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Macro, Submicro, and Symbolic: The many faces of the chemistry “triplet”
Vicente Talanquera
a
Department of Chemistry and Biochemistry, University of Arizona, Tucson, USA
First published on: 08 January 2010
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International Journal of Science Education
Vol. 33, No. 2, 15 January 2011, pp. 179–195
RESEARCH REPORT
Macro, Submicro, and Symbolic: The
many faces of the chemistry “triplet”
Vicente Talanquer*
Department of Chemistry and Biochemistry, University of Arizona, Tucson, USA
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0VicenteTalanquer
Vicente@u.arizona.edu
000002009
International
10.1080/09500690903386435
TSED_A_438821.sgm
0950-0693
Original
Taylor
2009
00
and
&
Article
Francis
(print)/1464-5289
Francis
Journal of Science
(online)
Education
The idea that chemical knowledge can be represented in three main ways: macro, submicro, and
symbolic (chemistry triplet) has become paradigmatic in chemistry and science education. It has
served both as the base of theoretical frameworks that guide research in chemical education and as
a central idea in various curriculum projects. However, this triplet relationship has been the subject
of different adaptations and reinterpretations that sometimes lead to confusion and misunderstanding, which complicates the analysis of the triplet’s nature and scope. Thus, the central goal of this
paper is to describe some of the existing views of the triplet relationship in chemistry and science
education and critically analyse their underlying assumptions. We also propose a general structure
of our chemistry knowledge intended to better situate the chemistry triplet in relationship with the
different types, scales, dimensions, and approaches that seem to characterise such knowledge. Our
proposed model may be useful in the analysis, evaluation, and reflection of educational research
results and teaching practices centred on the triplet relationship.
Keywords: Chemistry education; Knowledge structure; Learning; Pedagogical content
knowledge; Position paper; Science education
Introduction
The suggestion that chemical knowledge and understanding of our world is generated, expressed, taught, and communicated at three different “levels”, traditionally
called the macroscopic, the submicroscopic, and the symbolic levels, has been one of
the most powerful and productive ideas in chemical education for the past 25 years
(Gabel, 1999; Gilbert & Treagust, 2009a; Johnstone, 1982). The triplet relationship, as it has recently been called by Gilbert and Treagust (2009b), has served as a
framework for many research studies in the field and guided the work of chemistry
instructors, curriculum and software developers, and textbook writers across the
*Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ 85721, USA.
Email: vicente@u.arizona.edu
ISSN 0950-0693 (print)/ISSN 1464-5289 (online)/11/020179–17
© 2011 Taylor & Francis
DOI: 10.1080/09500690903386435
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180 V. Talanquer
world. It has also influenced discussions about modelling (Gilbert & Boulter, 2000)
and visualisation (Gilbert, 2005) in science education in general. However, as often
happens to many powerful and insightful concepts and ideas, this triplet view of our
chemical knowledge has been adopted and adapted by many people who, through
personal or collective reinterpretations, have generated what can be identified as
different faces, personalities or manifestations of the triplet. Many of these reconceptualisations actually expand and enrich the original idea, forcing us to think more
deeply about the challenges involved in chemistry teaching and learning. Nevertheless, they sometimes also generate confusion and misunderstanding as people tend
to use different terms and concepts when describing the nature and scope of the
major components of the triplet.
The central goal of this work is to describe some of the existing views of the triplet
relationship in chemistry and science education and critically analyse their underlying assumptions. The purpose is not to evaluate whether the interpretations are right
or wrong, or whether some are better or worse than others. As already pointed out,
different views tend to challenge and enrich our understanding of the nature of
chemical knowledge, which is beneficial in teaching and educational research. The
main intention is to instigate further thinking, discussion, and reflection on this
topic, particularly among chemistry teachers, chemistry teacher educators, and
chemical education researchers. As a chemistry teacher educator I often find
prospective teachers either uncritical of the existence of the “triplet” or confused by
the different ways in which its main components are described in their course readings (levels of description, levels of representation, levels of thought, different worlds,
etc.). Thus, this work seeks to provide an opportunity for science and chemical
educators to critically reflect on what has become a central paradigm in our field. In
the process, I will not resist the temptation to generate my own pedagogical interpretation of the nature and structure of chemical knowledge. From my perspective, this
is the type of personal reconstruction of knowledge and understanding that science
educators should be encouraged to do to enhance and develop our pedagogical
content knowledge in a given discipline.
Back to the Beginning
The relevance of the triplet relationship in chemical education was explicitly highlighted by Johnstone in 1982. In this work, Johnstone (1982) pointed out that expert
chemists can view their subject matter on at least three different levels:
●
●
●
Descriptive and functional: The level at which phenomena are experienced,
observed, and described.
