Alternative Use for the Refined Consensus Model of Pedagogical

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Alternative Use for the Refined Consensus Model of Pedagogical Content Knowledge: Suggestions for Contextualizing Chemistry Education Research Jon-Marc G. Rodriguez*,† and Marcy H. Towns

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Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States ABSTRACT: The primary goal of chemistry education research should be to improve the teaching and learning of chemistry; however, in some cases, the implications of research are too abstract to readily apply to the classroom. In this commentary, we provide suggestions to help researchers contextualize their work for practitioners, asserting the utility of situating research using the framework outlined in the refined consensus model of pedagogical content knowledge, which describes the dynamic interactions among different knowledge bases as instructors engage in planning, teaching, and reflecting. Although it provides a productive avenue for research, the premise of this paper is not to advocate for more studies designed using this framework; rather, a suggestion is made to consult this framework during dissemination, that is, when considering the relevance of the results for practitioners.

KEYWORDS: General Public, Chemical Education Research, Pedagogical Content Knowledge

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Chemical Education CER articles5 and in an editorial in this Journal that emphasizes that research should be intentional and should move the field forward.6 Nevertheless, in some cases, the implications of a research study might not be stated explicitly or its application to the classroom might not be obvious to practitioners, particularly if the work is overshadowed by technical jargon.7 We posit that one way to help researchers contextualize their work is through the use of the refined consensus model of pedagogical content knowledge, a framework from the science education research community that characterizes the knowledge used by an instructor during processes associated with teaching.8 That stated, the goal of this commentary is to (1) provide a brief overview of the refined consensus model of pedagogical content knowledge and (2) describe the utility of this framework in helping researchers draw connections between their work and practical applications for instructors.

s discussed by the National Research Council,1 disciplinebased education research, such as chemistry education research (CER), serves a critical role in improving undergraduate education. Through the process of careful design, implementation, analysis, and communication of results, insights are provided that can inform the teaching and learning of chemistry, as well as help address related concerns that are inherent to the discipline.2,3 Given the importance of chemistry education research in supporting students in developing a sophisticated understanding of phenomena and fostering competency in skills with broad applicability, special attention should be given to the “Conclusion and Implications” sections of manuscripts. This sentiment is reflected in an ACS Symposium Series book, The Nuts and Bolts of Chemical Education Research:4 The ultimate goal of a chemistry education research project is that the scholarly work resulting from the research will have an impact on our understanding of teaching and learning, and will result in more effective and meaningful learning in the chemistry classroom. The idea regarding the importance of the relevance and application of research results is also echoed in a recent editorial in Chemistry Education Research and Practice,2 with similar arguments made in the guidelines for Journal of © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: April 27, 2019 Revised: July 15, 2019

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DOI: 10.1021/acs.jchemed.9b00415 J. Chem. Educ. XXXX, XXX, XXX−XXX

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Commentary

REFINED CONSENSUS MODEL OF PEDAGOGICAL CONTENT KNOWLEDGE As a construct, pedagogical content knowledge (PCK) was originally conceptualized by Shulman,9 who framed PCK as the knowledge needed to transform content (disciplinary expertise) into teaching. As discussed recently by Chan and Hume,10 there is a large body of literature grounded in ideas related to pedagogical content knowledge; however, multiple models for PCK exist, and related terms have been operationalized differently:8 PCK has generated particular interest as it represents the unique province of knowledge for teaching that distinguishes teachers from content specialists, and the idea has spawned many empirical studies on teachers’ knowledge, particularly in the domains of science and mathematics. Yet, despite its potential to move the field forward, the diverse understanding and interpretation of PCK that has occurred since its inception have greatly limited its utility in research, teacher education and policy. Stemming from the varied ways in which PCK has been used, recent efforts have moved toward explicitly defining PCK and related constructs, resulting in the refined consensus model of PCK.11 Within the current model, different types of knowledge are defined (professional knowledge bases) that interact and inform an individual’s pedagogical content knowledge, including assessment knowledge, content knowledge, curricular knowledge, knowledge of students, and pedagogical knowledge.8 Each of the professional knowledge bases are provided and defined in Box 1. As an additional note,

