Loraine P. Snead
Difficulties Teaching Abstract Concepts in Secondary Chemistry Classroom
Abstract
Examining research surrounding the difficulties teaching abstract chemistry
concepts to students in secondary school classrooms, suggests that the lack of
comprehension and emerging misconceptions warrants new research. While the abstract
concepts in chemistry are many, two are discussed in this paper: chemical bonding and
atomic orbitals.
Piaget (1958) introduces four stages of cognitive growth which determine the
reasoning and mental development skills of which a child or adolescent is capable.
While a large portion of development and capability is linked to gene inheritance, many
secondary-school-aged children have not yet reached the capacity to understand abstract
concepts without a concrete basis. Most researchers agree on the issues that abstraction
presents, however, they differ on the most appropriate way to stimulate this development.
Duschl and Hamilton (2011) introduce three frameworks, or learning progressions, which
define how material is presented in an educational context. These learning progressions
can be used to understand how students’ comprehension develop over time, and can help
instructors create appropriate educational instruction and curricula for the classroom.
In the face of critique on teaching abstract concepts in introductory science
classes, Tsarpalis (1997) of the University of Ioannina in Greece, presents several
convincing arguments about the origin of students’ misconceptions. He suggests that
many students enter higher-level education with an incomplete or incorrect knowledge of
chemistry concepts. In a five-year study, he provided different groups of students with a
conventional lecture-based curriculum, and in each trial, the students performed poorly,
likely due, he said, to incomplete secondary education (Tsarpalis, 1997).
As a pre-requisite secondary course for students desiring a future in the sciences,
the question is whether to teach the students adequate and correct theory in secondary
school in order for them to be better prepared in college, or to forego teaching them
abstract concepts at all. Sanchez Gomez et al. (2003), argue that current scientists are
limited by their lack of understanding abstract knowledge, especially in the area of
quantum mechanics. He goes on to infer that it is important that students learn quantum
principles as soon as possible (Sanchez Gomez, 2003). Many other scientists mentioned
in this review suggest that conceptual (as opposed to mathematical) approaches are
necessary to teach students correct interpretations of quantum theories, an example of
which is chemical bonding.
While a large part of cognitive development and capability is linked to genes and
maturity, many students can be taught abstract thinking through learning progressions
using concrete and practical links. The link or model that is used should be based on
helping students visualize and form conceptual image of the abstraction. Spectroscopy is
an excellent tool to use to complete the understanding of chemical bonding and atomic
orbitals. This review summarizes the research that supports the potential benefits of
using spectroscopy to teach secondary school students chemical bonding is needed.
Introduction
This paper briefly examines research surrounding the difficulties teaching abstract
chemistry concepts in secondary classrooms and suggest that research into using
spectroscopy to teach these concepts is one solution. The difficulties may be based on a
L.Snead
lack of physical concrete visuals and/or appropriate pedagogical methods. Recent
research in the area of visual thinking holds promise for helping students “see” the
“unseen” (Barry, 1997) Concepts such as chemical bonding and electron arrangement
that have their underpinnings in quantum chemistry can be taught through spectroscopy.
First, in order to address the abstract thinking issue, it is important to understand the
cognitive research surrounding it.
Jean Piaget, well-known child psychologist, postulates that there are four stages
of cognitive growth: sensory-motor intelligence (from birth to age two), preoperational
thought (from age two until eight), concrete-operations (from age eight to twelve) and
formal reasoning, which begin during adolescence (Inhelder and Piaget, 1958). Piaget
labeled the final stage of intellectual growth from concrete to abstract thinking the
“formal operational stage” (Inhelder and Piaget, 1958). It is believed that only two-thirds
of adults ever reach this state of abstract thinking. Moreover, this formal operational
thought, or the ability to generate creative solutions for abstract issues, may not appear
until age twenty or thirty (Healy, 2004). How, then, are instructors expected to teach
undergraduate and secondary age students abstract science concepts? A large part of
intellectual growth stems from inherited traits, but can this specific type of intellect be
taught if the inherited links are weak or delayed in development? The future of science,
indeed the future of our society, is contingent upon more students developing these
capabilities earlier in their developmental cognitive abilities (National Commission on
Excellence in Education, 1983). Americans can appreciate the urgency of this matter by
examining the comparative international indicators of complex learning and applied
knowledge published by the Organization for Economic Co-operation and Development
(OECD) PISA program. The 2006 Program for International Student Assessment (PISA)
focused on science literacy including an evaluation of students’ ability to interpret data,
critique scientific evidence, and apply knowledge of scientific concepts to current topics
such as DNA fingerprinting and biodiversity (Songer et al., 2009). On the 2006 test, 15year old Americans performed poorly overall, ranking 29th out of 57 countries. Finland,
Hong Kong, and Canada ranked first, second and third respectively.
