A question of pattern recognition: investigating the impact of structure variation on students’ proficiency in deciding about resonance stabilization
Irina
Braun
a,
Scott E.
Lewis
b and
Nicole
Graulich
*a
aJustus-Liebig-University Giessen, Institute of Chemistry Education, Heinrich-Buff-Ring 17, D-35392 Giessen, Germany. E-mail: nicole.graulich@didaktik.chemie.uni-giessen.de
bDepartment of Chemistry, University of South Florida, Tampa, USA
First published on 27th August 2024
Abstract
The ability to reason with representations is pivotal for successful learning in Organic Chemistry and is closely linked to representational competence. Given the visual nature of this discipline, this comprises competency in extracting and processing relevant visual information. With regard to the resonance concept, proficiency in identifying whether electron delocalization applies in a molecule is an essential prerequisite to using this concept in problem-solving. However, prior research shows that students struggle to recognize whether molecules profit from electron delocalization, and seldom use this concept in problem-solving. As it remains unclear how the variation of structural features affects students’ consideration of resonance, this quantitative study seeks to identify characteristics regarding students’ perception of electron delocalization. To this end, undergraduate students enrolled in an Organic Chemistry I course (N = 699) completed an online survey in which they had to decide on resonance stabilization for molecular structures with varying structural features. K-means cluster analysis was performed to explore patterns in students’ proficiency in discerning resonance stabilization and how they relate to other performance variables (e.g., time-on-task). The results suggest pattern recognition approaches with students’ attention being guided by singular structural features or structures’ visual similarity to familiar patterns (i.e., allylic carbocations), with less attention to implicit features.
Introduction
Much of the knowledge one acquires in Organic Chemistry relies on making sense of representations and visualizations. While one works through chapters in textbooks related to, for instance, specific reaction mechanisms or listens to instructors’ explanations, the concepts and facts encountered are usually linked to specific representations, making imperceptible processes and abstract concepts accessible to the learner (Bodner and Domin, 2000; Justi and Gilbert, 2002; Gilbert, 2005). Representations are a crucial aspect of disciplinary discourse in chemistry (Hoffmann and Laszlo, 1991; Kozma et al., 2000; Goodwin, 2008; Airey and Linder, 2009). They facilitate communication and serve as a sense-making tool in problem-solving. As such, various types of representations are used in Organic Chemistry to provide complementary information on chemical phenomena (Ainsworth, 2006; Rau et al., 2015). The SN2-reaction of 2-bromobutane with a hydroxide ion can serve as an example (Fig. 1). While the electron-pushing formalism in a mechanistic representation illustrates the processes and interactions between entities during the reaction, dash-wedge representations showcase the stereochemistry. In contrast, reaction coordinate diagrams reveal the energetic and kinetic aspects of this specific reaction type. Given that varying degrees of explicit and implicit information are encoded within representations, their processing may necessitate different cognitive operations and inferences (Cooper et al., 2012a, 2012b; Talanquer, 2022). Learners must become adept in navigating through the varying complexity of representations (e.g., a representation's granularity or iconicity) to successfully deal and reason with representations in Organic Chemistry (e.g., choose suitable representations for problem-solving dependent on their affordances and limitations) (Kozma and Russell, 1997; Kozma and Russell, 2005; Talanquer, 2022). As part of that, learners must become proficient in decoding representations and linking relevant visual cues to chemical concepts (Rau, 2018; Talanquer, 2022). Resonance, for instance, is a concept that enables reasoning about electron density distribution in a molecule. As it is closely linked to the use of different representations, one must be able to decipher these representations, e.g., connect the variation in colour in electrostatic potential maps to electron density distribution, or differentiate resonance hybrids from depictions of single resonance structures. When solving mechanistic problems in Organic Chemistry, learners usually encounter Lewis structures or skeletal formulas. To apply resonance, here, it is essential to be able to locate and recognize conjugated systems in structures in the form of different patterns (e.g., allylic positive charges, lone pairs adjacent to positive charges), all indicating the possibility of electron delocalization (Klein, 2020) (Fig. 2). | ||
| Fig. 1 Different representation types illustrate different aspects of a chemical phenomenon. | ||
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| Fig. 2 Different structural features in a molecule enable resonance to occur. | ||
Theoretical background
Sense-making skills and perceptual fluency as integral parts of representational competence
In general, successfully engaging with and using representations is governed by two broad, interrelated representational competencies: sense-making skills and perceptual fluency (Kellman and Massey, 2013; Rau, 2018). Sense-making skills refer to one's conceptual and procedural competencies in terms of a given representation. This involves, for instance, the knowledge and competency to connect or map visual features in representations to chemical principles and concepts, to make inferences based on representations, to explain the connections or differences between representations, and to choose particular representations for a specific purpose (Kozma and Russell, 2005; Rau, 2018; Talanquer, 2022). Thus, these skills pertain to one's knowledge of representations that can be explicitly verbally expressed (Rau, 2017).Besides sense-making skills, fluency in decoding representations is also crucial for learning with representations. Hence, perceptual fluency builds another essential part of representational competence (Rau, 2018). It comprises the ability to effortlessly and quickly perceive and selectively attach meaning to relevant visual cues across varying representations as a result of experience-induced perceptual learning (Gibson, 2000; Kellman and Massey, 2013; Rau et al., 2015). This competency refers to one's fluency in processing visual information in a specific type of representation (e.g., recognizing patterns), one's use of representations to solve tasks (e.g., distinguishing relevant from irrelevant visual features in a representation for further cognitive processing), and one's ability to automatically detect connections across different (types of) representations (e.g., deciding at a glance whether two representations show the same or different entities) (Gibson, 2000; Kellman et al., 2008; Airey and Linder, 2009; Koedinger et al., 2012; Kellman and Massey, 2013; Rau, 2018). Unlike sense-making skills, which are acquired via explicit instruction such as (self-)explanations (Koedinger et al., 2012; Rau, 2017), gaining fluency in perception undergoes a non-verbal, inductive process enhanced by extensive practice and exposure to representations in order to develop sensitivity to relevant perceptual features in a representation (Richman et al., 1996; Koedinger et al., 2012; Kellman and Massey, 2013). In fact, research across different disciplines has shown that the perception of representations distinguishes experts from novices. Experts are able to pick up relevant patterns in representations and abstract relationships which are invisible to novices (e.g., Chi et al., 1981; Richman et al., 1996; Kellman and Garrigan, 2009; Gegenfurtner et al., 2011; Kellman and Massey, 2013; Stieff et al., 2020; Connor et al., 2021). Being efficient in discerning patterns and extracting relevant information involves increased attentional filtering and automaticity in selecting meaningful features, which results in encoding visual information in the form of larger perceptual chunks, eventually decreasing cognitive load and freeing up cognitive capacity (Kellman and Garrigan, 2009; Rau et al., 2015; Stieff et al., 2020). This allows one to recognize familiar cases and categorize new instances with more ease, and to engage in higher-order conceptual reasoning such as solving more complex and creative problems or enabling more parallel processing (Richman et al., 1996; Goldstone and Barsalou, 1998; Kellman et al., 2008; Kellman and Garrigan, 2009; Kellman and Massey, 2013). Perceptual fluency is not limited to perceiving low-level sensory features in a representation (e.g., discerning a certain functional group in a molecule), but also extends to detecting high-level, deeper structural relations within a given problem (e.g., perceiving the possibility of reaction pathways given the arrangement of different entities in a system) (Kellman et al., 2008; Kellman and Massey, 2013).
Developing proficiency in representational competence
Even though sense-making skills and perceptual fluency have built separate lines of research for years (Rau, 2017), perception and cognition are closely related (Goldstone and Barsalou, 1998; Wu et al., 2001; Kellman et al., 2010; Kellman and Massey, 2013). More specifically, with regard to representational competence in chemistry, the different skills discussed by Kozma and Russell (2005) involve both sense-making skills and perceptual fluency. For example, to translate representations (e.g., draw different resonance structures), one must not only know the conventions for different representations but must also perceive specific, relevant cues and patterns in the starting representation (e.g., identifying the conjugated system) to subsequently generate a corresponding representation. Consequently, besides conceptual knowledge about specific representations, fluency in extracting relevant information builds a crucial aspect underlying reasoning with representations (Kozma and Russell, 2005).It becomes apparent that the interplay of sense-making skills and perceptual fluency characterizes proficiency in representational competence. It is not only crucial to have conceptual knowledge about a representation, but also necessary for this knowledge to be readily accessible in order to be flexibly applied across varying contexts. Given their mutually dependent character, it is not possible to characterize proficiency only in terms of sense-making skills or perceptual fluency. When reasoning with representations, it is important to be able to perceive relevant features in a representation in order to activate corresponding conceptual knowledge (DiSessa et al., 2016); however, prior conceptual knowledge is required to attend to these features. Hence, they rather build integrated skills that develop on a continuum when learning chemistry and, furthermore, may be context-dependent. For instance, when learners have a sound conceptual understanding of a representation and have often encountered it in their courses, they can quickly make sense of the representation. In contrast, when learners have been introduced to a novel representation, they have not gained perceptual fluency yet; instead, their reasoning about this newly encountered representation rather relies on sense-making, requiring more time to come to a valid conclusion (e.g., by explicitly thinking about the meaning of the representational features). Therefore, perceptual fluency (indicated by the time to answer tasks correctly) does not suffice to measure learners’ developing representational proficiency, especially at the introductory level of Organic Chemistry, where novices are introduced to a number of new representation types (Anderson and Bodner, 2008). Instead, one can assume that the interplay of sense-making skills and perceptual fluency may increase one's performance (i.e., learners’ success in correctly answering tasks). Consequently, learners’ performance scores across different tasks may reflect their developing proficiency in representational competence more adequately.
