Plurality and identity: on the educational relations between chemistry and physics

Abstract

We present an approach to the question of the educational relations between chemistry and physics based on the one hand, on an inferentialist account of scientific representation (Suárez M., (2024), Inference and Representation. A Study in Modelling Science, Chicago and London: The University of Chicago Press). On the other, we have drawn on the notion of science identities, as is currently used in science education. We argue that the representational practices of chemistry are the key competencies for the development of a chemistry identity. We extrapolate this conclusion to physics. The problem of representational plurality, that is, that some objects can be represented divergently in these sciences is thus linked to that of identity plurality, to the question of whether it is possible for a person to simultaneously hold a chemistry and a physics identity. We study the educational implications of this situation within the framework of Lev Vygotsky's sociocultural pedagogy to conclude that the difficulties inherent to representational plurality in chemistry and physics are sociological: university degrees are built around a single, well-defined, identity, thus tending to exclude any form of plurality that compromises this uniformity. As an application of these conclusions, we have studied the question of the introduction of the quantum description of molecules in chemistry education at an undergraduate level. We conclude that this introduction should not be based on the molecular orbitals approach but, instead, on the valence bond method.

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1. Introduction

A recent on-line debate on the differences between physics and chemistry in teaching and thinking† was opened with the question: “Do chemists and physicists think differently?”. The answer of the speakers was affirmative but next they both added that chemistry and physics are closely related. They agreed that the expression “linked, but distinct” correctly expresses the relationship between both disciplines. The interest of the answer does not lie in this agreement, which we think that any person who has treated chemists and physicists in a professional setting will find hardly surprising. What is revealing, as we see it, is the way both speakers automatically shifted from the ways of thinking of chemists and physicists to the structure of these disciplines themselves. For them, the thought of chemists reproduces the models employed in chemistry, and, of course, the same for physicists and physics.

The idea that chemists and physicists, qua such, mentally represent their objects of study according to the rules and usages sanctioned in their respective sciences seems, in fact, a piece of the most ordinary commonsense. There seems to be an obvious parallelism between the individual thinking of chemists and physicists and the models employed in their respective sciences. On the other hand, a closer look shows that the question is far from being so evident. For there is no need to be a radical constructivist to consider problematic the notion that the mental contents of a person reflect the knowledge validated in her or his cultural environment. A professional physicist can, for example, be fully competent in the mathematical representation of a specific object, but does this competence imply that her or his mental representation of this object is also mathematical? And thus, the conclusion that chemists and physicists think differently is, perhaps, a little bit hurried. In fact, even considering that chemistry and physics are linked is not a fair description of the relationship between them. Chemistry and physics are not just linked, they are overlapping sciences. There is a number of problems that can be represented and explained from the point of view of both disciplines. The most conspicuous example is, perhaps, the description of molecules.

What we are trying to point out is that the question about the educational relationship between physics and chemistry must be formulated at two levels. On the one hand, there is the micro level of the individual. A problem that immediately arises here is whether a person can simultaneously think about an object from the point of view of physics and chemistry. More in general, can a person hold alternative mental representations of a natural phenomenon, and if so, what are the educational implications of such a plurality of conceptions? On the other hand, there is the macro level of the community of experts in each discipline. In this case, the question refers to how different models or theories about the same phenomenon coexist within the same curriculum. More specifically, if one of these models is presented to the students as correct, or more adequate, what is the didactic treatment to be given to the alternative ones? Let us think, for example, again, of the representations of molecules in chemistry and in physics. If a physical, quantum–mechanical description in terms of wave functions is introduced, perhaps in an approximated or even partial way, and since considering that this representation of a molecule is the right one is not an extravagant dogmatic stance, how is a chemistry teacher expected to present Lewis structures, or any other way of representing a molecule in chemistry?

In this work, we present an approach to the problem of the educational relationship between chemistry and physics that aims to account for both the micro and the macro levels. We will focus on chemistry education, specifically on the representation of molecules at the higher secondary-initial tertiary chemistry courses. Given the centrality of this issue in the chemical theory, we think that our conclusions can be extrapolated to other questions. Our analysis is based on the one hand, on an inferentialist view of scientific representations (Suárez, 2024). On the other, it draws on the notion of science identity, as is currently used in science education (Carlone and Johnson, 2007). In a nutshell, we consider that both chemistry and physics identities are characterized by a set of representational competencies. In this view, the question about the relationship between the representation of an object in chemistry and in physics is thus linked to whether it is possible for a person to concurrently develop a chemistry and a physics identity in an educational context.

In the next section we briefly review the inferentialist conception of scientific representation, and in Section 3 we show that this view is coherent with the notion of science identities. In Section 4 we study the didactic implications of these ideas from the point of view of Lev Vygotsky's socio-cultural pedagogy (Vygotsky, 1978). In Section 5, we will use our conclusions to study the case of the plurality of representations of molecules in chemistry education.

2. The inferentialist conception of scientific representation

Since we will focus on the way molecules are represented in chemistry and in physics, it seems sensible to adopt a consistent account of scientific representations as a framework to develop our ideas. To delve into this point, we will first briefly review the role that this question plays within our current understanding of the sciences.

Perhaps the most relevant trend in the contemporary philosophy of science is a shift from a syntactic view to semantic and pragmatic approaches. In a rather synthetic way, “syntax [of a theory] concerns grammar and abstract structures; semantics investigates meaning and representation; and pragmatics explores use” (Winther, 2021, Section 1). In sum, the focus has widened from the structure of scientific theories to their content, and to the way they are employed by the actual scientists. Without ignoring the importance of the logical form of theories, the semantic and pragmatic facets seem much more relevant for the study of science education. From this point of view, the philosophy of science and the research and practice in science education are now closer than a few decades ago.

