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DOI: 10.1039/D4RP00086B (Paper) Chem. Educ. Res. Pract., 2025, 26, 112-125

“That's not a super important point”: second-semester organic chemistry students’ lines of reasoning when comparing substitution reactions

Ina Zaimi a, Field M. Watts b, David Kranz c, Nicole Graulich c and Ginger V. Shultz *a
aDepartment of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA. E-mail: gshultz@umich.edu
bDepartment of Chemistry and Biochemistry, University of Wisconsin – Milwaukee, Milwaukee, Wisconsin 53211, USA
cJustus-Liebig-University Giessen, Institute of Chemistry Education, Heinrich-Buff-Ring 17, 35392 Giessen, Germany

Received 16th March 2024 , Accepted 6th August 2024

First published on 14th August 2024

Abstract

Solving organic chemistry reactions requires reasoning with multiple concepts and data (i.e., multivariate reasoning). However, studies have reported that organic chemistry students typically demonstrate univariate reasoning. Case comparisons, where students compare two or more tasks, have been reported to support students’ multivariate reasoning. Using a case-comparison task, we explored students’ multivariate reasoning. Our study was guided by the resources framework. One conceptual resource activates another conceptual resource and, successively, a set of conceptual resources. This successively activated set of resources is expressed in a line of reasoning. Pairing this framework with qualitative methods, we interviewed eleven second-semester organic chemistry students while they compared two substitution reaction mechanisms and chose the mechanism with the lower activation energy. We analysed what conceptual resources and lines of reasoning were activated and the variation to which students engaged in multivariate reasoning. Students activated multiple conceptual resources and, moreover, extended their activated resources into both developed and undeveloped lines of reasoning. When constructing their explanations, most students engaged in univariate reasoning. These students provided a developed line of reasoning selected from multiple activated resources, or they provided an undeveloped line of reasoning constructed from only one activated resource. Few students engaged in multivariate reasoning. These students provided both developed and undeveloped lines of reasoning from multiple activated resources. Our findings highlight the variation with which students engage in both univariate and multivariate reasoning. Therefore, we recommend that case-comparison activities scaffold engagement with multiple lines of reasoning in addition to activating and developing them.

Introduction

The first-semester and second-semester organic chemistry curricula are arranged around reactions, and substitution reactions are typically placed at the start of the first-semester organic chemistry curriculum. While substitution reactions are first and fundamental, substitution reactions are not simple, and they have been pushed to the end of Flynn and Ogilvie's (2015) second-semester organic chemistry curriculum. Flynn and Ogilvie (2015) argued that addition reactions are simpler than substitution reactions are: addition reactions combine species; contrastingly, substitution reactions combine and create species with requirements of regiochemistry, stereochemistry, and competing pathways. Approaching substitution reactions requires understanding of concepts at the surface level defined by explicit, structural representations and at the deep level defined by implicit, chemical and physical properties. Additionally, approaching substitution reactions requires reasoning with multiple concepts (i.e., multivariate reasoning). Herein, we explore second-semester organic chemistry students’ multivariate reasoning when comparing substitution reactions.

Approaching substitution reactions requires understanding of concepts at the surface level and at the deep level

An important aspect of approaching substitution reactions is characterizing the nucleophile and the electrophile. Studies reported that most students characterized nucleophiles by their feature of having negative charges and electrophiles by their feature of having positive charges (Anzovino and Bretz, 2015, 2016; Galloway et al., 2017; Caspari et al., 2018a). However, these studies reported that some students characterized nucleophiles by their function of donating electrons and electrophiles by their function of accepting electrons (Anzovino and Bretz, 2015, 2016; Galloway et al., 2017; Caspari et al., 2018a). The considerations of charges around features indicate the conceptualization of charges at the surface level; however, the considerations of charges around function indicate the conceptualization of charges at the deep level, where charges hold the electronic properties of electrophilicity and nucleophilicity.

Moreover, Bodé et al. (2019) reported that some students characterized nucleophiles and electrophiles by considering steric effects. The considerations of steric effects cite “bulkiness” more than electronic attraction and electronic repulsion, which indicate the conceptualization of steric effects at the surface level more than at the deep level.

Few students characterized nucleophiles and electrophiles by considering induction effects (Anzovino and Bretz, 2016) or by considering resonance effects (Anzovino and Bretz, 2016; Galloway et al., 2017; Caspari et al., 2018a). Induction effects lack a structural feature (e.g., having partial negative charges or having partial positive charges), and, requiring the consideration of multiple bonds or functional groups (Braun et al., 2022), resonance effects demand a structural representation (e.g., drawing the resonance hybrid or the resonance structures). Therefore, induction effects and resonance effects are implicit and must be related back to a structural feature. These conceptualizations at the deep level could elucidate students’ few considerations of induction effects and resonance effects. These studies documented that students tended to focus on form for charges, steric effects, induction effects, and resonance effects and, accordingly, tended to demonstrate surface-level understandings of these concepts.

Another important aspect of approaching substitution reactions is characterizing the leaving group. Studies reported that some students characterized a leaving group by its size because size impacts the bond length between the carbon atom and leaving group (Popova and Bretz, 2018; Caspari and Graulich, 2019). Additionally, these studies reported that some students characterized a leaving group by its electronegativity because its electronegativity impacts the stability of negative charge on the conjugate base (Popova and Bretz, 2018; Caspari and Graulich, 2019). The leaving group's size weakening the leaving group's bond and, similarly, the leaving group's electronegativity stabilizing the conjugate base's charge connect form and function. These connections of form and function indicate the conceptualizations of size and electronegativity at the deep level.

Like induction effects and resonance effects, size and electronegativity are implicit and must be related back to a structural feature. Unlike induction effects and resonance effects, size and electronegativity could be related back to a structural feature (e.g., having a halogen leaving group) with trends and without manipulation of the structural representation. Thus, Popova and Bretz (2018) reported that students relied on absolutes (e.g., the bromine atom is a good leaving group) rather than comparatives (e.g., the bromine atom is a better leaving group than the chlorine atom) within one concept or between multiple concepts. Absolutes prove problematic: size increases as electronegativity decreases, and size impacts leaving group ability more than electronegativity does due to this size change (Popova and Bretz, 2018; Caspari and Graulich, 2019). These studies documented that students tended to focus on function for size and electronegativity and, accordingly, tended to demonstrate deep-level understandings of these concepts. However, considering size and electronegativity jointly rather than considering them separately affected understanding.

Approaching substitution reactions requires reasoning with multiple concepts

In studies focusing on students’ reasoning, most students reasoned with one concept (i.e., univariate reasoning), and few students reasoning with multiple concepts, despite the task requiring multivariate reasoning (Kraft et al., 2010; Strickland et al., 2010; Weinrich and Talanquer, 2016; Galloway et al., 2017; Caspari et al., 2018a, b; Bodé et al., 2019; Moreira et al., 2019; Crandell et al., 2020; Deng and Flynn, 2020; Watts et al., 2021). Multivariate reasoning has been reported to support students’ conceptual understanding (Deng and Flynn, 2020; Kranz et al., 2022). However, these studies recommended scaffolding this reasoning.

