Multi-framework case study characterizing organic chemistry instructors’ approaches toward teaching about representations
Tamera
Jones
a,
Anastasia
Romanov
a,
Justin M.
Pratt
b and
Maia
Popova
*a
aUniversity of North Carolina at Greensboro, Greensboro, North Carolina, USA. E-mail: m_popova@uncg.edu
bUniversity of Rhode Island, Kingston, Rhode Island, USA
First published on 1st August 2022
Abstract
Representational competence (RC) is a set of skills to reflectively use a variety of representations to draw inferences, make predictions, and support claims. Despite the important role RC plays in student success in chemistry and the considerable number of investigations into student ability to reason with representations, little is known about instructors’ approaches toward developing student RC skills. This case study characterizes organic chemistry instructors’ intentions and practices toward cultivating their students’ RC. Three organic chemistry instructors participated in semi-structured interviews that explored their Pedagogical Content Knowledge (PCK) and goals for developing student RC. Interview data were triangulated with course artifacts data, including lecture slides and assessments. Several frameworks were used to deductively code the interviews and course artifacts: Kozma and Russell's RC, Geddis’ PCK, Ainsworth's functional taxonomy, and Johnstone's triplet. Through triangulation of different data sources and theories, we found differences in instructors’ PCK for teaching with representations, despite teaching the same course at the same institution. There were also differences in the alignment between each participant's instructional goals and what they enact when teaching and assessing representations. Specifically, two of the three instructors expressed explicit goals for developing student RC skills, which mostly aligned with the focus of their course artifacts. One participant, however, did not articulate any RC skills that they aim to teach and assess; yet, course artifacts revealed that they do use activities and assessment items that target some RC skills. This suggests that this instructor teaches and assesses RC skills without realizing it. Implications for instructors and education researchers are presented in light of these findings.
Introduction and significance
Organic Chemistry is associated with high failure and attrition rates (Lovecchio and Dundes, 2002; Jones and Gellene, 2005; Grove et al., 2008). Therefore, it is critical to reconceptualize curricular, instructional, and assessment practices within the course. To effectively transform organic chemistry education, professional development programs are needed to equip instructors with literature-based resources and supports that can meaningfully impact instructors’ pedagogical knowledge and teaching practices (Gess-Newsome et al., 2003; Henderson et al., 2011). One critical direction for these initiatives is on representational competence (RC) as learning and communicating with visualizations is essential to chemistry instruction (Kozma and Russell, 2005; Ainsworth, 2006; Gilbert, 2007; Stieff, 2007; Keehner et al., 2008). Focusing on RC is particularly appropriate for Organic Chemistry as this course introduces students to a wide variety of representations that they have not experienced in previous courses: skeletal structures, dash–wedge diagrams, Newman projections, chair conformations, Kekulé structures, IUPAC formulas, various kinds of spectra, and others. A historical analysis of 18 organic chemistry American Chemical Society (ACS) exams showed that since 1982 more than 90% of exam items include representations (Raker and Holme, 2013).Although a wide body of literature has explored organic chemistry students’ RC (Bodner and Domin, 2000; Cooper et al., 2010; Grove et al., 2012; Stull et al., 2012; Popova and Bretz, 2018a, 2018b, 2018c), no studies have examined organic chemistry instructors’ goals, Pedagogical Content Knowledge (PCK), or practices toward developing student RC. Therefore, it is critical to fill this gap as previous research has shown that instructors’ intentions around student learning with representations directly impact the curriculum they enact (Bussey and Orgill, 2019). Additionally, developing student RC is not a trivial task, and expert blind spots can make instruction about representations ineffective. Specifically, instructors’ high levels of expertise may limit their awareness of the skills required to understand and use a representation (Nathan et al., 2001; Gilbert and Eilam, 2014). For this reason, instructors may select representations that are too challenging for students to understand, overlook scaffolding representations to support student learning, and/or assume that students understand the affordances and limitations of various representations (Schönborn and Anderson, 2010; Gilbert and Eilam, 2014; Baldwin and Orgill, 2019).
Several studies have evidenced chemistry instructors’ blind spots and unawareness about teaching with representations. For example, Linenberger and Holme characterized 494 biochemistry instructors’ views toward developing and assessing visual literacy in their courses (Linenberger and Holme, 2015); half of the biochemistry instructors assumed visual literacy on their assessments. Additionally, these instructors selected interpreting and generating representations as the two most important skills for students to develop in a biochemistry course, putting little to no emphasis on other skills (Linenberger and Holme, 2015). Xue and Stains (2020) found that only one of two instructors in their study focused on explaining affordances and limitations of representations when teaching about resonance, which lead to a significant difference in student understanding of resonance. Patron and colleagues found that secondary chemistry teachers in Sweeden were unable to give the explicit reasoning that guided their choice of representations to teach about bonding (Patron et al., 2017). Finally, our previous work studied the intentions of thirteen chemistry instructors, teaching a variety of chemistry courses, toward developing student RC (Popova and Jones, 2021). Through the analysis of participants’ descriptions of their instructional and assessment practices, we found that, without realizing it, most were likely to teach and assess several RC skills. A closer examination of these skills revealed a focus on lower-level RC skills (e.g., interpreting and generating representations) and a lack of a focus on higher-level meta-RC skills (e.g., describing affordances and limitations of representations). Additionally, some instructors were self-aware of their lack of knowledge about effective teaching about representations and expressed a desire for professional development opportunities to learn about differences in how experts and novices conceptualize representations, evidence-based practices for teaching about representations, and how to assess student mastery of RC skills.
The case study described herein triangulated interview data with course artifacts through the lens of multiple analytic frameworks to provide richer characterizations of how instructors teach about representations, whereas our previous work only analyzed interview data, and only through the lens of one framework. In addition, this study extends the analysis to also characterize instructors’ PCK and practices while our previous study only focused on goals and intentions around developing student RC. Understanding the interconnection of faculty goals, PCK, and practices around teaching with representations will allow for the development of evidence-based professional development for faculty and empirically tested teaching interventions to support student RC. Unless faculty are intentional about developing student RC and are equipped with tools to support the development of these skills, student RC is unlikely to grow in sophistication. For example, Nitz et al. (2014) explored the development of RC along with the development of conceptual understanding when learning about photosynthesis. They found that while the two constructs are related, biology students had a significant increase in their content knowledge but not in their RC, likely due to only moderate focus on supporting students in developing RC. However, when intentionally cultivated, student RC can grow in sophistication; Kohl and Finkelstein (2006) found that students in a reformed introductory physics course that placed a higher emphasis on supporting students in mastering multiple representations learned a broader set of RC skills than students in a traditional course. Finally, while our previous study focused on chemistry instructors teaching a variety of chemistry subjects, this case study zooms in on a more homogeneous sample of three organic chemistry instructors. As such, this study seeks to address the following research questions (RQ):
(1) What are organic chemistry instructors' goals and PCK around teaching about representations?
