Reasoning through uncertainty: expert chemists’ analogical thinking on a novel problem

Abstract

Chemistry education has begun to consider disciplinary practices as complementary to traditional instruction of content knowledge. A challenge in this, however, is that our understanding of the latter is far more developed: given a canonical question, it is more obvious to instructors whether a student's reasoning is correct than if it reflects productive approaches to sensemaking. In this study, we investigated how expert chemists approach sensemaking when challenged with a novel question. Here we focus on a prominent aspect of the results, the experts’ pervasive use of analogies, defined as explicit references to previous knowledge from other situations. The findings reinforce the importance of analogical reasoning in disciplinary expertise. Descriptions of how chemists’ reason in novel situations will help educators recognize the productivity of students’ sensemaking independent of its correctness.

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I. Introduction

Curriculum and instruction focus almost exclusively on guiding students toward expert-like understanding, supported by chemistry education research (Lenzer et al., 2020) on the nature of that understanding (Taber, 2014; Cooper and Stowe, 2018). Most introductory chemistry classes continue to build students’ mental bank of chemistry knowledge in restricted instructional time. At times, the imperative of broad context coverage inhibits essential features of disciplinary practice (Scudder, 1997; Van Berkel et al., 2000).

There is no question that the traditional material of introductory chemistry is an important base for students to build their knowledge on. In fact, expertise in any field develops on a strong fundamental foundation. Following earlier research in physics education (Larkin et al., 1980; Chi et al., 1981), chemistry education research (CER) has studied the nature of experts’ knowledge compared with novices’ (e.g. Heyworth, 1999; Krieter et al., 2016; Gulacar et al., 2022). The general approach of this work has been to create a comparative platform of experts and novices, where the same task is presented to individuals at different levels of expertise. Across these studies, experts’ knowledge is found to have a different structure and organization from novices, with implications for the organization of course curriculum, such as the order of topics in instruction.

These results have also argued for reforming curricula and teaching to engage students more actively in working to connect and organize what they learn. Gulacar et al., for example, suggest that reforming chemistry curricula “to promote… expert level concept connections… should also enhance students’ metacognitive abilities and make them successful lifelong learners.” (Gulacar et al., 2022) Similarly, Khan recommends redesigning science teacher education programs to place greater emphasis on scientific reasoning in their trainings, with the goal of promoting more reasoning by students in the classrooms (Khan, 2025). In this way, CER has recognized that expertise in chemistry goes beyond the body of knowledge alone (Claesgens et al., 2008; NGSS, 2013; Brooks et al., 2016; Lenzer et al., 2020; DeGlopper et al., 2022). For a key example, the expertise of professional chemists centres on inclinations and abilities to engage with what they do not already know: “Doing chemistry” is a disciplined activity of sensemaking of novel phenomena. Chemists are experts at learning, including at recognizing gaps and inconsistencies in their current understanding (Evans et al., 2006; Sevian and Talanquer, 2014). This uncertainty, which is inherent to science in general, (Firestein, 2012), gets lost in well-defined sections of the curricula, designed to deliver facts to learners (Dávila and Talanquer, 2010). The contrast is stark: within chemistry research, a matter of uncertainty is an opportunity; within a typical chemistry course, it is a liability.

The challenge for chemistry education is in coordinating attention to these other aspects (such as sense-making and self-reflection) with the traditional focus on content knowledge. At this point, the community has a far better understanding of the body of knowledge than of experts’ practices as learners. For instructors, as for students, the obvious “material” of introductory chemistry is the set of concepts, models, and laws listed week-by-week in syllabi and textbook tables of contents. There is a need for more understanding of the nature of implicit skills of chemistry expertise.

One approach to researching expertise has been to study scientists at work, drawing on the history and philosophy of science (Niaz, 2016) and ethnographic studies (Knorr-Cetina, 1999; Dunbar and Blanchette, 2001a, 2001b). Kozma et al. (2000), for example, drew on both historical accounts and ethnographic observations of chemists in their laboratories to identify abilities that can be cultivated in students (Kozma et al., 2000).

Another approach is less connected to the genuine work of scientists but closer to the contexts that students experience in school. Rather than giving experts and novices the same task, the researchers posed questions to experts that challenged them to think beyond what they already knew. Discipline-based education researchers in physics (Clement, 1994a, 1994b; Clement, 1998a, 1998b; Singh, 2002), mathematics (Schoenfeld, 1985), and engineering (Cross and Cross, 1998; Ball et al., 2004) have taken this approach to focus on expert reasoning strategies.

Across these studies, expert reasoning involved considering and coordinating multiple lines of thinking, including searching prior knowledge and experience for possibly relevant connections. The relevant knowledge, of course, reflected the disciplinary contexts. Clement (1994a, 1994b), for example, showed a central role for imagistic and kinaesthetic simulation in the physicists’ reasoning about springs. However, his work also revealed that expertise involved metacognition, habits of assessing the quality and coherence of those connections (Clement, 1994a, 1994b). Physics experts chose how to proceed based on those assessments, such as when coordinating qualitative, physical intuition with formal calculations. Singh (2002) showed that when experts generated conflicting lines of reasoning through intuitive thinking, they shifted from qualitative reasoning to formal calculation (Singh, 2002).

We set out to conduct a comparable study of expert reasoning in chemistry, motivated by a general, initial question: How would chemists reason about a problem that is novel and challenging for them? Button et al. (Button et al., 2023), summarized below, focused on the experts’ metacognitive and socio-emotional management of not knowing in their response to the novel question. Here, we focus on the substance and flow of their reasoning. As we recount below, we began with an open exploration and found significant complexity, involving both “fast” and “slow” thinking (Kahneman, 2011). Analogical reasoning was prominent throughout, in chemists’ quick, intuitive associations as well as in their slow, effortful analyses. We decided for this paper to focus on experts’ use of analogies.

The plan for the remainder of this article is as follows: first, in the rest of Section I, we recount our path to conducting this study, including our positionalities as scholars, and a summary of initial explorations that led us to focus on analogies. In Section II, we review prior research on analogical reasoning and its use in professional science. We then turn in Section III, to our methodology, data, and analyses of expert use of analogies in reasoning about the novel problem we posed. Finally, we close with Section IV to summarize our conclusions and discuss potential implications for CE and CER.

Formation of this study

The two faculty authors, Diren and David, have worked together for six years, both in The Listening Project (Tobin, 2017), which was a professional development initiative focused on science faculty attending to student thinking, and in the Institute for Research on Learning and Instruction (IRLI) at Tufts University. During a meeting of The Listening Project, they happened on a question that challenged chemists in the room: Why doesn’t the molecule FBO exist naturally as a stable compound? They refined this question to be more open, to ask about the structure of a compound made up of fluorine, boron, and oxygen.

Diren used this question in her teaching by posing it to students without requiring them to come to a single “correct” answer. They had ideas, but Diren wondered how experts would respond. She and David made a plan to interview PhD chemists, inspired by earlier discipline-based education research (DBER) studies of expert reasoning. Diren recruited an undergraduate, John Button, as a research assistant to help with interviewing the experts and analysing results. Diren and David developed the interview protocol that we describe below.