Multiple studies captured reasoning with a single case that provided a single task, such as “provide the product” tasks (Kraft et al., 2010; Strickland et al., 2010; Galloway et al., 2017; Decocq and Bhattacharyya, 2019) and “propose the mechanism” tasks (Kraft et al., 2010; Strickland et al., 2010; Galloway et al., 2017; Decocq and Bhattacharyya, 2019). These studies found that the single case tended to elicit univariate reasoning (Kraft et al., 2010; Strickland et al., 2010; Galloway et al., 2017; Decocq and Bhattacharyya, 2019). Contrastingly, multiple studies captured reasoning with a case comparison that provided two or more tasks, such as “which reaction has the lower activation energy” tasks (Caspari et al., 2018a; Caspari and Graulich, 2019; Graulich and Caspari, 2021; Watts et al., 2021; Kranz et al., 2022) and “which molecules have a similar reactivity” tasks (Graulich et al., 2019). These studies found that the case comparison tended to elicit multivariate reasoning (Alfieri et al., 2013; Caspari et al., 2018a; Graulich and Schween, 2018; Caspari and Graulich, 2019; Graulich and Caspari, 2021; Watts et al., 2021; Kranz et al., 2022).

Motivated by these results, Caspari and Graulich (2019) created a scaffolded case comparison and showed that the scaffolded case comparison helped students collect more influential factors of a reaction than the non-scaffolded case comparisons (Caspari and Graulich, 2019). However, they found that the scaffolded case comparison did not help students “modify their reasoning toward higher plausibility” (Caspari and Graulich, 2019). Students incorporating but not discarding concepts could be futile if the concepts conflict instead of support, such as size decreasing, electronegativity increasing, and both influencing leaving group ability (Popova and Bretz, 2018; Caspari and Graulich, 2019). They noted that “we need to know how to facilitate students’ progress toward the identification of plausible influences” (Caspari and Graulich, 2019). These studies demonstrated the usefulness of case comparisons in engaging students in collecting multiple concepts but also motivated the exploration of case comparisons in engaging students with using multiple concepts in multivariate reasoning. Thus, using a case comparison on substitution reactions, our study builds on prior studies and describes how students may activate lines of reasoning and, ultimately, may or may not use them in their explanations.

Resources framework

Our study was grounded in the resources framework (Hammer, 2000; Hammer and Elby, 2002; Hammer et al., 2005). This framework proposed that explanations are constructions of “pieces of knowledge” or resources (Hammer, 2000; Hammer and Elby, 2002; Hammer et al., 2005). Defining these resources, conceptual resources are what students know (e.g., the leaving group's electronegativity, the leaving group's size, etc.) (Hammer et al., 2005), and epistemological resources are why students know (e.g., “knowledge as fabricated stuff” or reasoning) (Hammer and Elby, 2002; Hammer et al., 2005). Organizing these resources, one resource activates another resource and successively a set of resources. This set of resources is modified and applied. Informally, Hammer (2000) termed this successively activated set of resources a “line of reasoning” or a “way of thinking.” Formally, we term a successively activated set of resources a line of reasoning, in reference to Hammer (2000), as a path (i.e., “of reasoning”) instead of a pattern (i.e., “a line,” a circle, a cluster, a constellation, etc.). Thus, activating resources depends on knowing the content.

Activating resources also depends on framing the task. A frame is how students know “what is going on here” (Hammer et al., 2005), which is often tacit but can be interpreted through the task itself as well as students’ knowledge of and their experiences with the task. In an unfamiliar frame, Hammer (2000) posited that students laboriously activate a set of resources, including weighing resources, incorporating resources that support, and discarding resources that conflict. Learning requires repetition, and a repeatedly activated set of resources is a “cognitive unit” or resource itself (Hammer et al., 2005). Therefore, in a familiar frame, Hammer (2000) posited that students automatically, less laboriously activate a set of resources.

Framing not only affects activating resources but also affects applying them. A line of reasoning may be appropriate, productive, and correct in one frame, but that line of reasoning may be inappropriate, unproductive, and incorrect in another frame (Hammer, 2000; Hammer and Elby, 2002; Hammer et al., 2005). However, while the line of reasoning may be incorrect or may lead to unproductive problem solving, the resources themselves cannot be and may be “instincts” that instructors can guide (Hammer, 2000). Furthermore, multiple lines of reasoning may be appropriate, for example, in an organic chemistry course where the case-comparison task elicits multivariate explanations (Alfieri et al., 2013; Caspari et al., 2018a; Caspari and Graulich, 2019; Graulich and Caspari, 2021; Watts et al., 2021). Therefore, the resources framework is a powerful framework for our study.

In our study, we explored second-semester organic chemistry students’ reasoning, framing their reasoning with a case-comparison task on substitution reactions in a second-semester organic chemistry course. Substitution reactions could activate the leaving group's electronegativity, the leaving group's size, etc. as conceptual resources. Moreover, the case comparison should activate reasoning as an epistemological resource. However, students’ frame – their knowledge of and their experiences with substitution reactions, case comparisons, organic chemistry, etc. – will affect their activation. The resources framework provided this language (i.e., resources, line of reasoning, and activating) as well as the organization of conceptual resources into lines of reasoning.

Research questions

We interviewed second-semester organic chemistry students and tasked them to compare two substitution reaction mechanisms. Analysing their explanations, we explored what lines of reasoning students activated and how students used them in their explanations in order to characterize multivariate reasoning. Our study was guided by the following research questions:

(1) What lines of reasoning are second-semester organic chemistry students activating when they compare two substitution reaction mechanisms?

(2) What activated lines of reasoning are second-semester organic chemistry students using in their explanations for the substitution reaction mechanism case-comparison task?

Methods

Institutional context

Our study was situated in a large-enrolment (∼800 students), second-semester laboratory course at a research-intensive (R1), Midwestern university. The second-semester laboratory course was composed of a one-hour, once-a-week lecture that was taught by faculty instructors and a four-hour, once-a-week laboratory that was facilitated by graduate student teaching assistants. In-lab, graded requirements included lab work, lab reports, and quizzes. Out-of-lab, graded requirements included lab pages, lab write-ups, and Writing-to-Learn assignments (Schmidt-Mccormack et al., 2019; Watts et al., 2020; Gupte et al., 2021; Zaimi et al., 2024). In addition to these, in-lecture, ungraded requirements included case-comparison activities (Watts et al., 2021).