The major questions that guide this study, relate to how abstract thinking is
defined in the scientific world, especially on the topics addressed in most high school
chemistry classes. Why is abstract thinking important in understanding chemistry? Is
abstract thinking developmental and if so, are high school students psychologically ready
to think this way? Can a more practical and visual technique such as spectroscopy be
used to teach conceptual quantum chemical principles in high school classrooms?
Abstract and Concrete Thinking
Most cognitive psychologists define abstract thinking as characterized by the
ability to use concepts and to make and understand generalizations. According to experts
from the Brain Injury Association of New York State, abstract thinking involves the
ability to think about ideas that are removed from the facts of the “here and now” and
from specific examples of the things or concepts being thought about (Ylvisaker et al.,
2006). In essence, it is what the mind is able to form when stimulated in the absence of a
concrete subject.
The mid-1990s provide better insight on the history of abstract thinking in
educational psychology. As previously mentioned, Piaget suggested that a child’s
cognitive abilities or intellect proceed through four distinct stages: sensory-motor, preoperational, concrete operational, and formal operational adolescence (Inhelder and
Piaget, 1958). Piaget further noted that development precedes learning and that the
2
L.Snead
developmental stages are discrete. His main views in cognitive intellect suggested that
non-developmental stage learning could not take place unless the child was on the verge
of moving to the next stage. Currently, however, critics argue that Piaget underestimated
children’s abilities (Lawson, 1985). Children are more competent than Piaget thought
and, more importantly, their skills develop individually on different tasks – the progress
of one student cannot be used to track the development of another the same age. In
addition, their formal educational experiences have changed, especially as teachers
become better trained in using various researched methodologies to improve higher order
thinking. Higher order thinking in this context is understood to be when students can
take information and ideas from one context and infer their meaning and implications in
another. The pedagogy used in the classroom can have a strong influence on the pace of
development (Byrnes, 1988;Gelman, et al., 1983; Overton, 1984). Children in the preformal operational stage can form concepts that are independent of physical reality. As
Gelman and Baillergeon assert, “the experimental evidence available today no longer
supports the hypothesis of a major qualitative shift from preoperational to formal
operational thought.” In other cognitive research, Pribyl (1995) documented that young
children in groups of three to five year-olds are able to think in abstract terms, making
sense of their world through creating intuitive models. These scientists concluded that
young children are able to engage in experimentation to develop their ideas.
There are many other views on the stimuli behind progressing through the four
stages. While many think maturation is a pre-requisite for abstract thinking, there are
many alternate beliefs. Some view an appropriately stimulating physical and social
environment will provide the necessary neurological development (Lawson, 1985).
Again, it is possible for the pedagogy used in the classroom to enable the transition from
concrete to abstract thinking.
The following example illustrates the difference between concrete and abstract
thinking. A concrete thinking adolescent can recognize that the organization of an essay
in English class needs a thesis statement and several points or arguments that support the
thesis statement. An abstract thinker can recognize that this strategy in an English class
essay is the same as using the idea of a thesis statement as the purpose and the arguments
as evidence in a Chemistry class laboratory report. In a review of research on formal
reasoning and science teaching, Lawson (1985) argues “biological maturation during late
childhood or early adolescence may not play a significant role in the development of
formal reasoning.” With respect to Piaget’s groundbreaking work in cognitive
development, it must be noted that the aforementioned formal operational thinking does
not necessarily occur in adolescence and as mentioned earlier, it may be that it doesn’t
appear until well into adulthood.