John was intrigued by the chemists’ saying “I don’t know” (IDK), which became the focus of the first analysis (Button et al., 2023). The evidence suggested that saying IDK served the experts as a kind of socio-emotional shield from judgment, as well as to mark their perception of a gap or inconsistency in their reasoning. The implications from that analysis highlighted a need for students and educators to consider not-knowing, confusion, and uncertainty as valuable opportunities for sensemaking rather than as embarrassing situations to avoid.

There remains more to study in the collected interview data beyond what was presented in Button et al., 2023, including the original motivation to study expert problem-solving. For experts, questions in introductory chemistry are usually familiar “exercises” (Bodner, 2003), which they can answer efficiently. Therefore, while watching a student struggle with those types of questions, they “are tempted to intervene, to show the ‘correct’ way of obtaining the answer” (Bodner, 2003). A study of how experts handle an unfamiliar problem may help instructors recognize productive struggles in students. To delve deeper into experts’ problem-solving strategies, Diren recruited Kyle to help analyse the substance of the experts’ reasoning on FBO.

Authors positionalities

At the time of this study, Kyle was a senior at Tufts, majoring in biology. He had taken two courses with Diren and served both as a Learning Assistant and Learning Researcher in introductory chemistry courses. In those roles, he was trained to look closely at the thinking moves of his peers in the classroom. Kyle has been interested in the epistemology of teaching and learning from his first days at Tufts (Bergeron, 2020). Currently, he is a medical student at the Larner College of Medicine at the University of Vermont. Kyle retains both a professional interest as well as a personal stake in the education of future physicians, all of whom must complete undergraduate instruction in general chemistry, organic chemistry, and biochemistry.

Diren is a senior lecturer in the Department of Chemistry, with 14 years of teaching experience, a long-standing interest in developing curriculum and practices of instruction, and growing involvement in chemistry education research. She is especially interested in the role of intuitive expertise (Kahneman and Klein, 2009) in both students’ and experts’ problem-solving processes. Having taught both pre-medical students and other introductory chemistry and biochemistry students for many years, she is intrigued with how her students, many of whom are on track to be future doctors and scientists, display fast and slow thinking (Kahneman, 2011) as they grapple with problems and when making decisions. Diren and Kyle conducted the analyses throughout this study, meeting with David occasionally to consult.

David is a professor of Education and Physics, one of the leaders of the Listening Project and of the IRLI. His research has focused for many years on students’ learning in STEM, and he regularly teaches introductory physics. He has a long-standing interest in helping students learn how to learn, including their noticing, articulating, and engaging productively with confusion, an emphasis in his syllabi and threaded through research publications (Hammer, 1995; Hammer, 1997; Phillips et al., 2018; Radoff et al., 2019). This continued partnership with Diren is his first involvement in a study of expert reasoning.

Initial exploration & analysis

We began an exploration of the data through the lens of “two systems of the mind” (Kahneman, 2011), similar to “dual process theory” (Wason and Evans, 1975; Evans, 2008). System I is fast and automatic; “it is something that happens to you, it is not something that you do” (Kahneman, 2012, p. 55). System II is slow and effortful, something “you have to do” (Kahneman, 2012).

Throughout the interviews, as the experts thought aloud, there was evidence of both Systems at play. Expert fast thinking included spontaneous recognition and naming of prior knowledge, which we called “recognizing patterns”. This occurrence often took the form of analogies as we discuss below. Other facets of experts’ System I-style thinking contained claims or conjectures the experts produced without evidence of deliberation, which we called “proposing ideas”. There was also evidence of slow thinking in the interviews, when the experts talked through details of their understandings and uncertainties. We simply called this “chemical reasoning”, which also included the moments of “mental simulations” in the experts’ explanations to visualize dynamic processes, similar to Clement's (1994a, 1994b) account of imagistic simulation. (Clement, 1994a, 1994b) Chemical reasoning of the experts overall involved examining the quality of spontaneous recognitions and ideas, as well as deliberative searching for related knowledge.

We constructed circular flow maps of each chemists’ interview to look for patterns, as illustrated in Fig. 1. These maps included each of the thinking moves (described above) as nodes and traced the chemists’ movement between the nodes as they reasoned through the FBO question. The colour of each line matches the starting node, and the arrow points to the finishing node of each path. The thickness of the lines indicates the relative frequency of that particular path. Each map begins with the initial FBO question on the right and includes the chemists’ expressions of uncertainty and resolutions of thoughts.

Fig. 1 Annotated map for participant #9's reasoning and problem solving process.

This analysis invited the possibility that comparable patterns might emerge across the set, as illustrated in Fig. 2. The data from every interview showed complexity. In each interview, we saw the expert making evidently fast connections to other knowledge as well as slow, deliberate examination and development of those connections. Fig. 2 shows the range of complexity in our interpretations of the data. One interesting variation was in the experts’ choices; with some (such as #6, blue arrow) moving to conclusions more directly from the fast pattern recognitions dominated, while others (such as #3, green then orange arrow) habitually checked those connections before coming to a resolution. This variation between experts and the possibility of experts having distinct, characteristic patterns in how they approach novel problems is an area for further study.

Fig. 2 Variation in experts’ problem solving and decision-making patterns. Samples are from participants #6, #1, #2, #3.

Each map reflected the first two authors’ collaborative analyses, yet it was difficult for the third author to replicate specific interpretations, turn-by-turn in the data. It was clear in the data, however, when the experts made explicit mention of other knowledge as it applies to the problem at hand, which we are calling analogies.

In this study, we define analogies as any explicit reference to knowledge from other situations, whether expressed as simile or metaphor, including in a question (e.g. to ask if fluorine might be like chlorine), and in mentions for contrast (e.g. to say that fluorine is not like iodine). We include references expressed as similes or as metaphors (e.g. “a bond is like a spring” or “a bond is a spring”). Such references were central in how the experts handled not-knowing, in order to find and evaluate connections to what they did know.

Analogies happened both in quick recognition and focused deliberation. In other words, we saw them in fast thinking, for example when expert #13 started a new train of thought saying,

“I know you can make chloronium. So, can we make fluoronium?”

And we saw analogical reasoning in slow thinking, such as when expert #5 narrated their reasoning,

“I don't know how boronic acid is made, probably it's… or, I don't know if… to see if there's any analogous compounds known. Is there anything X-BO? How's it made? I mean, I would have to search the literature. How do you even make anything like this? Is there anything where this is iodide? where it's bromine? where it's chlorine? Is there anything…?”

Interestingly, the analogies were certainly not all “correct”; experts often considered analogies that could be misleading. Mostly, though, the experts tended to question, examine, and critically analyse each analogy as they followed wherever it led.

Focusing on analogical reasoning

We entered this project with the broad research question of how chemists reason when they are in a position that is common for students—thinking about a problem that is new to them. What do experts do when they do not know? We hoped to gain insights into the nature of chemists’ expertise beyond content knowledge that can inform curriculum and instruction.

We chose to focus on one aspect of the dynamics, namely the chemists’ use of analogies, for several reasons. First, explicit references to other knowledge are straightforward to identify in the data. Second, they seem to arise out of both fast and slow thinking. Finally, there is prior work on analogies in science and science education.

For this study, we refine our research question to ask, more specifically, “How do chemists use analogical reasoning in thinking about a novel question?” We return to the data from our interviews below. First, we review prior work on analogical reasoning.

