WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
“LEARNERS’ MATHEMATCAL DIFFICULTIES IN GENERAL PHYSICS 1: BASES FOR
DEVELOPMENT OF PHEASYCS WORKBOOK”
by
Jamil E. Lindong
CHAPTER 1
INTRODUCTION OF THE STUDY
Chapter one consists of five parts: (1): Background of the Study, (2) Theoretical
Framework of the Study, (3) Statement of the Problem, (4) Definition of terms (5) Significance
of the Study.
Part One, Background of the Study presents and illustrates the overview of the study.
Part Two, Theoretical Framework of the Study, presents the theories from which the
study is based to.
Part Three, Statement of the Problem, states the existing questions that needs to be
investigated.
Part Four, Definition of Terms, provides conceptual meanings and operational definition
of the study.
Part five, Significance of the Study, discuss the purpose of the study ad explains the
benefits that may derive from the findings to the beneficiaries of the study.
1
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Background of the Study
As what most expert would say, Mathematics is the language of Physics. From solving
physics problems to defining physics terms, we use Math. The beauty of Mathematics opens
new discovery to Physics and the more complex the equations are the deeper the
provide citation
understanding scientist unravels.
Educators need to make sure that our learners are comfortable with the subject.
However, that is the sad truth, a lot of learners doesn’t have the confidence and ability to utilize
Math in Science. Teachers may miss some lessons because there are some cases in which
learners are stuck on the same lesson having hard time on problem solving. Based on the result
of the Programme for International Students Assessment 2018 (PISA, 2018), the Philippines
performed poorly in terms of academic in math and science. The Philippines scored 353 points
in mathematics compared to an average of 489 points in OECD countries. With these scores,
the Philippines ranked second to the lowest both in Mathematics and Science among 79
countries who participated (PISA, 2018). This is very alarming.
Mathematical difficulty refers to cognitive deficits such as ineffective problem-solving
strategies and a lack of computational fluency (Lebens, Graff & Mayer. If a student has poor
performance in Mathematics, the performance in Physics will be affected as well. We know that
concepts and theories in Physics are associated with Mathematics. (Reddy, 2017) revealed that
students’ inability to understand basic subject matter content, principles of physics formulas
result to high failure rate in Physics. The results of their study also stated that one factor is the
lack of remembering problem-based equations in Physics (Reddy & Panacharoensawad, 2017).
2
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
It was also recommended that students should be given the ample time and opportunity to
solve the physics problems during the process of learning physics and for science educators and
curriculum developers they need to incorporate and emphasize on mathematical concepts
(Reddy & Panacharoensawad, 2017).
Overcoming mathematical difficulty means having a deeper understanding to the
mathematical concepts. It is a set of principles in the aspect of mathematical systems than is
used to understand patterns, interpret quantities and describe the structures of the
relationships between variables. In other words, the ability of conceptual understanding once
possessed by the students will provides them problem solving skills, communication skills and
the ability to use mathematical representations (Lestari & Surya, 2017).
According to Talikan (2021), it is evident that back-to-basic Mathematics is effective in
improving the Physics performance of the students. This reflected on the level of effectiveness
of back-to-basic Mathematics as perceived by the students which is highly effective. This means
the students believe they learn better in Physics if the basic Mathematics lessons will be
renewed to them (Talikan, 2021). However, this study is a survey-based study. This concept
will be more effective if there is an assessment to be given to the students that will measure
the students’ performance after using such instructional material.
One solution that may help students’ mathematical skills in Physics is the use of
instructional materials. In the study of Okpe (2018), instructional material plays a great role on
students’ academic performance. The result of the study shows the academic achievement of
students in Physics depends on the use of instructional material and the teacher way of
delivering it during classes. Instructional materials are very important (Jacob, 2014). Physics
3
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
formulas can be remembered easily if learners’ have access to it or they can practice with it.
The use of instructional materials in terms of problem solving helps students’ retention and
improves learners’ problem-solving ability. In the study of Adebule and Ayoola (2015), it is
revealed that there is a significant difference between students’ performance taught with
instructional materials and resources in schools (Adebule & Ayoola, 2015). This tells us that as
the educational system continues to evolve and become modernize, new sets of materials,
tools, teaching style, learning approach and more will change as well. Educators’ responsibility
is to provide solution to an existing problem and so this study.