enacted PCK, the application of an individual’s knowledge and skills during the process of planning, teaching, and reflecting.8 Thus, enacted PCK can be conceptualized as a subset of personal PCK, which involves a subset of collective PCK, and is informed by the professional knowledge bases described in Box 1. For a summary of the three realms of PCK, see Box 2. Box 2. Descriptions of the PCK Realms. Adapted from ref 8. • Collective PCK: Cumulative knowledge held by a community of professionals, including practitioners and researchers • Personal PCK: An individual’s cumulative PCK (when an individual accesses or utilizes part of their personal PCK, it becomes enacted PCK) • Enacted PCK: Application of an individual’s PCK during planning, teaching, and reflecting Moreover, within this model, the different realms of PCK can be analyzed at various levels of grain-size (discipline, topic, and concept), and knowledge is posited to move dynamically among the three PCK realms, which is mediated by the specific educational context.8 The relationships among the constructs identified in the current PCK model is provided in Figure 1, which is a modified version of the representation provided by

Box 1. Descriptions for the Professional Knowledge Bases That Inform PCK. Adapted from ref 10. • Assessment Knowledge: Knowledge of how to design formative and summative assessments, including actiontaking based on assessment data • Content Knowledge: Subject matter knowledge that is pertinent to the teaching task, including key ideas and their relationships • Curricular Knowledge: Knowledge of the goals of a curriculum as well as its structures, scope, and sequence • Knowledge of Students: Knowledge of students’ cognitive development and variations in their approaches to learning and general characteristics • Pedagogical Knowledge: General knowledge and skills related to teaching, including learning theories, instructional principles, and classroom management we are using a nuanced definition for the professional knowledge base content knowledge, favoring a broader interpretation that encompasses knowledge and skills, reflecting an understanding of and ability to engage in science practices.12 Another important feature of the refined consensus model of PCK is the distinction between three different levels or realms of PCK: (1) collective PCK, the cumulative knowledge held by a community of professionals that is informed by empirical and anecdotal evidence and involves ideas related to pedagogy, student learning, assessment, and curricular context (i.e., professional knowledge bases); (2) personal PCK, the subset of collective PCK held by an individual combined with an individual’s experiences and interactions with peers; and (3)

Figure 1. Refined consensus model of pedagogical content knowledge, simplified and adapted from a model presented by Carlson and Daehler.8 The professional knowledge bases reflect different types of knowledge that inform collective PCK; personal PCK involves a subset of collective PCK (specific to an individual), and enacted PCK is the result of an individual applying their personal PCK to a teaching context. The arrow emphasizes the dynamic nature of knowledge and its movement across different realms of PCK. In the original model, the arrow goes in both directions; here, a single arrow is used to emphasize the importance of moving knowledge from collective PCK (e.g., that which is informed by research) to personal and enacted PCK. The silhouette of a person in the center emphasizes the idiosyncratic and individualized nature of PCK. B

DOI: 10.1021/acs.jchemed.9b00415 J. Chem. Educ. XXXX, XXX, XXX−XXX

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Figure 2. Reframing the implications of research by asking the question, “To what extent does this research inform each professional knowledge base?” Addressing this question contributes to the professional knowledge bases, which then informs collective PCK. Additional questions related to each of the professional knowledge bases are provided. The core ideas, crosscutting concepts, and science practices referenced in the content knowledge question are a reference to the three dimensions of the Next Generation Science Standards released by the National Research Council.12

Carlson and Daehler.8 In Figure 1, we used nested pentagons (instead of the concentric circles used by Carlson and Daehler8) in order to draw attention to the five professional knowledge bases, which are particularly important for the discussion framed in this commentary. Moreover, the pentagon is not drawn to scale, that is, the equilateral pentagon is not intended to imply that the proportion of knowledge in each knowledge base is equivalent. In addition, Carlson and Daehler8 utilized double-sided arrows to illustrate the dynamic nature of knowledge that moves in both directions (between collective PCK and enacted PCK and between enacted PCK and collective PCK), but here we used a single arrow to emphasize the importance of ensuring that disseminated research, which informs and contributes to collective PCK, reaches individual instructors and is applied to classroom practice. Moreover, although not depicted in Figure 1, an individual’s compilation of knowledge (i.e., personal PCK) and their application of this knowledge (i.e., enacted PCK) is informed and mediated by the learning context; thus, instructional decisions are highly dependent on the educational environment.8