II. Literature review

Analogies and analogical reasoning in professional science

Science philosopher Schummer writes on the structure of chemical knowledge, “Chemistry at the core is a science of peculiar relations. Instead of studying isolated objects to be measured, compared and put into a classificatory scheme, dynamic relations between objects constitute the basic set of chemical knowledge” (Schummer, 1998). Given this highly connected structure of chemical knowledge, it is perhaps unsurprising that analogies are pervasive in chemistry, both past and present, and more broadly in science as well. In chemistry, textbooks routinely describe the progression of models of the atom with analogies to plum pudding, to the solar system, and to shells and clouds. In the early 19th century, decades before Mendeleev's periodic table, German chemist Döbereiner grouped many of the known elements into threes based on chemical and physical analogies which he called the Law of Triads. (Döbereiner, 1829) These triads now form the first three elements in the groups of the modern periodic table.

Later, British chemist John Newlands (1884), again saw elements as analogous to one another, and described the periodicity of analogous elements with an analogy to musical octaves:

“It will also be seen that the number of analogous elements generally differ either by 7 or by some multiple of seven; in other words, members of the same group stand to each other in the same relation as the extremities of one or more octaves in music.” (Newlands, 1865).

At the molecular level, analogical reasoning also helped discoveries in medicinal chemistry (Farber, 1950; Fischer et al., 2010). Schaumann saw pethidine as analogous to morphine, which motivated testing and proving pethidine to be a pain medication (Schaumann, 1940; Schaumann, 1956). Other researchers later extended that analogy to other substances (Woolfe and Macdonald, 1944; Wong, 1993), leading to the formation of an entire category of analgesics (cf. Atkins, 2004).

As common as analogies are in textbooks and publications, there is good reason to expect that a great deal of analogical reasoning in science has gone unreported or unrecognized. As Feynman put it in his Nobel lecture,

“We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. So, there isn’t any place to publish, in a dignified manner, what you actually did…” (Feynman, 1966).

He took the opportunity of the Nobel lecture to speak about what he actually did, and his account included analogies that he did not describe in publications. Feynman's remarks notwithstanding, there have been scholars who describe their thought processes, and researchers in cognitive and learning sciences have taken advantage of their accounts.

In many ways, medical education research is more advanced in its attention to analogical reasoning. Analogical reasoning is utilized as an efficient tool for educating new doctors, directly implemented by doctors in their medical practice, and even for official nomenclature of medical terms (Eva et al., 1998; Ark et al., 2007; Norman et al., 2007; Speicher and Kehrhahn, 2009; Pena and de Souza Andrade-Filho, 2010). A series of publications by Andrade-Filho catalogues commonly used medical analogies and their practical utility (de Souza Andrade Filho and Pena, 2001). Ever-changing conditions in clinical practice require doctors to attend to the developing details of the situation for what needs to be modified in response to emerging problems (Cristancho et al., 2016). Analogies under these circumstances serve as the most readily available line of resources, almost like a first aid kit. This behaviour parallels the moves of scientists who work with unknowns in their field and potentially mirrors Maxwell's progression towards making sense of electromagnetism with analogies (Nersessian, 1992). While the context of a physicist's work might differ drastically from a surgeon's time-pressured and high-stakes decision-making, they converge in their basic nature of uncertainty and working in an ambiguous territory (Shepherd et al., 2020).

“Case-Based Reasoning” (CBR) is a related construct in chemistry and medical education research, discussed as complementary to rule-based, theoretical reasoning. Kovac, for example, defines “practical reasoning” as a process that “begins with a detailed description of the facts of the particular case under consideration, then uses general warrants based on similar precedents to draw a provisional conclusion” (Kovac, 2002). He suggests that analysing CBR in chemistry would help educators to use this type of reasoning in the classroom. Similarly in engineering design, analogical reasoning as a process of problem solving has been defined as “the use of ‘source’ information from a previous problem-solving episode as a means to facilitate attempts at solving a current, ‘target’ problem.” (Ball et al., 2004). Ball et al. analyse CBR at a more granular level by introducing the schema-based analogizing as a sign of intuitive expertise. Stéphane and Marc (2008), in their engineering design work put forward analogical reasoning as the basis of CBR, and suggest a cyclical reasoning process involving retrieval, reuse, and revision of the previous information (Stéphane and Marc, 2008). These examples merge on Neisser's previous study on the uses of analogies as dynamic rounds, or ‘perceptual cycles’ that are modifiable internal experiences of the problem solver (Neisser, 1976). Like Stéphane and Marc, and others (Kolodner, 1997), we see CBR as a subset of analogical reasoning. We use the latter as the more general term.

Cyclical iteration of ideas to facilitate the problem solving has been identified in more recent studies of medical education as well (Cristancho et al., 2016). In a 2016 analysis of surgeons in operating rooms, Cristancho describes a cyclical process by which doctors course-correct and adapt during a surgery. Interestingly, during these iterative cycles, one of the surgeons’ problem-solving moves is to ‘‘transform’’ the incoming information by comparing it against what is typical to make sense of new developments in the operating room (Cristancho et al., 2016). On these accounts, expertise involves repertoires of familiar cases as evolving knowledge bases, along with practices of tapping into those resources for reasoning about novel situations.

Studies of scientists’ analogies in cognitive and learning sciences

Nersessian's, 1992 “cognitive-historical” study of physicist James Clerk Maxwell's writings showed the central importance of analogical reasoning in Maxwell's thinking (Nersessian, 1992). She documented the difficulty he encountered in modelling magnetic vortices all rotating in the same direction: these rotations would jam against each other. One idea for resolving the difficulty was an analogy to idle wheels in physical machines, and another to the idea of fluid vortices, the latter coming closer to the account he was developing of magnetic fields. “The method of physical analogy” was central to Maxwell's research.

Gentner et al.'s case-study of Johannes Kepler (Gentner et al., 1997) is an application of Gentner's structure-mapping theory of analogical reasoning (Gentner, 1983; Gentner and Gentner, 1983). Their analyses show Kepler's analogical reasoning as central to his process of conceptual change, which led to a radical shift in conceptualization of the solar system:

“Kepler was a prolific analogizer. In his books, journals, and letters he constantly used analogies, some only fleetingly and others with tenacious persistence. In some cases, he returned to an analogy repeatedly across different works, extending and analyzing it further on successive bouts.” (p. 5).

Cavicchi (1997) studied physicist Michael Faraday's inquiries based on his extensive notebooks, which he kept to record his “experimental efforts, observations, speculations, and wonder” (p. 869) (Cavicchi, 1997). Dunbar pursued research into analogies by observing molecular biologists at work, including video recording conversations (Dunbar, 1995; Dunbar, 2000; Blanchette and Dunbar, 2001; Dunbar and Blanchette, 2001a, 2001b). He found analogical reasoning was abundant, in a similar range as Gentner et al. (1997) described of Kepler, with some analogies used “only fleetingly” and others persistently. We also found similarly short-lived analogies interspersed in our interviews and included examples below. Another of Dunbar's findings (Dunbar, 1995) was that most of the biologists’ analogies were to similar experiments and organisms within the discipline, “local analogies,” in contrast with “distant analogies” outside the discipline, which were used mainly for explaining ideas to others.