Representational: The level in which signs are used to represent and communicate
concepts and ideas.
Explanatory: The level at which phenomena are explained.
Given the particular nature of chemistry, Johnstone built a strong association
between the “descriptive and functional” level and what he called macrochemistry,
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Macro, Submicro, and Symbolic 181
the “representational” level and the symbolic language of the discipline, and the
“explanatory” level and the particulate theories and models of matter (initially
referred to as microchemistry, and more recently as submicrochemistry). From discussions in later works (Johnstone, 1991, 1993, 2000), it is clear that this author-related
macrochemistry, or the macro level, to the entities and phenomena that are tangible
and visible in our world, that he used submicrochemistry to refer to particulate models
of matter, and that his definition of the representational level, also referred to as the
symbolic level in one of his works (Johnstone, 1991), encompassed both chemical
and mathematical signs and their relationships (i.e. equations). Johnstone’s main
educational argument was that expert chemists build “reality” as a dynamic blend of
macro, submicro, and symbolic elements, while novice learners mainly operate at
the macro level and struggle to meaningfully relate the other levels. Unfortunately,
most chemistry teaching is focused on the submicro–symbolic pair of the triplet and
rarely helps students to build bridges to comfortably move between the three levels.
This teaching approach often results in confusion and information overload, with
negative consequences on student motivation and achievement in the chemistry
classroom.
Although Johnstone’s chemistry triplet has been extremely appealing to chemical
and science educators and very useful in highlighting core components of our chemical knowledge, we need to be careful in its application and interpretation. From my
perspective, more discussion is needed about what the three major components
represent and encompass. For example, the analysis of Johnstone’s own writings
reveals that he refers to the components of the chemistry triplet in various ways:
levels of thought (Johnstone, 1991), components or modes (Johnstone, 1993), and
forms of the subject matter (Johnstone, 2000). Additional labels have been used by
researchers such as Gabel and co-workers who have espoused a very similar view of
the chemistry triplet to that of Johnstone: levels of description (Gabel, Samuel, &
Hunn, 1987), levels of teaching (Gabel, 1993), and levels of representation (Gabel,
1999). Now, if the components of the triplet are levels of representation, a view that
has become dominant in recent years (Gilbert & Treagust, 2009a), in which way can
the macro level, of the things that are visible and tangible, be called a “representation”? Or, why should we single out the representational level as one of the major
components of the triplet if the other two major elements are also “levels of
representation”? These types of questions need to be addressed if we want to have a
clearer understanding of the meaning and educational implications of the triplet
relationship.
The analysis of the specific nature and actual scope of each of the different levels
of the triplet is also critically important. For example, by only focusing on the particulate models of matter (submicro) in the explanatory component, Johnstone’s triplet
seems to exclude the wide variety of macroscopic theories and models that chemists
use to explain and predict the properties of substances and chemical processes (e.g.
chemical kinetics and thermodynamics). From Johnstone’s own writings it is not
clear whether these types of models are assumed to be part of the descriptive
(macro) or the representational (symbolic) levels, given that he claims that classical
182 V. Talanquer
thermodynamics operates on these two levels only (Johnstone, 1982, 1991).
Although classical thermodynamics is certainly a phenomenological theory, it has a
major explanatory component that, even if it does not rely on atomic assumptions, is
built on many abstract constructs (e.g. internal energy, entropy). How can we use
then the triplet relationship to make sense of this type of knowledge? To try to
answer these questions it is useful to explore how other science educators have
approached the analysis of modern chemistry knowledge.
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Other Faces
Several authors, either based on Johnstone’s ideas or in an independent manner,
have recognised the need to identify different forms or levels in which chemical
knowledge is built, portrayed, taught, or communicated. In some of these works, the
central arguments reveal different interpretations of the components of the triplet,
both of their nature and scope, or suggest a more complex structure for our chemical
knowledge. In the following subsections I describe contentious issues that emerge
from the analysis of these related studies and that demand a clearer characterisation
of each of the components of the chemistry triplet.
Rethinking the Explanatory (Submicro)
Chemists rely on a variety of models of matter to describe, explain, and make predictions about the properties of chemical substances and processes. These models represent matter at different scales, and thus some authors have considered it important to
distinguish among different modelling levels. For example, in analysing the sources
of students’ difficulties when learning chemistry Ben-Zvi, Eylon, and Silberstein
(1988) considered the relationship between chemical symbolism and three distinct
levels of description of matter: the macroscopic (of the phenomena), the atomicmolecular (one single-particle), and the multi-atomic (many particles). These authors
found it important to distinguish between the single- and the multiple-particle
modelling levels because while chemical properties may be explained at the singleparticle level, many physical properties of macroscopic substances, such as their
density or state of matter, can only be justified considering moles of atoms or
molecules.