(2) What are organic chemistry instructors' approaches toward teaching and assessing representational competence skills?
(3) How (if at all) do organic chemistry instructors' goals and PCK around teaching about representations align with their instructional and assessment practices?
Analytical frameworks
Four analytical frameworks were used to provide a rich characterization of organic chemistry instructors’ thinking and practices around teaching about representations and developing student RC: Kozma and Russell's RC (2005) to understand what skills organic chemistry instructors intend to support students in developing (RQ 1) and what skills they teach and assess (RQ 2), Geddis’ PCK to understand instructors’ knowledge of how to most effectively teach about representations (Gess-Newsome, 2015) (RQ 1), Johnstone's triplet (1991) to analyze the types of representations instructors include in their lecture slides and assessments (RQ 2), and Ainsworth's functional taxonomy (2006) to understand what functions these representations serve in their instructional materials (RQ 2). Below, we describe each framework in more detail as well as how we used them in our study.In the context of this work, we are focusing on the instructor's ability to transform their content knowledge about representations into a teachable form that supports student development of RC. Geddis (1993) described five criteria for this transformation to occur: (1) careful selection of representations, which includes analogies, illustrations, examples, explanations, and demonstrations to be used in teaching; (2) consideration of learners’ prior knowledge, or the understanding that learners bring prior ideas and conceptions into the learning environment; (3) consideration of what makes the learning about something difficult (in this context about domain-specific representations); (4) knowledge of effective teaching strategies that support student understanding and development of domain-specific skills; and (5) evaluation of curricular saliency, or what key concepts associated with a specific topic should be scaffolded to achieve the greatest understanding of this topic. Since representations are not a discrete chemistry topic and are used across the entire curriculum to support explanations of various topics and concepts, we could not analyze for the last criterium – curricular saliency. The remaining four criteria were used to analyze instructors’ PCK around teaching with representations and developing student RC. It should be noted that the fourth criterium – knowledge of effective teaching strategies – is not only an articulation of instructors’ PCK but also a description of their instructional practices (if the described strategies are actually used in instruction). However, to remain consistent with Geddis’ PCK framework, we will position the knowledge of effective teaching strategies as a component of instructors’ PCK.
Methods
Sample
Three organic chemistry instructors from the same research-intensive institution in the midwestern United States participated in this study. To protect the identities of the participants, each has been assigned a pseudonym: Sid, Mai, and Dan. At the time of the interview, Sid had twelve years of teaching experience and taught organic chemistry for both chemistry major and nonmajor students. Mai had seven years of teaching experience and only taught organic chemistry for nonmajors. Dan had five years of teaching experience and taught organic chemistry only for chemistry majors. When necessary to make this distinction, pseudonyms are also accompanied by a course designation: M for chemistry majors and NM for nonmajors (e.g., Mai-NM, Dan-M). When it comes to course textbooks, Sid used Organic Chemistry by Klein (2015) in his nonmajor course and Organic Chemistry by Bruice (2010) in his major course. Mai also used Organic Chemistry by Klein (2016) in her nonmajor course. Dan used Organic Chemistry by Jones and Fleming (2014) in his major course.Data collection
The three instructors participated in semi-structured interviews in Spring 2019 using Skype (Herrington and Daubenmire, 2014). Institutional Review Board approval was obtained before data collection. Prior to interviewing participants, they were given a consent form that described their rights and how data would be treated to ensure confidentiality. At the start of the interview, participants were told that they will be asked questions about how they teach about representations. To ensure that the participants interpreted the term “representation” as intended, the following definition was read aloud to each participant at the beginning of the interview:Representations are perceptible, symbolic images and objects in the physical world that are useful to represent aspects of chemical phenomena, much of which cannot be seen (Kozma and Russell, 2005, p. 123). Representations can be static or dynamic and include diagrams, graphs, pictures, physical models, animations, simulations, and others (Schönborn and Anderson, 2010, p. 347).
The interview protocol contained multiple questions probing how the three instructors teach about representations. The full interview protocol can be found in the Appendix. The length of the interviews varied: Sid's interview lasted 42 minutes, Mai's lasted 37 minutes, and Dan's lasted 78 minutes. Along with the interview data, each participant provided course artifacts associated with the beginning chapters in their course(s), covering topics such as Lewis structures, the octet rule, formal charges, molecular orbital theory, hybridization, and molecular representations. The beginning chapters were selected as they introduce various representations used to depict chemical structures that are heavily used in Organic Chemistry. The course artifacts provided by participants included (a) a syllabus for the whole course, (b) PowerPoint lecture slides covering the beginning chapters material, and (c) the first midterm exam. These artifacts were used to characterize each participant's instructional and assessment practices. Mai provided artifacts for her nonmajor course, Dan provided artifacts for his major course, and Sid provided artifacts for both his major and nonmajor courses.
Data analysis
Multiple analytical frameworks were used to analyze the data to provide a rich characterization of instructors’ thinking and practices around developing student RC. These frameworks target four constructs: (1) goals, (2) PCK, (3) instructional practices, and (4) assessment practices. Interviews and course artifacts comprised the data sources for these analyses. Table 1 summarizes the data sources and the various analytical frameworks used for the analyses.| Target constructs | Data source | Data analysis methods and analytical frameworks |
|---|---|---|
| Goals | • Interview | • Inductive coding |
| • Deductive coding with Kozma and Russell's RC framework | ||
| PCK | • Interview | • Deductive coding with Geddis’ PCK criteria |
| Instructional practices | • Interview | • Inductive coding |
| • Lecture slides | • Deductive coding with (1) Kozma and Russell's RC framework, (2) Ainsworth's functional taxonomy, and (3) Johnstone's triplet | |
| Assessment practices | • Interview | • Inductive coding |
| • Midterm exam | • Deductive coding with (1) Kozma and Russell's RC framework and (2) Johnstone's triplet |
Two researchers collaboratively coded all data sources using a combination of inductive and deductive coding (Fereday and Muir-Cochrane, 2006; Soiferman, 2010). Inductive coding was used to analyze the interview data to characterize participants’ instructional goals and course artifact data to capture how often representations appeared in slides and midterm exams, which type(s) of representations appeared, and how representations were used in lecture slides and midterm exams. Data were also deductively coded using codes defined by the analytical frameworks (Table 2).