In this respect, Gentner et al. (1997) found differences between Kepler and the scientists in Dunbar's study:

“[I]n contrast to the microbiologists, Kepler used many distant analogies. This stems in part from the different historical stages of the domains. Kepler was forming the new science of astrophysics, more or less in the absence of a usable physics. Distant analogies were in many cases his only option…. Local analogies are useful for filling in an established framework, whereas distant analogies are used for creating a new framework.” (p. 33).

For example, as Kepler tried to make sense of why gravity decreases in intensity as objects get far away from each other, he reasoned by analogy, how the intensity of light decreases with distance. Newland's analogy to musical octaves and Maxwell's to machines and fluids are other examples of distant analogies, reflecting the scarcity of local resources the scientists had available.

The common dynamic in all is the scientists’ “deliberately seeking out and developing analogies” (p. 879) (Cavicchi, 1997), connections to other knowledge, apparently seeking outward from the target phenomena. The microbiologists in Dunbar's study (Dunbar, 1995), chemists like (Schaumann, 1940) and Woolfe, (Woolfe and Macdonald, 1944) had ample knowledge similar to the targets of their research: their analogies were mostly local. Explaining their ideas to others, however, the microbiologists made use of distant analogies: they found connections to what non-specialists would know.

Studies of analogies and analogical reasoning in science education

Writing more than 30 years ago, Duit (1991) reviewed the previous 15 years of research on analogies and metaphors in science education, citing rich connections to more general research in cognitive science (Duit, 1991). The start of the article reflects the field's broad emphasis on goals of conceptual understanding: “It has frequently been argued that analogies may be valuable tools in teaching and learning difficult science concepts… but there are also more sceptical positions,” citing concerns that analogies can lead to misconceptions (Spiro, 1988; Glynn, 1989). The review went on to raise broader considerations, and the final words argued for considerations beyond content knowledge:

“If it is accepted that science instruction should not only teach scientific knowledge but also scientific metaknowledge, then the role of analogies and metaphors in science must be considered to be an essential aspect of science instruction.” (p. 655).

It stands to reason that analogies contribute to students’ developing expert-like understanding, given the historical evidence of their role in expert thinking. There is now broad consensus that they are essential (Gabel and Sherwood, 1980; Brown and Clement, 1989; Glynn, 1989; Ingham and Gilbert, 1991; Orgill and Bodner, 2004; Glynn, 2012; Orgill et al., 2015) with support from a wide range of empirical studies. For recent examples, Shana and El Shareef (2022), showed that guiding high school students to reason about capacitors by analogy to springs led to dramatic improvement in measures of their conceptual understanding (Shana and El Shareef, 2022). Shahani and Jenkinson (2016) explored springs as an analogy for undergraduate students learning about bond energy curves (Shahani and Jenkinson, 2016).

The concerns remain that “analogies are two-edged swords” that can inform as well as mislead (Taber, 2001; Harrison and Treagust, 2006). Rather than to avoid analogies, however, the consensus is to recommend care in their use (Orgill and Bodner, 2004; Harrison and Treagust, 2006), to include multiple analogies for a given concept (Spiro, 1988; Christidou et al., 2018) and to provide explicit discussion about where analogies break down (Harrison and De Jong, 2005). In these ways, research on the value of instructional analogies for students’ conceptual learning has pointed toward the relevance of students’ meta-knowledge about analogical reasoning, in line with Duit's (1991) closing call (Duit, 1991). Wang recently found that eighth graders gained conceptual understanding from instructional analogies comparing heat to water, but these gains depended on the students’ metacognitive abilities (Wang, 2023). This finding suggests those abilities might be important targets in their own right.

Since Duit's (1991) review, research has moved in the direction of including students’ analogical reasoning as essential for them to do science, which is part of a larger shift of attention in science education toward disciplinary practices (Ford and Forman, 2006) as student learning goals. Research has attended to students’ abilities to generate and to reflect on analogies (Haglund, 2013). Evidence shows these abilities begin early, as studies of elementary school children show their generating analogies to construct explanations (May et al., 2006; Haglund et al., 2012; Tang and Hammer, 2024). Wong (1993) studied older students’ reasoning, documenting their self-generated analogies leading them not only to construct explanations but also to raise new questions. (Wong, 1993). Indeed Clement's (1998a, 1998b) research, cited above, found the “shared natural use of analogies for unfamiliar problems is an expert-novice similarity“ (Clement, 1998a, 1998b) (p. 1271). Cavicchi (1997), also cited above, compared Faraday's inquiries with those of an undergraduate student. (Cavicchi, 1997). Both showed extensive analogical reasoning in their efforts to make sense of observations, but Faraday's notebooks showed a more refined “practice of deliberately seeking out and developing analogies” (p. 879). Within chemistry, Jeppsson et al. (2015) posed pairs of undergraduate and doctoral students problems on entropy with an interest in studying the students’ use of conceptual metaphors. (Jeppsson et al., 2015). Their analyses showed significantly greater use of metaphor by the PhD students, leading them to suggest metaphorical reasoning is a learnable aspect of expertise for students. Clearly, the use of analogies can be spontaneous even in novices but requires cultivating to reach the expert level.

As science educators work toward balancing both traditional content and disciplinary practices in the learning objectives for students, they encounter tensions (Hammer, 1997): Students’ inquiries inevitably take them in multiple, conflicting directions, very much like scientists’ historical accounts. If instructional analogies can be double-edged swords, student-generated analogies only risk greater divergence from the canon of established knowledge. The debate Duit (1991) reviewed, over whether instructional analogies help or hurt student understandings, becomes a challenge for instructors to coordinate objectives, which often pull in opposite directions in particular moments. (Duit, 1991). Talanquer (2014) wrote of this tension in chemistry, identifying “heuristics to tame”, including analogical reasoning among “fundamental associative processes” (Talanquer, 2014).

This study's contribution

Analogies emerged for us in what was a broader exploration of how chemists handle novel problems of the sort we give students, following prior work cited above in physics, mathematics, and history. Reviewing the literature, we see our results reinforcing prior findings, including analogical reasoning as central to disciplinary expertise.

Existing literature has much to say about established analogies as part of chemists’ knowledge, yet we found little prior study of chemists’ analogical reasoning on novel questions, novel to them in the way that questions in coursework are novel for students. While recent research supports building classroom environments that more closely resemble the disciplinary practices of science, the vast majority of chemistry courses continue to function in a more traditional style. We sought to study how expert habits of mind might present in situations like those students experience. Having these habits of mind in evidence will perhaps influence what instructors notice about their students’ thinking.

It may also contribute more broadly. While previous research has focused on identifying analogical reasoning from publications, notebooks, and laboratory observations, (Gentner et al., 2001) there has been limited investigation into chemists’ real-time, individual reasoning processes. The think-aloud interviews conducted in this study offer an opportunity to capture the spontaneous generation of analogies in real-time. By recording participants’ immediate, minimally filtered thoughts, these interviews provide a closer view of the authentic problem-solving, rather than the more refined reasoning typically shared in writing or among peers.

We turn now to analyses of chemists’ interviews with respect to the research question: How do chemists use analogical reasoning in thinking about a novel question?