Research on science learning appears to be moving away from a focus on general
principles of learning science to a focus on the psychological, social, and cultural factors
that influence the development of domain specific science knowledge. According to
Duschl and Hamilton (2011) there are three frameworks in the current research on the
learning of science: theory and research on core knowledge, learning progressions, and
domain-specific and domain-general learning frameworks. Duschl and Hamilton also
noted that these frameworks overlap: learning progressions (LPs) are embedded into the
domain-specific and the core knowledge frameworks. Learning progressions can be seen
as tracking the progress of how students’ understandings of and abilities to use core ideas
grow and become more sophisticated over time. A key component of learning
progressions is also embedded in the notion of instruction-assisted development like that
described in the learning pathway on matter and the atomic molecular theory (Smith et al.
3
L.Snead
1985). Assisted development can be utilized when learning is stalled, because of the need
for abstract reasoning even in elementary age children. Here, thoughtful and informed
curriculum designs and effective remediation on the part of teachers can move learners
forward. (Leher et al. 2008; Metz, 2008).
Recently, Duschl and Hamilton (2011) stated that there are several areas of
science learning that haven’t been researched fully and need more investigation. The
future research on science learning and teaching needs to focus more on learning in
context. Research is needed on developmental trajectories/progressions that examine
learning and reasoning. Also, research is needed to develop a better understanding of
whether (and how) instruction should change with children’s development. In addition,
their findings conclude that research on new curriculum materials is a critical area.
Teaching abstract concepts to concrete thinkers can theoretically be accelerated,
but only through purposeful planned interactions between the concrete thinker and a more
mature and well-trained adult. High school science teachers can teach students abstract
chemistry, such as quantum mechanics, using a combination of learning methods and in
many cases using visual and spatial representations (Schwartz et al., 2006).
Common orbital concept in high school textbooks
In most high school chemistry textbooks, the concept of orbitals is taught as a
precursor, or as a necessary mean to an end. The end being that “the atoms of each
element have a unique arrangement of electrons” (Buthelezi et al., 2008). The usual
treatise by the authors in efforts to arrive at the electron configuration of atoms starts with
Light and Quantized Energy and then Quantum Theory and the Atom. Buthelezi et al.
(2008) depict an atomic orbital as a “density map” representing the probability of finding
an electron in a region around the nucleus, similar to Figure 1.
Figure 1. Electron cloud model depicts a density map of electrons in an atom.
(Time Line, http://hi.fi.tripod.com/timeline/timeline.htm)
There is also a short discussion about Schrödinger’s wave equation in the same textbook
sections (Buthelezi et al., 2008). In summary, the treatise states that the equation treats
the hydrogen atom’s electron as a wave, but the equation is too complex to be considered
in the text.
4
L.Snead
Alternative Conceptions (misconceptions) in Chemistry
According to a research review provided by Tsaparlis (1997) students start
undergraduate quantum chemistry courses with either incomplete knowledge or
alternative conceptions (misconceptions) about quantum-chemical concepts. He
attributed these conceptual difficulties to ill-informed secondary teachers, poorly written
textbooks and ineffective teaching pedagogy. Tsaparlis suggests that because of the
misconceptions that undergraduate students bring to college, lecturers are against the use
of certain concepts being taught in high school, based on the limited explanations and
predictions found in high school chemistry textbooks. He concludes that the imprecise
and elementary pictorial coverage of quantum concepts is the primary cause of students’
misconceptions. This is not a solitary view, even to the extent of critics commenting that
atomic orbitals should not be taught at all, because orbitals simply don’t exist. One
scientist speaks for many critical perspectives, arguing that there is no “right” way or best
way to depict orbitals, that orbitals are constructs, and at best unproven theory (Ogilvie,
1990). This belief, among many other statements made by Ogilvie was strongly
criticized by Linus Pauling (Pauling, 1992). While Pauling agreed that orbitals should not
be taught in introductory chemistry courses he maintained that they could be represented
through quantum mechanical expressions. There have been several other theorists
expounding against teaching orbitals and related quantum mechanical concepts in
introductory courses (Bent, 1984; Berry, 1996; Gillespie, 1991; Hawkes, 1992). They
believe that these concepts are highly abstract and beyond the understanding of most
students. Tsaparlis defends this belief, and supports it by tracking undergraduate students
in a required fourth semester quantum chemistry course of the four-year chemistry degree
program at the University of Ioannina (Greece). Tsaparlis taught the course in a
traditional university lecture-based class. He administered a cumulative final exam to the
students in the form of mostly free-response questions with a limited number of multiplechoice questions. All of the questions on the exam were deemed typical and suitable for
an undergraduate quantum chemistry course by several professors at the University. The
results of 506 students’ assessments show that only 41.9% of the students passed with at
least a 45.0% minimum grade. According to Tsaparlis their lack of success points to
“misconceptions, errors, and lack of knowledge that may prevail among future secondary
school chemistry teachers”. He further asserts that these deeply held misconceptions
couldn’t be easily corrected by later and more advanced instruction. One revealing
misconception came from a question about atomic-orbital shapes. The question referred
to four representations of atomic orbitals from Tsaparlis’ paper, shown below in Figure 2.