The importance of identifying and differentiating between relevant size or length
scales for the chemical theories and models of matter (the explanatory level according to Johnstone) has been recognised by other authors. In particular, Jensen (1998),
in his analysis of the logical structure of chemistry, divided the concepts and models
of chemistry into three conceptual levels, the molar, the molecular, and the electrical.
The molar level includes concepts and models that are used to describe, explain, and
predict the bulk properties of substances and processes without any reference to
their submicroscopic structure. The molecular level refers to models of matter based
on the characterisation of the number and types of atoms, molecules, or ions in a
system and their dynamic interactions, while the electrical level focuses on the
Macro, Submicro, and Symbolic 183
subatomic components, particularly electron distribution and dynamics. Recently,
Gilbert and Treagust (2009c) also emphasised the importance of recognising this
gradation of models based on length scale, highlighting the existence of models at
mesoscopic levels that are useful in understanding the properties of many modern
materials (Meijer, Bulte, & Pilot, 2008). All of these studies reveal the multi-layered
nature of the explanatory level in chemistry, which is not captured by a one-to-one
association with the so-called submicro models of matter.
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Rethinking the Descriptive (Macro)
The nature of the macro level has also been the subject of various interpretations.
Some authors characterise the macro level as mainly including the actual phenomena
that we experience in our daily lives or in the laboratory; it is the level of the observable and tangible (Gabel, 1999; Treagust, Chittleborough, & Mamiala, 2003).
However, others describe the macro level as representational in nature, mainly
shaped by those concepts and ideas used to describe the bulk properties of matter,
such as pH, temperature, pressure, density, and concentration (Chandrasegaran,
Treagust, & Mocerino, 2007; Gilbert & Treagust, 2009b; Nakhleh & Krajcik, 1994).
In some studies the macro level seems to encompass both the actual phenomena and
the concepts used to describe them (Dori & Hameiri, 2003; Hinton & Nakhleh,
1999; Johnstone, 1982, 1991, 2000). We even find authors who conceive the macroscopic level as mostly referring to those phenomena that students experience in
chemistry classrooms and laboratories, which are judged to be different from the
“real” macroscopic world of their daily lives (Bodner, 1992). The claim in this case
is that classroom chemistry is mostly about solving inconsequential academic
problems, which are different from those we encounter in everyday life.
Acknowledging the various meanings attributed to the macro level in the chemical
education literature is of central importance from a pedagogical perspective. Experience and research tell us that students have problems building bridges between the
phenomena they see or experience and the intellectual tools used in chemistry to
describe or explain them (Gabel, 1998, 1999). Although one may claim that our
description of natural phenomena cannot be separated from the mental constructs
that we use to make sense of what we observe, in learning chemistry students need to
be able to connect the phenomena they observe and describe in colloquial terms
their formal descriptions using scientific concepts. Observing and describing that a
balloon blows up when heated is not the same as characterising this phenomenon as
a result of an increase in temperature that caused the internal pressure of the balloon
to rise. This latter type of description relies on macroscopic conceptual constructs
and models of matter that belong to the molar level in Jensen’s categorisation
described above (Jensen, 1998), and would thus be better characterised as in the
“explanatory” level rather than in the “descriptive” level in Johnstone’s framework.
Calling the macro level a “level of representation” seems to imply that the macroscopic or molar concepts and models of matter used in chemistry are part of it. But if
that is the case, then we need to be very careful about claims that suggest that the
184 V. Talanquer
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macro level is more “concrete” than the submicro level (Rappoport & Ashkenazi,
2008), or that the students have an easier time grasping ideas at the macro than at
the submicro levels (Johnstone, 1982, 1993). Concepts used in chemistry to characterise the macroscopic properties of matter, such as substance, element, energy,
entropy are as abstract and conceptually challenging as the concepts of atom, molecule, and electron. Consider, just as an example, all the educational research
describing students’ difficulties in differentiating between the macroscopic concepts
of heat and temperature, or density and weight (Driver, Squires, Rushword, &
Wood-Robinson, 1994). From this perspective, suggestions such as those of
Kermen and Méheut (2009) or Levy and Wilensky (2009), who separate the empirical (macro) level of the experienced phenomena from the modelling (macro) level
used to interpret them are pedagogically more transparent.