Hence, this study aims to identify the mathematical difficulty of senior high school
students in Physics. This proposed study aims to determine the mathematical struggles of STEM
students in General Physics 1 and to provide an instructional material that will improve their
academic performance.
The researcher believes that there is a need in identifying the mathematical difficulties
of students in Physic because knowing and understanding their experiences towards the subject
is the right position for the researcher to offer possible course of action to the existing problem.
Indeed, it is only when the researcher performs some kind of diagnosis or assessments that
researcher can offer an achievable outcome. In the case of senior high school STEM students
taking Physics class, identifying students’ mathematical difficulty in Physics are the first step a
researcher should take to address the problem.
4
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Theoretical Framework
Input – Process – Output (IPO) Model
The Input – Process – Output (IPO) Model plays a great role in the field of educational
research. In breaks down the model into three components: inputs, process, and outputs.
Inputs refers to the conditions and context that shape the engagement process. This will
include who will participate, the intervention to be used, resources used and many more. The
process on the other hand represents the internal dynamics and interactions between
participants, the transformation of the system and the development of a product if there is on.
Lastly, the output refers to the effects or impact of participatory institutions that includes policy
formulation and implementation (Font et al. 2018; Ga;ais et al. 2021)
The IPO model can be applied in various situations where a process creates outputs or
by-products from inputs. Production is defined as the transformation of inputs into outputs
(Arnold, 2009; Iqbal 2021). The IPO model can also be used inside a simple classroom set ups.
This help student and teachers have a systematic approach when having a class. This also helps
both the learners and teachers create instructional materials such as digital visual aids, power
point presentations and more (Iqbal, 2021).
This study will use the same framework where inputs will be gathered from the learners
through the researcher made test. The process will focus on the development of PhEASYcs
workbook, this will include the context, illustrations, designs and validations. The output will
focus on the evaluation of the instructional materials.
5
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Dick and Carey’s Model of Instructional Design
In the lens of constructional design, the word model refers to an organized set of
procedures for solving a problem. These models based on theories and research findings, as
well as on experienced-based reasoning (Briggs, 1970; Briggs and Wagner, 1981; Seung Youn
Chyung, 2008). Dick and Carey’s instructional design model is thus a systematic instructional
design model that also provides a systemic perspective: it takes a comprehensive view of
instructional design in those various components of the instructional system (such as the
instructor, the learners, the instructional materials, and the learning environment) interact with
one another in order to achieve the instructional goal. (Seung Youn Chyung, 2008).
Bakri and Muliyati (2018) conducted a study “Design of multiple representations elearning resources based on contextual approach for the basic physics course”. The researcher
followed the Dick & Carey research and development model. The steps are as follows:
1. Identify Instructional Goal 2. Conducting Instructional Analysis 3. Analyze Learners and
Contexts 4. Writing Performance Objectives 5. Develop Assessments Instruments 6. Develop
Instructional Strategy 7. Develop and Select Instructional Materials 8. Design and conduct
formative evaluation of Instruction 9. Revise instructional. Following the Dick and Carey’s model
allowed the researcher create and present instructional materials in the form of concept map,
figure, table, video experiments results, the graphs of the data table, the study of the verbal,
mathematical equations, examples of matter, and matter of practice. The result of the study
after presenting multiple representations in the e-learning basic physics course shows an
increase in students understanding of the concept of the study.
6
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Dick and Carey’s Model of Instructional design provide a systematic guide to develop an
instructional design. Following such steps will provide the development of PhEASYcs workbook
its focus on the most important area of the General Physics 1 from which the learners have
difficulties. After gathering the data from the least learned skills of the learners in General
Physics 1 measured through Researcher-made test, the researcher will develop an instructional
strategy developed in PhEASYcs workbook created from the General Physics 1 subject.
Exercises and activities will then be added to the workbook to measure students improvement
on a certain topic.
Metacognitive Theory
Learning is a complex process. It is more than memorization or simple recall. The
human mind is unique because the way they think about a specific matter may differ from one
another. Metacognition, mostly defined as “thinking about thinking” or “learning how to learn” is
the ability of a person to have awareness of his or her own cognition.