Developing proficiency in using different representations requires learners’ repeated use and exposure to different types of representations when learning chemistry. However, traditional instruction often emphasizes learning facts and procedures, while the acquisition of perceptual fluency usually takes a minor, implicit role in teaching (Anderson and Bodner, 2008; Kellman et al., 2008; Kellman and Garrigan, 2009). As a result, learners gain relevant knowledge about concepts or reactions but may not be able to successfully use and apply it (Wise et al., 2000; Kellman et al., 2010). Due to the tacit process of becoming perceptually fluent, beginners might face slow visual processing and cognitive overload when dealing with representations, eventually leading to superficial interpretations and a strong focus on salient, familiar features (Ealy and Hermanson, 2006; Anderson and Bodner, 2008; Hinze et al., 2013). This may cause difficulties in extracting relevant information when interpreting representations.
Students’ challenges in the extraction of resonance-related information
Throughout their Organic Chemistry courses, learners are introduced to a number of new representations. Despite unfamiliarity, they are expected to use these representations to learn about novel chemistry concepts (Rau, 2017). As a result, identifying relevant structural features and activating and integrating respective conceptual knowledge may be difficult for beginners in Organic Chemistry. This becomes even more challenging as representations might be used inconsistently and without explicit instructional training (Wise et al., 2000; Graulich, 2015; Baldwin and Orgill, 2019; Patron et al., 2021; Talanquer, 2022). Abundant literature in chemical education research reports that learners are often overwhelmed by this discipline's visual language and experience difficulties in extracting relevant information in representations, eventually hindering their problem-solving (e.g., Keig and Rubba, 1993; Wu and Shah, 2004; Bhattacharyya and Bodner, 2005; Anderson and Bodner, 2008; Strickland et al., 2010; Grove et al., 2012; Anzovino and Bretz, 2016). This is problematic as the fluent extraction of relevant information builds the basis for reasoning with and learning of domain knowledge (DiSessa et al., 2016). Concerning the resonance concept, in particular, proficiency in identifying whether electron delocalization occurs in a molecule builds an essential prerequisite to successfully apply this concept in problem-solving (e.g., to draw reasonable resonance structures, to approximate the geometry of a molecule or to identify electrophilic or nucleophilic sites in a molecule to predict reaction pathways) (Carle and Flynn, 2020). However, several studies have shown that students face challenges while deciding if resonance applies, resulting in a scarce integration of this concept in their reasoning processes (Carle et al., 2020; Finkenstaedt-Quinn et al., 2020; Petterson et al., 2020; Braun et al., 2022). In this regard, it has also been shown that students struggle to identify the correct place to start the electron movement, focus on unrelated structural features, or do not consider the octet rule or hybridization when generating resonance structures (Betancourt-Pérez et al., 2010; Finkenstaedt-Quinn et al., 2020; Petterson et al., 2020; Braun et al., 2022; Tetschner and Nedungadi, 2023). However, the structures’ geometry, the saliency, and the explicitness of the given structural features (i.e., lone pairs, hetero atoms) seem to influence whether learners can recognize and apply the resonance concept correctly, and how they distribute their visual attention to the structures (Carle et al., 2020; Finkenstaedt-Quinn et al., 2020; Braun et al., 2022; Farheen et al., 2024). Despite these exploratory results, it remains unknown how the variation of structural features affects students’ consideration of resonance. While prior studies have identified general difficulties and pointed to potential influencing factors, the impact of varying structural features on students’ ability to recognize and apply resonance has not been explored yet. Specifically, how differences in structural features make the recognition of resonance more difficult or what considerations guide students’ resonance-related information extraction have not been systematically examined in previous studies. Such insights, however, are valuable in informing teaching practices and better supporting students in their learning process.Research questions
Successfully learning Organic Chemistry necessitates a significant degree of proficiency in attending to and interpreting relevant features in representations, eventually affecting concept learning and use. Pertaining to this, learners’ ability to perceive structural features indicating the possibility of electron delocalization builds the basis for successfully using resonance in problem-solving (Braun and Graulich, 2024). Even though literature provides insights into students’ challenges in drawing and using resonance structures in problem-solving, it remains unclear how the variation of structural features impacts students’ decision-making on resonance stabilization in molecules (e.g., to which extent they pay attention to explicit and implicit structural properties when considering resonance), and how students’ developing proficiency in resonance-related considerations is related to other performance metrics such as prior knowledge and time-on-task. To this end, the quantitative study presented herein is guided by the following research questions:1. How do different combinations of structural features influence students’ ability to discern resonance stabilization in molecules?
2. What trends regarding students’ proficiency in making decisions on resonance stabilization in molecular structures emerge?
3. How do the emerging trends relate to other performance variables (i.e., time-on-task, prior knowledge, cognitive load)?
Methods
Participants and research setting
The study was conducted at a large, research-intensive university in the southeastern region of the United States. The study population comprised first-semester Organic Chemistry students enrolled across five classes, taught by three different instructors using a common syllabus and textbook (Klein, 2020). Through lectures and discussion sections, the course covered fundamental concepts of structure, bonding, reactivity, and mechanisms of organic chemistry. All participants were informed about their rights and data handling beforehand. The students were recruited voluntarily via e-mail announcements and had a week to take the online survey (described below). As an incentive, the students received extra credit worth approximately 0.4% of their course grade upon survey completion, irrespective of consent to the study or the correctness of the provided answers to the tasks. Of 899 students enrolled in the Organic Chemistry I course, 699 students completed the survey giving informed consent for their data being anonymously analysed and published by the research team. As the survey was conducted near the end of the course, it followed the presentation of the resonance concept and the construction of resonance structures, which were covered within the first weeks of the course. Altogether, 1.5 lectures were delivered on the topic of resonance. The instruction followed the presentation of the concept in the textbook (Klein, 2020) and targeted different learning objectives. Students should be able to explain resonance stabilization and electron delocalization, use curved arrows to construct resonance structures, compare the significance of different resonance structures, construct resonance hybrids, and distinguish between delocalized and localized lone pairs in structures. Students were also expected to recognize the five resonance patterns described in the textbook (e.g., lone pair adjacent to a carbocation) (Klein, 2020). Clicker questions during the lectures, virtual homework questions, and exam questions were used to assess whether students met the learning objectives. Furthermore, the Klein textbook offered students different scaffolded worked examples (i.e., with an indication of step-by-step strategies) and practice problems for the various learning objectives (e.g., how to draw significant resonance structures) (Klein, 2020).Ethical considerations
Students were provided a written consent form detailing the data processing prior to study participation, and it was clarified to the students that they had the right to opt out from the survey at any time. No identifying information was collected that allowed participants to re-identify.Research instrument and data collection
Data was collected via an online survey implemented in Qualtrics, which consisted of three parts (Fig. 3). The first part assessed students’ conceptual prior knowledge of resonance. Based on the resonance-related learning outcomes described by Carle and Flynn (2020), students first self-assessed their confidence in dealing with different aspects around resonance (e.g., “I can identify whether resonance is possible in a molecule”, or “I can assess the thermodynamic stability of molecules based on their structural formulas”) on a five-point Likert scale. Besides their self-reported knowledge, the students also solved different designed tasks to assess their understanding and use of resonance in concrete tasks (Fig. 3, part I). The tasks were informed by both Carle and Flynn's (2020) described learning outcomes on resonance, and conceptual difficulties regarding resonance reported in previous research studies (Taber, 2002; Kim et al., 2019; Xue and Stains, 2020; Brandfonbrener et al., 2021; Tetschner and Nedungadi, 2023; Braun and Graulich, 2024). For instance, students had to choose the energetically most favourable structural formula among different resonance structures of dinitrogen oxide, had to indicate the correct product of a reaction using the electron-pushing formalism (Flynn and Featherstone, 2017), or had to mark in a multiple-choice task all correct statements regarding resonance (cf. Appendix for the complete list of tasks). When designing the tasks, we avoided using structures similar to those in the subsequent survey part to avoid priming the students. | ||
| Fig. 3 Survey design with exemplary items for every survey part. | ||
In the second part of the study (Fig. 3, part II), students were asked to decide whether a molecular structure profits from resonance stabilization. By deciding on resonance stabilization, students had to decide on the possibility of reasonable resonance structures. In some molecules, delocalization was theoretically possible but would result in energetically unfavourable resonance structures and would not contribute to charge stabilization. Applying resonance in these cases would not be reasonable. Following research on perceptual fluency (Kellman and Massey, 2013), the students were asked to decide whether resonance stabilization applies as intuitively as possible in order to avoid overthinking and consulting textbooks. To prevent fatigue effects, students were presented a subset of 37 molecules, one at a time, that were randomly selected from a database of 72 molecules. The first two molecules were identical for all students. When deciding on resonance stabilization, students could also express uncertainty by choosing among the answers yes; probably yes; probably no; or no. During this survey part, student log data was collected comprising their time spent on each item and the click count when answering the questions.