Rethinking the Representational (Symbolic)
The third component of the triplet has also been conceptualised in different
manners by various authors. In many cases, as originally proposed by Johnstone
(1982), this level is assumed to include all types of signs, chemical or mathematical,
used to represent concepts and ideas in the discipline. However, some authors have
preferred to separate the symbolic system, in which substances and processes are
symbolised using chemical language and drawings, from the algebraic system, in
which relationships between the properties of matter are expressed using formulas
and graphs (Nakhleh & Krajcik, 1994). Of even a more complex nature is the sometimes implicit classification of the symbolic components of the chemical language as
belonging to the representational (symbolic) level while its more iconic components
are associated with the explanatory (submicro) level. Let us explore this issue in
further detail.
The visual language of chemistry can be thought of as comprised of symbols and
icons used to represent the properties and behaviour of chemical substances and
processes. Symbols include those signs used by convention to represent, for example,
the composition of matter (e.g. H, O, H2O), or its properties and behaviour (e.g. +,
(g), →). On the other hand, icons are signs that are thought to resemble in some
fashion the object or event that they are designed to represent (e.g. space-filling or
ball-and-stick representations of molecules; particulate drawings of a chemical
substance or reaction). Now, in many cases, the signs used in chemistry combine
both symbolic and iconic values (Hoffmann & Laszlo, 1991). Consider a typical
representation of the geometry of a molecule using its Lewis structure combined with
wedges and dashes to communicate perspective. While the types of atoms and bonds
that comprise the system are represented using symbols, the drawing has an iconic
value as it tries to represent the three-dimensional structure of the modelled
molecule.
The semi-symbolic, semi-iconic nature of many visual representations in chemistry
gives them a hybrid status between signs and models; between convention-based ways
to communicate concepts and ideas and actual attempts to represent things as they
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Macro, Submicro, and Symbolic 185
are, either in the external world or as conceived within a certain theoretical framework
(Hoffmann & Laszlo, 1991). If we think of them as mere signs, then we may be
inclined to classify them as belonging to the representational (symbolic) level; if we
think of them as models with descriptive, explanatory, and predictive power we may
prefer to think of them as part of the explanatory (submicro) level. This ambiguity
needs to be recognised, and if possible resolved at least from a pedagogical perspective. Otherwise, we may fail to address students’ difficulties in differentiating between
the world we experience, the theoretical models we develop to understand it, and the
visual tools we use to facilitate thinking and the communication of ideas.
To illustrate this latter point, consider the underlying assumptions made in the analysis of the results of studies designed to investigate students’ difficulties translating
between symbolic and submicroscopic representations of substances or chemical reactions (Nurrenbern & Pickering, 1987; Sanger, 2005). In many of these investigations,
students are asked to build or identify the iconic representation of a system (particulate
drawings) that corresponds to a given symbolic representation (chemical formulas and
equations). Does this task require the ability to move between the representational
and the explanatory levels in Johnstone’s triplet, or mainly to move between symbolic
and iconic forms within the representational level? Can we claim that a student who
is successful in these types of tasks actually understands the assumptions and implications of the explanatory model that the particulate drawings are trying to represent?
I would argue that in many educational discussions the difference between understanding the actual theoretical models used in chemistry to explain phenomena on the
one hand, and manipulating the iconic representations that attempt to capture their
most essential features on the other, has been blurred by many educators and that we
need to study and analyse more carefully whether this is a valid assumption.
Rethinking Other Assumptions
There are additional implicit or explicit assumptions associated with the triplet relationship in chemistry that are important to recognise and question if we want to
develop a better understanding of the discipline as it is taught. For example, the
contrasting differences between students’ abilities to solve algorithmic and conceptual questions or problems have played a central role in the chemical education
research literature in the past 20 years (Bodner & Herron, 2002). These types of studies have led people to build a strong one-to-one association between the algorithmic
aspects of chemistry teaching and the symbolic component of the triplet (e.g. stoichiometric calculations based on chemical equations), and between the conceptual
facets of chemistry and the submicroscopic level (e.g. representation of chemical reactions using particulate drawings). To some extent, these strong associations seem to
imply that quantitative theories and models in chemistry cannot be approached
conceptually unless we refer to some sort of submicroscopic model, and that
particulate representations of matter are impervious to algorithmic manipulation.
However, I would claim that each of the components of the triplet can be approached
qualitatively or quantitatively, conceptually or algorithmically, depending on the
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186 V. Talanquer
nature of the task and the particular characteristics of the teacher and the learner. We
need to distinguish between traditional teaching practices in the discussion of certain
topics, which may favour some approaches over others (e.g. algorithmic balancing of
chemical equations versus reflective application of conservation principles), and the
inherent nature of the components of the triplet.