Representations play a crucial role in both the semantic and the pragmatic approaches to the scientific theories. How we represent the objects studied by a scientific discipline strongly conditions, or, perhaps, even determines, what we can say about them. Besides, the way we employ the scientific ideas cannot be separated from the way we represent them. We cannot of course review here the different theories of scientific representation that have been put forward (see, for a recent review, Frigg and Nguyen, 2021). For our purposes in this paper, and focusing on the authors that consider that there is a clear divide between scientific and other kinds of representations,‡ it suffices to point out that while some authors have proposed necessary and sufficient conditions for a representation to be deemed as scientific, others have taken a deflationary approach. That is, instead of looking for their inner structural properties, these latter authors focus on the elements of practice and patterns of use that underlie scientific representations in general. This latter strategy is, in principle, better suited to explore the role of representations in an educational context, where the point is not what a specific representation is, but how it is employed by both teachers and learners. Following this line of thought, in this work we will adopt a deflationary approach. More specifically, we will adhere to the inferentialist conception put forward by Mauricio Suárez (Suárez, 2024, and references therein) because it is consistent with a Vygotskian pedagogy, which is the didactic framework that we will employ to develop the educational implications of our ideas. We elaborate on this point below in Section 4.

Suárez considers that, in practical terms, the main role of scientific theories is to provide inferences about the phenomena deemed as relevant in a specific field, either in the form of explanations or in that of predictions. Besides, this author adopts a representational semantic view, according to which theories are aggregates of representations (Suárez and Pero, 2019). Regarding his vision of representation, in Suarez's inferentialist account, for a source A to successfully represent a target B, some features of A must permit a competent person to develop explanations and to draw inferences about features of B. That is, scientific representations must enable surrogate reasoning, a consideration about the target whose task is partially taken over by operations on the source. Suarez calls inferential capacity this relational property of a source and a target. Obviously, a source that has some inferential capacities towards its intended target may lack them for any other object. Besides, the relation of representation cannot be established by mere stipulation. Four sp³ hybrid orbitals do not represent the valence shell of the carbon atom of methane just because the guild of quantum chemists has conventionally so decided, very much like the IUPAC has stipulated that the symbol of the element with an atomic number of 6 is C. These orbitals represent the valence electrons of carbon atoms in CH₄ because they license inferences about the molecule, while, for example, the word ‘methane’ does not.

The inferential capacity of a source does not suffice to successfully represent a target. Let us think, for example, of a graph like this:

Although its inferential capacity will be evident for many readers, without any further information it is, in fact, inert. It is just a fanciful shape unless it is perceived, at least in a specific context, as pointing towards a target, very much like a symbol points towards the object it stands for. To account for this directionality, Suárez introduces the idea of representational force, which, in his own words, “is the capacity of a source to lead a competent and informed user to a consideration of the target. Force is a relational and contextual property of the source, fixed and maintained in part by the intended representational uses of the source on the part of agents: no object or system may be said to possess representational force in the absence of any such uses” (Suárez, 2004, p. 768). In our example, outside the conventions adopted in organic chemistry to represent the conformation of cyclic alkanes, the graph presented above is forceless.

For a scientific representation to be effective some intended uses of an agent are required, and this implies some pragmatic considerations in the interpretation of the model sources. There are also pragmatic skills involved in the appropriate descriptions of the targets and on how sources can be employed to draw inferences regarding the target. This inherently pragmatic character accounts for the remarkable fact that schematic representations can lead to accurate conclusions about complex phenomena. Let us think, for example, of the properties of a substance, such as polarity and solubility, that can be inferred from a three-dimensional model of its molecules by means of simple electrostatic arguments. These conclusions, in the inferentialist view, are not somehow enciphered in the molecular representation, although they are of course based on its structural properties. Rather, this source enables social interactions within the community of chemists that eventually yield conclusions about the substance. It is in this community of experts, not in the source, where the information that leads to relevant inferences lies. Representations provide a medium into which reasoning can be outsourced, so that it can be shared and collectively done. Within the inferentialist approach, scientific representations are not realistic depictions, but tools for surrogate reasoning. They should not be assessed in terms of accuracy but in terms of efficacy.

From an inferentialist point of view, since the representational uses of a discipline are validated within its community of practitioners, no scientific knowledge is possible outside this community. The content of the scientific ideas (their semantics) cannot be separated from the way they are socially employed (their pragmatics). Another important corollary is that since a source is not intended to be a figurative depiction of its target, there is not a single, not even a preferent way of representing an object. Pluralism is an essential feature of inferentialism. What is effective in a context may be useless if embedded into an alternative representational practice.

3. Scientific representation and science identity

3.1 Science identities

The notion of identity is central in contemporary sociology and anthropology. Identity theory was introduced to provide a unified vision of the self that could account for both macro and micro processes in the interplay between the individual and their environment (Thoits, 1995, and references therein). In a nutshell, in sociology the term ‘identity’ refers to the possible answers to the question “How would you define this person?” that can be expected in a specific context, both from the person we are asking about and from others. This definition, if synthetic, is not as simplistic as it may seem. For although we usually believe that we are unique and that this unicity manifests coherently in every aspect of our lives, the fact is that we do not usually employ the same definition to present ourselves in different contexts (not to speak about definitions from other people). Besides, what a person is changes with time, so that saying that I am the same individual as I was ten years ago is true only in an approximated way. Identity, in sum, is a complex and fluid construct that can rarely be exhausted by specifying the individual traits of a person in a given context at a given time.