Finally, the third part of the survey (Fig. 3, part III) asked the participants to rate their perceived cognitive load on a seven-point Likert scale for different items regarding the second survey part. Specifically, the instrument developed by Klepsch et al. (2017) has been adapted to measure students’ intrinsic, extraneous, and germane cognitive load. For instance, students had to decide to which extent they agreed that the display of the molecules was inconvenient for identifying resonance. In the end, the students were given open-ended questions to report on how their task-solving approach changed during the survey completion and to provide feedback. Due to the low response rate for the open-ended questions, they remain unconsidered in the following analysis. The students were asked to answer the entire survey without external help or any additional tools (e.g., class material, textbooks). The median duration for completing the whole survey was 14 minutes and 29 seconds.
Item design
In the second part of the survey, the students had to decide whether electron delocalization (i.e., resonance) contributes to charge stabilization for different molecular structures. Based on previous research on students’ generation and understanding of structural representations, particularly involving resonance, the design of the molecular structures followed a systematic variation of different structural parameters, which could affect students’ perception of resonance. This comprises the degree of explicitness of given information, the structures’ complexity and geometry, and familiarity of structural features (Kraft et al., 2010; DeFever et al., 2015; Graulich and Bhattacharyya, 2017; Graulich et al., 2019; Carle et al., 2020; Finkenstaedt-Quinn et al., 2020; Braun et al., 2022; Talanquer, 2022). Specifically, in this study, the molecules differed in the indication of lone pairs of electrons, the explicit indication of bonds to hydrogen atoms, the distance of the charge to the conjugated system (i.e., γ-, β-, or α-position), the type of charge (i.e., positive or negative charge), the structure's carbon backbone (branched, linear, or cyclic structures), and the presence and familiarity of hetero atoms. For instance, 20 of the 72 items had a negative charge. Furthermore, some molecules required an explicit focus on additional aspects such as atoms’ hybridization or violation of the octet rule in case of electron delocalization. In general, all items had variations of the abovementioned features, as indicated in the examples in Fig. 4. | ||
| Fig. 4 Examples of structural variation for molecular structures. | ||
Data analysis
Selection of considered structural features
To examine students’ proficiency in dealing with different structural features when deciding on resonance stabilization, some decisions regarding the subsequent analysis (see section below) were made. Given that a molecule always fulfils multiple structural features (cf.Fig. 4), we simplified the data and reduced the number of initially encountered structural features to consider four structural characteristics that allowed the formation of distinct, non-overlapping combinations of structural features. While the integration of different structural parameters in the item design (see section Item design) permitted a variation of the molecular structures that might have affected students’ overall decoding of the representations, previous research findings indicate that learners tend to focus on the most salient features in a representation when making decisions (Graulich et al., 2019). Accordingly, we focused our analysis on rather salient, most meaningful structural characteristics that are directly related to electron delocalization, need to be considered, and, thus, might impact students’ ability to discern resonance in a molecule: the distance of the charge to the conjugated system (i.e., β- or α-position of the charge to the conjugated system, or the charge being on a hetero atom), the presence (or absence) of hetero atoms (i.e., lack of hetero atoms indicated by the label “carbon atoms”, or presence of hetero atoms, labelled as “hetero atom”), the type of charge (i.e., positive or negative charge), and additional implicit aspects underlying the presence of conjugated systems and the plausibility of resulting resonance structures (e.g., electronegativity, hybridization). Combining pairs of these abovementioned structural characteristics resulted in six categories that are exclusive in nature (i.e., each item falls into one of these categories): 1. β-position of charge (20 items), 2. carbon atoms & positive charge (i.e., allylic carbocations) (7 items), 3. hetero atom & positive charge (16 items), 4. hetero atom & negative charge (7 items), 5. hetero atom & positive charge & implicit considerations (7 items), and 6. positive charge on hetero atom (8 items) (cf.Fig. 5 for representative examples). Apart from the first and last category, the charge is adjacent to a hetero atom or double-bonded carbon atom for the remaining categories (α-position of the charge). As students were shown approximately 50% of all the items, some other possible combinations of structural features (e.g., carbon atoms & negative charge, γ-position of the charge) were discarded from further analysis as less than five survey items would be assigned to these categories. Keeping these categories would mean that most students only saw between 1 and 2 items, which would distort obtained results in terms of students’ performance on these variables. This would lead to extreme performance values (described in the section below). Consequently, of the initial 72 molecular structures, seven items were excluded from further analysis, overall resulting in 65 items included for cluster analysis (see section below). | ||
| Fig. 5 Item examples for the different clustering variables. Dark numbers indicate the possibility of resonance stabilization, whereas molecular structures with light numbers do not profit from electron delocalization. | ||
Cluster analysis
Cluster analysis was performed to uncover patterns and describe characteristics of students’ proficiency in recognizing resonance across different molecular structures. Cluster analysis is an exploratory statistical technique used to organize larger datasets by discovering meaningful groupings of objects (i.e., clusters) based on their similarity in clustering variables (Everitt et al., 2011). Irrespective of the specific clustering algorithm, the data is divided in a manner that objects similar in their characteristics are assigned to the same cluster. Objects within one cluster should, therefore, be as homogeneous as possible (i.e., internal cohesion) but as distinct as possible from objects in other clusters (i.e., external isolation) (Everitt et al., 2011; Sarstedt and Mooi, 2014). Identifying a smaller number of groupings allows a concise description of patterns in the data, which can serve as a basis for further interpretation and prediction (Everitt et al., 2011).In the study presented herein, K-means clustering served as a clustering approach using Euclidean distance as a measure of distance. Unlike hierarchical clustering approaches, K-means clustering is robust to outliers and applies to larger sample sizes (above 500) (Sarstedt and Mooi, 2014). K-means is a non-hierarchical, partitioning cluster algorithm which iteratively relocates each object by minimizing their distance to cluster centroids (i.e., grouping means). More specifically, the clustering process begins by dividing all objects simultaneously into a pre-specified number of clusters with a randomly selected initial cluster centre for each cluster. In the next steps, the cluster centroids are recalculated based on the objects forming the cluster, and the objects are successively reassigned to the closest cluster centroid. Objects can shift from one cluster to another during the clustering process to minimize the distance to the nearest cluster centroid. This process of cluster re-evaluation and optimization repeats until the cluster solution is stable, i.e., the within-cluster variation is minimized, and the affiliation of objects to clusters does not change (Clatworthy et al., 2005; Everitt et al., 2011; Sarstedt and Mooi, 2014). Different steps were taken for the K-means clustering which are described in the following. All statistical analyses were conducted in SPSS version 29.0.
| (Combination of) structural features | Mean (SD)a | Skewnessb | Kurtosisc | Number of outliersd |
|---|---|---|---|---|
| a N = 681. b Skewness standard error for this sample is 0.09. c Kurtosis standard error for this sample is 0.19. d More than two standard deviations from the mean. | ||||
| β-Position of charge | 65.34 (25.61) | −0.42 | −0.69 | 22 |
| Carbon atoms & positive charge | 75.22 (28.44) | −1.03 | 0.35 | 35 |
| Hetero atom & positive charge | 55.46 (27.28) | −0.09 | −0.82 | 26 |
| Hetero atom & negative charge | 54.37 (32.23) | −0.18 | −0.99 | 0 |
| Positive charge on hetero atom | 43.55 (28.82) | 0.20 | −0.68 | 0 |
Results
Students’ overall scores for the different structural feature categories
Descriptive statistics for the different categories were calculated and are displayed in Table 1 to describe students’ overall scores in recognizing resonance stabilization in molecular structures for each structural feature. The relatively large standard deviations for all variables suggest a wide range of students’ scores in answering the different items. Moreover, the variables exhibit a negative kurtosis, indicating a flatter data distribution than a normal distribution apart from the variable carbon atoms & positive charge (rather peaked distribution of the scores due to positive kurtosis). Regarding skewness, while the items belonging to the variable positive charge on hetero atom are positively skewed, i.e., have a more pronounced distribution of the data toward the lower end of the possible value range, students’ scores on the other variables show a negative skewness, thereby a higher rate of scores being clustered toward the higher end of the performance range with the tail pointing towards the lower end of the distribution range.The mean values across the study population reveal that students scored highest for items belonging to the structural feature carbon atoms & positive charge (75%). Students also scored relatively high on items in β-position of charge (65%); therefore, they could relatively well decide on non-conjugated systems. Students’ overall score on items involving hetero atoms was lower where students answered approximately half of the items correctly on average (55% for positive charge and 54% for negative charge). When additional implicit aspects (i.e., hybridization, violation of the octet rule) had to be clearly considered for a correct decision on the stabilization of a positive charge (i.e., positive charge on hetero atom), their score was relatively low at 44%. To test the statistical significance of these observed differences in students’ success rates, a repeated-measures analysis of variance (ANOVA) was conducted to compare the overall mean scores of the clustering variables. As the Mauchly-test indicates a violation of the assumption of sphericity (W = 0.89, X2 (9) = 82.65, p < 0.001), the Huynh–Feldt correction was applied. The repeated-measures ANOVA shows that the overall scores for the different variables differ significantly with a large effect size [F(3.82, 2599.75) = 123.37, p < 0.001, η2 = 0.15]. Follow-up paired-sample t-tests with a Bonferroni-adjusted α-level set at 0.005 as criterion for significance yielded significant differences (p < 0.001) between all categories except for the comparison of hetero atom & positive charge and hetero atom & negative charge (Table 2).