Case-comparison task design

We designed a case-comparison task, where students compared two substitution reaction mechanisms (Fig. 1) and chose the mechanism with the lower activation energy. We included explicit structural features: mechanistic arrows, the presence of a carbonyl group, and the identity of the leaving group. Additionally, the representations included implicit structural features: electron lone pairs and carbon atoms. Accordingly, we expected that the case-comparison task would elicit students’ multivariate reasoning and that students would engage in reasoning with a variety of conceptual resources (e.g., induction effects, electronegativity, resonance effects, etc.). Our choices are consistent with the instructional activities of our institution (Watts et al., 2021) and with the case-comparison tasks in research (Graulich and Caspari, 2021; Kranz et al., 2022).
image file: d4rp00086b-f1.tif
Fig. 1 The case-comparison task.

Data collection

The Institutional Review Board's approval (HUM00115139) was obtained, and students’ consent was obtained. We conducted eleven task-based (i.e., a case-comparison task), semi-structured, think-aloud interviews. The interviews were audio recorded and transcribed. The notes taken by the researchers (IZ and FMW) and the documents annotated by the students were collected and scanned. These notes and documents augmented the interview transcripts. Data were anonymized, and students were given pseudonyms, which were not reflective of their race, ethnicity, gender, or other identities.

Data analysis

Data analysis was a three-step process. First, we coded and memoed interview transcripts, capturing what conceptual resources students activated. We defined conceptual resources as surface-level structural features (e.g., the chlorine group), deep-level chemical and physical properties (e.g., the chlorine group's electronegativity), and effects (e.g., energy). Second, we wrote profiles, capturing what lines of reasoning students activated and how students used the lines of reasoning in their explanations. We defined that a line of reasoning starts with a surface-level structural feature (e.g., the chlorine group), continues with deep-level chemical and physical properties (e.g., the chlorine group's electronegativity), and ends with an effect (e.g., energy). Third, we compared students’ individual lines of reasoning, combined them, and created our comprehensive lines of reasoning, mapping students’ individual lines of reasoning onto our comprehensive lines of reasoning and comparing how students activated them.
Coding and memoing. Two researchers (IZ and FMW) coded and memoed (Saldaña, 2021; Braun and Clarke, 2022) the interview transcripts. Specifically, we coded the interview transcripts for the structural feature (e.g., the chlorine group) and the property that were immediately activated (e.g., the chlorine group's electronegativity). We memoed the interview transcripts for the properties that were additionally activated (e.g., bond polarization, bond strength, and electrophilicity). For example, Violet noticed the carbonyl group and activated induction effects: “[The] oxygen [draws] negative charge away from the carbon […].” Therefore, we coded Violet's interview transcript “the carbonyl group's induction effects.” Furthermore, Violet explained induction effects and activated charge stabilization and electrophilicity: “[The carbon] becomes even more partially positive, which makes it even more [electrophilic] […].” Therefore, we memoed Violet's interview transcript “charge stabilization” and “electrophilicity.” Additionally, we memoed the interview transcripts for the effects that were activated (e.g., energy). Some students activated energy; however, Violet and most students did not activate energy or any effects, or they did not verbalize that they did.

As we coded and memoed the interview transcripts, we negotiated consensus (Saldaña, 2021; Watts and Finkenstaedt-Quinn, 2021; Braun and Clarke, 2022). We re-coded the interview transcripts, producing codes of the functional group's induction effects, the leaving group's electronegativity, the functional group's resonance effects, the leaving group's size, and the leaving group's steric effects (Table 1). This process captured what conceptual resources students activated.

Table 1 The codebook
Code Definition
The functional group's induction effects The student activates the induction effects of the carbonyl group or the halogen leaving groups. A difference exists where Reaction 1 has two electron-withdrawing groups (C[double bond, length as m-dash]O, C–Cl) and Reaction 2 has one electron-withdrawing group (C–Br).
The leaving group's electronegativity The student activates the electronegativity effects of the halogen leaving groups. A difference exists where Reaction 1 has a chlorine atom, which is more electronegative, and Reaction 2 has a bromine atom. If electronegativity leads into induction, the statement is coded “the functional group's induction effects,” not “the leaving group's electronegativity.”
The functional group's resonance effects The student activates an alternate resonance structure of the carbonyl group. A difference exists where Reaction 1 has an alternate resonance structure (C[double bond, length as m-dash]O, C–O) and Reaction 2 does not have an alternate resonance structure.
The leaving group's size The student activates the size of the halogen leaving groups. A difference exists where Reaction 1 has a chlorine atom and Reaction 2 has a bromine atom, which is bigger.
The leaving group's steric effects The student activates the steric hindrance of the halogen leaving groups. A difference exists where Reaction 1 has a chlorine atom and Reaction 2 has a bromine atom, which is bigger. If “hindrance” or “bulkiness” is not mentioned, the statement is coded “the leaving group's size,” not “the leaving group's steric effects.”

Writing profiles. We organized the conceptual resources into a line of reasoning. We evoke a “line of reasoning” in reference to Hammer (2000), as a path (i.e., “of reasoning”), not as a pattern (i.e., “a line,” a circle, a cluster, a constellation, etc.). However, students activated direct, linear lines of reasoning, or they verbalized that they did. The structural feature and the property that were immediately activated (i.e., a code) started a line of reasoning (e.g., the chlorine group's electronegativity). Sometimes, additional properties were activated and continued a line of reasoning (e.g., bond polarization, bond strength, and electrophilicity). Here, students linked these properties, where they connected one property to the next and created a direct, linear line of reasoning. For example, Violet's line of reasoning for induction effects started with the carbonyl group, moved from induction effects to charge stabilization, and eventually ended with electrophilicity. We characterized this line of reasoning as a deep-level or developed line of reasoning, emphasizing deep-level chemical and physical properties and, therefore, deep-level understanding. Other times, additional properties were not activated and did not continue a line of reasoning. Here, students stated the property. For example, Violet's line of reasoning for size started with the bromine group and immediately ended with size. We characterized this line of reasoning as a surface-level or undeveloped line of reasoning, emphasizing surface-level structural features and, therefore, surface-level understanding. However, undeveloped connotes neither underdeveloped nor unproductive. Moreover, this case-comparison task did not have a straightforward answer, as most case-comparison tasks have not (Graulich and Caspari, 2021; Watts et al., 2021; Kranz et al., 2022). Therefore, based on the case-comparison task, both developed and undeveloped lines of reasoning were appropriate, and undeveloped lines of reasoning are productive “instincts” that instructors can guide (Hammer, 2000). This approach is an anti-deficit approach, which has been applied in a recent study (Haas et al., 2024), where second-semester organic chemistry students’ mechanistic reasoning was explored through the resources framework.

As exemplified by Violet, students activated lines of reasoning throughout the interview. Because students did, we compared students’ lines of reasoning throughout the interview to their lines of reasoning at the end of the interview in their final explanation for the case-comparison task. This comparison characterized how students used their activated and (un)developed lines of reasoning, either incorporating multiple lines of reasoning into explanations as multivariate reasoning or discarding lines of reasoning from explanations and selecting only one line of reasoning as univariate reasoning. For example, Violet's profile described them incorporating the developed line of reasoning for induction effects into their explanation. However, Violet's profile described them discarding the undeveloped line of reasoning for size from their explanation and noting size as “less significant [than induction effects].” Therefore, Violet's profile characterized univariate reasoning.