In this work we shall assume, with the mainstream in the current sociology and anthropology, that the self is reflexive, that is, it classifies itself according to categories taken from the environment of the individual (McCall and Simmons, 1978; Stryker and Serpe, 1982; Turner et al., 1987). In this view, the possible answers to the question “What are you?” are limited, and they are determined by the roles and relations that the respondent can take or stablish within the social groups in which she or he participates. Since, in general, an individual can adopt several of these available roles, the self is a multifaceted construct, and its components are usually referred to as identities. Identities are invoked to instill meaning into a given situation. For example, in some contexts an immigrant man is likely to use his nationality to define himself, as this permits him to make sense of his personal environment in terms of the compatriot/outsider dichotomy. On the other hand, in his family life it is perhaps more probable that he uses his gender, or his being head of household, to think of himself. There is no need to say that the attitudes and actions that can be expected from each role are essentially different. In sum, identities shape the interactions of the individual with other people and with her or his environment, both material and cultural.

Of all the roles that people tend to adopt, one that has a particular social relevance has to do with their occupation. Being a butcher, or a surgeon, or a police officer, or any other profession, are usual ways of defining oneself. More specifically, in some contexts people are likely to be identified as practitioners of an academic discipline: they are archaeologists, economists or geologists. In this work, in line with other authors (see Hyland, 2012), we will focus on the scientific disciplines as sources of possible academic identities.

Identity studies have been extended to science education by means of the notion of science identity, introduced by Carlone and Johnson (2007). These authors concluded that a crucial factor for a person to succeed in a scientific career is to develop a science identity, that is, being acknowledged as a “science person” at some point in her or his trajectory. In Carlone and Johnson's view, science people are individuals who are able to perform some required tasks in an academic or professional context, thus making their scientific competence evident, so that they are recognized, by themselves and by others, as proficient in a specific scientific discipline. Carlone and Johnson, in sum, put an emphasis on the social performance of relevant scientific practices in the formation of a science identity, thus bringing an evident pragmatic twist in the study of science education. Besides, if we consider the representational uses of a discipline as core competences for a person to be recognised as a practitioner of it, then the notion of science identity gains an obvious inferentialist reading.

In a much-cited paper, Zahra Hazari and co-workers adapted the notion of science identity so that it can be applied to non-professional scientists and to specific scientific disciplines (Hazari et al., 2010). Hazari's model of physics identity differs in several aspects from the original proposal by Carlone and Johnson, but it stills relies on a pragmatic vision of the scientific endeavour. This framework has been adapted to other scientific fields, including chemistry and chemical engineering (Godwin and Potvin, 2013; Hosbein and Barbera, 2020a, b), and to measure a generic science identity (Vincent-Ruz and Schunn, 2018; Chen and Wei, 2022). There are differences between these approaches, but they all keep a focus on the proficiency in some socially sanctioned practices as a key point of any disciplinary identity.

3.2 Representation and identity

In a recent paper, we have studied the role of the representational uses and practices in the formation of a chemistry identity (Sánchez Gómez, 2023). It may be interesting to review this argument in detail.

Let us focus on the usual representations of molecules in terms of bonds and lone pairs (see, for an example, Fig. 1). These molecular graphs are instrumental to any inference in chemistry, either through structural reasonings based on their three-dimensional configuration or through their usage to build reaction mechanisms. This explanatory scheme is far from being a mere introductory aid with didactic purposes. It can be found in any piece of chemical literature, from basic textbooks to state-of-the-art research papers. Using molecular graphs to draw inferences is a key skill for a person to be a chemist.

Fig. 1 A molecular graph of methyl isocyanate.§

From an inferentialist point of view, for molecular graphs to be effective representations of molecules, some intended uses are required. The requisites for a correct molecular representation, the Meccano-like vision of the molecular frame as a three-dimensional construction that can be dismantled and re-arranged, and the rules of construction of reaction mechanisms are part of the least common background shared by all the chemists that enables the representational force of molecular graphs. On the other hand, instantiating the structure of a molecule as it occurs in nature, as it were regardless of description, is not within their purview. This latter point takes us to yet another convention implicit in the representations of molecules in chemistry. Since molecular graphs are not realist depictions of molecules, the conclusions that they yield cannot be taken literally. For example, the formal charges of the different resonant Lewis forms of a molecule, which are instrumental to locate its reaction sites in the usual chemical way of reasoning, cannot be expected to be observed by any experimental method. Consequently, any argument based solely on inferences drawn from molecular graphs provides, at most, a proof of the consistency of a given inference with the rest of the accepted chemical theory, but not an absolute measure of its validity. Sometimes the person who uses the molecular graph can her or himself design and perform such a validity test, but usually this task is deferred to other experts. In sum, when somebody draws an inference from molecular graphs, she or he is always ceding the decision about its validity to the community of professional chemists. This epistemic deference is part of the uses and practices that enable the representational force of molecular graphs. Without it, chemical theory would degenerate into a self-referential game and its conclusions could not be deemed as inferences, but as interpolations.