| Framework | Codes/categories and their definitions |
|---|---|
| Geddis’ PCK criteria | Representations – analogies, illustrations, examples, instructional tools, explanations, and demonstrations used |
| Learner prior knowledge – ideas that learners bring to the topic | |
| What makes the learning difficult – ideas that are considered difficult to grasp but that leads to greater understanding | |
| Knowledge of teaching strategies most likely to be fruitful – strategies that allow for the greatest understanding | |
| Curricular saliency – big ideas or main concepts that bring a topic together/allow for the main topic to be scaffolded | |
| Kozma and Russell's RC framework | Interpret representations – ability to decode surface features of a representation |
| Generate representations – ability to draw/build a representation | |
| Translate between representations – ability to make connections between different kinds of representations or between two or more representations of the same kind | |
| Use representations – ability to use representations to make predictions, draw inferences, and/or solve problems | |
| Understand affordances and limitations of representations – ability to identify what a representation shows that other representations do not show and identify the shortcomings of a representation | |
| Choose representation – ability to select the most appropriate representation type for a particular purpose | |
| Epistemological understanding – realization that representations depict chemical phenomena but are not the chemical phenomena itself | |
| Ainsworth's functional taxonomy | Complementary – representations of two different molecules or two conformations of the same molecule that are meant to be contrasted with one another to draw meaning |
| Constraining – representations that depict the same molecule or same information in several different ways. In this case, one representation is more familiar and straightforward than the other | |
| Constructing – multiple representations being integrated to achieve deeper understanding which would otherwise be difficult to attain with a single representation | |
| Scaffolding – representations that are used to guide students toward skill-building and understanding of concepts | |
| Johnstone's triplet | Macroscopic level – phenomena that are perceptible to the senses (e.g., can be seen, touched, and smelled) |
| Symbolic level – symbols, formulas, equations, mathematical expressions, graphs | |
| Submicroscopic level – phenomena that cannot be seen with a naked eye (e.g., atoms, molecules, ions, etc.) | |
| Hybrid – representations that contain characteristics of two or more levels that coexist and complement each other as one representation | |
The researchers discussed every case of coding disagreement until a 100% inter-rater agreement was achieved (Lee, 2017). Constant comparative analysis was then used to explore the relationships between codes to create hierarchies of codes and categories (Fram, 2013). Thematic analysis was used to identify themes that crosscut the data (Fereday and Muir-Cochrane, 2006). These coding analyses were also accompanied by written reflective memos to help the researchers engage with the data more deeply and assist in communicating about the analyses. These periodic discussions about codes, memos, and analyses add credibility to the findings by rectifying any inconsistencies in the interpretations of the data by the researchers (Anney, 2014). The overall trustworthiness of the findings was further supported by comparing and contrasting all code applications until consensus was reached (Lincoln and Guba, 1986); this allowed for the creation of a unified codebook and consistent coding across every interview and course artifact. Below is a description of how we coded the interview and course artifacts data.
Results
This section is structured around the three research questions that guided the study. To answer the first research question, we present the results from the analysis of the organic chemistry instructors’ goals and PCK around teaching with representations. To answer the second research question, we present the results from the analysis of instructors’ approaches toward teaching about representations and assessing RC skills. Finally, to answer the third research question, we present the results from the analysis of the alignment of instructors’ goals and PCK around teaching about representations with their teaching and assessment practices. Throughout this section, the text in italics surrounded by single quotation marks represents ‘codes,’ whereas the text in italics surrounded by double quotation marks represents “quotes.”RQ 1: What are organic chemistry instructors’ goals and Pedagogical Content Knowledge around teaching about representations?
Goals around teaching about representations
Deductive coding of interview data with Kozma and Russell's RC framework (Table 2) was used to identify participants’ teaching and assessment goals around student RC. Table 3 summarizes these results.| Mai | Sid | Dan | ||||
|---|---|---|---|---|---|---|
| Teaching goals | Assessment goals | Teaching goals | Assessment goals | Teaching goals | Assessment goals | |
| Interpret | ✓ | ✓ | ✓ | Did not articulate | Did not articulate | |
| Generate | ✓ | ✓ | ✓ | |||
| Translate | ✓ | ✓ | ✓ | |||
| Use | ✓ | ✓ | ||||
| Afford./limit. | ✓ | |||||
| Select | ✓ | |||||
| Epistemol. | ||||||
As shown, Mai and Sid were intentional about supporting students in developing RC skills, as they articulated concrete teaching and assessment goals for students learning about representations (Table 3). For example, when asked about the skills that she wants to help students develop when they learn about representations, Mai responded:
Being able to read the graphs is important. We also make them play with their model kit and make different molecules with it, cause there's definitely a little bit of a learning curve to using the model kit…And also for drawing mechanisms, you know, learning how to draw the arrows properly. Those are things that we try to develop in them.
As illustrated in this quote, Mai articulated concrete goals around supporting students' ability to interpret representations (“being able to read graphs”) and generate representations (use “model kit and make different molecules with it” and “drawing mechanisms”). Mai and Sid also reported that they assess these skills on exams. For example, when asked about how he knows that his students understand the representations that he introduced in his course, Sid responded:
Well, primarily through assessments…On exams, we have questions explicitly about representations which would just be sort of converting from one to another, which early on in the course are more appropriate because that's actually the skill we're trying to develop, you know, how to convey chemical structures through different sorts of representations.
As illustrated in the quote, Sid articulated assessing students’ ability to translate between representations (“converting from one to another”). Sid explicitly stated that he includes questions of this nature on his exams because that is “actually the skill we’re trying to develop.” In summary, the quotes above support that Mai and Sid articulated concrete goals around developing student RC, and that they are intentional about supporting students in developing RC skills and assessing RC skills.
In contrast, Dan did not articulate any explicit goals for developing student RC skills. When asked whether there are any specific skills that he wants his students to develop when they learn about representations, Dan responded:
I think the overall goal is to understand the characteristics of that particular structural reaction and it's very much utilitarian. How do we utilize different techniques to achieve that kind of goal? So it's more tools to, you know, hopefully understanding reaction process or you know, the chemical process itself.
Here, Dan wants to help students understand reactions and “the chemical process itself.” Even though RC might be an important component of this, Dan did not articulate any concrete RC skills when asked about teaching about representations. Dan also did not articulate any concrete RC skills that he assesses on his exams. Instead, he discussed accessing students’ ability to apply learned chemical principles to solve new problems. It should be noted that when asked about how he introduces new representations in his course, Dan described some practices consistent with helping students interpret, generate, and translate representations. This shows that Dan might be teaching some RC skills without realizing it.
Overall, Mai and Sid articulated concrete RC skills that they teach and assess. Contrastingly, Dan did not articulate any concrete RC skills that he hopes to help his students develop, nor any skills that he might assess.
Pedagogical content knowledge around teaching about representations
In addition to coding the interviews with Kozma and Russell's RC framework, data was also coded using Geddis’ criteria to capture each participant's PCK around teaching with representations and developing student RC.When it comes to the sources of representations, all three participants discussed obtaining them from ‘textbooks.’ Sid also discussed that he likes to ‘produce his own representations’ (either by hand or using ChemDraw), whereas Dan and Mai find additional representations using ‘internet search engines’ (e.g., Google, YouTube).