III. Design, methods and theoretical framework

Methodology & theoretical framework

This study continues research on the same data analysed in Button et al. (2023) (Button et al., 2023). As reviewed in that article, Diren sent emails to 18 PhD chemists asking for their participation in an “interview” of their reasoning about a novel question. 16 agreed; two declined, and a third was not able to schedule a time. One participant found the interview uncomfortable and withdrew. In the end, there were 14 participants. Almost all were in academia; one was from industry. Three described themselves as organic chemists, one as a physical chemist, one as an inorganic chemist, and one as a chemical engineer.

The question was to consider a molecule made up of a single atom each of boron, oxygen, and fluorine, FBO. In one form or another, every participant expressed discomfort about FBO, saying it was strange and/or that it could not be stable. John Button, the undergraduate research assistant, conducted eight of the interviews, and Diren the remaining six, all on Zoom during the COVID-19 pandemic. We recorded the interview sessions for subsequent analysis, with the participants’ consent, as approved by the Tufts Institutional Review Board (IRB). The interviews lasted an average of 50 minutes and followed semi-structured, “think-aloud” methods (Ericsson and Simon, 1998), with the chemist leading the flow of reasoning after the initial question.

For the purposes of this study, we identified evidence of analogical reasoning in any explicit reference to knowledge from some other situation than FBO, whether as similes or metaphors, and whether the reference was for similarity or contrast. From there, Kyle and Diren analysed the roles of the analogies using methods of constant comparison and grounded theory (Henwood and Pidgeon, 2003; Mills and Gay, 2019; Saldaña, 2021). Two main categories emerged from our discussions about the utility of analogies, in iteration with applying the refined categories to the data (Glaser and Strauss, 2017).

Data analysis

There were analogies evident in every interview. Kyle and Diren converged on two main patterns of analogical reasoning evident in the interviews: evaluative and generative. Evaluative analogies follow and assess claims or conjectures the chemists had already formed, most often in support of those claims. This pattern of analogical reasoning seems to be a key strategy chemists use to manage uncertainty over an idea, and the data often showed chemists introducing the idea with indications that they are not convinced. In some cases, the role of the analogy seems mainly to support their clarifying ideas for their audience.

Generative analogies preceded a claim or conjecture as part of the chemists’ search for relevant prior knowledge to help them generate ideas. Often this pattern came along with markers of uncertainty, such as “I don’t know” statements. As we describe below, these patterns are not mutually exclusive: an analogy that begins as evaluative may be generative of new possibilities. As well, in some cases when a conjecture follows an analogy, it seemed possible that the chemist thought of the conjecture first without verbally expressing it.

Kyle and Diren analysed the transcripts independently to code for either of the categories, which resulted in an initial 74% agreement. They then returned to the data together, considered agreements and disagreements, and revised the coding criteria. Each coded independently a second time, and found >95% inter-rater reliability, which was sufficient to support the qualitative claims regarding participants’ various uses of analogies.

We also note that in some moments, the evidence of analogical reasoning was too fleeting for us to interpret, perhaps because the chemist did not express the fullness of their thinking, or perhaps because it was only a quick passing thought.

In what follows, we present examples of analogical reasoning from seven of the interviews. We present them within excerpts of participants’ reasoning, to stay closer to the phenomena as we observed them, noting along the way our interpretations of how the analogies seemed to function. We chose the examples for their brevity and clarity, which allows us to present them without omitting any intermittent text within that section of the interview. We use ellipses (‘‘…’’) to indicate brief pauses of speech.

Example 1 – Participant #4. Participant #4 offered the idea that FBO:

“…could form, oligomeric or polymeric structures. Oxygen lone pairs, fluorine lone pairs can certainly react with a boron centre and start forming aggregates, microcyclic or linear polymeric structures, there could be sort of… Hm…if it forms micro cycles if the geometry permits, you could start forming sort of regular oligomers.” (Fig. 3a).

Fig. 3 (a) Potential polymeric structure of FBO as proposed by Participant #4. (b) Dimeric structure of borane brought up as an analogy to justify FBO's polymeric structure.

They followed that proposal with an analogy to borane, BH₃, a well-known compound.

“That kind of reminds me that boron forms some really peculiar aggregates to fulfil its octet… trying to remember… to draw it properly … I think. So. So. So borane [two BH₃ molecules shown] forms a dimeric structure (Fig. 3b). The stable borane is a dimeric structure where, it's a Sigma bond between boron and hydrogen that provides electron density to fulfill effectively, boron's octet preference. So it's not as available electrons as lone pairs on oxygen and fluorine. It's actually Sigma bond that still completes the octet for each boron in this dimeric structure so that's how the diborane looks like. That is how it typically is drawn in organic chemistry textbooks. And borane as you know, it's difficult to form species. Diborane is in equilibrium with just borane, BH₃, but the equilibrium favors diborane at least under ambient conditions. So that that's another you know that's another reason why I suspect that your structure forms, forms oligomers. (points to Fig. 3a again)”

Participant #4 proposed that FBO could form stable oligomeric or polymeric structures, first with hedging language (“could form”, “could be sort of”, etc.). They then thought about borane as an analogy, which they were confident has a stable dimeric structure (Fig. 3b). This provided an opportunity to evaluate the proposed oligomeric structure of FBO and eventually use the analogy to support their previous idea.

Borane was a common analogy across the interviews, coming up in eight of the fourteen interviews. Another common analogy was carbonyl, in six interviews. Here, the expert uses the carbonyl analogy when considering the reactivity of FBO, rather than the structural features.

Example 2 – Participant #2. Participant #2 gave their quick first impression:

“I think even if it is formed, it's gonna be quite reactive.”

They went on to reflect on the nature of their expertise, in effect providing their own analysis, to explain that pattern recognition is a part of it:

“The more you see, you recognize patterns and say: you know, so… for organic chemists, this might seem like a… um… [points to the structures in Fig. 4a] uh… this um… piece of um… this segment of the molecule [highlights the B=O in Fig. 4b], uh… one can think of this is not actually… this looks like a carbonyl, so, we say, ‘well carbonyl has this dipole moment going towards oxygen’ and, [draws the carbonyl and dipole arrow in Fig. 4c] therefore, this carbon here is electrophilic [highlights the carbon atom in Fig. 4c]. And so, the… that's, that's one way to approach this. And boron is going to be even more electrophilic—and, in fact, it's even connected to another uh… fluorine, so that is really hot, that particular atom.”

Fig. 4 Electron pushing model showing possible reaction mechanism between two FBO monomers (a) and (b) due to boron's high electrophilicity. C=O is drawn after the electron pushing proposal as a back-up (c).

We saw evidence of more careful deliberation in the pace and substance when #2 paused and restarted, introducing the analogy to carbonyl (C=O in reference to B=O). They seemed convinced by the analogy, which supports their first impression that FBO would be highly reactive.

At another moment, #2 made a claim about fluorine:

“But, once again, because fluorine is so nonpolarizable and so electronegative as a… as a… as an element, uh… it is usually not very happy to give up its electron density…”

We deliberated over whether to consider the statement that fluorine is not “happy” as a reference to other knowledge, that is an “analogy.” It is rather a metaphorical anthropomorphism, thinking of the atom as ‘wanting to keep’ its electrons nearby, but the statement fell short of explicit comparison. #4 continued with a much clearer analogy:

“So, it [fluorine] requires it because the nucleus has so much positive charge that… they are… [Fig. 5] they are actually very tightly bound to the nucleus; so, they don’t want to be in this fuzzy, like… iodine, you know? So far-away from the nucleus that uh… they are kinda renegade, and you know, the nucleus has no control over those electrons.”