| Comparison | Mean difference | SE | t(680) | p | d | Effect sizeb |
|---|---|---|---|---|---|---|
| a Bonferroni-adjusted significance level at 0.005. b Effect size according to Cohen (1992). | ||||||
| Carbon atoms & positive charge – β-position of charge | 9.88 | 1.34 | 7.39 | <0.001 | 0.28 | Small |
| β-Position of charge – hetero atom & positive charge | 9.88 | 1.52 | 6.52 | <0.001 | 0.25 | Small |
| β-Position of charge – hetero atom & negative charge | 10.97 | 1.50 | 7.29 | <0.001 | 0.28 | Small |
| β-Position of charge – positive charge on hetero atom | 21.79 | 1.54 | 14.18 | <0.001 | 0.54 | Medium |
| Carbon atoms & positive charge – hetero atom & positive charge | 19.76 | 1.35 | 14.67 | <0.001 | 0.56 | Medium |
| Carbon atoms & positive charge – hetero atom & negative charge | 20.86 | 1.62 | 12.91 | <0.001 | 0.50 | Medium |
| Carbon atoms & positive charge – positive charge on hetero atom | 31.67 | 1.60 | 19.76 | <0.001 | 0.76 | Medium–large |
| Hetero atom & positive charge – hetero atom & negative charge | 1.09 | 1.56 | 0.70 | 0.48 | 0.03 | — |
| Hetero atom & positive charge – positive charge on hetero atom | 11.91 | 1.52 | 7.86 | <0.001 | 0.30 | Small |
| Hetero atom & negative charge – positive charge on hetero atom | 10.82 | 1.70 | 6.35 | <0.001 | 0.24 | Small |
Cluster solution
K-means cluster analysis yielded a five-cluster solution reported in Table 3. It displays the means and standard deviations for each group's scores for each clustering variable and the distribution of students in each cluster. Finding the standard deviations within each cluster generally lower than the overall standard deviation supports the internal cohesion of the clusters.
|
Table 3 shows that each cluster can be characterized by the average scores on the different cluster variables. While cluster I shows rather moderate scores for all combinations of structural features not exceeding 52% on any variable, cluster II is characterized by relatively high scores for the variables β-position of charge (69%), carbon atoms & positive charge (80%), and positive charge on hetero atom (66%). In contrast, they score substantially lower on the remaining variables. Cluster III achieves even higher scores on the variables β-position of charge (80%) and carbon atoms & positive charge (81%), and also has a high average for the variable hetero atom & negative charge (79%). Cluster IV scores high on the variables carbon atoms & positive charge (89%) as well as hetero atom & positive charge (76%), but shows, compared to clusters II and III, a lower score for the variable β-position of charge (63%) and low scores for the remaining cluster variables (<31%). Finally, similar to cluster IV, cluster V shows a lower average for the variable β-position of charge (62%). While students in this cluster score well on the variables carbon atoms & positive charge, hetero atom & positive charge, and hetero atom & negative charge (>75%), average scores for positive charge on hetero atom were lower (62%). These cluster-specific score differences permit the inference of different profiles regarding students’ proficiency in dealing with structural features. They are portrayed in detail in the Discussion section.
Relationship to other variables
Cluster assignments were related to other external variables as evidence of external validity; that is, the clusters represent meaningful groupings of students. The external variables investigated were the average time spent on the items, students’ prior conceptual knowledge, students’ confidence, and their perceived cognitive load when solving the tasks. The expectation is that higher performance on the resonance tasks will be associated with higher prior conceptual knowledge, higher confidence, and lower perceived cognitive load. Furthermore, informed by previous eye-tracking research contrasting decoding behaviours of experts and novices (e.g., Gegenfurtner et al., 2011; Lindner et al., 2014), one can assume that clusters having more proficiency in discerning resonance stabilization will be associated with less time spent on the items. Inferential statistics were used to examine the extent of differences among the clusters on these external variables match these expected relationships.| Cluster | I | II | III | IV | V | Overall |
|---|---|---|---|---|---|---|
| Prior knowledge score | 7.51 (2.23) | 8.09 (2.04) | 8.05 (2.04) | 8.53 (2.03) | 8.50 (2.13) | 8.17 (2.12) |
| Cluster | Identify resonance in molecules | Assess thermodynamic stability of molecules | Determine atoms’ hybridization | Draw curved electron arrows | Define the resonance concept | Assess the influence of electron delocalization on molecule stability |
|---|---|---|---|---|---|---|
| I | 3.78 (0.99) | 3.42 (1.11) | 3.86 (1.07) | 4.01 (0.94) | 3.76 (1.02) | 3.55 (1.11) |
| II | 3.91 (1.02) | 3.41 (1.08) | 3.98 (1.07) | 4.20 (0.97) | 3.95 (1.05) | 3.68 (1.06) |
| III | 4.15 (0.86) | 3.56 (1.00) | 4.03 (1.06) | 4.29 (0.83) | 4.02 (0.93) | 3.80 (1.03) |
| IV | 4.12 (0.86) | 3.52 (1.06) | 4.01 (1.06) | 4.33 (0.84) | 4.03 (0.97) | 3.78 (1.01) |
| V | 4.01 (0.94) | 3.62 (1.05) | 3.98 (1.04) | 4.28 (0.96) | 4.07 (0.96) | 3.75 (1.07) |
| Overall | 4.01 (0.94) | 3.51 (1.06) | 3.98 (1.06) | 4.23 (0.91) | 3.98 (0.99) | 3.72 (1.05) |
| Cluster | I | II | III | IV | V | Overall |
|---|---|---|---|---|---|---|
| Time on item | 5.15 (5.46) | 6.64 (5.07) | 5.95 (3.55) | 7.67 (6.83) | 8.24 (6.59) | 6.82 (5.74) |
| Cluster | Intrinsic cognitive load | Extraneous cognitive load | Germane cognitive load | Confidence | |||
|---|---|---|---|---|---|---|---|
| Difficult to recognize resonance | Molecules were complex | Problem-solving process was complex | Inconvenient display of molecules | Exhausting to find important information | Effort in task solving | ||
| I | 4.46 (1.46) | 4.29 (1.54) | 4.23 (1.45) | 3.58 (1.73) | 3.88 (1.59) | 4.86 (1.67) | 3.22 (1.64) |
| II | 4.42 (1.51) | 4.48 (1.63) | 4.29 (1.53) | 3.48 (1.86) | 3.90 (1.72) | 4.72 (1.45) | 2.90 (1.41) |
| III | 4.44 (1.30) | 4.30 (1.37) | 3.99 (1.44) | 3.12 (1.68) | 3.49 (1.62) | 4.55 (1.35) | 3.12 (1.26) |
| IV | 4.44 (1.31) | 4.12 (1.44) | 3.69 (1.32) | 3.19 (1.61) | 3.57 (1.50) | 4.42 (1.47) | 3.03 (1.25) |
| V | 4.44 (1.47) | 4.34 (1.63) | 4.15 (1.62) | 3.35 (1.80) | 3.64 (1.76) | 4.58 (1.38) | 3.29 (1.42) |
| Overall | 4.44 (1.40) | 4.30 (1.52) | 4.06 (1.49) | 3.33 (1.74) | 3.68 (1.65) | 4.61 (1.46) | 3.11 (1.39) |
Discussion
RQ 1: How do different combinations of structural features influence students’ ability to discern resonance stabilization in molecules?
A closer inspection of the variables’ mean values (cf.Table 1) indicates that different structural features make it significantly easier or more challenging for the students to correctly decide on resonance stabilization. While students across the entire study cohort achieved high scores for items belonging to the variable carbon atoms & positive charge (i.e., allylic carbocations) (75%) and were also relatively proficient in deciding on no application of resonance stabilization in molecular structures bearing a charge in β-position to the conjugated system (65%), items involving hetero atoms related to lower scores (<56%). If, additionally, implicit aspects such as the violation of the octet rule had to be clearly considered to correctly decide on resonance stabilization, students’ scores decreased even more (44%).An analytic consideration of the molecular structures’ characteristics and affordances could explain this varying performance. Given that items belonging to the category β-position of charge do not represent conjugated systems (cf.Fig. 5, items 1–4), resonance stabilization is not possible here. To answer these items correctly, one must have basic knowledge of conjugated systems, i.e., that they represent arrays of aligning p-orbitals, resulting in π-bonding overlap along the whole system and enabling electron delocalization. Consequently, when the chain is interrupted (i.e., positions of carbon atoms with sp3-hybridization), no conjugated system is possible. With regard to the molecular structures and the processing of structural features, one must be proficient in estimating the distance of the charge, i.e., knowing that the charge must be in direct adjacency to an electron-donating or -deficient source.