The criteria for selecting representations varied for each participant. Sid discussed three criteria: ‘based on personal preferences,’ ‘what aligns with the course,’ and ‘what the instructor cannot create themselves.’ Mai discussed different criteria for selecting representations: ‘accuracy,’ ‘clarity,’ and ‘quality.’ Finally, Dan discussed only one criterion – whether the representation ‘highlights a key concept well’ or not.
Participants were also asked why they incorporate representations into their teaching (i.e., the purposes of representations). All three participants highlighted various affordances of representations. For example, Sid stated that ‘representations help students focus on fundamental chemical ideas’ and that ‘different representations are useful because they each communicate different information:’ “All the [representations] that we typically used…have their place [and] are intended to convey different kinds of information.” This idea was also expressed by Dan. Mai stated that representations ‘serve as tools to spark student interest’ and that they ‘help students visualize chemical phenomena.’ Mai gave a further explanation for this: “For organic chemistry, I think like having pictures is really important. [It's] a lot more spatial. And so, having actual visuals is really important just to kind of see what's happening.”
| Mai | Sid | Dan | |
|---|---|---|---|
| Difficulties developing specific RC skills and visuospatial ability | |||
| Ability to interpret representations | ✓ | ||
| Ability to generate representations | ✓ | ||
| Ability to translate between representations | ✓ | ✓ | |
| Ability to understand affordances and limitations of representations | ✓ | ✓ | |
| Ability to visualize molecules from different perspectives | ✓ | ✓ | |
| Difficulties intrinsic to chemistry | |||
| Abstract nature of chemistry | ✓ | ✓ | |
| Representing 3D structures in the form of 2D representations | ✓ | ✓ | |
| No one true representation in chemistry | ✓ | ||
| Difficulties related to providing instruction | |||
| Representations are a source of misconceptions | ✓ | ||
| Limited class time is a barrier to teach about representations well | ✓ | ||
Overall, all three participants described that it is difficult to develop some skills such as the ability to interpret representations, generate representations, translate between representations, understand affordances and limitations of representations, and visualize molecules from different perspectives. In addition to these difficulties, Sid and Mai discussed difficulties intrinsic to chemistry itself. They both shared the sentiment that chemistry is difficult to learn because of its ‘abstract nature’ and because chemists often ‘represent 3D structures in the form of 2D representations.’ Sid also discussed that there is ‘no one true representation’ in chemistry because chemical phenomena can be represented in different ways, and this can make learning chemistry complicated for students. Dan, on the other hand, highlighted difficulties related to providing instruction. He expressed that teaching with representations can be challenging because sometimes ‘representations are a source of misconceptions.’ He also articulated a barrier to providing high-quality instruction around representations; he expressed that limited time is an issue in ensuring sufficient explanations are provided for the different representations taught in an organic chemistry course. The idea of time being a barrier to quality teaching has been previously reported in other contexts. For example, Shadle et al. (2017) identified time as the main barrier to using evidence-based instructional practices in science classrooms.
Finally, Mai was the only participant who also addressed what makes learning about representations easy, stating that certain representations (Lewis structures, bond-line structures, and molecular formulas) are very clear and easy for students to understand. Although these representations might be relatively simple, previous research has shown that Lewis structures can be very challenging for students (Cooper et al., 2010; Grove et al., 2012). Therefore, Mai might be assuming that these representations are easy for students to understand.
| Teaching Strategy | Mai | Sid | Dan |
|---|---|---|---|
| Explains the rationale for using various representations | 1 | 4 | 1 |
| Draws/builds representations for students | 1 | 1 | 2 |
| Explains new representations in light of familiar representations/ideas | 2 | 4 | |
| Uses a combination of formative and summative assessments | 1 | 1 | |
| Starts from simpler molecules/representations and slowly builds complexity | 1 | 1 | |
| Asks students to practice drawing/building representations | 2 | 2 | |
| Uses different representations together to enhance learning | 1 | 1 | |
| Carefully chooses the representations to introduce new ideas | 1 | ||
| Scaffolds all the features of new representations | 2 | ||
| Uses multiple representations to explain a difficult concept or ideas | 2 | ||
| Spends more time explaining complex representations and ideas | 1 | ||
| Teaches representations in tandem without overwhelming the lecture | 2 | ||
| Covers less but better | 1 | ||
| Uses repetition | 1 | ||
| Teaches students how to use representations to make predictions and inferences | 1 | ||
| Teaches multiple representations due to their limitations | 1 | ||
| Explains a general rule followed by specific examples | 1 |
All three participants stated that they ‘explain the rationale for using representations’ and ‘draw/build representations for students.’ Sid explained that he draws representations to allow for proper pacing for students. Sid and Mai shared four additional strategies: ‘explains new representations in light of familiar representations/ideas,’ ‘uses a combination of formative and summative assessments,’ ‘starts from simpler molecules/representations and slowly builds complexity’, and ‘asks students to practice drawing/building representations.’ These overlapping ideas show that Mai and Sid use multiple similar strategies when teaching about representations. In comparison to Dan, based on their descriptions, Mai and Sid also rely on a much wider variety of teaching strategies.
A more nuanced analysis of codes and quotes provided evidence that Sid was very reflective when describing strategies for teaching with representations. Table 5 represents the number of times each participant described each strategy during their interview. The table shows that most teaching strategies were mentioned one or two times throughout the interview. At the same time, Sid discussed two strategies four times throughout his interview: ‘explains the rationale for using various representations’ and ‘explains new representations in light of familiar representations/ideas.’ These strategies provide great insight into Sid's PCK for teaching about representations. Consider the following quote from Sid that highlights both of these aforementioned codes:
“So there are a lot of different new representations that get introduced in organic chemistry or at least you don’t assume that they’ve seen [them] before. They’ve probably seen some of them before. Um, you know, the first one is probably the bond-line structures, which are really kind of the foundation for the whole course. I mean that's usually in lecture one or two or something, something early on. So, um, it's a question of sort of going back over what a, uh, essentially what a Lewis structure is and then, and then abstracting it a little bit from there and trying to emphasize sort of the importance of, or why we use bond-line structures, you know, to eliminate clutter and to emphasize parts of the molecule we think are more important than to just because they're easier to draw quickly.”
As can be seen from this quote, Sid introduces bond-line structures in the context of being similar to Lewis structures, which should be familiar to students from General Chemistry. He explains how the two representations are similar and different from each other. In addition, Sid emphasizes the purposes and affordances of bond-line structures, helping students develop meta-representational competence (diSessa, 2004; Schönborn and Anderson, 2006).