As we wrote the profiles, we negotiated consensus (Saldaña, 2021; Watts and Finkenstaedt-Quinn, 2021; Braun and Clarke, 2022), and re-wrote the profiles. This process captured what lines of reasoning students activated, how students developed them (i.e., undeveloped and developed lines of reasoning), and how students used or did not use them in their explanations (i.e., multivariate and univariate reasoning).

Mapping students’ individual lines of reasoning onto our comprehensive line of reasoning. We compared students’ individual lines of reasoning. Sometimes, they matched, activating the same conceptual resources. For example, Violet's and Brooke's lines of reasoning for induction effects started with the carbonyl group, moved from induction effects to charge stabilization, and ended with electrophilicity. Other times, they did not, activating either more or less conceptual resources. Representing as many conceptual resources as we could, we combined students’ individual lines of reasoning into our comprehensive lines of reasoning. Moreover, we compared our comprehensive lines of reasoning, modifying them. For example, Violet's and Brooke's individual lines of reasoning for induction effects did not include bond strength between charge stabilization and electrophilicity. However, students’ individual lines of reasoning for electronegativity included bond strength between charge stabilization and electrophilicity. We reasoned that, although students did not verbalize the property, the property played a comparable role in both lines of reasoning and would be an appropriate, productive property in this line of reasoning. Thus, our comprehensive line of reasoning for induction effects included bond strength.

As we created our comprehensive lines of reasoning, we negotiated consensus (Saldaña, 2021; Watts and Finkenstaedt-Quinn, 2021; Braun and Clarke, 2022). We mapped students’ individual lines of reasoning onto our comprehensive lines of reasoning, producing lines of reasoning for the carbonyl group's induction effects, the chlorine group's electronegativity, and the bromine group's size. This process compared how students activated lines of reasoning.

The results are arranged by students’ individual lines of reasoning mapped onto our comprehensive lines of reasoning. We discuss the lines of reasoning for the carbonyl group's induction effects and the chlorine group's electronegativity, as students linked them. Subsequently, we discuss the line of reasoning for the bromine group's size. This analysis points out leaps in students’ individual lines of reasoning but also links from other students’ individual lines of reasoning.

Results and discussion

We interviewed eleven second-semester organic chemistry students, where they compared two substitution reaction mechanisms (Fig. 1) throughout the interview and chose the mechanism with the lower activation energy throughout the interview and, in order to prompt evaluation, at the end of the interview. We explored students’ multivariate reasoning, analysing their explanations. Addressing the first research question, we discuss what lines of reasoning students activated. Students activated lines of reasoning for the carbonyl group's induction effects, the chlorine group's electronegativity, and the bromine group's size. While all lines of reasoning were productive (i.e., the line of reasoning answered the question), some were developed (i.e., the line of reasoning started with a structural feature and a property that were immediately activated and continued with properties that were additionally activated), and others were undeveloped (i.e., the line of reasoning started with a structural feature and a property that were immediately activated but not continued). Addressing the second research question, we discuss how students used their activated and (un)developed lines of reasoning in their final explanation for the case-comparison task. Generally, students used developed lines of reasoning for the carbonyl group's induction effects and the chlorine group's electronegativity to select Reaction 1. Using multiple lines of reasoning for their final explanation demonstrated multivariate reasoning. Contrastingly, generally, students used undeveloped lines of reasoning for size to select Reaction 2. Using one line of reasoning for their final explanation demonstrated univariate reasoning. Thus, we sectioned the results and discussion by what reaction students selected and sub-sectioned the results and discussion by what conceptual resources students activated, what lines of reasoning students activated, and how students used the lines of reasoning in their final explanations. We concluded the results and discussion with an overview of the variation in students’ univariate and multivariate reasoning.

Activating and incorporating lines of reasoning for the carbonyl group's induction effects and the chlorine group's electronegativity resulted in selecting Reaction 1

Most students (N = 6) stated that Reaction 1 – with its carbonyl group and its chlorine atom – had a lower activation energy than Reaction 2. Honing in on these functional groups, students activated the induction effects (N = 1) of the carbonyl group, the electronegativity (N = 4) of the chlorine atom, or both (N = 1) (Table 2). They activated productive, developed lines of reasoning for induction effects (Fig. 2) as well as productive, developed and productive, undeveloped lines of reasoning for electronegativity (Fig. 3). Comparing these functional groups, students activated the steric effects (N = 4) or the size (N = 1) of the bromine atom (Table 2). They activated productive, undeveloped lines of reasoning for steric effects and size. Students’ lines of reasoning were productive lines of reasoning. However, evaluating their lines of reasoning, most of these students (N = 4) used their (more) developed lines of reasoning for induction effects and/or electronegativity, instead of their undeveloped lines of reasoning for steric effects or size.
Table 2 Students who selected Reaction 1 activated these conceptual resources. image file: d4rp00086b-u1.tif = the student activated the resource, activated a developed line of reasoning, and incorporated it in their final explanation. image file: d4rp00086b-u2.tif = the student activated the resource, activated an undeveloped line of reasoning, and incorporated it in their explanation. image file: d4rp00086b-u3.tif = the student activated the resource, activated an undeveloped line of reasoning, but did not use it in their final explanation. Blank cell = the student did not activate the conceptual resource
Student Induction effects Electronegativity Steric effects Size
Violet image file: d4rp00086b-u4.tif image file: d4rp00086b-u5.tif
Brooke image file: d4rp00086b-u6.tif image file: d4rp00086b-u7.tif image file: d4rp00086b-u8.tif
Jade image file: d4rp00086b-u9.tif image file: d4rp00086b-u10.tif
Naomi image file: d4rp00086b-u11.tif
Chad image file: d4rp00086b-u12.tif image file: d4rp00086b-u13.tif
Gigi image file: d4rp00086b-u14.tif image file: d4rp00086b-u15.tif


image file: d4rp00086b-f2.tif
Fig. 2 The lines of reasoning for the carbonyl group's induction effects. The conceptual resource is activated if its box is coloured grey. The top line of reasoning is our comprehensive line of reasoning, and the bottom lines of reasoning are students’ individual lines of reasoning mapped onto our comprehensive line of reasoning. Thus, the shades of grey on our comprehensive line of reasoning are additives of the shade of grey on students’ individual lines of reasoning. The activation of one resource triggers the activation of another resource, shown by the black arrow.

image file: d4rp00086b-f3.tif
Fig. 3 The lines of reasoning for the chlorine atom's electronegativity. The conceptual resource is activated if its box is coloured grey. The top line of reasoning is our comprehensive line of reasoning, and the bottom lines of reasoning are students’ individual lines of reasoning mapped onto our comprehensive line of reasoning. Thus, the shades of grey on our comprehensive line of reasoning are additives of the shade of grey on students’ individual lines of reasoning. The activation of one resource triggers the activation of another resource, shown by the black arrow.