Fig. 5 Participant #2's FBO structure.

Chemists often compare halogens for similarity. Here, #2 compares for contrast, iodine being unlike fluorine with respect to the electron density. #2's language included more anthropomorphism, now more explicitly: the electrons in iodine are “so far away from the nucleus” that “they are kinda renegade.” This mention of electrons as ‘renegades’ is an analogy to informal knowledge, describing iodine's large electron shell and its polarizability.

One final example of interest from this participant was a rare example of a distant analogy in our data set:

“So, I think um… and, we also have to remember that atoms vibrate uh… so the bond is like a spring. But, these are all constructs that we create to understand the system.”

The analogy between chemical bonds and springs is another common analogy made in chemistry classrooms to explain the behavior of certain bonds. (Fig. 6) The chemist gave it only a fleeting mention, and so it is difficult to have a sense of what role it played in their reasoning.

Fig. 6 Participant #2's diagram of the attractive and repulsive forces for chemical bonds as they explore the probability of B, O, F atoms to bond.

Example 3 – Participant #13. Participant #13 decided FBO (F–B=O) could not be stable as a monomer but thought it might form a polymer. They proposed their idea and then supported it with an analogy to silicone:

“You know, that's not uncommon to see like polymers that looks something like this [Fig. 4], you know, like I know silicone is a polymer, you know? It has a whole bunch of oxygens around it, things like that, so I thought, maybe boron could do the same type of thing.” (Fig. 7)

Fig. 7 Participant #13's proposed polymeric structure of FBO.

The analogy followed the initial idea in #13's statement, suggesting an instance of evaluative analogy, here to support the idea. But this is an example of how interpretation can be challenging. #13's narration of their thinking with the past tense, “so I thought, maybe,” suggests the possibility that they may have first thought of the analogy to silicone in a generative way but silently. This is something we cannot infer from the interview. Therefore, we took it at face value that the silicone analogy is used to convince the expert, or maybe the interviewer, that the idea of polymers is valid in this case.

Another moment from #13's interview shows a clearer instance of evaluative analogical reasoning. The following exchange began with the chemist's claim that fluorides can make fluoronium ions, but they expressed it with some uncertainty. In considering that idea, #13 thought of chloronium as a supportive analogy.

Interviewee: “I don't know… I mean, I know fluorides also can make fluoronium ions, it can be positive. Right?”

Interviewer: “Really?”

Interviewee: “You can make… I believe so, let me see. I know you…”

Interviewer: “I’ve never heard of that.”

Interviewee: “…you can a chloron—so, I know you can make chloronium. So, can we make fluoronium?”

The chlorine–fluorine comparison is a clear and often-used analogy between the two most common halogens. Here, it supported #13 in the idea that a fluoronium ion could be part of FBO. Later in the interview, #13 decided to reject that possibility after a more detailed evaluation.

Example 4 – Participant #1. Participant #1 began with their ‘first intuition’, expressing uncertainty as they narrated their reasoning.

Interviewee: “So, my first intuition would be that it (enthalpy) is smaller than zero, so favourable from an enthalpy perspective. Then, I would look at the entropy. So, this (F₂) is a gas, this (O₂) is the gas, this (B) is a solid, obviously now, I think this (FBO) would be a gas, but that's an assumption.”

Interviewer: “How did you assume it? Before getting…”

Interviewee: [Laughs for eight seconds] “…I was again, thinking about methane, and methane is a gas and it doesn't have many… so, like I mean it doesn't have…

Wait! Now, I think… so, that's what I thought. I again had methane in my mind. I had: it's small, it doesn't have much London dispersion forces, but now I need to think about, is there any like polar interactions? Or like even… I mean, no hydrogen bonds…” (Fig. 8)

Fig. 8 Participant #1's chemical equation for the synthesis of FBO from fluorine gas, oxygen gas, and solid boron.

Like #13 in the earlier example, #1 expressed the idea first, that enthalpy is negative (our interpretation of “smaller than zero”) and then the analogy to methane, potentially to support it, but they described the analogy in the past tense. Where #13 had said “so I thought,” #1 was more explicit, saying “I was again, thinking” in reference to their mention of methane earlier in the interview. Later, there is also clear evidence of their new thinking after reporting the analogy (“but now I need to think about”), generating more paths to consider.

Participant #1 provided another example of a short-lived analogy but this time through a very close comparison instead of a distant one that participant #2 mentioned. It begins when they ask the interviewer to look up Boron's elemental form in a book.

Interviewer: “Boron's apparently solid. B, just B. Solid.”

Interviewee: “Just B, a solid? [writes B with the state symbol]. Okay like, like carbon?”

Interviewer: “Yeah, like carbon…” (Fig. 9)

Fig. 9 Participant #3 thinking about the elemental forms of the component elements of the FBO molecule. F2 and O2 are written rather quickly by the expert (a), but boron, B, is looked up, written down, then likened to carbon (b).

While this analogy appears to be a valid comparison, boron being a solid ‘like carbon’ is not pursued by the expert any further and does not make a reappearance at any point later in their reasoning. This is not to say this, or any other short-lived analogy served no purpose, but instead, whatever they might have done for the experts’ thinking was not made obvious to us observers. Interestingly, these kinds of analogies were also seen in Kepler's notebooks by Gentner, which were then defined as ‘fleeting’ analogies due to their short-lived appearance (Gentner et al., 1997).

Example 5 – Participant #11. Participant #11 was sharing their computer screen in the Zoom call, to show the interviewer their search in Google, which they did with the comment: “Maybe this will make students feel better about themselves because faculty chemists do stuff like this.” They typed “borate” into the search and focused on the Lewis structures that came up in the results.

Interviewee: “Right, so I would go to borates. Right, okay so, so here's, so here's this, here's this guy here, right? [pointing to the boric acid in Fig. 10a, then clicking on other images with borate structures, which led them to finding b & c.]”

Fig. 10 Participant #11's borate analogy helps them advance their thinking about the structure they were trying to generate. (a), (b) and (c) show results from the Google search; (d) is what #11 drew.

Interviewee: “And so, I go okay so, so boron it seems to like that. Boron, it seems, like to have three bonds. Three bonds to oxygen. And so, I would do something like… ah, you know… [starts to draw manually] Basically make this… [points to a borate he found online, Fig. 10b] …and think… And, and now I’m thinking like, okay, is it—would it be just as easy to… like you know, can I make an oxygen–fluorine bond or not? And then, so I would Google… [Googles “oxygen fluorine bond” and finds a structure of oxygen difluoride, F–O–F, Fig. 10c].