The actual question is written below the figures, asking: what does each of the figures
represent for a hydrogen-like pz orbital? Less than half of the students answered
correctly. Tsaparlis was particularly disappointed that one of the statistically lowest
performance (N=52, M=29.4% with SD=36.5%) was for descriptions of (a) and (d). He
attributes the incorrect descriptions of Figure 2a to students’ holding on to previously
learned instruction that the pz orbital has the shape of a “figure-eight.” Tsaparlis uses the
data accumulated from this study to further substantiate his claim that incomplete and/or
incorrect previous instruction may develop misconceptions that are very hard to correct
by later, advanced instruction. Figure 2(a) is a cross-section of the graph of  (, ) for
the pz atomic orbital, not the shape of a pz orbital.
5
L.Snead
Figure 2. The actual question about atomic-orbital shapes in two examinations: What
does each one of the representations, (a), (b) and (c) represent for a hydrogenic pz orbital?
What does (d) represent for the 2py orbital? (Tsaparlis, 1997)
More recently, Talanquer, associate chemistry professor at the University of
Arizona reasoned that it is “common sense” that interferes with students’ scientific
learning. He lists the numerous misconceptions students bring to chemistry courses,
including the mole concept, changes of state, chemical reactions and, atomic and
molecular structure (Talanquer, 2002). Talanquer develops “eight patterns of reasoning”,
one of which suggests that there is a one-to-one correlation between models or images
that represent abstract concepts to the concrete model or image. Bliss supports Talanquer,
6
L.Snead
through a twenty-year study on reasoning and thinking in adolescents in the United
Kingdom. The study aimed to determine how students reason in the everyday physical
world (Bliss, 2008). Initially, her research was concerned with the difficulties students
experienced in reasoning about concepts involving force and motion. The results showed
that the students were using everyday knowledge to explain and reason about these
physical areas. It was clear that instead of the students using concepts and ideas that they
learned in school to reason about force and motion, they consistently fell back on their
“common sense.” learned from the physical world. Bliss further proposed that an
important part of human reasoning uses concrete physical schemes to explain the physical
world.
It appears, then, that Talanquer’s characterization has merit. Following his logic,
it is possible that common sense is what causes students to misunderstand the various
abstract chemistry concepts such as chemical bonding.
Chemical Bonding
Chemical bonding is commonly defined as a net attractive force that joins two or
more atoms (Buthelezi et al., 2008). It is better described as an attraction that occurs
when one or more electrons are simultaneously attracted to two nuclei. The subsequent
compound made is stable when the total energy of the combination of atoms has lower
energy than the separated atoms. This minimum energy exists at a specific equilibrium
length, or inter-nuclear distance between the atoms and that distance is called the bond
length. A bond (or attraction) between the atoms is not static, and is often introduced in
the classroom in comparison to a spring that vibrates about its equilibrium position. The
molecules are constantly vibrating, which involves a displacement of the atoms from
their equilibrium positions (Engel, 2006). The bond energy is a direct measure of the
strength of this bond. The value of bond energy of electrons in free atoms is calculated by
wave functions (i.e., quantum mechanical methods), but it is difficult to determine the
energy of bonds in molecules this way because the electrons and nucleus energy changes
during hybridization (Korablev et al., 2006).