Any inference from molecular graphs is thus an implicit act of pledging epistemic allegiance to the community of chemists. A similar argument can be made regarding the rest of the representational practices of chemistry (such as, for example, the usage of chemical equations). But allegiance alone is not enough to belong to a community. Full membership requires acknowledgement by the rest of the members. Three conditions, therefore, appear to be necessary and jointly sufficient to take a part in the guild of chemists: representational competence (the knowledge and understanding of the content conveyed in chemical representations), representational performance (the social engagement in the representational practices of chemistry) and representational recognition (acknowledging oneself and getting acknowledged by others as a ‘chemistry person’ by means of the usage of chemical representations). These three factors are closely intertwined. Competence and performance go hand in hand in any pragmatic account of scientific representations, such is the inferentialist view. Regarding recognition, a person is acknowledged as a chemist on the basis of her or his competence/performance. Recognition is not anointment; it stems from a previous assessment, usually implicit, of the competence of an individual. Engaging in the representational practices that characterize chemistry, in turn, is a social endeavour that requires, and implies, a recognition of/from the rest of the practitioners of a discipline. If somebody uses the Fischer reaction mechanism to explain to us the outcome of mixing acetic acid and ethanol in the presence of sulphuric acid, she or he, though implicitly, is acknowledging us as chemists. They will not use this explanation with, for example, a physicist, or with a science lay person. This implicit recognition does not operate in the rest of the competencies that we usually deem as inherent of being a chemist, such as, among others, laboratory skills. If I see a person performing, for example, a titration I cannot know whether she or he is a chemist unless they provide an explanation, no matter how simple, of the chemistry implied. She or he may perhaps have been trained to follow a fixed series of steps without any chemical knowledge (or, perhaps, they operate a machine that performs the technique automatically). What qualifies as a chemist is not the technical competence in the laboratory but being able to engage in the representational practices of chemistry, that is, on an inferentialist view, to contribute to an inference about the outcome of a chemical experiment. This conclusion may be shocking, or even provoking, for some readers, but it is in fact coherent with the much-cited Ian Abraham's findings on the value of practical work in science education (Abrahams, 2009). In his own words, “whilst practical work generates short-term engagement, it is relatively ineffective in generating motivation to study science post compulsion or longer-term personal interest in the subject” (Abrahams, 2009, p. 2335). In our view, this result can be easily explained if it is considered that practical work alone, independently of the representational proficiency, does not contribute to the consolidation of a science identity.

Let us now assume, as it seems sensible, that the membership to the community of chemists is equivalent to a chemistry identity.¶ What we have is thus a model for this identity based on three tightly joint dimensions, namely (representational) recognition, (representational) competence and (representational) performance. We will call this view the Trinity Model: three distinct facets and only one true identity.

Playing devil's advocate, it can be said that within the Trinity Model only people who have studied chemistry academically can develop a chemistry identity. Such a class-conscious interpretation can be deactivated by considering, on the one hand, that chemistry identity, or any disciplinary identity, for that matter, is not a dichotomic variable. Although in our ordinary language we tend to classify people into chemists and non-chemists (and the same for any other discipline or group of pertenence), that fact is that chemistry unfolds in a variety of circumstances that can seldom be reduced to an all or nothing scheme. Even if we restrict the focus on education, it makes little sense to consider that there is a line to be crossed to be a chemist. Considering that a university degree acts as such a landmark is granting academic recognitions a sacramental character that has little value other than the merely parodic. Besides, and in fact closely related to the previous, representations in chemistry can be formulated at different levels. Let us think, to stick to the example that we are focusing on this work, of the alternative representations that can be employed to represent a molecule, from simple, schematic Lewis structures, to elaborated three-dimensional depictions including atomic orbitals or other technicalities to account for the molecular geometry, through ball-and-stick models intended to allow students the manipulation and the direct visualization of the representation. Moreover, on an inferentialist view, representation is a social endeavour. Producing, or interpreting, a molecular graph requires the insertion in a community, that of chemists, where a manifold or roles coexist. In the words of Ken Hyland, speaking about disciplinary identities in general, “identity does not belong within the individual but between persons and within social relations […]. Identity is not the state of being a particular person but a process, […] an ongoing project as opposed to a fixed product” (Hyland, 2012, pp. 2–3). In sum, in our view, there is an alternative to thinking about chemistry identity as something an individual person may lack, a condition to exclude somebody from the guild of chemists. For it can be, in fact, quite the opposite: a way of integrating divergent stories into the collective enterprise we have come to call chemistry. A laboratory technician may not be able to give a full theoretical account of the underlying chemistry of an experimental technique, but as long as she or he plays a role in the representational practices that take place in the laboratory, understood as a complex social setting, they does participate in a chemistry identity. This conclusion is not restricted to the individual experience. As we understand identity, groups that have traditionally received little academic acknowledgement are entitled to claim their role in the development of chemistry. Women, for example, have been always indispensable in the usages and institutions that enable the representational practices of chemistry. The lack of recognition should not obscure the fact that without their contribution, in a variety of roles, chemists had never been able to engage in the complex network of interactions that underlie their practice. A similar argument can be made regarding other minorities underrepresented not just in the history of chemistry, but also, regrettably, in its present state.

3.3 Empirical implications of the Trinity Model

Some facets of the Trinity Model can be empirically tested. To start with, educational factors related to representations should show a stronger positive correlation with constructs that are assumed to be concurrent or convergent with chemistry identity (such as, respectively, science-related attitudes -Fraser, 1978; 1981; Navarro et al., 2016- and science career interest or science self-concept -Kier et al., 2014-) than other not explicitly representational competencies. For example, visuospatial thinking has been shown to be critical in chemistry learning (Wu and Shah, 2004; Kiernan et al., 2021), a conclusion that can be readily explained from an inferentialist point of view, given the instrumental value of spatial reasoning in the generation and usage of molecular representations. Well then, in the Trinity Model, when compared with constructs concurrent with chemistry identity, spatial intelligence will show, among other measures, a Pearson's r correlation coefficient closer to 1 than, let us say, manipulative skills, which are expected to be connected with the proficiency in the laboratory. Regarding its internal structure, a structural equation model (SEM) of the construct ‘Science Identity’ based on the one we represent in Fig. 2 should show a strong correlation between representational competence, performance and recognition, each of them, on its side, predicting identity. That is, while our analysis supports the original proposal of Carlone and Johnson (2007), we conclude that neither ‘Interest’ nor any other attitudinal construct plays any role in the conformation of a chemistry identity.

Fig. 2 Model of chemistry identity within the trinity model.

A further testable consequence of the Trinity Model is that educational interventions focused on representations should produce, under equivalent conditions, larger educational effects than other non-explicitly inferential approaches. For example, a chemistry laboratory course in which molecular representations are systematically used to explain the experiments is expected to yield a sounder engagement with the subject, both more intense and more persistent, than other approaches in which representations are not explicitly employed to draw inferences.