Two students (Violet and Brooke) noticed the carbonyl group and activated induction effects (Table 2). These lines of reasoning are examples of a developed line of reasoning (Fig. 2), where the line of reasoning starts with a structural feature and continues with properties. For example, Violet started with the carbonyl group and reasoned that the carbonyl withdraws “negative charge away” from the bond between the carbon and the chlorine and leaves a “partially positive charge” on the carbon. Violet moved from induction effects to a charge dipole and reasoned that this dipole “makes it more favourable for the iodine to come in and react with [the carbon].” Eventually, Violet ended with electrophilicity. For another example, Brooke reasoned:

“I'm […] trying to think if the resonance contributors are going to […] impact what's going on. Since oxygen is the more electronegative atom in the carbonyl, the other [resonance structure] could put a negative charge on the oxygen and a positive charge on the carbon. […] Because the carbon [that's in the carbonyl] has a positive charge, it might pull […] more electrons away from the carbon that's involved in the reaction itself, which could make it more electrophilic itself.”

This line of reasoning is also a developed line of reasoning, starting with the carbonyl group, moving from induction effects to a charge dipole, and eventually ending with electrophilicity. Both Violet's and Brooke's lines of reasoning flow from a structural feature (i.e., the carbonyl group) to a series of properties (i.e., the induction effects, a stronger charge dipole, and a stronger electrophile). This stepwise flow gives form a function, working toward weakening the leaving group's bond. Therefore, Violet's and Brooke's developed lines of reasoning for induction effects showcased their deep-level understandings of induction effects. This finding contrasts Anzovino and Bretz's (2016) finding, where students centred charges and induction effects itself, and suggests that the activation of the charge dipole could activate a developed line of reasoning.

Additionally, five students (Brooke, Jade, Naomi, Chad, and Gigi) noticed the chlorine atom and activated electronegativity (Table 2). These lines of reasoning are examples of a developed line of reasoning, where the line of reasoning starts with a structural feature and continues with several properties, as well as an undeveloped line of reasoning, where the line of reasoning starts with a structural feature but continues with few properties (Fig. 3). For example, Jade's line of reasoning is an undeveloped line of reasoning. Jade knew that the “trend of the periodic table for electronegativity” increases up the column, so Jade reasoned that “chlorine is more electronegative than bromine” and that “chlorine wants to hold onto its electrons more” than bromine. This line of reasoning connects a structural feature (i.e., the chlorine atom) and a property (i.e., the electronegativity) based on a rule (i.e., the periodic trend of electronegativity), not a series of properties (e.g., a stronger bond polarization, a stronger charge stabilization, a weaker bond strength, or a stronger electrophile). For another example, Naomi moved from electronegativity to charge stabilization and reasoned that “chlorine is more electronegative than bromine” and that chlorine “would take on the negative charge more readily.” Both Jade's and Naomi's lines of reasoning flow from a structural feature (i.e., the chlorine atom) to a few properties (i.e., the electronegativity and a stronger charge stabilization). This flow stops short of giving form a function, working toward weakening the leaving group's bond. Therefore, Jade's and Naomi's undeveloped lines of reasoning for electronegativity showed their surface-level understanding of electronegativity in these instances.

Contrastingly, Brooke's, Chad's, and Gigi's lines of reasoning are developed lines of reasoning. For example, Chad started with the chlorine atom and reasoned that “chlorine is more electronegative than bromine.” Chad moved from electronegativity to bond strength and reasoned, “[Chlorine] wants to hog the electrons between the carbon and chlorine bond. If chlorine hogs the electrons, then that bond is more willing to break.” Eventually, Chad ended with electrophilicity. Notably, bond strength can continue from electronegativity, as depicted by Chad's line of reasoning, or from bond polarization and charge stabilization, as depicted by Brooke's line of reasoning. Brooke moved from electronegativity to bond polarization and bond strength and reasoned, “Chlorine […] is more electronegative. The bond between the chlorine and the carbon [is] more polarized and, probably as a result, easier to break.” Therefore, Brooke's, Chad's, and Gigi's developed lines of reasoning for electronegativity showcased their deep-level understandings of electronegativity. This finding contrasts previous studies’ (Popova and Bretz, 2018; Caspari and Graulich, 2019) findings, where students centred charges and electronegativity itself, and suggests that the activation of the charge stabilization, the bond polarization, or the bond strength could activate a developed line of reasoning.

As described, students noticed the carbonyl group and the chlorine atom, and they activated developed lines of reasoning for induction effects and (un)developed lines of reasoning for electronegativity. One student (Brooke) not only incorporated but also linked their developed lines of reasoning for induction effects and electronegativity, demonstrating multivariate reasoning. Analysing Brooke's interview transcript, linking lines of reasoning proposes to be as stepwise as activating a line of reasoning is. First, Brooke reasoned with electronegativity:

“The first thing that comes to mind for me is that chlorine […] is more electronegative. The bond between the chlorine and the carbon [is] more polarized and, probably as a result, easier to break.”

Importantly, this line of reasoning involved creating a bond dipole or a weaker bond. Second, Brooke reasoned with induction effects:

“I’m looking at the carbonyl […] and trying to think if the resonance contributors […] are going to have any impact on what's going on. Since oxygen is the more electronegative atom, [that] puts a negative charge on the oxygen and a positive charge on the carbon. I don’t see [how] that should necessarily have any real impact on the rate of the reaction. […] I suppose it could? The carbon has a partial positive charge. It might pull […] more electrons in – away from the carbon that's directly involved in the reaction. [It] could make it[self] more electrophilic and […] also pull the reaction more easily to completion.”

Importantly, this line of reasoning involved creating a charge dipole or a weaker bond. Because both lines of reasoning involved a weaker bond, they overlapped, and Brooke combined them. However, while Brooke activated developed lines of reasoning for induction effects and electronegativity, they activated an undeveloped line of reasoning for steric effects. They mentioned that “[the sterics of the carbonyl] is not a super important point” and moved on. Therefore, Brooke claimed that “that Reaction 1 will have the lower activation energy because […] the chlorine-carbon bond [in Reaction 1] is going to be easier to break than the carbon–bromine bond in Reaction 2.” Linking lines of reasoning proposes to be not only as stepwise but also as laborious as activating a line of reasoning. This finding encourages activating and developing as many lines of reasoning as possible.