Another assumption that we need to challenge is the idea that the empirical or
descriptive level of the observable and tangible phenomena is constrained to the
macroscopic scale. Although it is true that most students’ experiences inside and
outside the chemistry classroom are likely to involve macroscopic samples of objects
and events, modern technologies now allow chemists to explore matter at a wide
variety of scales, from the macro- to the nano-level. Using techniques such as scanning tunnelling microscopy and optical tweezers scientists are able to directly
explore the surface of materials at the atomic level and manipulate nanometre-sized
particles (Cang, Xu, & Yang, 2008). Nowadays, the world that can be experienced
can no longer be captured using a “macro” label. In a century in which the scientific
and technological exploration and manipulation of the nanoworld is becoming a
reality, the tangible component of the chemistry triplet demands some reconceptualisation. Failing to do so may create additional confusion as people look for ways to
incorporate the “reality” of the submicroscopic level into the existing framework
(see, e.g. Davidowitz & Chittleborough, 2009).
Finally, I would like to discuss the challenges that context-based approaches to
chemistry teaching have posed for the triplet relationship. In recent years, the increasing emphasis on developing contextualised chemistry curricula that address topics
relevant to students in ways that may better prepare them to be informed and critical
participants in modern societies has led some authors to question the extent to which
the triplet relationship opens spaces for such approaches in the chemistry classroom
(Mahaffy, 2004, 2006). Thus, it has been suggested that a fourth component, the
human element, should be added to the mix to emphasise the need to integrate
the learning of the discipline within the broader contexts in which chemistry affects
the lives of citizens and communities. Without denying the central importance of
connecting chemistry to students’ daily lives and societal issues and needs, the question to discuss is whether it is better to conceive the human component as a fourth
level to be added to the triplet rather than as a particular approach to the way in which
the other three levels can be introduced, explored, and discussed in the classroom. If
we need to add a human component to the triplet relationship, why not also consider
philosophical, historical, or technological components?
A Complex Knowledge Space
I propose that the existence of many faces, interpretations or manifestations of the
chemistry triplet (or quadruplet, or quintuplet, depending on the conceptualisation)
as discussed in the previous sections is, in many cases, the result of either selectively
choosing or combining different pieces of chemical knowledge that actually exist in a
more complex, multi-dimensional knowledge space that the triplet relationship
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Macro, Submicro, and Symbolic 187
cannot capture. This purposeful selection or combination of relevant areas of
knowledge is pedagogically advantageous as it allows educators to highlight those
pieces that are considered most relevant for the teaching of the discipline (e.g. the
submicroscopic models of matter). However, it may become the source of confusion
or misinterpretation if we do not recognise that different authors may actually be
talking about different, although sometimes overlapping, portions of this multidimensional knowledge space when referring to the same component of the triplet.
In the following paragraphs I will try to characterise this multi-dimensional knowledge space for chemistry. In particular, I will propose that this space is characterised
by different types, scales, dimensions, and approaches of our chemical knowledge. The
terms that I have chosen to label the relevant components of this space deviate in
some aspects from those used in the current chemical educational literature related
to the chemistry triplet. My intent is not to claim that these are better labels than
those currently used, but to clearly differentiate among the elements that I consider
most relevant in the proposed model for the structure of our chemistry knowledge.
For example, I will not use the term “representation” to refer to any of the main
components of the knowledge space because, from my perspective, this term is illdefined in the science education literature. In particular, it sometimes refers to the
actual theoretical models used to “represent” reality, while in other occasions it is
used to describe the symbols or icons created to “represent” relevant elements of
such theoretical models in visual ways. However, I will try to identify those regions
of the proposed knowledge space that are “representational” in nature.
Types
Similarly to Johnstone (1982), I would suggest that the chemistry knowledge that is
relevant for teaching can be characterised as being of three main “types”:
●
●
●
Experiences: Which includes our descriptive knowledge of chemical substances
and processes as acquired in direct (through the senses) or indirect (using instrumentation) ways. Experiences refer to the actual empirical knowledge that we
have or gather about chemical systems.
Models: Which includes the descriptive, explanatory, and predictive theoretical
models that chemists have developed to make sense of the experienced world.
Models refer to the theoretical entities, and the underlying assumptions, that are
used to describe chemical systems by attributing to them some sort of internal
structure, composition, and/or mechanism that serve the purpose of explaining or
predicting the various properties of those systems.
Visualisations: Which encompasses the static and dynamic visual signs (from
symbols to icons) developed to facilitate qualitative and quantitative thinking and
communication about both experiences and models in chemistry. Visualisations
refer to the chemical symbols and formulas, particulate drawings, mathematical
equations, graphs, animations, simulations, physical models, etc., used to visually
represent core components of the theoretical model.
