a
constant for any two media. TRUE/FALSE
13. Refraction can produce images. TRUE/FALSE
14. The speed of light is the same in all media. TRUE/FALSE
15. If light travels from air into water, the speed increases. TRUE/FALSE
167
Appendix D
SCHOOL ATTACHMENT SCHEME
LESSON OBSERVATION AND EVALUATION CHECK LIST
IDENTIFICATION PROFILE
COLLEGE OF TRAINEE
………………………………………………………………
DATE:
……………………………………………………………………………………
SUBJECT:
………………………………………………………………………………
TOPIC:
……………………………………………………………………………………
168
AREAS FOR OBSERVATION AND EVALUATION
Tick ( ) the appropriate column and comment as necessary based on a 5-point scale
(5-Excellent; 4-Very Good; 3-Good; 2-Fairly Good; 1- Poor)
A
LESSON PLAN (20MARKS)
1. Objectives clearly stated in measurable terms
2. Appropriate RPK linked to new lesson
3. Very well stated core points
4
Logically organized TLA and TLMs for
effective delivery
Sub-total
B
LESSON PRESENTATION / DELIVERY
(80MARKS)
1. Effective and relevant introduction linked with
RPK.
2. Systematic and orderly delivery of lesson
3. Mastery of subject matter (understanding)
through delivery and confidence level
4. Proper and effective use of language (scientific
terms)
5. Use of vary feed back techniques and Clearly
explain settings
6. Adequate topic content coverage for the level
and use of time
7. Active students’ participation and involvement
8. Application of the concept and closure
169
5 4 3 2 1 REMARKS