While one needs to be able to differentiate between a conjugated system and a non-conjugated system by analysing a broader part of the structure, items with the charge being in α-position need the learner to inspect the given structural features in more detail to decide on the possibility of resonance stabilization. In terms of the category carbon atoms & positive charge, items in this variable only involve allylic positive charges (cf.Fig. 5, items 5–8), which often serve as introductory examples for resonance (stabilization) (e.g., in some textbooks such as in Ogilvie et al., 2018; Klein, 2020). Allylic carbocations are also often encountered and discussed when addressing aromaticity (e.g., electrophilic aromatic substitutions). As such, students’ higher success in deciding on resonance stabilization for items belonging to the variable carbon atoms & positive charge could stem from their familiarity. By containing chains of a single type of atom (i.e., carbon atoms), they require less information processing than those molecular structures comprising atoms other than carbon and hydrogen atoms. In these cases, the number of aspects to encounter exceeds the amount of information necessary to keep in mind when dealing with cations only involving carbon atom chains (i.e., the same atom type). Logically, the more information must be processed, the more difficult the answering of items can become (Paas and van Merriënboer, 2020). Consequently, answering items that only involve carbon atoms (and hydrogen atoms) appears less demanding and easier to process.
Handling different atom types necessitates, for instance, the estimation of an atom's hybridization or the calculation of atoms’ octets, thereby requiring a closer inspection and connection of different structural cues (i.e., bonds, and lone pairs of electrons), which, possibly, need to be inferred first when not explicitly depicted (Cooper et al., 2012a, 2012b; Graulich et al., 2019). For instance, molecular structures belonging to the category hetero atom & positive charge necessitate more implicit structural considerations as all items in this variable depict single bonds adjacent to the charges (cf.Fig. 5, items 9–12). Unlike the previous category with the explicit indication of double bonds, here, learners have to reflect on the structures and possible π-bonding interactions (e.g., by explicitly paying attention to electron pairs of the hetero atom as a source for electron delocalization). Consequently, to answer these items correctly, one must master a different pattern of molecular structure (Klein, 2020).
Items in the category hetero atom & negative charge involve the depiction of double bonds, similar to the allylic charges (cf.Fig. 5, items 13–16). However, here, a different approach is necessary. First, unlike items belonging to carbon atoms & positive charge, items in this category necessitate a broader consideration of the conjugated system due to the greater abundance of delocalized π-electrons. In contrast to allylic positive charges, these items require the electron delocalization in the reverse direction, thus not in the direction of the positive charge but starting from the negative charge towards the depicted double bonds. Second, as indicated by the two curved arrows in Fig. 6, one must mentally keep track of the electron delocalization, thereby, the hetero atoms must be taken closer into account (e.g., fulfilment of the octet rule) (cf.Fig. 6). Hence, this pattern in electron delocalization is more complex than, for instance, allylic carbocations.
 | ||
| Fig. 6 Varying complexity and approaches when delocalizing a negative or positive charge adjacent to double bonds (e.g., allylic carbocation or double-bonded hetero atom). | ||
Items in the category positive charge on hetero atom require to include even more aspects when deciding on resonance stabilization. Here, one has to consider the feasibility of electron delocalization with regard to the hetero atom's properties. The protonated 1,2,3,4-tetrahydropyridine can serve as an example (Fig. 5, item 23). On a surface level, this structure resembles an allylic positive charge (cf. the variable carbon atoms & positive charge); nonetheless, electron delocalization is impossible because the nitrogen atom's octet would be exceeded. Unlike this example, the charged enamine compound (1,2,3,4-tetrahydro-6-methyl-1-(1-methylethyl)pyridine) (cf.Fig. 5, item 24) would profit from electron delocalization given the sp2-hybridization of the nitrogen atom. Altogether, these analytic considerations illustrate that the items’ inherent characteristics may account for students’ varying ability in recognizing the possibility of resonance stabilization.
Despite these overall tendencies in students’ performance on different structural features, the cluster analysis suggests that this trend does not necessarily apply to all students equally (cf.Table 3). Instead, differences in students’ proficiency to deal with varying structural features prevail. These cluster-specific characteristics will be discussed next to identify underlying patterns within the wide range of student performance scores.
RQ 2 & 3: What trends regarding students' proficiency in making decisions on resonance stabilization in molecular structures emerge and how do they relate to other performance variables (i.e., time-on-task, prior knowledge, cognitive load)?
A closer look into the groupings’ average performance scores on the various clustering variables (cf.Table 3) allows a qualitative description of emerging characteristics and difficulties within the five clusters. While cluster I does not show pronounced proficiency in any structural feature, the other four clusters are reasonably proficient in discerning no possibility of resonance stabilization with the charge being in β-position and with recognizing resonance stabilization for allylic carbocations (i.e., items belonging to the variable carbon atoms & positive charge). With regard to hetero atoms, cluster III is also proficient with the structural features hetero atom & negative charge, whereas cluster IV shows higher proficiency for hetero atom & positive charge. Cluster V is proficient in both hetero atom & positive charge and hetero atom & negative charge. This permits the inference of different profiles regarding students’ guiding principles in deciding on resonance stabilization, and to characterize students’ proficiency in handling different structural features related to resonance.Cluster I: no proficiency demonstrated
Cluster I, comprising 16% of the students (Table 3), is denoted by a score on most clustering variables that approach the chance guessing mark of 50%. The substantial deviation from chance guessing was with carbon atoms & positive charge (28%). This variable was scored the highest by the overall sample and markedly distinguished this cluster from the other clusters. It is possible that these students were enacting an alternative process for identifying resonance that led to predictions inconsistent with the canonical process or that these students were not engaging with the survey meaningfully. It is not possible to distinguish these explanations with the current data. Students in cluster I spent markedly less time on the task (5.15 seconds) compared to the other clusters, which could evidence either possibility. However, the consideration of the other external variables supports the assumption that students in cluster I might perceive difficulties in conceptualizing and, consequently, applying resonance, which might have induced a fast decision-making and chance-guessing approach. Students in cluster I show a substantially lower score on tasks targeting students’ conceptual understanding of resonance (7.51) compared to the other clusters. Moreover, even though not differing significantly, they self-report the lowest resonance-related competencies for all items among the clusters (cf.Table 5). This emerging conceptual uncertainty reflects potential difficulties in their sense-making skills (e.g., knowing how resonance can be encoded in structural features). Consequently, students might have found it harder to focus on the structural information necessary to make decisions on resonance stabilization, accounting for their lower performance in the various variables. Overall, these observed difficulties align with different studies showcasing that difficulties in understanding resonance hinder its successful application in problem-solving (e.g., Petterson et al., 2020; Brandfonbrener et al., 2021; Braun et al., 2022).Cluster II: focus on allylic positive charges
Approximately 19% of the students belong to this cluster (Table 3). It is characterized by above average scores on the variables β-position of charge (69%), carbon atoms & positive charge (80%), and positive charge on hetero atom (66%), whereas showing low scores for the remaining two variables involving hetero atoms (i.e., hetero atom & positive charge and hetero atom & negative charge) (<37%). This indicates that students within this group are proficient in discerning conjugated systems and are more adept in dealing with molecules without hetero atoms. When comparing the different characteristics with regard to the molecular structures’ features, it becomes evident that students in this cluster are guided by specific structural features when deciding on resonance stabilization. They approach the items in a visual way. More concretely, they seem to base their decision on the presence of allylic positive charges, therefore relying on one specific pattern of electron delocalization. As such, they achieve relatively high scores in identifying resonance stabilization for molecules of the variable carbon atoms & positive charge. The guiding principle of allylic positive charges might also explain students’ scores on the other variables. Half of the items belonging to the variable positive charge on hetero atom involve double-bonded hetero atoms bearing a positive charge, whereas the remaining items in this variable resemble the allylic carbocation pattern except for the presence of a hetero atom (cf.Fig. 5, items 21–24). Given the students’ relatively high proficiency with this variable, it may be that the pattern of allylic carbocation has cued students to correctly decide on resonance stabilization, either triggered by the explicit presence of a double bond next to a positive charge (i.e., deciding in favour of resonance stabilization for items such as items 22 and 24 in Fig. 5), or being irritated by the presence of a charged hetero atom adjacent to a double bond. Consequently, even though items might resemble allylic carbocations (such as items 21 and 23 in Fig. 5), it is possible that students correctly decided against resonance stabilization being bothered by the presence of a hetero atom. This suggests that students might make a difference between molecular structures involving only a carbon backbone, and structures additionally comprising hetero atoms when deciding on resonance stabilization. Although students’ strategies in handling items in this variable cannot be ultimately determined, and require further investigation, it is reasonable to assume that students base their decision-making regarding these items on structural features inherent to allylic carbocations. This assumption is further strengthened by the low scores on the other variables involving hetero atoms. While the items in the category hetero atom & positive charge comprise single bonded hetero atoms and require another pattern of electron delocalization, items belonging to hetero atom & negative charge necessitate the delocalization of electrons in the reverse direction (cf.Fig. 6), therefore making it impossible to apply the typically used resonance pattern in this cluster (i.e., delocalizing a double bond toward a positive charge). Lastly, being cued by adjacent positive charges to double bonds, students might have found it easier to estimate the distance of the charge and, therefore, to recognize conjugated systems regarding the variable β-position of charge.The emergent strategy in decision-making, focusing solely on allylic positive charges, might also stem from uncertainty. Though not differing significantly, students in this cluster indicated the lowest confidence for correctly solving the tasks (2.90/7) and rated the perceived complexity of the molecules and the problem-solving process (i.e., intrinsic cognitive load) higher than the other clusters (cf.Table 7). This suggests that students might have found it more difficult to decide on resonance stabilization and, therefore, possibly recurred to a familiar pattern of electron delocalization. As students in cluster II might have searched for the presence of allylic carbocations, they limited their attention to structural features, thereby facilitating the decision on resonance stabilization due to processing less information (Paas and van Merriënboer, 2020).