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188 V. Talanquer
With these definitions I intend to make a clearer distinction between the empirical knowledge that we have about chemical substances and processes in our world
(experiences), typically described using colloquial terms and intuitive ideas by our
students, and the theoretical models developed to describe, explain, and predict
their properties and behaviour (models). For example, the knowledge that iron
tends to rust over time (experience) is different from the knowledge that iron and
oxygen, two chemical elements, react to form iron oxide, a chemical compound
(model). I also think that it is crucial to differentiate between the theoretical models
of matter developed by chemists to describe, explain, or predict the properties of
chemical systems and all of the different visual signs created to facilitate the interpretation and communication of concepts and ideas. Although it is common for
people to refer to visualisations as “models”, most theoretical models used in chemistry, and even those developed by our students, are multi-component entities that
rely on a variety of assumptions that are difficult to capture by a single visualisation.
For example, the drawings of an atom as electrons moving in spherical orbits
around a nucleus, or the energy diagram of an atom showing a sequence of quantised states, are visualisations of core elements of Bohr’s model of the atom, but
they are not the model per se.
If we try to create a visual image of the proposed knowledge space, we may begin
by placing the three main types of knowledge on the corners of a “chemistry triangle” (see Figure 1). Experiences define the “experiential” or empirical regions of this
space, while models and visualisations demarcate the more “representational” areas.
To illustrate the pedagogical significance of differentiating between these three types
of knowledge, let us discuss an application of these ideas. Consider, for example, this
piece of experiential knowledge:
Experience: Natural gas burns in the presence of air and can be used to warm things up.
This is the type of concrete empirical knowledge that people develop through their
interactions with their surrounding world. Now, this phenomenon is traditionally
reinterpreted in chemistry in the following manner, looking through the lenses of
macroscopic theories about the composition and reactivity of matter:
Model: Natural gas is mainly composed of methane, a chemical compound that undergoes a combustion reaction with a chemical element in the air, oxygen, producing
two new substances, carbon dioxide and water, and releasing energy in the forms
of heat and light.
The scientific concepts used to build this theoretical model (chemical compound,
chemical element, combustion reaction, substance, energy, heat, light), although
“macroscopic” in nature, are far from being tangible and visible. The actual model
can be thought of as both descriptive and explanatory in nature. A meaningful
translation from the experience to the model requires the understanding of many
complex concepts and ideas developed by chemists to explain the properties and
behaviour of matter. From my perspective, the experience and the model are two
clearly distinctive types of knowledge, and educational research tells us that
Macro, Submicro, and Symbolic 189
students will need considerable help and support in learning how to translate from
one to the other (Driver et al., 1994).
The experience and the model just described are often represented using the
following set of visual signs (a chemical equation in symbolic form):
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Visualisation: CH 4 (g ) + 2O2(g ) → CO2(g ) + 2H2O(g ) + Energy
This representation conveys specific information about the composition and states of
matter of the substances involved. To fully give sense to it, without resorting to any
submicroscopic type of model, one needs not only to understand the meaning of the
symbols and their relationships, but to have a clear idea of how chemists quantify
amount of substance for the different types of elements present in a given compound.
However, one may become pretty proficient at manipulating the chemical equation
without meaningfully understanding the underlying concepts and assumptions of the
models of matter to which it is associated. In that sense, it is pedagogically sound to
also make a clear distinction between models and visualisations.
Figure 1. Chemistry knowledge space. The image represents a multi-dimensional space defined
by the different scales/levels, dimensions, and approaches in which each of the three main
knowledge types (experiences, models, and visualisations) can be conceptualised
190 V. Talanquer
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Scales
Given that chemists explore, model, and build visualisations of the properties and
behaviour of matter at different length scales, from the macroscopic to the
subatomic, one can argue that each of the three main types of knowledge just
described span these multiple scales or levels (see Figure 1). For example, the burning of methane may be explored using a calorimeter at the macroscopic level or via
ultrafast laser spectroscopy at the molecular scale (Gord, Meyer, & Roy, 2008). The
process may be modelled using kinetic molecular theory at the multiple-particle level,
or using Lewis bonding theory to track bond breaking and bond formation at the
molecular (single-particle) scale. Particulate drawings or animations may be used to
visualise the reaction at the multi-particle scale, while Lewis structures can be useful
to communicate ideas at the molecular level.