dissemination phase of a study, not during the design phase. The way in which the refined consensus model of PCK outlines different types of knowledge that are useful for instructors readily lends itself to be used as a lens to help contextualize research in a way that is practical for the classroom. Thus, we are focusing on contributing to the knowledge bases that inform PCK, not PCK itself. When considering how the PCK framework could be applied to help support researchers, we were careful to consider the extent to which this tool would help improve the discussion of our research. Initially this began as simply thinking about our research in relation to each of the professional knowledge bases, but ultimately this was not fruitful; attempting to relate our research to the abstract constructs yielded vague implications for instruction. After discussions with colleagues, this led us to consider specific questions to promote deeper reflection. For example, in terms of considering the implications of a research project for instruction, it might be useful to reframe this discussion around the question, “To what extent does this research inform each professional knowledge base?” Building off this initial question, more detailed questions could be asked about each of the different knowledge bases, as shown in Figure 2. Thus, the idea is to use the different knowledge bases as an initial starting point to help researchers reflect more deeply about the implications of their work, and ultimately, addressing these questions and disseminating the results would contribute to our shared knowledge, which informs collective PCK. For clarification, this does not necessarily mean researchers need to cite and discuss PCK or related constructs in their work; instead, researchers should consult the PCK framework and use it as a



RETHINKING THE ROLE OF THE FRAMEWORK Given that the refined consensus model of PCK clarifies the constructs that influence PCK and their relationships to one other, utilizing this framework to design future studies would be particularly productive to provide support for instructors and graduate teaching assistants. Indeed the PCK framework has been used in a variety of topics across chemistry education research;13−22 however, the intention of this commentary is to draw attention to using the PCK framework during the C

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Figure 3. Illustration depicting the relationships among the different realms of PCK, along with questions to help move knowledge between the different realms. Moving knowledge from collective PCK to personal PCK is an issue of accessibility, and moving knowledge from personal PCK to enacted PCK is an issue of practicality.

the professional knowledge bases in the refined model of PCK, that does not necessarily mean the research is not relevant for the chemistry education community. Given that the PCK framework was developed primarily to characterize formal learning environments, we acknowledge the framework does not adequately address and encompass all types of chemistry education research. This does not invalidate other research; it simply highlights a limitation related to applying the framework. Another aspect of the framework worth drawing attention to is the nested nature of PCK, in which enacted PCK is part of personal PCK, and personal PCK involves a subset of collective PCK. One way of framing this is that once chemistry education research is published, it becomes part of the knowledge bases that inform collective PCK, but the extent to which this translates into personal PCK is an issue of accessibility (in terms of making the research both available and understandable), and even if an instructor has access to the research, the extent in which this translates into enacted PCK is an issue of practicality (see Figure 3). Therefore, as an additional consideration, researchers should be concerned if instructors are aware of emerging research and if instructors find the implications to be practical and achievable for implementation. One way to accomplish this is to work closely with the instructors involved in a particular study and share the results with the relevant stakeholders. Researchers should communicate directly with and discuss the implications with the instructor or graduate teaching assistant for the course from which the participants were sampled and then ask questions, elicit concerns, and determine in what ways they find the research results to be transferable to the classroom (i.e., Would they actually implement what is suggested by the research?). Movement among the different realms of PCK is

tool to consider the implications of their work for the classroom. Furthermore, in terms of the content that composes each professional knowledge base, it could be argued there is some overlap, which is largely a result of the highly interconnected nature of the various elements of this model. From the perspective of using the PCK framework to contextualize research, it is less important to be able to categorize an implication into a particular professional knowledge base category; what is more important is that the questions provided in Figure 2 are used to reconsider the research results from different perspectives to provide specific implications for instruction. Considering the different categories of professional knowledge bases, it is also worth considering how many of the professional knowledge bases are discussed in the implications section of a research paper. For example, if a study only adds to the knowledge of students category (i.e., the researchers only discuss topics that are challenging for the students), this may suggest the research focuses too much on what students do not know, as discussed by Cooper and Stowe in a recent review paper:23 “...there is little to be gained by simply cataloging misconceptions without paying heed to the mechanisms of their emergence, their organization, and their character.” Thus, by reflecting on which knowledge base or bases the research has an effect on, fruitful discussions can be generated that encourage meaningful results. However, it is important to focus on both quality and quantity, in terms of the number of professional knowledge bases addressed in a study. If researchers make surface-level connections to each knowledge base, it does not solve the problem of making research more relevant to practitioners. At the same time, if a study dived into detail and provided practical examples related to one of the knowledge bases, it would still be a valuable contribution to the community. Nevertheless, if research does not fit into any of D