Sid's interview included multiple detailed reflections and explanations of this nature. In comparison, Mai mentioned that she explains the purpose of representations only once, very briefly, in the context of Fisher projections: “Um, but yeah, I definitely stress to them, you know, why are Fischer projections helpful.” This quote has less detail and only briefly states that Mai explains to students the usefulness of Fischer projections. Dan also stated that he explains the rationale for using representations, but unlike Sid and Mai he did not specify any specific representation he was referring to: “I think I always say that you know, in some ways we need to be familiar with multiple versions so we, you know, communicate effectively, say using the shorthand to communicate accurately by recognizing the shorthand in fact represents the more detailed representation.” This quotation is representative of Dan's vague reflections when describing his instructional practices for teaching about representations.
Even though all three instructors are from the same institution and are all teaching undergraduate organic chemistry, we see clear differences in their PCK. Mai, and Sid especially, were much more descriptive and reflective during their interviews, whereas Dan only briefly expressed a limited number of ideas. The analysis also revealed that there were variations in responses across most of Geddis’ PCK criteria, with the biggest differences observed for criterion 4, conceptual teaching strategies for teaching with representations. Sid and Mai articulated over ten different strategies that they use to support students in developing understanding while learning about representations; Dan, on the other hand, only expressed four unique strategies. In addition, Dan was the only participant who shared that a ‘limited class time is a barrier to teaching about representations well.’
RQ2: What are the organic chemistry instructors’ approaches toward teaching and assessing representational competence skills?
Approaches toward teaching about representations
To get an insight into Mai's, Sid's, and Dan's instructional practices, using the codes in Table 2, we analyzed every PowerPoint slide in their lecture(s) for the beginning chapter(s) covering the following topics: bonding, Lewis structures, formal charges, molecular orbitals, hybridization, and molecular representations. We used three frameworks to code representations in their lecture slides: Johnstone's three levels to characterize the types of representations in the slides, Ainsworth's functional taxonomy to understand the pedagogical function of representations in the slides, and the RC framework to understand what RC skills are taught in the slides. The results below reflect our analyses of course artifacts of Mai's nonmajor course, Dan's major course, and Sid's nonmajor and major courses. | ||
| Fig. 1 Analysis of slides with Johnstone's three levels. M indicates that the instructor teaches a major course. NM indicates that the instructor teaches a nonmajor course. | ||
 | ||
| Fig. 2 Analysis of slides with the Ainsworth's functional taxonomy. M indicates that the instructor teaches a major course. NM indicates that the instructor teaches a nonmajor course. | ||
 | ||
| Fig. 3 Analysis of all slides (with or without activities) with the RC framework. M indicates that the instructor teaches a major course. NM indicates that the instructor teaches a nonmajor course. | ||
A more detailed analysis of the participant's lecture slides with the RC framework included examining any activity, practice problem, clicker question, and discussion question embedded in the lecture slides (referred to as activities for the rest of the paper). The three participants used similar activities in their slides but presented them in different formats. For example, Mai tended to ask questions with an accompanying representation, while Sid framed his activities as example practice problems for both the nonmajor and major courses. Dan also framed his activities as example practice problems, while also using clicker questions to check student understanding. This analysis revealed that the topics Lewis structures and formal charges had the most activities associated with them. Overall, Sid included almost twice as many activities in the lecture slides for his nonmajor course (Sid-NM, n = 11 activities) in comparison to Dan and Mai, who each included 6 activities in their lecture slides. Interestingly, Sid also only included 6 activities in the lecture slides of his major course (Sid-M). This highlights differences between Sid's lecture slides for his Organic Chemistry course for majors and nonmajors. Note that although Sid included twice as many activities in his slides for his nonmajor course, these activities targeted the same RC skills. In addition, we found that no instructor included activities that support students in developing higher-level meta-representational skills, such as the ability to ‘select’ an appropriate representation for a particular purpose, the ability to explain ‘affordances and limitations’ of different representations, as well as the ability to take the ‘epistemological position’ that representations correspond to but are distinct from the phenomena they represent (diSessa, 2004; Schönborn and Anderson, 2006).
Approaches toward assessing representational competence
To gain insight into Mai's, Sid's, and Dan's assessment practices, we analyzed the first midterm exam in their courses. The first midterm exam was chosen because the questions on this assessment align well with the analyzed content in participants' lecture slides. Two frameworks were used to code exam questions: the RC framework to understand what RC skills were assessed and Johnstone's three levels to characterize the types of representations used (Table 2).Analysis of midterm exam questions with the RC framework
To understand what RC skills each instructor assessed, we coded their first midterm exam with the RC framework; all three instructors assessed the same four RC skills (Fig. 4). Overall, 85–90% of all of the midterm exam items asked students to ‘interpret’ and ‘use’ representations, and 10–20% of the items asked students to ‘generate’ representations and ‘translate’ between representations. One possible reason for such a low number of items asking students to ‘generate’ representations is because most of the midterm exam items were multiple-choice. Additionally, the ‘interpret’ skill may have had the highest percentage across all three instructors because it was often double coded along with other skills; one cannot ‘use’ representations or ‘translate’ between representations without first ‘interpreting’ them. In comparing Sid's exams for his major and nonmajor courses, the major course had more questions that asked students to ‘generate’ representations than the nonmajor course. Sid also assessed the ‘translate’ RC skill more than his colleagues, in both his major and nonmajor courses. Other RC skills, like higher-level meta-RC skills, were not assessed on the midterm exams of the three instructors. In addition, even though a fairly large proportion of the items assessed the ‘use’ skill, the items focused on asking students to make inferences about structure–property relationships, as opposed to on more sophisticated ideas such as using representations to predict and explain phenomena. | ||
| Fig. 4 Graph showing the percentage of the four RC skills found in the exams that the participants assess. M indicates that the instructor teaches a major course. NM indicates that the instructor teaches a nonmajor course. | ||
Analysis of representations in the midterm exam questions with the Johnstone's three levels and beyond
Analysis with Johnstone's framework revealed that all representations in the first midterm exam of the three instructors were at the symbolic level. When it comes to the types of representations, Sid incorporated nine different types of representations, Mai included seven, and Dan included six. Generally, each exam item focused on one type of representation, with some items focusing on two. Skeletal structures were the most used representation by the three instructors on their first midterm exams. Further analysis showed that there was no relationship between the types of representations used on the midterm exam and the RC skills assessed, except for the ‘translate’ skill. Most of Dan's ‘translate’ items asked students to translate from an IUPAC name to a different type of representation. Most of Mai's ‘translate’ items asked students to translate between two different skeletal structures, while most of Sid's ‘translate’ items asked students to translate from a skeletal structure to different types of representations, and vice versa.RQ3: How (if at all) do organic chemistry instructors' goals and PCK around teaching about representations align with their instructional and assessment practices?