Moreover, while one student (Brooke) incorporated two developed lines of reasoning into their final explanation, three students (Violet, Jade, and Gigi) incorporated one (un)developed line of reasoning into their final explanations. Specifically, Jade and Gigi activated undeveloped lines of reasoning for steric effects. For example, Gigi activated a developed line of reasoning for electronegativity, but they mentioned that “[bromine is] just one atom” and moved on. Similarly, Violet activated an undeveloped line of reasoning for size. For example, Violet activated a developed line of reasoning for induction effects, and they considered that “[the bromine is] bigger than the chlorine,” but they decided that size is “less significant” than induction effects and moved on. Ultimately, these students incorporated their more developed line of reasoning for induction effects or electronegativity into and discarded their undeveloped line of reasoning for size or steric effects from their final explanations. Therefore, they demonstrated univariate reasoning. However, while Chad activated a developed line of reasoning for electronegativity and an undeveloped line of reasoning for steric effects, they did not discard the undeveloped line of reasoning. Chad argued, “Chlorine is a smaller atom than bromine, so iodine would have an easier time attacking that carbon.” Therefore, the lines of reasoning were incorporated, but they were not linked, which can be considered multivariate reasoning.

Furthermore, these students commented that induction effects or electronegativity were more “important,” “significant” (e.g., size is “less significant” than induction effects), and productive than steric effects or size. Thus, using our analysis (i.e., developed and undeveloped lines of reasoning) and identifying words (e.g., “important” and “significant”) that equate productiveness and development, we suppose that these students weighed based on development. Students could have used statements (e.g., “I know” or “I remember”) that equate productiveness and frame (i.e., their knowledge of and their experiences with substitution reactions, case comparisons, organic chemistry courses, etc.). Indeed, the frame of these substitution reactions requires the consideration of size (Popova and Bretz, 2018; Caspari and Graulich, 2019). However, we did not capture that students used these statements and weighed based on the frame of these substitution reactions or the organic chemistry course. We assume that these students have not yet had the repeated learning experiences that would “tip students into the desired frame” (Hammer et al., 2005) and activate size. These findings indicate that instructors and instructional materials should encourage not only activating and developing lines of reasoning as much as possible but also explicitly weighing them.

Activating and incorporating the line of reasoning for the bromine group's size resulted in selecting Reaction 2

Some students (N = 4) stated that Reaction 2 – with its bromine atom – had a lower activation energy than Reaction 1. Honing in on this functional group, students activated the size (N = 4) of the bromine atom (Table 3). They activated productive, developed lines of reasoning for size as well as productive, undeveloped lines of reasoning for size (Fig. 4). Moreover, students activated the electronegativity (N = 2) of the bromine atom (Table 3), and they activated productive, undeveloped lines of reasoning for electronegativity. Students’ lines of reasoning were productive lines of reasoning. However, evaluating their lines of reasoning, students (N = 2) used their (un)developed lines of reasoning for size, instead of their undeveloped lines of reasoning for electronegativity.
Table 3 Students who selected Reaction 2 activated these conceptual resources. image file: d4rp00086b-u16.tif = the student activated the resource, activated a developed line of reasoning, and incorporated it in their final explanation. image file: d4rp00086b-u17.tif = the student activated the resource, activated an undeveloped line of reasoning, and incorporated it in their explanation. image file: d4rp00086b-u18.tif = the student activated the resource, activated an undeveloped line of reasoning, but did not use it in their final explanation. Blank cell = the student did not activate the conceptual resource
Student Induction effects Electronegativity Steric effects Size
Ivy image file: d4rp00086b-u19.tif image file: d4rp00086b-u20.tif
Shea image file: d4rp00086b-u21.tif image file: d4rp00086b-u22.tif
Ben image file: d4rp00086b-u23.tif
Willam image file: d4rp00086b-u24.tif image file: d4rp00086b-u25.tif


image file: d4rp00086b-f4.tif
Fig. 4 The lines of reasoning for the bromine atom's size. The conceptual resource is activated if its box is coloured grey. The top line of reasoning is our comprehensive line of reasoning, and the bottom lines of reasoning are students’ individual lines of reasoning mapped onto our comprehensive line of reasoning. Thus, the shades of grey on our comprehensive line of reasoning are additives of the shade of grey on students’ individual lines of reasoning. The activation of one resource triggers the activation of another resource, shown by the black arrow.

Four students (Ivy, Shea, Ben, and Willam) noticed the bromine atom and activated size (Table 3). These lines of reasoning are examples of an undeveloped line of reasoning as well as a developed line of reasoning (Fig. 4). For example, Ivy's line of reasoning is an undeveloped line of reasoning. Ivy moved from the bromine atom to the atomic radius, and they reasoned:

“Bromine is larger than chlorine, and that would make [the bromine] a better leaving group” because “[the] atomic radius increases down the column. [The bromine] would be farther away from the carbon [and] easier to […] leave.”

For another example, Shea moved from the bromine atom to the atomic radius, and they reasoned that the bromine is “a bigger atom than the chlorine” because “[bromine] is a bigger atom, has more protons, has more electrons.” Furthermore, Shea reasoned:

“[Bromine] has an extra shell of electrons. […] I can't think of the name. It's on the periodic table? It's a row down? [Bromine] has an extra shell of valence electrons. [Bromine] has more orbitals of electrons. There it is – orbitals! […] There's more shielding [where] the electrons are less… being pulled in by the nucleus. [Bromine's] going to have a bigger atomic radius. […] Also, because bromine has an extra shell of electrons, […] [bromine's] going to be bulkier. I'm saying the same things over and over. […] Bromine is going to be a better leaving group than chlorine.”

Both lines of reasoning connect a structural feature (i.e., the bromine atom) and a property (i.e., the size) based on a rule (i.e., the periodic trend of size), not a series of properties (e.g., a stronger charge stabilization, a weaker bond strength, or a stronger leaving group). This flow leaves leaps, and Shea's hesitation (e.g., “It's on the periodic table?”) and repetition (e.g., “I’m saying the same things over and over.”) hint that students can recognize the leaps. Accordingly, this flow stops short of giving form a function, working toward weakening the leaving group's bond. Therefore, Ivy's, Shea's, and Ben's undeveloped lines of reasoning for size showed their surface-level understanding of size in these instances.

Contrastingly, Willam's line of reasoning for size is a developed line of reasoning. For example, Willam started with the bromine atom, moved from size to the atomic radius, and reasoned that “going down the periodic table,” the bromine has a larger atomic radius than the chlorine, “preferring the electrons returned to [the bromine].” Willam continued with charge stabilization and reasoned that “the bromine has more space to spread out the electrons,” so “the bromine better stabilizes the negative charge” than the chlorine. Eventually, Willam ended with leaving group ability. Willam's line of reasoning flows from a structural feature (i.e., the bromine group) to a series of properties (i.e., the size, a bigger atomic radius, and a stronger charge stabilization). This stepwise flow gives form a function, working toward weakening the leaving group's bond. Therefore, Willam's developed, continued line of reasoning for size showcased their deep-level understanding of size. This finding supports Popova and Bretz's (2018) finding and suggests that the activation of the charge stabilization could activate a developed line of reasoning. Moreover, Willam activated a developed line of reasoning for steric effects, and argued, “I think, it's possible that the […] iodine tags freely from [the] front or [the] back side and donates the electrons back to the bromine.” Therefore, the lines of reasoning were incorporated, but they were not linked, which can be considered multivariate reasoning.