Cluster III: flexible resonance recognition involving charges adjacent to double bonds
This cluster group (22% of students, Table 3) is characterized by an even more pronounced proficiency in handling the β-position of charges (i.e., discerning conjugated systems) (80%) and dealing with allylic carbocations (i.e., carbon atoms & positive charge) (81%) than cluster II. In contrast to the previously presented clusters, students within this group also perform better on items related to the variable hetero atom & negative charge (79%), whereas with a lower score on the variable hetero atom & positive charge (37%). Among all clusters, they score lowest on the variable positive charge on hetero atom (19%). With regard to the structural properties of the molecules, it becomes evident that the students in this cluster are also guided by the presence of double bonds when deciding on resonance but are able to operate with different charges more flexibly, indicating a higher proficiency over various structural features. More specifically, most items bearing a negative charge comprise double bonds, resembling the allylic carbocations pattern. However, unlike allylic carbocations, which permit a source-to-sink – approach by delocalizing electron density towards electron-deficient centres (i.e., the positive charge) (Bhattacharyya, 2013), delocalizing a negative charge requires a different approach, with the negative charge being the starting point to delocalize electron density. As such, the delocalization of the π-electrons in the reverse direction necessitates more complex thinking (i.e., interrelated consideration of structural features, cf.Fig. 6). This reflects an important learning outcome described by Carle and Flynn (2020), as students in this cluster seem to be able to track electron delocalization. This assumption matches students’ relatively fast decision-making (5.95 seconds), suggesting that students in this cluster might show beginning fluency in dealing with molecules involving positive and negative charges adjacent to double bonds. In this regard, being able to keep track of the electrons in the molecular structure is an important learning objective. Betancourt-Pérez et al. (2010) have shown that students who master electron movement can better compare stabilities of different Lewis structures. This arising proficiency in dealing with different charges in this specific structural motive might also be leveraged by students’ perceived competence in identifying resonance in molecules (4.15/5), with a score being the highest among all clusters.Being guided by patterns involving double bonds might also explain students’ varying scores in the other variables. While the presence of charges adjacent to double bonds might facilitate the decision on electron delocalization for molecular structures belonging to the variable β-position of charge, it might be conversely responsible for students’ relatively low scores for items bearing a positive charge adjacent to a hetero atom. These molecular structures are displayed with single bonds and might cause confusion for not following the same pattern (Fig. 5, items 9–12). Interestingly, students show, among all clusters, the lowest performance in correctly answering items belonging to the variable positive charge on hetero atom, even though these items also comprise double bonds and charges. An explanation for this might be the more reflective consideration of potential electron delocalization. It might be that students have applied learnt patterns involving allylic charges without further reflecting on the actual possibility of electron delocalization. Therefore, they might not have thoroughly examined the nature of involved atoms in the conjugated systems. This reinforces previous studies related to the fragmented use of resonance when reasoning through different organic chemistry tasks (Brandfonbrener et al., 2021; Braun and Graulich, 2024). Another explanation for students’ challenges with the variables hetero atom & positive charge and positive charge on hetero atom might be the hetero atoms’ hybridization. Unlike the other variables, displaying sp2-hybridized hetero atoms, all items in hetero atom & positive charge and half the items of positive charge on hetero atom show sp3-hybridized hetero atoms (cf.Fig. 5).
Cluster IV: consideration of different resonance patterns involving positive charges
About 21% of the students belong to cluster IV (Table 3). With regard to hetero atoms, unlike cluster III, cluster IV shows high proficiency in dealing with molecular structures involving positive charges adjacent to hetero atoms (i.e., the variable hetero atom & positive charge). It appears that students in this cluster are able to deal more flexibly with positive charges when deciding on resonance. As such, unlike the previous clusters, they discern resonance in molecular structures displaying different patterns of electron delocalization in relation to positive charges, i.e., also in molecules involving single-bonded hetero atoms in which the possibility of electron delocalization must be inferred (e.g., in terms of delocalizable lone pairs of electrons, or the consideration of possible steric constraints regarding π-bonding interactions). While students in the third cluster also master different resonance patterns, overall, these patterns relate to double bonds (i.e., double bonds adjacent to a positive or negative charge). In contrast to that, students’ proficiency with different resonance patterns related to positive charges in cluster IV indicates that they seem to be considerate of different aspects and structural features and, therefore, might handle the structural features in a more interrelated, thorough manner (Betancourt-Pérez et al., 2010). Being more proficient in considering different structural features could be associated with students’ significantly higher score on tasks assessing their conceptual understanding (8.53) and their above-average self-reported competency in identifying resonance in molecules (4.12/5).The more differentiated consideration of structural features might also account for their slightly lower mean score in discerning conjugated systems in contrast to the previous clusters (i.e., β-position of charge). While other clusters could simply check by searching for certain features (i.e., predominantly the presence of double bonds adjacent to charges), students in this group might experience more difficulties due to the higher degree of information to encounter and weigh (e.g., estimate the distance and connection of charges to single-bonded hetero atoms), which may also be the reason for the higher amount of time spent on the items (7.67 seconds on average). Even though students seem to be more attentive to hetero atoms in terms of resonance, they seem to limit their consideration of resonance stabilization to the delocalization of positive charges. Given the low value for hetero atom & negative charge (31%), it seems that students in this group face difficulties in assessing the impact of resonance on the delocalization of negative charges. Thus, they might not associate resonance stabilization with the delocalization of negative charges, but instead with the compensation of electron deficiency with electron density. This is not surprising as delocalizing electrons from an electron-donating to a -deficient centre is a typical approach in (organic) chemistry, for instance, with regard to the electron-pushing formalism (Bhattacharyya, 2013; Flynn and Featherstone, 2017). Consequently, students’ varying performance on items related to negative and positive charges indicates that students may mimic electron delocalization following a sink-to-source – approach but struggle to actually interpret the impact of electron delocalization (i.e., the energetic meaning of delocalizing electron density and how negative charge distribution contributes to the molecule's stability). This assumption aligns with existing research emphasizing students’ challenges in conceptual understanding of the resonance concept (e.g., Kim et al., 2019; Xue and Stains, 2020), their fragmented ideas about how resonance relates to stability and reactivity (Brandfonbrener et al., 2021; Tetschner and Nedungadi, 2023), and might be related to an overall operational teaching of resonance in Organic Chemistry courses (Xue and Stains, 2020; Barakat and Orgill, 2024). Comparing the students’ varying performance for the variables hetero atom & positive charge and hetero atom & negative charge and positive charge on hetero atom further indicates that students might perceive difficulties in dealing with sp2-hybridized hetero atoms. More specifically, all items of the variable hetero atom & negative charge and half of the items in the variable positive charge on hetero atom show sp2-hybridized hetero atoms.