A learners’ ability to solve problems successfully depends on number of factors related
to the way human process information (Hardin, 2003). In the world of physics, troubleshooting
is essential. It is among the most common types of problem solving. In fact, when people think
about problem-solving, they associate it strongly with problem-solving diagnosis (Jonassen,
2011). You can see physics problems covered with numbers, variables and sets of formulas you
need to integrate to come up with an accurate outcome. But there is more to that. These
numbers are representation of real-world scenarios which include physics concepts. The set of
formulas you have memorize is not enough to solve such problems, you need to think beyond
that and create a new formula that will satisfy the unknown from your problem. Hence, it is
7
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
important for you to have a set of formulas in your mind, and it is up to you how are you going
to utilize them. Combining cognitive and metacognitive strategies can issue a new revolution in
teaching-learning process in mathematics. Since mathematical concepts and subjects are
abstract therefore it needs that learner inform of effective strategies for deep learning because
mathematical concepts have relations altogether and if learners forget previous concept, he/she
cannot learn and grasps new concepts (Lofi, 2014).
The ability of the students to create their own strategies when doing problem solving is
a big factor. This will help them provide their own understanding of the topic and will help them
follow their own phase. Learners’ have unique minds; they have different ways of gaining the
knowledge presented to them. This is a big factor that educators need to consider, that is why
the best way fulfill the different needs of the learners are to provide them with a variety of
teaching strategies, exposed them from different classroom set ups, and of course provide
them with a variety of instructional materials. This study aims to expose the students to
different mathematical activities before delving into the physics topic itself. The exercises,
activities, and problem sets provided from the PhEASYcs workbook will help them develop
different set of skills and strategies when tackling a physics topic.
Piaget’s Cognitive Learning Theory
According to Duchesne and McMaugh (2013) the development of cognitive skills such as
perceiving, understanding, remembering, problem-solving and reasoning are influenced by the
child experiences, both with objects and events in the physical world (Duchesne & McMaugh,
2013). Students of different grade level performs on different level of academic difficulty. The
higher the grade level is the more difficult a particular subject would be. Piaget believed that
8
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
knowledge is a result of a life-long constructive process in which learners organize, try to
structure, and restructure experiences from existing schemes to modify and expand them
(Bodner, 2019). Learners’ ability in problem solving and physics concepts and understanding
may develop through time. In the Philippines K-12 curriculum, students have glimpse of physics
concepts as early as Grade 5 and Grade 6. These are then developed in Junior High School
where students are thought to integrate their understanding to their mathematical ability.
Those students who would pursue the STEM strand will continue to study higher level physics
General Physics 1 and General Physics 2. With previous topics and concepts thought during
Junior High School, learners will be tested on constructing their knowledge in physics into much
deeper level of problem solving. These will be a challenge to them, but since learners are being
mold to become better problem solvers, experiences from the past grade level will help the
learners. Workbooks or problem-solving exercises as instructional materials will develop
learners’ mathematical skills through time. According to Inocencio & Calimlim (2021), learners
perform better after the utilization of teacher made workbook from satisfactory to very
satisfactory. The workbook is useful as well according to teachers’ evaluation (Inocencio &
Calimlim, 2021).
Physics and mathematics and as well as different subjects, are thought each quarter in
the K-12 Junior High School. Learners are thought physics lessons with different level of
difficulty each year. Though this is a great strategy of the curriculum to provide students with
limited sets of topics so that learners skills will not be bombarded by a large amount of physics
lessons, the gap each year may affect the development of the learners’ mathematical skill.
According to Munro (2022), the summer months affects students’ performance. Summer
learning loss occurs in regions with a lengthy summer break which results in a loss of academic
9
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
knowledge and skills. The learning loss typically affects most students, the extent of knowledge
loss varies throughout math, science, reading and writing (Munro, 2022). But according to
Munro (2022) greater losses are seen in math compared to reading. Students lose two months
of previously learned math skills every summer (Boulay & McChesney, 2021; Munro 2022). One
of the objectives the PhEASYcs workbook presents is that for every topic a review and exercises
will be given to the learners for them to have better retention. In some words, a fresh review of
the mathematical concepts will help them not only in the problem solving aspect of the physics
but as well as in the application physics concepts and theories.
Research Paradigm
Research Paradigm
Input
Least learned
Competencies
Involving
Mathematical
concepts in General
Physics 1
Process
•
Development
& Evaluation of
PhEASYcs
Contextualized
Workbook
Output
Enhanced PhEASYcs
Contextualized
workbook
Fig. 1 In this diagram the IPO model is used for the development of PhEASYcs workbook.