The different scales I propose in Figure 1 are not meant to be exhaustive, but
rather highlight the importance of recognising the different scales of description and
explanation that may be necessary or fruitful to consider in the analysis of a given
system or problem. The traditional division into macro and submicro (which tends to
combine the multi-particle, supramolecular, molecular, and subatomic scales in
Figure 1 into a single level) does not explicitly recognise that students may not only
have problems connecting or translating ideas between these two major levels, but
that they are likely to experience difficulties whenever we move from one scale to
another in which “emergent” properties or processes arise (Jacobson & Wilensky,
2006; Penner, 2000). I use emergence here to refer to those properties or processes
of a composite system that result from the interactions between its parts, but differ
from those of the individual components (Deacon, 2003; Luisi, 2002). In this sense,
the properties of a single molecule, such as its geometry, are emergent from those of
the composing electrons and nuclei; the porosity of a supramolecular object, such as
cell membrane, is emergent from those of molecules in the aggregate; and the viscosity of a liquid emerges from the multiple interactions among the particles of the fluid.
The scales or levels that are relevant in analysing the properties of a system will
depend on its chemical nature. However, current teaching practices tend to emphasise the molecular (single-particle) and subatomic levels regardless of the nature of
the system. Seldom are students exposed to mesoscopic models and visualisations of
matter, which are very useful in analysing the properties of common materials such
as polymers and ceramics (Meijer et al., 2008). Exploration, analysis, and discussions of supramolecular systems are rare in the traditional chemistry curriculum
despite their central importance for understanding life. Even the discussion of the
transition from multiple-particle to macroscopic descriptions of matter is commonly
avoided, which may be one of the reasons why so many students hold a static view of
the submicroscopic world (Driver et al., 1994).
Dimensions
Beyond knowledge types and scales of exploration and analysis, following Jensen
(1998) I think that it is important to recognise that our knowledge about chemical
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Macro, Submicro, and Symbolic 191
substances and processes spans three major dimensions: composition/structure,
energy, and time (see Figure 1). Going back to our example, in studying the
combustion of methane we may be interested in analysing changes in the composition of the system, the amount of energy released, or the time it takes for the
process to end. We may carry out experiments to find the desired answers, build
and use thermodynamic, molecular or electronic models of matter to generate
explanations and make predictions, and use multiple forms of visualisation (from
mathematical equations, to reaction coordinate diagrams, to particulate drawings,
to computer simulations, to electron energy level graphs) to represent, manipulate,
and communicate ideas.
Chemical education research and practice has put a lot of emphasis on studying
and developing students’ ability to connect and translate between experiences,
models, and visualisations at different length scales, emphasising the composition/
structure dimension in Figure 1. Much less effort has been invested in exploring
students’ ideas and fostering understanding of properties and processes that occur in
different energy and time scales. How many of our students have a sense of the time
scale in which molecular vibrations occur or chemical bonds are broken compared to
the time in which a chemical reaction takes place? How many of them have a clear
idea of the relative amounts of energy needed to induce a molecular vibration, break
a bond, or overcome an intermolecular force? Recognising the different dimensions
of our chemical knowledge may help educators broaden their view of the central
ideas and concepts to be explored and discussed in the classroom.
Approaches
The proposed multi-type, multi-level, and multi-dimensional nature of the chemistry
knowledge space becomes even more complex if we recognise that we may take
different “approaches” in the teaching of chemistry (see Figure 1). For example, we
may want to emphasise the conceptual understanding of core ideas in a given area or
we may favour a more mathematical approach to the analysis of certain problems.
We could use relevant personal and societal issues to contextualise discussion of
ideas, or analyse historical cases as a way to introduce the human element into the
curriculum. We may take other approaches not included in Figure 1, for example,
philosophical or technological. However, we cannot think of any of these approaches
as restricted to any of the particular types, scales, or dimensions of chemistry
knowledge just described. Quantitative aspects can be introduced in discussing experiences, models, or visualisations. Conceptual understanding may be fostered in the
analysis of macro, molecular, or subatomic models of matter or their associated visualisations. Contextual issues may be addressed in the composition/structure, energy,
or time dimensions for most relevant situations (e.g. greenhouse gases and global
warming, conventional versus alternative fuels, drug action). Without neglecting the
interrelationships among the types, levels, dimensions, and approaches summarised
in Figure 1, more problems and confusions seem to arise from trying to merge
categories or build rigid links between them (e.g. symbolic with mathematical;
192 V. Talanquer
submicroscopic with conceptual; experiences with macroscopic) than from granting
them some degree of independence.