Table 6 summarizes the goals, PCK, instructional practices, and assessment practices of the three instructors around teaching about representations and developing student RC.
| Mai | |
| “Being able to read the graphs is important. We also make them play with their model kit and make different molecules with it. Cause there's definitely a little bit of a learning curve to using the model kit. And also for drawing mechanisms, learning how to draw the arrows properly. Those are things that we try to develop in them.” | |
| Goals | • Articulated concrete teaching & assessment goals for RC |
| • Teaching & assessment goals are mostly aligned | |
| PCK | • Uses multiple representations to help visualize chemical phenomena |
| • Does not assume student RC | |
| • Recognizes student difficulties in developing skills and chemistry in general | |
| • Articulated 11 strategies for teaching about representations | |
| Instructional practices | • Mostly symbolic representations in slides |
| • Most representations serve the scaffolding and constraining functions | |
| • Strong focus on interpreting with some focus on translating and generating representations | |
| • Little to no focus on higher-level RC skills | |
| Assessment practices | • Only symbolic representations on the midterm exam |
| • Strong focus on interpreting and using representations | |
| • Little to no focus on higher-level RC skills | |
| Sid | |
| “On exams, we have questions explicitly about representations which would just be sort of converting from one to another, which early on in the course are more appropriate because that's actually the skill we're trying to develop, you know, how to convey chemical structures through different sorts of representations.” | |
| Goals | • Articulated concrete teaching & assessment goals for RC |
| • Teaching & assessment goals are somewhat maligned | |
| PCK | • Uses multiple representations to help focus on fundamental ideas & communicate different info |
| • Does not assume student RC | |
| • Recognizes student difficulties in developing various skills and chemistry in general | |
| • Articulated 11 strategies for teaching about representations (reflective, intentional descriptions) | |
| Instructional practices | • Mostly symbolic representations in slides for NM course; a higher proportion of submicro and hybrid representations in M course |
| • Most representations in NM slides serve the constraining and complementary functions | |
| • M course included constraining, scaffolding, and complementary functions | |
| • Strong focus on interpreting representations with some focus on translating and generating representations, in both courses; M course more strongly focused on interpretation | |
| • Little to no focus on higher-level RC skills | |
| Assessment practices | • Only symbolic representations on the midterm exam |
| • Strong focus on interpreting and using representations, some on translating | |
| • No focus on higher-level RC skills | |
| Dan | |
| “A big part of the problem is a volume of material expected to be covered. We spend less time on different, you know, representations, going in them in detail because of the volume of content. You know, there's an expectation that in two semesters we'll cover basically the whole textbook.” | |
| Goals | • Did not articulate any concrete teaching or assessment goals for RC |
| PCK | • Uses multiple representations to communicate different information |
| • Does not assume student RC | |
| • Recognizes student difficulties in developing various skills and in providing instruction | |
| • Articulated 4 strategies for teaching about representations (short and vague descriptions) | |
| Instructional practices | • Slides included symbolic, submicroscopic, and hybrid representations |
| • Half of the representations serve the constraining function; the other half serve a variety of other functions | |
| • Strong focus on interpreting with some focus on translating and generating representations | |
| • Little to no focus on higher-level RC skills | |
| Assessment practices | • Only symbolic representations on the midterm exam |
| • Strong focus on interpreting and using representations | |
| • No focus on higher-level RC skills | |
The vast majority of the representations that each instructor discussed using in the interview appeared in their lecture slides. Some representations mentioned in the interview, like 3D models and animations, were not captured in the analysis of the course artifacts. There were also several representations that each participant incorporated in their lecture slides and assessments that they did not mention during the interview. This was particularly evident for Dan who failed to discuss using multiple representations in his course artifacts (e.g., Kekulé structures, electrostatic potential maps, dash-wedge diagrams, skeletal structures, and condensed structures). The misalignment between the representations Dan discussed during the interview and the representations that appeared in his course artifacts shows further evidence that he was less reflective, particularly when compared to Mai and Sid.
Finally, some of the teaching strategies that were discussed during the interview could be evidenced in the lecture slides of the three instructors. Note that we did not expect to detect all of the described teaching strategies as we did not collect classroom observation data. Sid discussed using 11 different strategies to teach about representations, and three of these strategies were evidenced in his lecture slides. Specifically, he used ‘repetition’ by showing representations and concepts multiple times, included activities in his slides to allow ‘students to practice drawing/building representations’, and scaffolded complex representations because it's important to ‘start from simpler molecules/representations and slowly build complexity.’ Mai also discussed using 11 strategies when teaching about representations, and four of these strategies were evidenced in her lecture slides. Specifically, she broke down complex representations that she introduced to ‘scaffold all the features of the new representations’, and ‘start from simpler molecules/representations and slowly build complexity’, included activities in her slides to allow ‘students to practice drawing/building representations’ and ‘used different representations together to enhance learning’. Dan only discussed 4 different teaching strategies and of these strategies, one strategy was evidenced in his lecture slides. He ‘uses different representations together to enhance learning'. This analysis shows that there is some alignment between participants’ described and enacted teaching strategies.
| Mai | Sid | Dan | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TG | TP | AG | AP | TG | TP | AG | AP | TG | TP | AG | AP | |
| Interpret | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||
| Generate | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||
| Translate | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||
| Use | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||
| Aff./lim. | ✓ | ✓ | ✓ | ✓ | ||||||||
| Select | ✓ | |||||||||||
| Epistem. | ||||||||||||
Sid described teaching his students four RC skills: (1) ability to interpret representations, (2) ability to generate representations, (3) ability to translate between representations, and (4) ability to understand the affordances and limitations of representations. The analysis of his lecture slides revealed that he teaches the aforementioned four RC skills in addition to (5) the ability to use representations to make inferences, draw conclusions, and solve problems. When it comes to the assessment goals, Sid described assessing students on two RC skills: (1) ability to translate between representations and (2) ability to select the most appropriate representation for a particular purpose. The analysis of his first midterm exam revealed that he assesses four RC skills (on exams for both of his courses): (1) ability to interpret representations, (2) ability to generate representations, (3) ability to translate between representations, and (4) ability to use representations to make inferences, draw conclusions, and solve problems. This analysis demonstrates a high level of alignment and intentionality when it comes to Sid's teaching practices, but not in the context of his assessment practices.
Dan did not articulate any goals for teaching and assessing student RC. However, the analysis of his lecture slides and his first midterm exam revealed that he does in fact teach and assess RC skills. Specifically, his lecture slides have the potential to support students in developing the same five RC skills as the ones taught by Mai and Sid. His first midterm exam assessed the same RC skills, except for the ability to understand the affordances and limitations of representations. This confirms that Dan teaches and assesses RC skills without realizing it. This can be problematic because unless specific skills are identified as intentional goals in a course, it is unlikely that these skills will be effectively taught and assessed (Stowe and Cooper, 2017).