However, while Willam incorporated two developed lines of reasoning into their final explanation, two students (Ivy and Shea) incorporated one undeveloped line of reasoning into their final explanations. For example, Ivy activated an undeveloped line of reasoning for size, but they mentioned that “chlorine is more electronegative” than bromine and that “electronegativity could make [the chlorine] a better leaving group” and moved on. Ivy discarded electronegativity because they “wouldn’t know” if “[electronegativity] is a bigger factor than size.” For another example, Shea activated an undeveloped line of reasoning for size, but they mentioned electronegativity and moved on. Shea discarded electronegativity because the halides have “the same” electronegativity, so the difference in size is more important than the difference in electronegativity. Ultimately, these students incorporated their undeveloped line of reasoning for size into and discarded their undeveloped line of reasoning for electronegativity from their final explanations. Therefore, they demonstrated univariate reasoning. Furthermore, demonstrating univariate reasoning, Ben only activated and used their undeveloped line of reasoning for size.

Unlike the students who selected Reaction 1, these students did not use “importance,” and they did not activate developed and undeveloped lines of reasoning. We do not suppose that these students weighed based on development. However, like the students who selected Reaction 1, these students did not intentionally, externally weigh based on the frame of these substitution reactions or the organic chemistry course. Students used statements (e.g., “wouldn’t know” and “the same”) that hint that size is important, but they did not use statements (e.g. “I know”) that equate productiveness and frame. Thus, size seemed an instinct, and they could have instinctively, internally weighed based on the frame. We assume that these students have begun to have the repeated learning experiences that would “tip students into the desired frame” (Hammer et al., 2005), activate size, and result in “chemical intuition” (Hammer et al., 2005). These findings pose the question: What ways of weighing are helpful?

Not weighing resulted in not selecting either Reaction 1 or Reaction 2

Analysing Morgan's interview exemplifies this question. Morgan noticed the halogen leaving groups and activated steric effects. Activating an undeveloped line of reasoning for steric effects, Morgan reasoned, “Bromine is bigger. […] Chlorine is smaller. […] I feel [that] bromine is more hindered [than chlorine] – not too sure. Since [bromine] is more hindered, […] [b]romine would be harder to get off.” Moreover, activating another undeveloped line of reasoning for steric effects, Morgan reasoned, “I guess [the carbonyl] would [contribute steric effects] – not sure.” These undeveloped lines of reasoning supported Reaction 1. However, Morgan noticed the carbonyl group and activated resonance effects. Morgan described a resonance structure that creates a double bond between the carbon and chlorine atoms of the leaving group and that creates a single bond between the oxygen and carbon atoms of the carbonyl group. Activating an undeveloped line of reasoning for resonance effects, Morgan reasoned, “[A]ttraction happens” between the negative oxygen and the positive chlorine. The attraction “might require more energy to separate the oxygen and the chlorine.” This undeveloped line of reasoning supported Reaction 2. The lines of reasoning for steric effects are as developed and productive as the line of reasoning for resonance effects are, although the line of reasoning for steric effects is more correct than the line of reasoning for resonance effects is. Weighing based on development would not have been helpful. Moreover, the lines of reasoning for steric effects and resonance effects are relevant and productive. Weighing based on the frame of these substitution reactions or the organic chemistry course would not have been helpful. Activating more conceptual resources could have been helpful, although activating more conceptual resources than the already activated conceptual resources has not ensured weighing (Watts et al., 2021). Therefore, Morgan doubted weighing (e.g., “I’m not entirely sure.”) and could not proceed. This weighing requires resources that students already have, such as their knowledge of and their experiences with substitution reactions, case comparisons, organic chemistry, etc., but also that instructors could provide, such as the data from experiments.

Variation in how students demonstrated univariate and multivariate reasoning

We found variation in how students demonstrated univariate and multivariate reasoning in their final explanations. Demonstrating univariate reasoning, few students activated a single conceptual resource, which they activated into either a developed or an undeveloped line of reasoning. Additionally, demonstrating univariate reasoning, most students activated multiple conceptual resources, which they activated into either developed or undeveloped lines of reasoning. Despite these variations in activation, all of these students used a single line of reasoning in their final explanations. These variations of univariate reasoning are evident in the examples of: Naomi and Ben, who activated and reasoned with a single undeveloped line of reasoning; Ivy and Shea, who activated multiple lines of reasoning but reasoned with a single undeveloped line of reasoning; and Violet, Jade, and Gigi, who activated multiple lines of reasoning but reasoned with a single developed line of reasoning. Therefore, these findings characterize that univariate reasoning can include students who activate multiple conceptual resources, in addition to previous characterizations of univariate reasoning where students used a single concept (e.g., Watts et al., 2021 and Kranz et al., 2022).

Demonstrating multivariate reasoning, some students activated multiple conceptual resources, which they activated into either developed or undeveloped lines of reasoning. Despite these variations in development, all of these students used multiple lines of reasoning in their final explanations. The variations of multivariate reasoning are evident in the examples of: Chad, who activated and reasoned with developed and undeveloped lines of reasoning; Willam, who activated and reasoned with developed lines of reasoning; and Brooke, who activated developed and undeveloped lines of reasoning but only reasoned with the developed lines of reasoning. Therefore, these findings characterize that multivariate reasoning can include students who activate and use undeveloped and developed lines of reasoning, in addition to previous expectations of multivariate reasoning (Haas et al., 2024), where students activate and use multiple developed lines of reasoning (Bodé et al., 2019; Caspari and Graulich, 2019; Deng and Flynn, 2020).

Together, these findings present the variation in how students engaged in univariate and multivariate reasoning, and they motivate scaffolded support. Some students could need support with activating multiple conceptual resources. Other students can activate multiple conceptual resources, but they could need support with developing them into lines of reasoning. Notably, Morgan activated multiple lines of reasoning, but did not use them, not demonstrating univariate or multivariate reasoning. These students may need support with weighing lines of reasoning.

Conclusion and implications

Organic chemistry reactions are challenging, requiring not only decoding structural features and connecting them to their chemical and physical properties (i.e., a line of reasoning) but also synthesizing multiple lines of reasoning (i.e., multivariate reasoning). Case comparisons, where students compare two or more tasks, have been reported to support students’ multivariate reasoning (Alfieri et al., 2013; Caspari et al., 2018a; Caspari and Graulich, 2019; Graulich and Caspari, 2021; Watts et al., 2021). Thus, we interviewed second-semester organic chemistry students and asked them to compare two substitution reaction mechanisms. Reaction 1 had a carbonyl group and a chlorine leaving group while Reaction 2 had a bromine leaving group. Analysing their interview transcripts, we explored what lines of reasoning students activated and how students used them in their explanations, characterizing univariate and multivariate reasoning.