The concept of chemical bonding is one of the most important topics in general
chemistry because it is related to so many other fundamental concepts that make up the
true nature of chemistry, for example, chemical reactions. The teaching and learning of
chemical bonding should be at the forefront of any secondary and undergraduate general
chemistry classroom. Chemical bonding is also one of the more abstract concepts that, if
not taught carefully, can help to proliferate the deeply imbedded misconceptions of
students. In fact, while researching this topic of teaching and learning chemical bonding,
Nahum’s group at the Weizmann Institute of Science found that there are many different
views among prominent scientists on the definition of chemical bonding and how it
should be taught (Nahum et al., 2010). One view shared by most scientists, however, is
that bonding is complex, and involves several factors. It is the very nature of a chemical
bond, whether covalent, ionic, or hydrogen, that relates directly to atomic and molecular
orbitals. Therefore, if chemical bonding is one of the more important concepts to learn,
but one of the more difficult concepts to teach, then it begs the question: when and how
should orbitals be taught? Should orbitals be taught in secondary chemistry classes?
If the majority of secondary chemistry teachers use textbooks as the main
(sometimes the only) source of information, chemistry teachers will become instructors in
the history of scientific development and discovery, for better or worse (Chamizo, 2007).
Realizing that there has been substantial debate on whether or not orbitals should be
taught in high school, the assertion is obvious; if we continue to teach orbitals and
7
L.Snead
chemical bonding as introduced by Pauling in 1922, these abstract and common-sensereasoned concepts will have to be replaced later, or unlearned in college.
Quantum Mechanics
According to Sanchez Gomez et al. (2003), if we are to thoroughly understand the
structure of matter, given the current state of knowledge we will need to use quantum
chemistry. Sanchez Gomez examined the future of learning chemistry and decided that
the old models proposed by the important historical figures such as G.N Lewis and Linus
Pauling, who introduced Lewis dot structures, Valence Shell Electron Pair Repulsion
(VSEPR) theory, and atomic orbital hybridization rules, are declining in terms of their
efficacy to explain current research. While quantum chemistry has been around for close
to a century, Sanchez Gomez argues that it has certain limitations for chemists. Most
would say that it is because chemists are concerned with physical reactions and making
various iterations of experimental methods and procedures (Sanchez Gomez, et al.,
2003). According to Sanchez Gomez, the true reason that chemists don’t embrace
quantum mechanics more is that they only have a superficial knowledge of how quantum
mechanics can be applied to chemistry problems. Moreover, using the old models to
depict molecular structure has limitation. He further states that during the last twenty
years advances in modern research fields such as the chemistry of plasmas and flames,
higher atmosphere and interstellar space challenge the explanatory power of old models.
There is reason to research new models to use when teaching molecular structure.
There is plenty of research describing methods to teach quantum mechanics to
undergraduate students and/or high school students (Deratzou et al., 2000; Fanaro, 2009;
Gomez-Herrero, 1999; Thaller, 2006; Zollman, 2001). It appears that the more
successful methods involve using some kind of visualization and that the emphasis is on
conceptual knowledge as opposed to a mathematical approach (Fanaro, 2009; Neto et al.
2007; Robblee, 1999). Zollman (2001) concludes that a good interpretation of the basic
concepts of quantum theory is what is important to learn in introductory chemistry
classes.
Deratzou (2006) reasoned that high school students learning about chemical
bonding and molecular structure improved significantly through visualization and
imagery. She concluded “students who learned the chemistry concepts more effectively
were better at visualizing structures and using molecular models to enhance their
knowledge”. She goes on to infer that visualization of molecular models provides a
“scaffold” between abstract and practical knowledge. In addition, her results show that
students who were not initially visual learners demonstrated spatial perception after being
trained in visualization.
Spectroscopy
Whereas quantum mechanics is a theoretical subject, its applications can be seen
in a more experimental and visual subject, namely spectroscopy. Spectroscopy is
associated with the absorption, emission, or scattering of electromagnetic radiation by
atoms or molecules. In absorption spectroscopy, a molecule absorbs the energy of
incident radiation and undergoes a transition from a state of lower energy to a state of
higher energy. An emission spectrum is produced when radiation is emitted from a higher
to a lower energy state. In both techniques, the change in the energy, E whether
absorbed or emitted is proportional to h (h= Planck’s constant and  = frequency). The
8
L.Snead
energy of a molecule can change as a result of molecular rotations and vibrations and can
be imaged on a graph called a spectrum. Hollas (2004) in Modern Spectroscopy
describes the basic molecular spectroscopic techniques as rotational, vibrational, and
electronic. Since the various forms of spectroscopy are among the most powerful tools
that chemists use to determine atomic and molecular characteristics, it can be used to
teach bonding and atomic orbitals.