Cluster V: beginning proficiency in various resonance patterns
This cluster, comprising 22% of the students, shows relatively high mean values for all variables (>61%) (Table 3). Consequently, students in this cluster combine the competencies regarding hetero atoms from clusters III and IV, with relatively high proficiency in dealing with both positive and negative charges adjacent to hetero atoms. As the items expose varying structural connectivity across the different variables, this showcases that students are more adept in handling different resonance patterns and dealing with different structural features in an interrelated manner (e.g., inspecting hetero atoms in terms of de-localizable lone pairs to stabilize charges). This flexibility and beginning proficiency are supported by students’ more advanced prior conceptual understanding (8.50), significantly outperforming other clusters. The students are also more confident in correctly answering the tasks on resonance stabilization (3.29/7), although this value does not differ markedly from the remaining clusters. Similar to cluster IV, being sensitive to different patterns and visual cues might also be the reason why students in this cluster perform slightly lower on items involving charges in β-position to the conjugated system (62%) and charged hetero atoms (62%). Processing and weighing more information in their interplay (instead of attending to mere structural features) might make the recognition of conjugated systems more difficult (Paas and van Merriënboer, 2020). This might account for students’ spent time-on-task. Given that it took students in this cluster the longest to come to a decision (8.24 seconds), the amount of time spent might be interpreted as an indicator of the number of structural features considered and weighed during the problem-solving process. Consequently, even though students show proficiency for most variables with different structural features, they seem to still explicitly make sense of the molecular structures in terms of resonance stabilization.General discussion
Different learning profiles can be inferred based on the clusters’ varying proficiency with different structural features, which are summarized in Fig. 7. A more general comparison of the five clusters’ characteristics and relationships with external variables permits the synthesis of different, broader inferences regarding students’ development of proficiency in resonance-related structure decoding, how they deal with different structural features when deciding on resonance stabilization, and how underlying, guiding principles impact students’ ability to discern resonance. These are described in the following. | ||
| Fig. 7 Summary of the different learner profiles based on the cluster characteristics. | ||
Students’ limited consideration of further, implicit features could also be related to the presentation of resonance in the textbook used in the course. Compared to other common Organic Chemistry textbooks, on average, the Klein textbook addresses more representational competencies (e.g., the interpretation, translation, generation, and limitations of representations) and offers a higher degree of highly scaffolded worked examples and practice problems to build these skills (Gurung et al., 2022). However, a closer look into the corresponding practice problems for the course's resonance-related learning objectives reveals that the exercises are limited to the identification and use of resonance patterns, in which resonance does apply. At least in the textbook chapter introducing and explicitly practising resonance, no exercises use examples in which resonance is not possible (Klein, 2020). Therefore, when answering these exercises, students were not required to question the feasibility of resonance structures when locating resonance patterns (e.g., deciding on the violation of the octet rule) apart from few exercises focusing on valid curved arrows (Klein, 2020). This may account for students’ lower success rate for items requiring such considerations.
Conclusion
The quantitative study presented herein aimed at exploring how the variation of structural features affects students’ consideration of electron delocalization and which (combinations of) structural features render students’ recognition of resonance stabilization difficult. Using K-means clustering, different profiles and characteristics regarding students’ proficiency and strategies in discerning resonance could be determined. Altogether, the data suggests no clear linear progression in terms of proficiency in recognizing resonance in molecular structures but rather indicates different paths in terms of emerging proficiency. While it became evident that dealing with allylic carbocations is much easier for the majority of students than with hetero atoms, a closer analysis of the different cluster affiliations revealed different individual challenges with regard to discerning resonance stabilization, which affect the time spent on items, and which relate to students’ conceptual understanding of resonance. Some students seem to base their decision on the possibility of electron delocalization on the presence of singular features (i.e., allylic systems), either due to low conceptual understanding and uncertainty or because of the visual resemblance of the structures to allylic carbocations. Moreover, across all clusters, it became apparent that students had difficulties in correctly answering items requiring further implicit considerations. However, students’ perceived cognitive load remained similar across all clusters. Based on these findings, different implications for teaching and future research can be inferred.Implications for practice
To successfully recognize and apply resonance across different types of molecular structures, one must be proficient in dealing with various structural features. While this study revealed that most students correctly decide on resonance stabilization for allylic carbocations, most students faced challenges in correctly deciding for molecules comprising other (combinations of) structural features (e.g., hetero atoms), even with increased prior knowledge. This is problematic as chemical problem-solving requires students to deal with more complex structures and flexibly use (implicit) structural information to consider the possibility of electron delocalization on their own (e.g., without explicitly indicating features such as lone pairs of electrons). In this regard, it is questionable whether students truly gain competence in discerning resonance by focusing on learning simple patterns of electron delocalization. Even though the students in this study learned about different critical aspects underlying resonance considerations in their Organic Chemistry I course (e.g., evaluate the significance of resonance contributors), the findings of the cluster analysis indicate that students had not fully applied their acquired knowledge to decide on resonance stabilization, both with regard to the recognition of resonance patterns and the plausibility of resulting resonance structures. At a broader level, the results implicate that it is crucial to reinforce and practice resonance considerations on a regular basis in order to promote learners’ connection and activation of concept-related resources, thus making them more available when confronted with molecular structures (DiSessa et al., 2016). However, at a more local level, students’ affiliation to the different clusters reveals different stages of proficiency in discerning resonance stabilization, requiring different approaches to enhance their sense-making skills and perceptual fluency. Based on that, specific implications can be derived for each cluster to develop their resonance-related proficiency.Since cluster I exposed conceptual difficulties, resulting in a low performance across all cluster variables, students in this cluster would benefit from sense-making activities (Rau et al., 2017). In this regard, Rau and colleagues (2017) and Rau (2018) have shown that sense-making activities should precede fluency-building activities when learners do not have sufficient prior knowledge. Consequently, these students could be supported with exercises explicitly making sense of electron delocalization and actively seeking explanations for resonance (Rau et al., 2017). Instead of a mere superficial recognition of resonance patterns, at this early stage of developing proficiency, emphasis should be placed on a thorough reflection on how different visual cues in the molecular structures relate to resonance (e.g., whether they build a conjugated system), and why the different structural feature combinations actually permit electron delocalization (Seufert, 2003; Xue and Stains, 2020). The concurrent consideration of aspects such as atoms’ electronegativity, hybridization, or the energetic impact of electron delocalization on hetero atoms could be discussed to a greater extent to connect existent different conceptual knowledge pieces (Betancourt-Pérez et al., 2010; DiSessa et al., 2016). In other words, instead of simply learning and applying different patterns, which may result in an overreliance on singular features resembling specific patterns, one could, at the beginning, inspect the molecular structures in more detail to raise students’ awareness of why electron delocalization is possible and energetically favourable; laying the ground for a more reflective approach to subsequent pattern recognition. One could also integrate different, complementary representations to illustrate the impact of electron delocalization and, therefore, support students’ understanding of electron density distribution (e.g., use of electrostatic potential maps) (Ainsworth, 2006; Rau, 2017). In this regard, it could be also addressed that electron delocalization does not necessarily equalize the compensation of positive charge but may also encompass the delocalization of negative charge (i.e., as shown by the reverse direction of curved electron arrows).
Students in clusters II to IV are more proficient in deciding on resonance stabilization, but they did not demonstrate proficiency with different structural feature combinations involving hetero atoms. To support these students, scaffolding (Kranz et al., 2023) or stepped-supporting tools (Hermanns and Schmidt, 2018) addressing these difficulties could be offered. For instance, when deciding on resonance stabilization for various molecular structures, students could be provided with different impulse questions and solution strategies (e.g., to consider the hybridization of (hetero) atoms, to determine the presence of conjugated systems, to check whether the octet rule is violated, or to expand the molecular structures to make atoms’ features more explicit). Accordingly, students can determine on their own whether they need help, ultimately allowing them to foster their sense-making of specific bonding patterns of resonance they still struggle with. Furthermore, different contrasting examples of (im-)plausible resonance structures with similar structure motives could be weighed and discussed in the classroom (cf.Fig. 6 for examples) (Graulich and Schween, 2018). For instance, eliciting comparisons of a positively and negatively charged molecular structure in terms of resonance stabilization could help students understand that in both cases, electron delocalization contributes to its stability (cf. cluster IV) but that negatively charged compounds require a different approach. Moreover, to enhance these students’ perceptual fluency, thus, being able to quickly focus on relevant structural cues, highlighting what to focus on (i.e., conjugated systems) could be a helpful guidance and prevent students from merely looking for singular structural features when deciding on resonance (cf. clusters II and III).
Finally, students in cluster V showed the most pronounced proficiency regarding resonance stabilization across varying combinations of structural features. However, in this cluster, it took the students the longest to come to a decision. This suggests that students’ proficiency is based on sense-making skills, thereby showing the need to engage students at this proficiency stage more in fluency-building activities (Rau, 2018) to become more fluent in their decision-making. This could be accomplished with short classification exercises following the principles of perceptual learning (Kellman and Massey, 2013), e.g., prompting students to decide on resonance for a sequence of molecules and providing immediate feedback. Here, existing practice exercises in Klein (2020) could be expanded by also exposing students to molecular structures where resonance is not applicable (e.g., due to the β-position of the charge, or the violation of the octet rule). Categorizing a variety of molecular structures in terms of resonance stabilization, not only by discriminating the different bonding patterns of resonance but also by considering their applicability, could help students become sensitive to a more reflective use of resonance patterns regarding molecules exposing similar structural feature motives.
Lastly, common teaching approaches to introduce and use resonance should be revisited. Students’ overall proficiency with allylic carbocations could stem from their familiarity with instructional contexts (e.g., the introduction of electron delocalization and discussion of aromaticity). While easier examples are certainly necessary at the beginning to help understanding, using more diverse examples and exercises could support students to become more adept in deciding on resonance for various molecular structures.