Students activated multiple conceptual resources. Comparing the presence or the absence of the carbonyl group, few students activated induction effects, but these students activated developed lines of reasoning for induction effects. These developed lines of reasoning emphasized deep-level properties and showcased their deep-level understanding. Additionally, comparing the presence of the chlorine leaving group or the presence of the bromine leaving group, some students activated electronegativity, and other students activated size. These students activated developed and undeveloped lines of reasoning for electronegativity and size. The developed lines of reasoning showcased their deep-level understanding, and the undeveloped lines of reasoning emphasized surface-level features and showed their surface-level understanding. Commonly, in undeveloped lines of reasoning, students started with the structural feature (e.g., the chlorine atom or the bromine atom) and ended with the first property (e.g., electronegativity or size). This leap implied that the presence of a functional group secures the effect of a functional group. Contrastingly, in developed lines of reasoning, students continued with charge stabilization and bond strength from the first property to the final effect (e.g., leaving group ability). These findings suggest encouraging students to activate as many conceptual resources as possible and to consider charge stabilization and bond strength. Furthermore, these findings add to previous studies that reported that students considered charges and induction effects itself (Anzovino and Bretz, 2016) or charges and electronegativity itself (Popova and Bretz, 2018; Caspari and Graulich, 2019), and they contribute to a previous study that reported that students considered size itself and orbitals (Popova and Bretz, 2018).

Moreover, most students activated developed lines of reasoning for induction effects and electronegativity and also undeveloped lines of reasoning for size. These students discarded their undeveloped lines of reasoning from their explanations, demonstrating univariate reasoning. Some students activated undeveloped lines of reasoning for size and also undeveloped lines of reasoning for electronegativity. These students discarded their lines of reasoning for electronegativity from their explanations, demonstrating univariate reasoning. Together, these findings suggest encouraging students to activate and develop lines of reasoning as much as possible and to weigh lines of reasoning, either based on development or based on the frame of the reactions or the organic chemistry course.

Supporting this suggestion, one student incorporated developed lines of reasoning for induction effects and electronegativity, and this student discarded an undeveloped line of reasoning for steric effects. They linked the developed lines of reasoning, demonstrating multivariate reasoning. Additionally, demonstrating multivariate reasoning, one student incorporated a developed line of reasoning for electronegativity and an undeveloped line of reasoning for steric effects, and one student incorporated developed lines of reasoning for steric effects and size. This infrequency adds to a previous study that reported multivariate reasoning often being missing (Kraft et al., 2010) and contributes to a previous recommendation that multivariate reasoning needs to be scaffolded (Caspari and Graulich, 2019).

However, countering this suggestion, one student activated undeveloped lines of reasoning for resonance effects and size. They doubted their own weighing and could not proceed. Without resources outside of the case-comparison task or the student themself, activating more conceptual resources would not have helped their weighing, and a previous study reported that activating more conceptual resources has not ensured weighing (Watts et al., 2021). These findings suggest that some ways of weighing (i.e., weighing either based on development or based on the frame) require resources that students already have (e.g., their knowledge of and their experiences with substitution reactions, case comparisons, organic chemistry, etc.); however, these findings suggest that other ways of weighing (i.e., weighing with finding a flaw) must exist and would require conceptual resources that instructors could provide (e.g., the data from experiments). Research is required to explore these ways of weighing and students’ decisions during the weighing process.

Grove and Bretz (2010) reported that the level of epistemological development that most first- and second-semester organic chemistry students had (i.e., dualistic thinking) and the level of epistemological sophistication that organic chemistry requires (i.e., multiplistic thinking) differed. They recommended that this epistemological dissonance catalyse and support students’ epistemological development. Thus, supporting students in engaging in multivariate reasoning and activating lines of reasoning, researchers created a case-comparison task that scaffolded collecting multiple concepts (Caspari and Graulich, 2019; Kranz et al., 2022). Similarly, supporting students in weighing lines of reasoning, researchers created a task that triggered weighing concepts (Lieber and Graulich, 2020, 2021). However, Lieber and Graulich (2020) reported that students might profit from peer discussion in addition to the task in order to deepen their weighing and reflection. Additional research is required to implement case-comparison tasks in the classroom and explore how social resources could support students’ weighing.

Additionally, the findings of this study provide implications for practice. Instructors could develop students’ explanations by providing links (e.g., bond polarization, bond strength, and charge stabilization) and by asking questions along the path of the study's lines of reasoning. Notably, students activated different lines of reasoning. One student's line of reasoning could provide the links for another student's line of reasoning. Peers could be an outside, social resource, so a case-comparison task would be an appropriate in-class activity for pairs or small groups. These collaborative discussions could provide opportunities for students to practice weighing their and others lines of reasoning.

Limitations

Our study's limitations stem from its data collection and interview design. We recruited students on a voluntary basis, resulting in a self-selecting bias, and we conducted eleven interviews, potentially resulting in a sampling bias. These interviews afforded a deep, rich exploration of students’ activation of resources, especially of conceptual resources, and their lines of reasoning. However, more resources could be activated than we reported, and more lines of reasoning could be activated than we reported, as those resources and lines of reasoning potentially were not demonstrated. The interview protocol captured (and was designed to capture) students’ activation of conceptual resources and lines of reasoning. While students’ responses suggested their activation of epistemological resources, the interview protocol only captured their verbalizations of the “importance” and “significance” of particular conceptual resources and lines of reasoning. For this reason, it was challenging to capture the weighing process (i.e., how and why students were weighing). We believe that students’ decisions in and ways of weighing would be valuable for future research to capture, analyse, and report. For a deeper, richer exploration of not only students’ activation but also their frame, future interview protocols could ask questions that encourage students to verbalize their weighing process (e.g., “How do you know that?” and “Why is this concept more important than that concept?”), and future research could follow the change in frame through a longitudinal study. Furthermore, as a final limitation to note, we interviewed students with a single case comparison at a single institution. Therefore, future research is required to evaluate the case comparison's transferability and our claims’ generalizability.

Author contributions

All authors contributed. IZ and FMW contributed to the conceptualization – the data collection, the data analysis, and the presentation – and the writing of this study. DK and NG contributed to the methods – the task and interview design – of this study. GVS contributed to the revising of this study. The manuscript was written by IZ, with extensive, valuable feedback from FMW, DK, NG, and GVS. All authors read and approved the manuscript.

Data availability

No shareable primary research results, software or code have been included and no new shareable data were generated or analysed as part of this study.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

GVS and IZ wish to thank the National Science Foundation Graduate Research Fellowship Program for funding (000884418). NG and DK wish to thank the German Research Foundation Deutsche Forschungsgemeinschaft for funding (446349713). Additionally, the authors wish to thank the organic chemistry students for participating as well as Brian J. Curtis and Shultz Group member Rebecca C. Fantone for providing feedback on our manuscript.

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