3.4 Plurality and identity

We can try now an inferentialist account of representational plurality, the fact that the same object can be represented divergently as it is studied by different sciences, and, in particular, of the case of the description of molecules in chemistry and in physics. To start with, we will assume, in principle as a hypothesis, that the Trinity Model, as it is represented in Fig. 2, also applies to physics. Using molecular graphs corresponds to implicitly claiming a membership to the community of chemists, more or less profound, depending on the level of complexity of the specific application. A wave function of a molecule, on its side, implies invoking a physics identity. Thus, the representational plurality of molecules, the fact a molecule is represented divergently as it is studied in chemistry and in physics, is thus linked to identity plurality, to the possibility of developing an identity with facets corresponding to both sciences. Such a multifaceted science identity does not seem, in principle, impossible. While both chemistry and physics identities are clearly delimited, cases of split personality are frequent at the border between them. A physicist, for example, can employ a representation of a molecule in terms of bonds and lone pairs to set out an approximation for its wave function. On the opposite direction, the topological properties of the energy hypersurface, obtained by solving the electronic Schrödinger equation for a molecular system, can be used by a chemist to elucidate the mechanism of a chemical reaction (see Simm et al., 2019). On the other hand, situations like these seem problematic in an educational setting. In such a context, plurality implies concurrently invoking two science identities by people who may have not developed, not even in an embryonic sense, neither of them yet.

4. A didactic framework for representational plurality: proximal development and identity

To explore the didactic implications of representational plurality we will resort to Lev Vygotsky's sociocultural theory of learning (Vygotsky, 1978). Given the centrality of the Vygotskyan framework in our current understanding of science education (see, for an excellent recent review, Murphy, 2022), it does not seem too restrictive a choice. We will focus on tertiary education since at this stage the process of identification with a scientific discipline seems more explicit and therefore more accessible for its study.

Vygotsky's crucial point is a distinction between development and learning (Vygotsky, 1978, p. 90). While development, for him, in a rather synthetic way, refers to individual understanding, learning is the ability to engage in some practices in a specific setting. Vygotsky's general genetic law of development states that learning precedes development: for an individual to develop some mental contents about something, she or he must first become competent in the usage of the cultural tools that stand for it, by participating in social interactions where these tools are employed.

It is easy to see that Vygotsky's ideas are coherent with the inferentialist approach to scientific representation.|| On the one hand, it seems simply obvious, independently of the psychological theory of learning that one subscribes to, that for a person to develop some mental contents about something she or he must first be able to internally represent it. In fact, at least in a rather prudent psychological vision, mental contents are nothing but representations of a part of the world.** Besides, we can hardly say to have an idea about something if we are not able to produce an explanation, not even a simple one, or draw an inference, no matter how limited, about it. Thus, taking these two conclusions together, the very notion of developing ideas about something presupposes a vision of representation coherent with the inferentialist tenets. On the other hand, from an inferentialist point of view, as we have seen in Section 2, representations are inseparable from some social practices sanctioned in a specific scientific community. In sum, if we accept the seemingly common-sense conception that representation is a prerequisite of thought, and if we adopt an inferentialist view of representation, then the general genetic law of development logically ensues.

The most important element of Vygotsky's pedagogy is the dialectics between meaningful social learning and individual understanding. The notion of Zone of Proximal Development (ZPD) grows out of this relation. According to Vygotsky, ZPD is “the distance between the actual developmental level [of the individual] as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers” (Vygotsky, 1978, p. 86). Vygotsky points out that two children with the same actual developmental level (that is, who could solve the same problems alone on a test) can show divergent educational performances due to differences in their respective ZPDs. Let us imagine, for example, that while one of them can engage in solving more complex problems, either with guidance of the educators or in collaboration with more capable peers, the other lacks this adequate environment. Obviously, the one who had a more supportive ZPD is more likely to learn through her or his social interactions than the other. The immediate conclusion, in Vygotsky's didactical approach, is that students must be provided with a fertile ZPD to promote learning and thus understanding.

The ideas of Vygotsky have been adapted into the framework of educational identity studies by means of the notion of Zone of Proximal Identity Development (ZPID) (Polman, 2006; 2010). The term ZPID refers to the distance between the actual identifications of an individual in a given context, at a given moment, and the identities that she or he can eventually develop through the interactions with the rest of the actors in that context. In a different way, ZPID is the potential evolution of a person in a learning environment where a disciplinary identity is invoked, so that the learner can be recognized, by her or himself and by the others, in this identity. The definition of ZPID builds on the concept of trajectories of identification (Dreier, 2000; Wortham, 2006), that accounts for the vision of identity not as a fixed trait, but as a process (Lemke, 2000), guided by the experiences of the individual as she or he takes part in different “communities of practice” (Lave and Wenger, 1991; Wenger, 1998). These communities are characterized by some cultural tools (including language and ideas) that enable social interactions within them. Obviously, the different scientific disciplines can be understood as communities of practice, their respective representational uses thus being a key part of the cultural tools shared by their practitioners. Considering the Trinity Model that we introduced in the previous section, the development of a chemistry (physics) identity can thus be favoured by the insertion of the learner in a suitable ZPID, that is, an environment in which she or he can get engaged, through an interaction with experts and more experienced peers based on mutual recognition, in gradually more complex tasks in which some representational practices of chemistry (physics) are put in practice.