Like okay, so they actually can make ethers out of using, using fluorines, too. So, it seems like we can, based on this structure here [F–O–F, Fig. 10c], you know this little thing here, this valence structure here, it seems like I can make that oxygen–fluorine bond, which means it would probably be… you know… [pauses to complete drawing 10 d] And I’ll stop sharing now so go back to this. [showing what they created in Fig. 10d]”

This is a clear example of generative analogical reasoning, as #11 saw borates as likely sources of insight into FBO and began to search for ideas with borate as the starting point. The results provided or confirmed the idea that “boron likes to have three bonds”, but the chemist was uncertain about how to place fluorine in the structure. They wondered if fluorine–oxygen bonds exist and turned back to Google. When they saw oxygen difluoride, F₂O, they completed their diagram.

Example 6 – Participant #3. Participant #3's first reaction to the question was to draw the diagram in 7a, which we saw come up in every interview. They immediately began to reason about the shape it would form and the distribution of electrons, then compared it to BF₃.

Interviewee: “I think that [pointing to what they drew in Fig. 11a] might be one way of fulfilling the…typical bonding patterns; although, this isn't typical because boron here will not be… boron will be… linear. It won't be trigonal planar. It’ll still be six electrons… um… And, it's very… it looks very reactive. So, you know, boron with its empty… you know, has, in this situation, is going to have… Some… it's going to be electro…it's one of like, you know, it's going to have an affinity for electrons—especially because of the electronegativity of O and F. So, this is going to be a very strong Lewis acid. So, this is gonna, this kind of is—looks a little bit to me, in some ways, like BF₃… [draws BF₃ in Fig. 11b]”

Fig. 11 Participant #3's comparison of their hypothetical structure of FBO (a) to the structure of BF₃ (b). Boxes up his final conclusion in (c).

Interviewer: “Oh yeah.”

Interviewee: “But, it's different, right? I mean, you know, it's a different geometry, but it has many of the same, you know—this sort of hypothetical structure [F–B=O in Fig. 11a]—has some of the same feel to it to me in terms of the boron is having electron density pulled away from it, it's always, you know, boron's generally, I think, a good Lewis acid, because it has an empty orbital, so it can always become tetra-coordinate…But, here, it's going to be really very reactive, I think… you know, because of… if for nothing else, because of boron's…you're sucking a lot of electron density, in this structure, away [puts the blue box around FBO in Fig. 11c].”

#3's analogy to BF₃ seemed to arise from their proposal that FBO is very reactive and “a very strong Lewis acid,” in line with the pattern of evaluative analogical reasoning. But they immediately shifted to questioning that analogy (“it's different, right?”). This cues or is a part of their cautious re-examination; the analogy seems to have generated new considerations. In this case, the analogy was the first part of the chemist's effort to assess a conjecture, in the evaluative pattern, but it was generative of new considerations later.

Example 7 – Participant #9. This example again shows an analogy arising in the context of a conjecture, that FBO is not a monomer, but in this instance, the comparison to another molecule contradicts the conjecture.

Interviewee: “Again, as I was saying, it seems a little hard to imagine it being monomeric, although you know why? I don't know… you have… carbon monoxide is, is perfectly happy as a molecule so FB is in some sense an okay replacement for C.”

Interviewer: “Yes.”

Interviewee: “I say that sort of in the context of boron–hydride clusters, where there's a whole set of rules for making boron hydride and you can always replace one BH unit with a carbon. And so, in the same way, this is sort of going in the reverse direction: you're replacing a C in carbon monoxide, with a BF, where F is acting sort of like H is. H and F are both more electronegative than boron, and so, they would both be… you know, the hydride would be acting like a halide, there.” (Fig. 12)

Fig. 12 Participant #9 compares the “BF” unit in FBO (a), with the “carbon” in the carbon monoxide molecule (b).

Most of the time, analogies chemists produced after a conjecture were supportive, or explanatory, but in this instance, it was an evaluative as a refutation: CO is “perfectly happy as a molecule.” From there, #9's confidence in their knowledge of CO generated the idea that FBO could be monomeric, and they supported that new idea with another analogy, to boron–hydride motif.

Shortly later in the interview, participant #9 was still searching their knowledge for ideas, which had them consider another analogy, this time to the molecule HBO.

Interviewee: “Right and so, then you can almost wonder: well, has HBO been made? That would be sort of the same analogue. I'm sure HBO is, you know, in some form, probably exists. I'm not sure of that exact stoichiometry… you know… Boric acid exists, where you have a one-to-one oxygen and a hydrogen, but of course, there's three of them per boron so…” (Fig. 13)

Fig. 13 Participant #9 thinks about HBO (a) and compares fluorine in FBO with hydrogen as an analog (b).

This was an instance of a chemist drawing an analogy to help generate ideas, but after only brief consideration #9 abandoned it, and HBO did not come up again.

IV. Findings & discussion

We set out to study how chemists respond to an unfamiliar question, to gain insight into their expertise beyond their specific content knowledge. We chose the FBO question, which has a form like questions students encounter in introductory courses but is novel for most chemists, including all 14 participants. The results were highly complex. Broadly, the first common feature we noticed across the interviews was that all involved a mix of fast, intuitive associations and slow, careful deliberation. Within that complexity, every chemist expressed and engaged with uncertainty, starting with initial unease over the idea of FBO as a molecule. (Button et al., 2023). Analogical reasoning, our focus here, emerged as another common feature. In this closing section, we review our findings and discuss their implications for instruction and further research.

Findings

The core finding was that every chemist reasoned with analogies, to evaluate ideas or to generate ideas. Example 2 above shows Participant #2 having a quick impression that FBO would be highly reactive, then finding an analogy to carbonyl that supported the idea. Example 5 shows #13 starting with an analogy to borates to generate ideas about FBO.

Within the dynamics of an individual's reasoning, the same analogy might function as both evaluative and generative. Example 6 is of participant #5 having the quick impression that FBO would be a strong Lewis acid, which motivated an analogy to BF₃, generating further ideas about electron density. Participant #3 initially used BF₃ to support their claim that FBO is very reactive and “a very strong Lewis acid”, but quickly switched to criticize that reasoning and generated new ideas.

Almost all of the analogies were ‘local’, that is to similar knowledge within the chemistry discipline, as opposed to ‘distant’ (Dunbar, 2000; Dunbar and Blanchette, 2001a, 2001b; Gentner et al., 2001). Like the biologists in Dunbar's studies, these chemists had rich knowledge within the domain that provided them many possible connections to consider, including extensive information about substances and phenomena as well as theoretical understandings of models, representational forms, processes and mechanisms. The only evidence we saw of distant analogies was fleeting, such as Participant #4's analogy between chemical bonds and springs.

These quick mentions might warrant further attention. Perhaps they were fleeting in the chemists’ minds; perhaps in some cases the chemists were not comfortable expressing them more thoroughly. It is not possible to discern the function of these analogies, and it was tempting to ignore them. But they suggest there is more analogical reasoning than we and others conducting similar studies have been able to see. Some research in medical education has noted ‘declarative analogies,’ passing mentions of similarities in cases without elaboration (Braude, 2012; Guallart, 2014). Further study might involve prompting subjects to explain these mentions, in the moment or in follow-up later.

While not the direct focus of our analyses here, the interviews show evidence of analogies involved in both ‘fast’ and ‘slow’ processes of thinking (Evans, 2008; Kahneman, 2011; Kahneman, 2012). In Example 3, Participant 13 had the idea of fluoronium ions, then shifted to consider it carefully. The search itself for prior relevant knowledge could also start as a slow and deliberate move, such as in Example 7, as Participant #11 looked intently for an analogy that might help.