Vibrational spectra are ordinarily measured by two different techniques: infrared
(IR) and Raman spectroscopy. The transitions between the set of energy levels
associated with molecular vibrations can give rise to absorptions in the IR part of the
electromagnetic spectrum. Changes in vibrational energy are accompanied by
simultaneous changes in rotational energy, but rotational energies are much smaller
(Atkins et al., 2002). Two features of vibrational spectroscopy that enable it to be useful
in discussions of bonding are 1) vibrational frequency of a molecule differs depending on
the identity of the atoms and 2) a particular vibrational mode in a molecule has only one
major characteristic frequency of any appreciable intensity (Engel, 2005). These
properties generate characteristic frequencies or what is commonly known as group
frequencies in IR spectroscopy. Therefore, the energy of a molecular vibration depends
on the internuclear distance of the atoms that constitute a chemical bond (Campaan et al.,
1994).
In rotational spectroscopy there are sets of energy levels associated with the
overall rotation of molecules; transitions between these levels give rise to spectra that
typically appear in the microwave section of the electromagnetic spectrum. In order to
predict which energy states are allowed, there are selection rules. Selection rules express
the allowed transitions in terms of quantum numbers (not discussed in this review). There
are also “gross selection rules” which specifies the general features a molecule must have
if it is to undergo a change in energy states. An example of a gross selection rule used in
when studying rotational spectroscopy is that in order for there to be transitions between
the rotational energy states, the molecule must contain a permanent dipole moment
(Atkins et al. 2002).
Last, electronic spectroscopy involves energy that causes electrons to transition
from one level to another while simultaneously promoting both vibrational and rotational
transitions. If the analyte is a liquid, the absorption bands are too broad to decipher
vibrational and rotational information (Harris et al., 1989). However, at low temperatures
and in the gas phase vibrational structure can be resolved. The energy transitions are
induced by visible and ultraviolet radiation. Electronic spectra are sometimes used in
high school classrooms to show that the emission spectra of certain elements consist of
several individual lines of color corresponding to visible radiation frequencies (Buthelezi
et al., 2008).
Figure 3 below, shows a potential energy curve of electronic, vibrations and
rotations of a diatomic molecule. The electronic transitions are the vertical lines;
vibrational transitions occur between different vibrational levels of the same electronic
state; rotational transitions occur between rotational levels of the same vibrational state.
9
L.Snead
Figure 3: Potential curve of electronic, vibrational and rotational transitions as a function
of internuclear separation. (http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html)
Conclusion
To improve understanding of abstract chemistry concepts, such as chemical
bonding, new models that are both practical and concrete, should be researched. The key
bonding concepts, such as orbitals, electron repulsions, internuclear attractions, and
Coulomb’s Law, are all non-tangible (nor visual) theories, and therefore difficult for
students to fully understand. As Sánchez Gómez et al., (2003) discussed, the most
advanced models available to chemists for understanding the structure of matter are
derived from quantum chemistry. Because spectroscopy is considered to be an
application of quantum chemistry, it may provide the needed “link” from concrete to
abstract thinking.
Raman spectroscopy is one example of a tool that illustrates the rotational
energies of simple gases, like O2 and N2 in the ground state. These Raman spectra can be
used to teach how molecular internuclear distances within gas molecules change
depending on atom identity (Campaan et al., 1994). The visual changes in the frequencies
of the different molecules can be observed readily on the spectra, giving students a
concrete and visual representation of a chemical bond.
Future research on the application of abstract chemistry concepts will help to
shape the methodology used to teach secondary school students abstract concepts. As
such, it is imperative that more research is conducted in order to improve methods of
chemistry instruction, especially at the secondary level.
10
L.Snead
References
Atkins, P. W., and J. DePaula. Physical Chemistry. Seventh Ed. New York, NY: W.H.
Freeman and Company, 2002. Print.