We can try now a sociocultural assessment of representational plurality in chemistry and physics. An ideal science career can be modelized as a trajectory of identification across a series of successive ZPID. This trajectory is not necessarily limited to a single discipline. At a specific point several identities can be simultaneously invoked, if their respective communities of practice are not mutually exclusive. We will assume that such is the case for the natural sciences at an introductory level. While professional science disciplinary identities are usually clearly delimited, we will consider that pre-university students, even at an upper secondary level, can identify, surely in a tentative way, with more than a single science. This assumption, on the other hand, is much less obvious in tertiary education. The existence of well-defined disciplinary academic degrees indicates that university education is designed as a linear process going deep into the community of practice of a specific science, at least in some cases. Specifically, although in recent decades there has been a proliferation of university degrees in which elements of different sciences are integrated, and without losing sight of the existence of time-honoured interstitial disciplines such as biochemistry or geophysics, this trend has not affected in depth the educational relationships between chemistry and physics. Physical chemistry is, of course, a well-established academic area, but its hyphenated name is somehow misleading since it is distinctly chemical.†† Besides, the academic life of both chemistry and physics continues to revolve around institutions (scientific societies, faculties, departments, etc.) specific of each area.

Summing up, tertiary chemistry education takes place within a distinct academic environment, and this leads us to think that, if not fully preordained, it is a teleological process. Although there are probably as many trajectories of identification as chemistry students, they all are expected to converge around a core of representational competencies that define, according to the Trinity Model, what being a chemist implies. It is this target identity what rules the curriculum of a chemistry degree, in the amplest acceptation of the noun ‘curriculum’. Chemistry identity dictates not only the contents to be taught, but also, and, in fact, primarily, the usages and competencies deemed as inherent to a chemist.

From a socio-cultural perspective, therefore, the implications of representational plurality vary dramatically as one ascends the academic ladder. This suggests that the difficulties that it brings about are neither individual nor, in fact, inherent to the community of chemists, but institutional. For there is no reason to think that people get less psychologically flexible, less apt to mentally deal with alternative frameworks, as they become expert chemists. Nor does it seem logical that the community of chemists is more tolerant to representational heresy in beginners, who have to stick to the uses and practices of the guild to be accepted in it, than in professionals, who, at least in principle, are expected to be critical with the received ideas.‡‡ Instead, as we see this question, the problem lies in that plurality introduces a potential bifurcation in the trajectory of identification of university students, thus challenging the teleology implicit in a chemistry academic degree.

5. An application: the representation of molecules in chemistry and in physics

Let us delve into the case of the representation of molecules in chemistry and in physics. We will focus on the higher secondary-initial tertiary chemistry education interface, as at this stage students are usually presented with both more complex applications of molecular graphs, and with the fundamentals of the quantum description of molecules. Let us think, for example, of a novice tertiary education student who is being taught, in parallel, a way of reasoning based on molecular graphs, such as that employed in reaction mechanisms in organic chemistry, and an alternative representation based on quantum mechanics, like the HOMO/LUMO approach to chemical reactivity. To keep the argument clear, we will not enter here into technical details, that can be found in any quantum chemistry textbook. To our present purposes, and at the risk of stating the obvious, it suffices to point out that drawing inferences from molecular graphs and from wave functions require radically different competences. It is not just that the simple, intuitive, visual rules employed with molecular graphs sharply contrast with the abstract mathematical approach needed to manipulate wave functions. The divergence gets to the point that that the compatibility between the inferences that can be drawn in both cases is problematic. While the reasoning based on molecular graphs is essentially structural, molecular structure, either in the sense of the geometry of the nuclear frame or in that of the distribution of electrons, is not a quantum observable and it is thus outside the inferential reach of the usual interpretations. Thus, in the terms that we introduced in the previous section, using a quantum description of molecules within at an introductory chemistry level induces a bifurcation in the trajectories of identification of the prospective chemists. Students must alternate between representational practices that imply radically different competencies. This is not perhaps an unfeasible task (although it does not seem the most promising didactic scenario, either), but it may imply a deep reformulation of a standard chemistry degree depending on the approach that is employed. Let us see it in detail.

In this work, we will restrict our analysis to the most common ways of approximating the wave function of a molecule, the molecular orbitals method (MO) and the valence bond (VB) method. The usual way of introducing the fundamentals of quantum mechanics in introductory chemistry textbooks follows the sequence: Lewis structures-VSEPR theory-VB method-MO method. In this approach, the main educational role of the VB method is to be a preparatory stage for the treatment of molecular orbitals. VB, in fact, is sometimes presented as a limited approach, an oversimplification of the problem of the quantum representation of molecules (Spencer et al., 2011, p. 170; Brown and LeMay, 2017, p. 368; Tro, 2018, pp. 267, 268). On the other hand, this opinion is, to say the least, debatable. To start with, it has been shown that both methods are formally equivalent (Galbraith et al., 2021; Shaik et al., 2021, and references therein). Besides, although, for historical reasons, most of the quantum calculations of molecules are done within the MO framework, the VB approach is currently included in many computer packages for quantum calculations of molecules (see Section 8 of Shaik et al., 2021). Finally, and from the point of view of our purposes in this work, most importantly, the VB method “is a chemical language” (Shaik et al., 2021, p. 10).

VB method thus provides a formally correct solution (or at least as correct as its main competitor's) for the Schrödinger equation for a molecular system (see Wu et al., 2011). It is computationally available, and, as Klein and Trinajstic put it more than thirty years ago, “VB views often merge naturally into basic qualitative (prequantum–mechanical) chemical bonding ideas that are taught” (Klein and Trinajstic, 1990). On the other hand, the role of notions such as bonding and lone pair within the MO approach is not clear, as can be seen in Fig. 3, where molecular orbitals of water are depicted together with a standard molecular graph. The relation between the bonding orbitals (2a₁ and 1b₂) and the two O–H bonds, and between the non-bonding orbitals (3a₁ and 1b₁) and the two lone pairs on the oxygen atom are anything but evident.§§ The connection with the chemical structural ideas is lost from the very beginning within a MO approach. Moreover, even a basic understanding of MOs requires some knowledge of mathematical subjects, such as complex analysis or group theory, that are of little use in other areas of chemistry. There is a gap between the representational practices in which university chemistry students are being enculturated and those specific of the MO method. As we interpret the situation, the MO approach fits into a chemistry identity, at least at an introductory stage, in a somehow eccentric way. It belongs to a rather idiosyncratic part of the community of practice of chemistry, that of quantum chemists, a tribe that dwells on the border with physics.