Limitations
This study provides a qualitative exploration of three undergraduate organic chemistry instructors' goals, PCK, and practices toward teaching and assessing student RC skills. As this is a case study, the sample size is small. Furthermore, all participants in this study were from the same institution. As such, these results are not generalizable and are not intended to suggest similar patterns in goals, PCK, and instructional and assessment practices for organic chemistry instructors at other institutions. Goals and PCK were elicited and characterized from what instructors described in the interview; the open-ended interview protocol allowed for follow-up questions and additional probing to minimize missing information. It is possible that with a longer interview period with a higher degree of probing, the instructors might have expressed more intricate PCKs or a wider range of goals. Additionally, we did not collect classroom observation data to analyze the participants’ enacted classroom practices. Therefore, all inferences about how participants teach about representations, and how they assess student understanding of representations, were made based on the analysis of interview responses and course artifacts. In the absence of classroom observations and student learning outcomes data, it is impossible to make definitive claims about the quality of how these instructors teach about representations and develop students' RC skills. Furthermore, given that PCK is a tacit and dynamic cognitive construct, thorough characterization of instructors’ thinking requires one to couple interview data with classroom observation data.Despite these limitations, this study offers a rich, multi-framework characterization of organic chemistry instructors' approaches to teaching about representations. Triangulation of multiple data sources (i.e., interviews and course artifacts) and the use of multiple analytical frameworks (i.e., Kozma and Russell's RC framework, Geddis PCK criteria, Ainsworth's functional taxonomy, and Johnstone's triplet) allowed us to interrogate the data and identify different ways of understanding instructors' goals, PCK, and practices; combined, these all enhance the trustworthiness and transferability of our findings (Lincoln and Guba, 1986).
Conclusions and discussion
The case study described herein triangulates multiple data sources (Table 1) and uses various frameworks (Table 2) to provide a rich, detailed characterization of the goals, PCK, and approaches toward teaching and assessing representations for three organic chemistry instructors. Although from the same institution and teaching the same subject, there were variations in instructors’ goals, PCK, and practices (Table 6). We found that Mai and Sid discussed explicit goals around developing student RC skills (Table 3). They also recognized that some students might struggle to develop different domain-specific skills, such as RC skills and visuospatial ability. In contrast, Dan did not articulate any concrete goals around developing student RC, despite recognizing that some students struggle to develop the ability to interpret and translate between representations. Interestingly, Dan's course artifacts revealed that, without realizing it, he does teach and assess several RC skills (Fig. 3 and 4). This finding corroborates previous results that showed a misalignment between the RC skills that instructors intend to develop and the RC skills that they teach and assess (Popova and Jones, 2021). This finding is also concerning because unless specific skills are identified as learning goals in a course, it is unlikely that these skills will be effectively taught and assessed (Stowe and Cooper, 2017). In other words, an instructor cannot effectively support their students in the acquisition of skills that the instructor is unaware of. To further test this assumption, future research should compare the learning outcomes of students taught by chemistry instructors who intentionally cultivate students’ RC and those who unintentionally teach and assess these skills.In addition to analyzing participants’ goals for teaching and assessing RC skills, we used Geddis’ four criteria to investigate similarities and differences in Mai, Sid, and Dan's PCK. Because Mai and Sid were much more reflective, their PCK was better understood when compared to Dan. Mai and Sid recognized that they needed many strategies and representations to aid in transforming their expert content knowledge into teachable forms. Not only were these ideas expressed by them multiple times during the interview, but they were also evidenced in their instructional practices. In addition, one of the most distinguishable characteristics of Mai and Sid's PCK is that they described using eleven different instructional strategies to teach about representations (Table 5). Unlike Dan, who was only able to articulate four strategies, Mai and Sid described possessing many more tools in their instructional toolbox. As Dan is a newer teacher, he may not have thought about his teaching practices to the same extent as his colleagues. Additionally, since Dan was not as reflective, it was hard to capture his PCK and how it affects his instructional practices. While Dan's interview was the longest of the participants, he struggled to elaborate on his ideas and stay on topic, despite the interviewer purposefully rephrasing questions to encourage elaboration. In summary, we found distinct differences in the PCK of the three organic chemistry instructors from the same institution for teaching about representations and developing student RC. Previous work by Park and Chen (2012) further corroborates these findings; they examined the process through which various components of personal PCK shaped the classroom practices of four biology teachers; even though the teachers worked at the same high school, taught the same topics (photosynthesis and heredity), and had similar lessons plans, their personal PCK differed. This finding is replicated by the study herein showing the complexities of PCK. Future research in this area needs to examine the relationships between chemistry instructors’ PCK and how it might affect their instructional practices, as well as student outcomes around developing RC.
Findings show that all three participants used symbolic and submicroscopic representations, or a hybrid of the two, in their instruction; no macroscopic representations were found in the data (Fig. 1). This shows similarity in the general approach these three participants have for incorporating representations into their instruction. Despite the similarity in the general types of representations, we found differences in the specific representations each instructor used and their pedagogical functions (Fig. 2). Interestingly, while Mai and Sid used the same textbook, they do not necessarily select the same representations; their selections are likely guided by the different pedagogical functions that these representations might serve. When comparing all three instructors, Mai utilized the scaffolding function more than the other two participants, which is a productive strategy; scaffolding supports students learning along the novice–expert continuum and allows for students to become increasingly fluent at linking abstraction elements to a more sophisticated schema (Offerdahl et al., 2017). In addition, the Ainsworth framework (Ainsworth, 2006) also allowed us to capture variation in the function of representations in Sid's slides for his courses (Fig. 2). His nonmajor course utilized a higher proportion of constraining representations (i.e., representations that depict the same molecule or same information in several different ways, where one representation is more familiar and straightforward than the other), whereas his major course utilized a higher proportion of scaffolding representations (i.e., representations that guide students step-by-step toward skill-building and understanding of concepts). Additionally, Sid's slides for his major course included fewer activities overall than his nonmajor course.
The RC skills that the participants focus on in their instruction are lower-level representational competence skills, such as the ability to interpret, generate, and translate between representations (Fig. 3 and 4). The focus on lower-level representational competence skills has been seen previously; for example, Xue and Stains (2020) found that one of the two organic chemistry instructors in their study focused on developing meta-RC, whereas the other did not. Similarly, Linenberger and Holme (2015) found that biochemistry instructors identify the ability to interpret and generate representations as key skills for their courses, without discussing higher-level skills. The finding that organic chemistry instructors do not teach meta-RC skills might be linked to the fact that meta-RC skills are not taught in organic chemistry textbooks (Gurung et al., 2022); this link is suspected because textbooks often serve as curricular guides and play a critical role in lesson planning and how the material is explained (Tulip and Cook, 1993; Bergqvist and Chang Rundgren (2017)). These findings suggest a gap in the current instruction because according to prior research, it is important to intentionally go beyond simple skills such as the ability to interpret representations and support students in the acquisition of higher-level meta-RC (diSessa, 2004; Schönborn and Anderson, 2006; Xue and Stains, 2020).