Barry, A. M. Visual Intelligence: Perception, Image, and Manipulation in Visual
Communication. Albany, NY: State University of New York Press, 1997. Print.
Bent, H. A. "Should Orbitals be X-Rated in Beginning Chemistry Courses?" Journal of
chemical education 61 (1984): 421. Print.
Berland, Leema K., and Katherine L. McNeill. "A Learning Progression for Scientific
Argumentation: Understanding Student Work and Designing Supportive
Instructional Contexts." Science Education 94.5 (2010): 765-93. Print.
Berry, K. O. "What should we teach them in High School?" Journal of chemical
education 63 (1986): 697. Print.
Bliss, J. "Commonsense Reasoning about the Physical World." Studies in Science
Education 44.2 (2008): 123-55. Web.
Buthelezi, T., et al. Chemistry Matter and Change. Columbus, Ohio: McGraw Hill
Glencoe, 2008. Print.
Byrnes, James P. "Formal Operations: A Systematic Reformulation." Developmental
Review 8 (1988): 66. Print.
Camelot Media Group, and Hibbard Ylvisaker Feeney. LEARNet A Program of the Brain
Injury Association of New York State. 2006. Web.
Chamizo, José. "Teaching Modern Chemistry through ‘Recurrent Historical Teaching
Models." Science & education 16.2 (2007): 197-216. Print.
Deratzou, Susan, Sheila R. Vaidya, and Drexel University. A Qualitative Inquiry into the
Effects of Visualization on High School Chemistry Students' Learning Process of
Molecular Structure. Philadelphia, Pa.: Drexel University, 2006. Print.
Engel, Thomas. "A Quantum Mechanical Model for the Vibration and Rotation of
Molecules." Quantum Chemistry and Spectroscopy. 2006. 103. Print.
Fanaro, M., M. Otero, and M. Arlego. "Teaching the Foundations of Quantum Mechanics
in Secondary School: A Proposed Conceptual Structure." Investigacoes em Ensino
de Ciencias 14.1 (2009): 37. Print.
Gelman, R., and R. Baillargeon. "A Review of some Piagetian Concepts." Carmichael's
Manual of Child Psychology (1983): 167. Print.
11
L.Snead
Gillespie, R. J. "What is Wrong with the General Chemistry Course?" Journal of
chemical education 68 (1991): 192. Print.
Harris, D. C., and M. D. Bertolucci. Symmetry and Spectroscopy an Introduction to
Vibrational and Electronic Spectroscopy. New York, NY: Oxford University Press,
1989. Print.
Hawkes, S. J. "Why should they know that?" Journal of chemical education 69 (1992):
178. Print.
Healy, Jane M. "Brain Development and Learning." Your Child's Growing Mind: Brain
Development and Learning from Birth to Adolescence. Third Ed. New York, NY:
Random House Inc., 2004. 125. Print.
Hobson, Brian. "Promoting Higher-Order Thinking Skills in Chemistry." Australian
science teachers' journal 43.4 (1997): 56. Print.
Hollas, Michael, J. Modern Spectroscopy. Fourth ed. West Sussex, England: John Wiley
& Sons, 2004. Print.
Hurwitz, Charles. Evaluating conceptual change in high school honors chemistry
students studying quantum concepts (2007) Print.
Inhelder, Barbel, and Jean Piaget. The Growth of Logical Thinking from Childhood to
Adolescence. Basic Books, Inc., 1958. Print.
Jiang, Bo. "Formal Reasoning and Spatial Ability: A Step Towards "Science for all"."
University of South Florida University of South Florida, 2008. Print. United States -Florida:
Kazerounian, Kazem. "Using LEDs and Phosphorescent Materials to Teach High School
Students Quantum Mechanics. A Guided-Inquiry Laboratory for Introductory High
School Chemistry." Journal of chemical education 86.3 (2009): 340. Print.
Korablev, G. A., and G. E. Zaikov. "Energy of Chemical Bonds and Spatial Energy
Principles of the Hybridization of Atom Orbitals." Journal of Applied Polymer
Science 101 (2006): 2101. Print.
Lawson, Anton E. "A Review of Research on Formal Reasoning and Science Teaching."
Journal of Research in Science Teaching 22.7 (1985): 569-617. Print.