Fig. 3 Molecular orbitals of H₂O.¶¶

Against this interpretation, it can be argued that since MO calculations are in fact heavily used by chemists in their daily practice outside the restricted field of quantum chemistry, this method is, in fact, genuinely chemical. MOs are as part of the standard representational implements of chemistry as, among others, molecular graphs or the quantum-like ideas associated to the VB method, such as the notions of orbital, hybridization, overlap, resonance and the so. Using MOs, in this view, does not imply pushing chemistry in the direction of physics. It is simply that the divide between chemistry and physics is, at least from the perspective of the representation of molecules, arbitrary. But this conclusion is, in fact, a mirage. Quantum chemistry computational packages are usually employed as black boxes, without a real insight into their foundations (Hirschi et al., 2023). As Gallegos et al. put it, “Today, most [chemical] researchers use [quantum] techniques in their essential post-calculation interpretation steps that are based on much cruder assumptions than those used in the simulations themselves” (Gallegos et al., 2024). What these authors point out is that for most non-theoretical chemists, quantum computations are basically instruments to quantify molecular graphs, chiefly to associate energy values to them and to set out bond lengths and other structural properties. They normally use quantum chemistry computer packages very much like experimental devices such as spectrometers or electron diffractometers, to fill in the blanks in their classical molecular models. It cannot be said, therefore, that non-theoretical chemists resort to a quantum representation of molecules when they employ the results of a quantum calculation. Instead, as we see it, they stick to classical molecular graphs, albeit enriched by including quantitative information obtained from quantum, usually MO, calculations.

Designing a ZPID based on the VB method to give a quantum coat to prospective chemists seems an obvious choice, in the sense that it does not require a heavy reformulation of the curriculum. This approach permits to use the standard chemical structural ideas to approximate the wave function of a molecule. The usual graphical representation of bonds and lone pairs by means of overlapping or doubly occupied atomic orbitals, respectively, can be seen as a preliminary stage in the development of a quantum thinking from basic chemical notions (Barradas-Solas and Sánchez Gómez, 2014). In a further step, the different resonant Lewis structures for a given system can be interpreted as the components of the wave function within a configuration interaction approach. Our point is that within the limits of the VB method, chemistry students can make use of their basic chemical background to set out gradually more complex approximations to the solution of the Schrödinger equation, either on their own or, more likely, in cooperation with other students or with the support of experts. In this approach, students are not expected to fully understand the quantum subtleties but, instead, to use Lewis structures to feed a standard computer program with an initial basis set to generate an approximated wave function, and then employing this function to draw inferences about a molecular system. On the other hand, the MO method could be fully ignored in chemistry education, at least at introductory levels, without any major harm. Moreover, as we see this question, students should not even use computer packages based on MOs. It is more productive, from the point of view of adding a quantum facet to a standard chemistry identity, to employ VB calculations. Putting it bluntly, a person does not need to know about MOs to become a chemist, at least a non-quantum one. It must be stressed that our position is not that the MO method is too difficult to be fully mastered by an average chemistry student. Our point is that for such a mastery to be achievable, the usual chemistry curriculum must be substantially reformulated to include in it subjects that are typical of a physical degree.

In sum, we advocate for getting rid of the ancillary role that the VB method has been traditionally granted in chemistry education. As we see this question, this approach is the natural way for a chemist to get in touch with quantum mechanics, and it should be extensively exploited in chemistry education. The MO method, again in our view, can be treated at a later educational stage, only after students are competent in the use of the VB model to represent molecules, including, of course, quantum calculations. If there is an educational role of the MO method in chemistry education, it should be providing prospective chemists with an alternative, bond-free vision, that aims not at the construction of a chemistry identity, but at allowing students to add a further physical facet to it. A notable consequence of this position is that, since the representation of molecules is arguably the most conspicuous overlap between chemistry and physics, an obvious way for prospective chemists to get in touch with a physics identity is through quantum mechanics. It is therefore possible, or even probable, that a chemistry student become competent in the inferentialist use of wave functions without a deep understanding of other areas such as classical mechanics or electrodynamics. This prospect can be deemed as limited, or even as dysfunctional, from the point of view of the traditional approach to physics education. On the other hand, we think it is the logical consequence of putting the representational competencies at the core of scientific identities. In a not completely metaphorical way, the shortest path between any two of these identities departs from, and ends at, their respective representational practices.

6. Conclusions

In this work we have presented an approach to the question of the educational relations between chemistry and physics based on three closely related lines: an inferentialist account of scientific representation; the notion of science identities, as it is employed in the current educational research; and Lev Vygotsky's sociocultural pedagogy. We argue that the representational practices of chemistry are the key competencies for developing an identity for this discipline. Specifically, in our view, chemistry identity is a construct with three different but inseparable facets: representational competence (the knowledge and understanding of the content conveyed in chemical representations), representational performance (the social engagement in the representational practices of chemistry) and representational recognition (acknowledging oneself and getting acknowledged by others as a ‘chemistry person’ by means of the usage of chemical representations). We have called this view the Trinity Model of chemistry identity and we assume that it can be extrapolated to physics. As an obvious corollary, representational plurality, the fact that the same object can be represented divergently as it is studied in chemistry and in physics, runs in parallel with identity plurality, the possibility of developing a science identity belonging to these two disciplines. We have adapted the Trinity Model into a Vygotskian framework, to conclude that the educational implications of representational plurality are neither psychological (a learner can employ alternative representations of an object from the point of view of chemistry and physics), nor anthropological (the representational uses and practices of chemistry and physics do not seem incompatible), but sociological: educational institutions are based on a clear distinction between chemistry and physics that is compromised by plurality. Chemistry and physics university degrees, in particular, rest on a well-defined separation of their respective disciplinary identities. Plurality challenges this academic disciplinary logic and thus it does not easily fit within the institutional embodiment of chemistry and physics.