Figure 1. Chemistry knowledge space. The image represents a multi-dimensional space defined by the different scales/levels, dimensions, and approaches in which each of the three main knowledge types (experiences, models, and visualisations) can be conceptualised
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Final Comments
There may be many other ways of conceptualising the structure of chemical knowledge different from that proposed in this paper. We may find some of them more or
less appealing or fruitful for educational purposes. However, the analysis, discussion,
and reflection of each of them is likely to enrich our understanding of the discipline
and challenge our assumptions about how best to teach chemistry and help others
learn it. Undoubtedly, the triplet relationship is a very powerful, productive, and
widely used metaphor for both teaching and doing educational research in chemistry, as well as in science in general. For these same reasons, we should be careful
when using it in making planning and assessment decisions in the classroom. The
abuse or misuse of the chemistry triplet as an instructional tool may increase
students’ confusion and lack of motivation towards chemistry (Johnstone, 1982,
2000). Given the different interpretations of the main components of the chemistry
triplet, we should also be cautious when interpreting the results and evaluating the
implications of research and curricular projects that rely on it as part of their
theoretical framework.
Research tells us, for example, that students have difficulties translating between
the macro and the submicro “levels of representation” of matter (Davidowitz &
Chittleborough, 2009; Gabel, 1998, 1999); does this mean that they have problems
translating between experiences and submicro models, between macro models and
submicro models, between experiences or macro models and submicro visualisations, or between all of the above? I would argue that we are not talking about subtle
distinctions between concepts. Research has clearly shown that there is a huge divide
between the world as we experience it and interpret it in real life, and the world as
modelled by science. Similarly, we cannot assume that because someone is proficient in using and manipulating different forms of visualisation for a given system or
model, that he or she understands the basic ideas and assumptions on which the
model is based.
Kozma and Russell (1997) indicated that the development of representational
competence, or the ability to transform one form of representation to another, is critical for meaningful understanding and successful problem solving in chemistry. Their
study was based on the comparative ability of expert and novice chemists to classify
and translate between different visualisations of the same phenomenon. Without
further analysis one may conclude that in order to develop students’ representational
competence we only need to train them in properly translating between different
visual representations used in chemistry. However, Kozma and Russell clearly indicated that experts were also able to meaningfully connect the different visualisations
to the theoretical constructs (models) in which they were based, using these connections as the base for their classifications. Representational competence thus depends
on the meaningful and skilful manipulation of both models and visualisations.
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Macro, Submicro, and Symbolic 193
The structure of our chemistry knowledge presented in Figure 1 reinforces the
idea that beyond the ability to translate between different visualisation forms, meaningful chemistry learning requires students to be able to translate within and across
knowledge types, scales, dimensions, and approaches. It is not just a question of
learning to transform from symbolic (e.g. chemical formulas) to iconic (e.g. particulate drawings) signs, or from real objects to submicro visualisations. Students need
to differentiate between experiences, models, and visualisations, while building
connections among them at different scales. They need to recognise the different
dimensions (structure, energy, time) in which chemical phenomena are explored,
modelled, and visualised, and try to build coherent and integrated mental models for
them. They should develop qualitative and quantitative understandings of these
phenomena, while being able to build bridges between what they study in the classroom and laboratory and the world in which they live.
The proposed chemistry knowledge space in Figure 1 may be too complex for
teachers to use as a practical tool in the actual classroom, or to be discussed with
their students. However, it can be a very useful instrument for teachers, curriculum
developers, and educational researchers in making more reflective decisions about
what to teach, assess, or investigate at different educational levels. For example,
many educators have suggested that chemistry teaching should start at the “macro”
level. However, our discussion highlights the need to more clearly define what we
mean by the term “macro”. I would suggest that results from educational research
(Gilbert & Treagust, 2009a) indicate that beginner chemistry students should have
opportunities to explore real life objects and events, build their own models to
describe, explain, and predict the properties and behaviours of these systems, and
discuss and communicate ideas making use of a variety of visualisation tools. These
experiences, models, and visualisations may initially be focused on the macro scale, with
particular emphasis on the composition/structure dimension, and following conceptual
and contextual approaches. This level of description is certainly less ambiguous than
that suggested by the single term “macro” and facilitates decision-making and planning of the next curricular steps (e.g. introduce a more quantitative approach in the
analysis of chemical systems or involve students in the development of multi-particle
models before asking them to generate molecular models).
It is undeniable that a big portion of traditional chemistry teaching can be located
in the representational region in the knowledge space in Figure 1. It is in this region
that many authors build the traditional triplet relationship, using the macro-modelling
scale as one of the corners of the conventional chemistry triangle (Gabel, 1999;
Johnstone, 1991), merging the other modelling scales into a single level (submicro)
to create the second point, and combining all of the visualisation scales into a single
“symbolic” level to construct the third corner. However, this is, to some extent, a
reduced and constrained space that cannot necessarily capture the richness and scope
of our modern chemistry knowledge. Despite these limitations, this paper is not a call
to revise or substitute a very productive and intellectually stimulating way of looking
at chemical knowledge; it is rather an invitation for discussion and reflection on a topic
that has become paradigmatic in chemistry and science education.
194 V. Talanquer
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