Overall, in comparison to Dan, Sid and Mai evidenced the most alignment between the goals they set for students and the types of representations, teaching strategies, and assessment tactics used in their courses (Table 7).
Implications
The findings described herein have implications for chemistry education practitioners and researchers. First and foremost, results suggest that there is a need for professional development programs that specifically target developing student RC. Such professional development programs must equip instructors with literature-based resources and supports that could meaningfully affect their PCK and teaching practices (Gess-Newsome et al., 2003; Henderson et al., 2011; Talanquer, 2014). As such, effective pedagogical training, customized to teaching about domain-specific representations, is needed to facilitate the professional growth of instructors. This type of pedagogical training could help instructors (1) understand relevant learning theories such as constructivism (Novak, 1993), dual-coding theory (Paivio, 1986) and the information processing model (Baddeley, 2003), as well as how to facilitate meaningful learning with chemical representations (e.g., Johnstone's triplet (Johnstone, 2010)); (2) learn about the key factors affecting students' ability to reason with representation (e.g., prior content knowledge, mode of external representations, understanding the visual language and conventions used in various external representations) (Schönborn and Anderson, 2006, 2010); and (3) promote awareness of RC skills and how to support students in developing both lower-level skills and higher-level meta-RC skills (diSessa, 2004; Kozma and Russell, 2005). The latter is particularly important given that one of the instructors in this study teaches and assesses RC without realizing it, and all three instructors described only teaching lower-level RC skills. In addition, even though the instructors taught and assessed students' ability to use representations, this often included only the ability to make inferences about structure–property relationships, as opposed to also predicting and explaining phenomena. This suggests that instructors need professional development to effectively support students in using representations as models as opposed to as just inert knowledge that does not carry the larger epistemic context within them (Gouvea and Passmore, 2017). The success of such faculty professional development initiatives needs to be studied to understand what constitutes effective training in this domain, and how to most appropriately structure programs to foster growth and development.To aid student learning, organic chemistry professors (and all instructors in general) must be purposeful and intentional when crafting and aligning goals for their courses. Understanding the skills that they want students to develop, and how to develop those skills, is key and necessary. From our data, we see that reflective instructors (Sid and Mai) were intentional about what they wanted students to learn and evidenced carrying out those goals in their teaching practices. As a result, Sid and Mai were able to describe how they knew students understood what they were learning, and the instructional strategies they use to aid students. However, as shown with Dan, some faculty members may have unknown and/or unintended learning outcomes embedded in their practice. As suggested by the limitations in Dan's discussion of his goals and practices, faculty may also want to consider student learning outcomes beyond traditional content knowledge (e.g., RC, scientific practices, affective learning, professional skills). To achieve this level of intentionality, instructors must engage with, and obtain a deeper understanding of, education research literature and evidence-supported teaching practices. This, combined with the suggested professional development opportunities, can guide, drive, and support instructors in crafting goals, and aligning them with their practice, to enhance student learning.
In addition, more research is needed to characterize the impact of instructor thinking and teaching practices on students’ developed RC skills. This analysis could include triangulating faculty interviews, classroom observations, and assessments of student learning outcomes. However, such an investigation requires a high-quality instrument to measure student learning outcomes related to RC. As such, an assessment instrument is needed to measure student RC skills in the context of chemical representations.
Additionally, findings related to Sid who approaches teaching major and nonmajor students differently are interesting but limited; future research should investigate how instructors approach teaching similar topics to different groups of students to further understand nuances in instructor goals, PCK, and practices.
Finally, this paper is an exemplar of how to use multiple theories as analytical frameworks to gain extensive insights into instructors’ PCK and teaching practices. Each theory served a unique role and provided a different lens with which to interrogate the data and glean insights. Using the theories in conjunction with each other also allowed for deeper and more comprehensive understandings than if used independently. We hope that this case study approach will provide a model for in-depth qualitative studies that seek to triangulate multiple data sources to understand abstract and complex ideas (such as instructor PCK).
Conflicts of interest
There are no conflicts to declare.Appendix
Interview ProtocolDemographic questions:
1. How many years have you been teaching? OChem specifically?
2. What types of OChem courses do you teach (OChem I/OChem II/graduate courses)?
3. What courses have you taught/are teaching this year?
4. How many students are typically enrolled in your course?
5. What types of students enroll in your course? (majors/nonmajors, sophomores/juniors)
Questions about the use of representations in the classroom:
1. What types of representations do you use to teach organic chemistry?
2. What is the purpose of the representations you use?
3. Where do you get the representations you use?
4. What criteria do you use to select representations?
5. How do you integrate representations in your teaching? (introduce, help students make sense of them)
– Is there anything that you know about student thinking that influences how you teach about representations?
6. Are there any specific skills that you want your students to develop when they learn about representations?
– Do you prefer exposing students to multiple representations of the same phenomena or do you choose one that you consider the most scientifically correct?
– Do you spend time teaching the students how to make sense of the representations or do you mostly focus on helping students understand concepts?
7. How do you know that your students understand representations that you introduce in your course?
– Do you use representations in your assessments?
– What types of representations do you use on your assessments?
– What is the purpose of representations that you use on your assessments?
8. What resources, support, or instructional materials do you wish you had access to that would help you teach about representations more effectively?
Questions about different representations of the same molecule:1. When preparing to teach about these representations, what do you take into consideration?
2. What do you intend students to learn about these representations?
3. What do you know about student thinking that influences how you teach about these representations?
4. What are the difficulties associated with teaching about these representations?
5. What resources, support, or instructional materials do you wish you had access to that would help you teach with representations more effectively?
Do you agree with the following statement? Why or why not?
1. Different students respond to representations differently.
2. Some people are more visual than others because of their learning styles.
3. Some students are better at understanding representations than others and there is not much the instructor can do about it.
4. More realistic images are more helpful for student understanding than abstract ones.
5. I assume that students come to my course already having developed representational competence in previous courses/high school and I can place a stronger focus on explaining concepts.
Acknowledgements
We thank the chemistry instructors who participated in this study. We also thank the Popova Research Group for assistance in transcribing the interviews and providing feedback on an earlier draft of this manuscript. Finally, we thank Richard H. McKinney for his assistance in creating original figures for the interview protocol.References
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