In sum, although there seems to be no fundamental hindrance for a person to develop a pluralistic representation of any question that can be studied alternatively from the point of view of chemistry and physics, this situation is unlikely in practical terms. Scientific disciplines, like any other social institution, are contingent, but not arbitrary. They embody the history of the knowledge about some specific problems, and thus they shape the ways this knowledge is employed in actual situations. In is not unthinkable that in the future the border between chemistry and physics gets blurred or dissolved, or even that a new hyphenated discipline emerges between them, very much like current biochemistry has gained some autonomy from both chemistry and biology. But as of today, chemistry and physics show distinct disciplinary logics that are particularly intense in an educational context. Specifically, a university degree does not seem the right place to challenge the separation between them, simply because tertiary education is primarily oriented towards the insertion of the students in the community of practitioners of a discipline, at least in the case of chemistry and physics.

We have applied these ideas to the question of the usage of quantum representations of molecules in chemistry education. We argue that the simplest way for a novice chemistry student to become competent in drawing quantum inferences about molecules is to stick to the valence bond method as an approximation for the wave function. That is, in our view, molecular orbitals should not be employed at preliminary stages of the teaching of the quantum foundations for chemists.

Finally, although our conclusions are in principle restricted to the relationship between chemistry and physics, they may be extrapolated, at least in part, to other disciplines. The potential generalization of the Trinity Model is one of the questions we plan to study in further works.

Author contributions

Pedro J. Sánchez Gómez have contributed to the CRediT roles: conceptualization; investigation; methodology; writing – original draft; and writing – review and editing. Mauricio Suárez has contributed to the CrediT role: writing – review and editing.

Data availability

The author confirms that no empirical data have been employed to support the findings of this study.

Conflicts of interest

The authors declare that they have no conflicts of interest.

Acknowledgements

This work has been supported by the Spanish Agency for Research (AEI) projects PGC2018-099423-B-100 and PID2021-126416NB-I00. Pedro J. Sánchez Gómez is member of the research group Grupo de Investigación en Filosofía de la Educación (GIFE), based at the Complutense University of Madrid. Mauricio Suárez is member of the research group Grupo Interdisciplinar de Sistemas Complejos (GISC-UCM), based at the Complutense University of Madrid.

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Footnotes

† https://edu.rsc.org/feature/what-are-the-differences-between-physics-and-chemistry-in-teaching-and-thinking/4016897.article. The speakers were Charles Tracey, a senior leader in education policy linked to the Institute of Physics (IOP), and Izzy Monk, an adviser of the Royal Society of Chemistry and former chemistry and physics teacher.

‡ Some authors have argued that the relation of representation is merely stipulative: A represents B if, and only if, so is stipulated in a given context. From this point of view, there is no essential difference between a scientific and any other kind of representation. Diego Velázquez's The Surrender of Breda can be taken to represent, for example, a many electrons atom if so is decided. As Frigg and Nguyen point out, this counterintuitive position fails to explain some evident features of the representations that are usually employed by the scientists (Frigg and Nguyen, 2021, Section 2) and we will not dwell upon it in this work.

§ Figure taken from: https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_General_Chemistry_%28Petrucci_et_al.%29/10%3A_Chemical_Bonding_I%3A_Basic_Concepts/10.7%3A_Shapes_of_Molecules.

¶ Linking social identity to the membership to a group is, in fact, the basis of social identity theory, a standard approach within social psychology. Social identity theory was originally developed by Henri Tajfel and John Turner in the 1970s and 1980s (see, to cite two classic references, Tajfel and Turner, 1979; Tajfel and Turner, 1986). Although the notion of identity is formulated differently in sociology and in social psychology, it has been shown that these differences lie more in the emphasis put on specific issues than in substantial divergences between them (Stets and Burke, 2000).

|| This coherence is surely coincidental. For, on the one hand, Lev Vygotsky died well before the problem of representation were put on the focus of the philosophical investigation. And, on the other, to the best of our knowledge, there is no evidence that the inferentialist authors have paid much attention to the work of Vygotsky and his followers.

** In the entry ‘Narrow Mental Content’ of the Stanford Encyclopaedia of Philosophy we read: “[…] Mental content simply means the content of a mental state such as a thought, a belief, a desire, a fear, an intention, or a wish. […]. A state with content is a state that represents some part or aspect of the world; its content is the way it represents the world as being.” (Brown, 2022, Section 1).

†† A few university degrees in physical chemistry can currently be found (see, for example, https://www.ucl.ac.uk/natural-sciences/core-streams/chemistry/physical-chemistry), but they are not a merger of elements of chemistry and physics degrees but, instead, a specialization on a specific area of chemistry.

‡‡ We guess that some readers may found this opinion debatable, but we think that even the staunchest Kuhnian will agree with us in that discrepancies with the orthodox views are much more likely to be tolerated if they come from a professional scientist than from a novice student.

§§ Molecular orbitals can be localized by means of a unitary transformation, without any change in the overall wave function (see, to cite a classical textbook, Section 15.9 of Levine, 2000), but this abstract algebraical procedure is as alien to the usual chemical way of reasoning as any other mathematical method of quantum mechanics such as, among others, the group theory that lies behind the nomenclature of molecular orbitals (e.g., a₁, b₂, a₁, b₁ are the labels of the irreducible representations within the C_2v point group).

¶¶ Figure taken from the web of the London South Bank University. URL: https://water.lsbu.ac.uk/water/h2o_orbitals.html.

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