10
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Statement of the Problem
The study aims to determine Mathematical difficulty in Physics of the Senior High School
STEM students. The following questions will serve as guide in the development of PhEASYcs
Workbook.
1. What are the least-learned competencies in General Physics 1 that involves
mathematical concepts?
2. What instructional material can be developed to address the least – learned
competencies in General Physics 1 involving mathematical skills?
3. What is the level of acceptability of PhEASYcs (Physics made Easy) workbook:
Addressing Mathematical Difficulties of Learners in General Physics 1 as evaluated by
experts in terms of content, understanding procedure, knowledge and application,
practical applications in its relevance, clarity of timely information, development of
higher order thinking skills?
11
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Definition of Terms
The following terms are further defined either operationally or conceptually:
Top 3 least Learned Competencies – the top 3 least learned competencies will be
the bases of the content for PhEASYcs workbook. This information will be gathered through the
learners’ assessment result from the researcher made test.
Workbook – it contains different features that include awareness raising, reading task
and guided exercises to help develop and practice the critical skills required to appraise papers
independently (Cambridge English Corpus, 2024).
In this study, the developed PhEASYcs workbook will be used to provide task and
exercises for the Grade 12 SHS students taking General Physics 1.
Physics – the scientific study of matter and energy and the effect that each has on the
other:
In this study, it refers to the subject taken by the Grade 12 SHS learners. Specifically,
the subject is known as General Physics 1 which focuses on mechanics of particles and motion
of the rigid bodies.
Learning Competencies – Learning competencies refers to knowledge,
understanding, skills, and attitudes that students need to demonstrate in every lesson and/or
learning activity (DepEd, 2020).
This will be based on DepEd’s Most Essential Learning Competencies for Grade 12 Senior
High School Students taking STEM strand.
12
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
Mathematical Difficulty – refers to cognitive deficits such as ineffective problemsolving strategies and a lack of computational fluency (Lebens, et. al, 2010).
In this study, it refers to problem encountered by the learners that may be hard to
understand or solve for some individuals. These can be basic mathematical computations to a
complex mathematical concepts and theories.
PhEASYcs Workbook – the developed instructional material Physics Made Easy
(PhEASYcs) Workbook aims to aid the students’ difficulty of General Physics 1 in terms of its
mathematical aspects. This will provide contextualize contents and mathematical concepts as
addition to the existing Physics topics.
Significance of the study
This study maybe beneficial to the Grade 12 STEM Learners, Seniors High School Physics
Teachers, Curriculum Developer and future researchers that will investigate related problems
from this study.
Learners. The result of this study may help learners’ mathematical skills in Physics. This
may develop students critical thinking skills and reason to a higher level. The students may
benefit on the practical exercises the workbook may offer.
Physics Teachers. The workbook may serve as a guidance to teachers’ preparation for
physics classes. This may help teachers provide a more contextualize activities and problemsolving exercises that will soon be used inside the classroom set-up.
Curriculum Developer. The result of the study may raise a question to our current
educational curriculum. Questions that may push our educational system to the development or
13
WEST VISAYAS STATE UNIVERSITY
COLLEGE OF EDUCATION
GRADUATE SCHOOL
Iloilo City
revisions of competencies, school textbooks/ workbooks or modules used by the schools under
the Department of Education (DepEd).
Policy Maker. The result of the study will provide data about the quality of education
from a small portion of students. This may raise questions about educational content, teaching
methods, and students’ performance. Once these data are gathered policy makers will play a
crucial role in policy formulation and implementation.
School Administrator / Department of Education (DepEd). This will serve as an
eye opener for the administration since the students’ performance and the quality of education
towards physics will be highlighted at the end of the study. The result may raise concerns and
pushed the Department of Education to provide educational program development in the field
of physics, student counselling to gather information about the external factors that may affect
the learner’s performance and policy making.
Textbook Writer. Textbook writers contribute significantly to educational materials to
ensure the accuracy and engagement of the learners and teachers inside the classroom. The
product of this study will provide textbook writers references to create a textbook content and
developed instructional materials that involves critical evaluation of information for reliability
and usefulness.
Researcher. This research will serve as a useful reference for the future researchers
that would take related studies about the development of instructional materials and Physics
related studies. The development of PhEASYcs Workbook stand for a significant advancement in
educational research providing future researchers the opportunity for further exploration and
innovation.
14