Implications for research
While this study yields first insights into how different structural features impact students’ consideration of resonance stabilization in a molecule, the analysis focused on a limited number of structural features in smaller, relatively simple molecular structures. Future work could delve deeper into more complex structures to further shed light on other (less salient) features, such as the impact of the familiarity of hetero atoms or the role of lone pairs on students’ application of resonance. It would also be interesting to investigate students’ strategies to perceive conjugated systems in more detail (e.g., through eye-tracking) or to look deeper into students’ certainty when answering different resonance tasks. Given that students in this study were explicitly prompted to consider and decide on resonance stabilization in provided structures, more research is needed investigating students’ proficiency in resonance recognition within reaction contexts.Not included in the analysis were changes in students’ perceptions and strategies as a result of being presented with a sequence of molecular structures. In this regard, it could also be worthwhile to look in more detail into how students’ proficiency develops across a semester or across different courses, e.g., model a learning progression or uncover the differences between novice learners and advanced learners in terms of resonance-related decoding of molecular structures. While this study indicates that the clusters differ in conceptual understanding, future studies could more systematically investigate how prior conceptual knowledge affects students’ proficiency in discerning resonance in molecular structures. Lastly, the effectivity of different teaching approaches needs to be investigated in more detail (e.g., does instruction focusing on a stronger connection of different concepts, such as hybridization, energy, and resonance, result in more reflective pattern recognition? Does perceptual learning with feedback settings help students to become proficient in discerning resonance?). This also comprises a more thorough examination of how instructors’ teaching practices impact learners’ proficiency in discerning resonance stabilization in molecules, e.g., whether they promote certain learning profiles.
Limitations
This quantitative study is explorative in nature; therefore, the results must be interpreted in light of several limitations. First, as the data were collected at one institution following a traditional curriculum, it remains unclear whether the findings can be generalized, given different teaching approaches at other universities. Second, the cluster analysis focused on a limited number of combinations of salient structural features, whereas each molecular structure also includes multiple less salient structural features (e.g., the complexity of the structure's carbon backbone of the structures, the explicit indication of bonds to hydrogen atoms). As such, their overall interplay might have influenced students’ decision-making on resonance as well. Given the reduction of structural features considered in the cluster analysis, students’ proficiency in resonance considerations for structures involving negative charges could not be resolved entirely. For instance, it remains unclear whether students are proficient with negative charges when the molecules do not involve hetero atoms. Given the randomized display of about 50% of the items for each student, students solved different items that could have influenced the findings in light of the interplay of different structural features. Due to the study's quantitative character, students' proficiency with different structural features was inferred from patterns in the cluster solution and could not be complemented with qualitative data. The interpretations drawn would benefit from further student validation (e.g., member checking) to verify the correctness of conclusions made regarding students’ proficiency and difficulties. At the time of data collection, no concept inventory to assess students’ prior resonance-related knowledge existed. Consequently, the assessment of students’ conceptual understanding could not be based on established instruments. Lastly, the remote completion of the survey bears different limitations that might have affected the inferred findings. On the one hand, students’ actual effort in solving the tasks remains unclear and could not be validated. For instance, although students were explicitly prompted to decide on the impact of electron delocalization on the molecule's stability, it remains unclear whether students interpreted the prompt as intended (e.g., whether they tried to look for resonance stabilization or the mere possibility of delocalizing electrons). The hypothetical interpretation of the prompt as deciding on the formal possibility of electron delocalization would not affect the inferences made based on the clustering variables. The decisions on stability contribution align with the possibility of electron delocalization for the variables included in the cluster analysis (cf.Fig. 5). However, conclusions drawn on implicit considerations based on the variable hetero atom & positive charge & implicit considerations (excluded from the cluster analysis due to low performance scores across all clusters, cf.Table 8 and section Cluster analysis) should be viewed with caution. On the other hand, even though students were explicitly asked to take the survey without external helping tools, it is uncertain whether students answered the items intuitively or whether they used supporting tools (e.g., lecture notes and textbooks). Eventually, the use of external tools might have affected students’ cluster affiliation (e.g., by more often correctly identifying resonance across the different cluster variables) and their cluster characteristics (e.g., time spent on the tasks). Finally, the conclusions regarding students’ proficiency in discerning resonance stabilization are constrained by being based on simple molecular structure items; therefore, it remains unknown whether they also apply to students’ proficiency in identifying the possibility of electron delocalization in reaction contexts.
|
Author contributions
Irina Braun: conceptualization, investigation, methodology, formal analysis, writing – original draft, visualization. Scott E. Lewis: resources, methodology, writing – review and editing. Nicole Graulich: conceptualization, methodology, supervision, writing – review and editing.Data availability
The data are not publicly available as participants of this study did not consent for their data to be shared publicly.Conflicts of interest
Researcher SEL receives funding from the Royal Society of Chemistry (RSC). The RSC played no role in the data collection, analysis or presentation of the research.Appendices
Tasks assessing students’ prior resonance-related knowledge
Based on the learning outcomes defined by Carle and Flynn (2020) and reported alternative conceptions on resonance (e.g., Brandfonbrener et al. (2021), Xue and Stains (2020)), nine tasks have been designed to assess students’ conceptual understanding of resonance (Fig. 8). For each correct answer, students received 1 point (altogether 15 points). Solutions are indicated in blue. | ||
| Fig. 8 Overview of the designed tasks to assess students' resonance-related prior knowledge. | ||
Initial cluster solution
The cluster analysis was initially performed with six clustering variables (Table 8). However, the variable hetero atom & positive charge & implicit considerations did not differentiate the clusters with overall low scores for all clusters. Consequently, the cluster analysis was redone, omitting this variable (cf.Table 3).Correlation matrix
The clustering variables exhibited low correlations (<0.9). They are summarized in Table 9.| (Combinations of) structural features | β-Position of charge | Carbon atoms & positive charge | Hetero atom & positive charge | Hetero atom & negative charge |
|---|---|---|---|---|
| **Significance level p = 0.01. *Significance level p = 0.05. | ||||
| Carbon atoms & positive charge | 0.17** | |||
| Hetero atom & positive charge | −0.12** | 0.21** | ||
| Hetero atom & negative charge | 0.09* | 0.04 | 0.07 | |
| Hetero atom & positive charge & implicit considerations | −0.03 | −0.29** | −0.20** | 0.01 |
| Positive charge on hetero atom | −0.08* | −0.07 | 0.01 | −0.06 |
Split-half reliability of the cluster solution
To test for reliability of the cluster analysis, the data was randomly divided in half. On each half, a K-means cluster analysis with K = 5 clusters was performed independently. The results of each cluster analysis are summarized in Table 10. Inspecting and comparing the two cluster solutions (Clatworthy et al., 2005), it was found that they agree qualitatively and correspond to the characteristics of the cluster solution reported in Table 3, thereby supporting the stability of the cluster analysis.| Cluster | % of N | β-Position of charge | Carbon atoms & positive charge | Hetero atom & positive charge | Hetero atom & negative charge | Positive charge on hetero atom |
|---|---|---|---|---|---|---|
| I | 16.3 | 52.04 | 23.15 | 47.67 | 41.93 | 47.65 |
| II | 14.3 | 74.19 | 84.46 | 46.56 | 25.78 | 73.59 |
| III | 22.7 | 80.90 | 76.44 | 29.66 | 77.02 | 22.66 |
| IV | 23.0 | 61.49 | 89.13 | 74.53 | 25.33 | 22.64 |
| V | 23.6 | 56.81 | 82.00 | 77.88 | 80.86 | 55.10 |
| Overall | 343 | 65.09 | 71.04 | 55.26 | 50.18 | 44.33 |
| I | 16.0 | 43.67 | 35.62 | 49.69 | 56.94 | 52.79 |
| II | 20.1 | 66.07 | 75.64 | 29.15 | 26.76 | 67.45 |
| III | 24.0 | 76.11 | 86.23 | 46.10 | 80.66 | 20.09 |
| IV | 18.0 | 67.41 | 88.03 | 67.20 | 25.59 | 24.02 |
| V | 21.9 | 68.24 | 90.90 | 78.52 | 79.28 | 65.38 |
| Overall | 338 | 64.3 | 75.28 | 54.13 | 53.85 | 45.95 |
Self-reported knowledge
Students self-reported on different competencies related to resonance-specific learning outcomes in the first survey part (Fig. 3). While Table 5 reports on learning outcomes directly related to the decision-making in the second survey part (Fig. 3), Table 11 gives an overview of the clusters’ self-assessment on the remaining items with indication of the means and standard deviations.| Cluster | Estimate molecules’ geometry | Determine aromaticity in a molecule | Estimate acid and base strength of molecules | Assess the influence of electron delocalization on molecule's reactivity |
|---|---|---|---|---|
| I | 3.83 (1.05) | 3.97 (1.11) | 3.60 (1.05) | 3.50 (1.07) |
| II | 3.89 (1.09) | 4.08 (1.21) | 3.58 (1.10) | 3.63 (1.16) |
| III | 3.90 (1.03) | 4.25 (1.02) | 3.56 (1.07) | 3.85 (1.04) |
| IV | 4.01 (0.99) | 4.26 (1.10) | 3.62 (1.02) | 3.74 (0.90) |
| V | 3.95 (1.02) | 4.07 (1.11) | 3.49 (1.06) | 3.75 (1.03) |
| Overall | 3.92 (1.03) | 4.14 (1.11) | 3.57 (1.06) | 3.71 (1.04) |
Acknowledgements
This publication represents a component of the first author's doctoral (Dr rer. nat.) thesis in the Faculty of Biology and Chemistry at the Justus-Liebig-University Giessen, Germany. The researchers would like to acknowledge the students at the research setting for their efforts with the survey and the instructors for facilitating data collection. IB would like to thank Prof. Richard Göttlich and Prof. Michael Schween for valuable feedback on the study design.References
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