Lehrer, R., L. Schauble, and D. Lucas. "Supporting Development of the Epistemology of
Inquiry." Cognitive Development 23 (2008): 512. Print.
Metz, K. "Narrowing the Gulf between the Practices of Science and the Elementary
School Classroom." Elementary School Journal 109.2 (2008): 138. Print.
12
L.Snead
Mintzes, J. J., J. J. Wandersee, and J. D. Novak. "Meaningful Learning in Science: The
Human Constructivist Perspective." Handbook of Academic Learning; Construction
of Knowledge. Ed. G. D. Phye. 1997th ed. San Diego, California: Academic Press,
Inc., 1997. 405-437. Print.
Nahum, Tami Levy, et al. "Teaching and Learning the Concept of Chemical Bonding."
Studies in Science Education 46.2 (2010): 179-207. Print.
A Nation at Risk. National Commission on Excellence in Education, 1983. Web. June 21,
2011.
Nave, C. R. "HyperPhysics Concepts." 2010.Web. <http://hyperphysics.phyastr.gsu.edu/hbase/hph.html>.
Neto, Francisco Milton Mendes, Francisco Vilar Brasileiro, and IGI Global. Advances in
Computer-Supported Learning. Hershey, PA: Information Science Pub., 2007. Print.
Overton, W. F. "World Views and their Influence on Psychological Theory and Research
" Advances in Child Development and Behavior 18 (1984): 191. Print.
Pauling, L.C., “The Nature of the Chemical Bond-1992.” Journal of chemical education
69 (1992): 519. Electronic
Pascual, J. I., et al. "Seeing Molecular Orbitals." Chemical Physics Letters 321.1-2
(2000): 78-82. Print.
Pribyl, Jeffrey. "Measuring with a Purpose." Journal of chemical education 72.2 (1995):
130. Print.
Robblee, K. M., P. Garik, and G. Abegg. "Using Computer Visualization Software to
Teach Quantum Science: Impact on Pedagogical Content Knowledge". National
Association for Research in Science Teaching. 1999, 11. Print.
Sanchez Gomez, P. J., and F. Martin. "Quantum Vs "Classical" Chemistry in University
Chemistry Education: A Case Study of the Role of History in Thinking the
Curriculum." Chemical Education: Research and Practice 4.2 (2003): 131. Print.
Sawyer, R., ed. The Cambridge Handbook of the Learning Sciences. New York, NY:
Cambridge University Press, 2006. Print.
Schwarz, Christina V., et al. "Developing a Learning Progression for Scientific
Modeling: Making Scientific Modeling Accessible and Meaningful for Learners."
Journal of Research in Science Teaching 46.6 (2009): 632-54. Print.
Sinfield, Melanie. "Teaching Abstract Mathematical Concepts: An Adult Student Unable
to Organize Mathematical Knowledge." The University of Regina (Canada) The
University of Regina (Canada), 2001. Print.Canada: .
13
L.Snead
Smith, C., S. Carey, and M. Wiser. "On Differentiation: A Case Study of the
Development of Size, Weight, and Density." Cognition 21.3 (1985): 337. Print.
Songer, Nancy Butler, Ben Kelcey, and Amelia Wenk Gotwals. "How and when does
Complex Reasoning Occur? Empirically Driven Development of a Learning
Progression Focused on Complex Reasoning about Biodiversity." Journal of
Research in Science Teaching 46.6 (2009): 610-31. Print.
Sousa, D. A. "Chapter 3 - Memory, Retention, and Learning." How the Brain Learns.
Second ed. Thousand Oaks, California: Corwin Press, Inc., 2000. 78-104. Print.
Thaller, Bernd. Visual Quantum Mechanics: Selected Topics with Computer- Generated
Animations of Quantum-Mechanical Phenomena. New York: Springer/TELOS,
2000. Print.
"Time Line."Web. 6/30/11 <http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html>.
Tsaparlis, Georgios. "Atomic Orbitals, Molecular Orbitals and Related Concepts:
Conceptual Difficulties among Chemistry Students." Research in science education
(Australasian Science Education Research Association) 27.2 (1997): 271-87. Print.
Zolllman, D. Visual Quantum Mechanics. Kentucky, USA, 2001. Print.
14