Overall, our results show the centrality of analogical reasoning in chemists’ grappling with novel questions. It is part of how chemists manage uncertainty, including uncertainty over the validity of a conjecture as well as the broader uncertainty of how to begin forming a conjecture. Throughout the interviews, there is evidence of chemists looking for possible connections to other knowledge for support and ideas.

Implications for instruction

Chemists’ expertise is not only in the body of knowledge they have developed; it is also in their abilities to engage with novel questions, with what they do not yet know. Analogical reasoning is part of sense-making, a continuity from novice to expert, but part of expertise is in “taming” (Sevian and Talanquer, 2014) or disciplining its use. Current practices in chemistry education dissuade students from generating analogies for themselves, except a few for whom it is already a robust habit of mind. Other than towards the canon of amassed chemical facts, traditional instruction does not in general provide students opportunities or guidance, for generating and reflecting on analogies to their prior knowledge.

The core implication for instruction is the need for a change in current practices. CER has called for attention to students’ engagement in disciplinary practices, to complement traditional objectives. Part of that should be analogical reasoning, not only as part of canonical understanding but also as an aspect of chemists’ expertise for arriving at new understandings. Like the prior research we reviewed above on the roles of analogies in other disciplines, this study will serve chemistry education with examples of how chemists handle questions that are new to them, to allow a different form of comparison with novices. Whereas chemists’ reasoning on standard questions looks refined and efficient, their reasoning on novel questions proceeds with tentative ideas, confusions, and consideration of multiple possibilities.

Much of the challenge of this implication is that to cultivate students’ practices of analogical reasoning, chemistry instructors will often need to defer or suspend traditional objectives: Students’ analogical reasoning will at times take them in directions at odds with the canon of established chemistry (Pena and de Souza Andrade-Filho, 2010; Taber, 2010; Talanquer, 2013). Of course, the same is true of chemists: in this study, as in historical chemistry, some analogies took experts in ‘wrong’ directions, ‘wrong’ in the sense that the ideas they considered would not hold up to further examination.

To support students learning to reason like chemists, instruction needs to expand and shift in objectives and assessment. Instructors need to learn to recognize the value of students’ disciplined analogical reasoning as productive for their learning. By “disciplined” here we mean to emphasize that expert analogical reasoning involved both fast ideation and slow deliberation. It is much of what the evidence showed for experts, and it is a feature of their expertise that they have learned to “tame” their reasoning (Talanquer, 2014).

As well, much of the challenge of this implication is in its conflict with instructional common sense that knowledge of chemistry must come before reasoning: until the students know some chemistry, how can they reason? That stance defers students’ engaging in their own sensemaking. We argue that disciplined sensemaking needs to become a goal in and of its own right, as part of students’ learning the discipline.

When a student generates an analogy, it is evidence they are engaging in sensemaking. Instead of viewing wrong analogies as traps to be avoided, instructors might view them as evidence of something important, whether or not in the moment they lead to correct knowledge.

Thus there will be moments of instructional tension, between supporting students’ engagement in analogical reasoning and making their reasoning correct. The implication here is that it will often be important to prioritize the former, in those moments. To be clear, in arguing for allowing ‘wrongness’ in moments we are not suggesting teachers abandon traditional objects. To the contrary, we are arguing that to support students’ progress in these less obvious aspects of expertise will ultimately support their progress toward canonical knowledge. As students develop disciplined practices of reasoning, they will—like chemists, or as nascent chemists—be better able to progress within the canon. Indeed, research suggests student-generated analogies may be more productive than the instructor-generated ones (Koretsky et al., 2015).

Needs for further research

There is a great deal more work to do, in further research on these less-salient features of expertise in chemistry, research on how students may or may not progress toward that expertise, as well as research on how curriculum and instruction may expand and shift in attention to include analogical reasoning and other disciplinary practices.

While we chose FBO to see how experts engaged with a novel problem, it was not as novel for the chemists as what students experience in an introductory chemistry course: the chemists we interviewed had extensive knowledge within the domain they could use as the bases for their analogies. Students in introductory chemistry do not have that base of knowledge. Like Kepler (Gentner et al., 1997), Faraday (Cavicchi, 1997), and Maxwell (Nersessian, 1992; Nersessian, 2002), their analogical reasoning would need to draw on more distant phenomena.

One direction for further study would be to understand more of when and how experts make more distant analogies. We have fleeting evidence they do, in these interviews. Perhaps follow-up study of these mentions would tell us more, as we noted above. Or perhaps there are other questions than FBO that might give more insight? In a similar direction, the evidence shows complex entanglement in their abilities for reasoning and their extensive knowledge base. That entanglement seems important for further study as well.

When considered from a dual systems perspective of fast and slow thinking (Kahneman, 2011), most education studies favour slow, deliberate thinking about problems (System II), while fast thinking (System I) is often linked to heuristics and biases (Taber, 2009; Maeyer and Talanquer, 2010). However, studies on expert decision-making argue that slow deliberation of concepts is often not the first line action for the experts. Instead, experts match the situation from a previously encountered case to retrieve a plausible path to solution quickly (Klein, 1998), a process known as “recognition-primed” decision-making. This approach closely resembles analogical thinking, where a familiar situation is mapped onto a new one. It is not surprising then, that some of the analogies emerged intuitively in our study, as a product of fast recognition. However, subsequent evaluation and refinement of these initial ideas still involved slower, more deliberate mental simulations, sometimes generating new analogies along the way.

One implication for research is the study of educators’ reasoning and experience, and how chemistry instructors may learn to appreciate students’ analogical reasoning (Khan, 2025). Research in mathematics and science education has studied teachers learning to notice, attend, and respond to productive beginnings in students’ thinking (Philipp et al., 2014; Robertson et al., 2015).

Finally, there is a need for further exploration of the dynamics of student learning. We argue, with others (Lieber et al., 2022; Button et al., 2023) that chemistry education needs to pay more attention to students’ expectations and abilities for reasoning through connections to what they already know. This position suggests the need for further research and development, especially at introductory levels, to understand possible formative dynamics of canonical knowledge in tandem with practices of inquiry. Above we argued that students’ progress in disciplinary practices of reasoning will support their progress in the canon, but we do not discard traditional expectations of the reverse. The dynamics are likely to be highly complex and sensitive to the features of particular moments. For these reasons, we are eager to pursue further study of students’ reasoning, and we anticipate it will be valuable to do so through case studies (Hammer et al., 2018).

Author contributions

Author contributions are stated within the ‘formation of this study’ section of the article.

Conflicts of interest

There are no conflicts to declare.

Data availability

All relevant data analysed for this study are included in the published article as the excerpts from participants. Due to ethical confidentiality requirements and to maintain anonymity, the full data (recorded or transcribed) have not been made publicly available.

Acknowledgements

The authors of this paper would like to thank Dr Milo Koretsky for his guidance and help, Mr John Button for his suggestions on the manuscript, and Mr Matthew Turner for his help with data visualization in Fig. 1 and 2. We are also grateful to all of the participants for their generosity with their time. This project was funded by the Tufts University Institute for Research on Learning and Instruction (IRLI).

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