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and is in contrast to viewing students as having stable ideas that are uniformly applied across contexts.25 Thus, as a general note regarding instruction, the specific word choice and context used have implications for how the students respond to a question and reason through a problem, which are closely related to understanding the knowledge and skills with which students need more support or are more likely to have difficulty (i.e., knowledge of students). On the basis of the analysis associated with the study discussed above, the following themes emerged: (1) students demonstrated an understanding of the mathematical definition of zero order in the form of equations, graphs, and the independence of rate on reaction concentration; (2) students tended to have difficulty describing the particulate-level phenomena modeled by zero-order reactions; (3) students were unsure how catalysts increased reaction rate and interacted with reactants, and they tended to state that catalysts do not influence reaction order; and (3) students tended to discuss and define half-life using first-order kinetics language (radioactivity, decay, carbon-dating, etc.), which negatively influenced how they solved the zero-order half-life problem. With respect to the students’ understanding of halflife, the results suggest students need more support applying half-life ideas across different contexts, which involves an emphasis on the definition of half-life in conjunction with examples from a variety of chemical systems with varying reaction orders. Being aware that students have these challenges is useful, but what’s more important is how this knowledge can be used and incorporated in different aspects of instruction, as discussed in the sections to follow.

critical, because the impact on student learning is diminished if the results are not translated into classroom practice.



TRANSLATING THEORY INTO PRACTICE In order to illustrate how the PCK framework could be applied to rethink the instructional implications of a research study, in this section we outline an implications-centered discussion involving a study we previously published in this Journal. In brief, the research study of interest involved interviews in which general chemistry and upper-level students worked through chemical kinetics problems, one of which involved a metal-catalyzed zero-order reaction, and students were prompted to reason about the half-life of the reaction.24 Because of limited space, further details will not be provided regarding the specifics of the study, but interested researchers and instructors are encouraged to read the paper. Using each of the professional knowledge bases that inform collective PCK, we provide specific suggestions based on the research results. As discussed previously, there is some overlap among the professional knowledge bases, so some are discussed together. Pedagogical Knowledge and Knowledge of Students

Pedagogical knowledge is a broad category that encompasses teaching techniques such as presentation of content and classroom management, but it also involves theoretical considerations about learning and cognition. The research discussed in the study above was designed around the resource-based model of cognition, which describes reasoning as involving the activation of context-specific ideas (resources) E

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engagement with the concepts.26,28,29 Therefore, any time researchers can distill and translate their work into a concrete product, such as by including a supplementary section with a concise summary of research results and “exam-ready” questions that assess target content and promote deeper conceptual reasoning, instructors will be more likely to use the research as a resource and implement evidence-based practices. As a closing thought, the importance of communicating research to instructors is nicely summarized by Richard Zare in “Questions to Chemical Educators from the Chemistry Community”:7 ...the answers provided by this community of scholars will have little impact unless chemists and chemical education researchers can communicate clearly to one another and gain not only each other’s respect but also the attention and respect of the wider chemistry community.

Assessment Knowledge, Content Knowledge, and Curricular Knowledge

One of the most practical applications of research is considering how it can be translated into assessment (assessment knowledge), which involves considerations regarding the scope of ideas relevant for a course (content knowledge), as well as the relationships with previous and future courses (curricular knowledge). For this discussion, informed by the 3D-LAP26 and best practices for designing multiple-choice items,27 we have designed some assessment questions that revolve around the themes that emerged from the study. Both constructed response (short answer and free response) and selected response (multiple choice) questions are provided in Box 3. In terms of the level of detail that should be discussed regarding reaction order, we posit that although discussions tend to revolve around first-order reactions in general chemistry courses (particularly in relation to half-life), zero-order reactions provide a unique opportunity to consider what is happening at the particulate level and apply ideas to new contexts, ideas that are important for future topics such as enzyme kinetics. Note how the assessment questions focus on drawing connections among zero-order reactions, rates, and catalysts and on considering the relationship between reaction order and half-life, with kinetics data (graphs) providing an opportunity for students to engage in the science practice analyzing and interpreting data. In broader terms, these items could easily be framed as opportunities for formative or summative assessments and could be adapted as homework, group work, or in-class (e.g., iClicker) questions.



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jon-Marc G. Rodriguez: 0000-0001-6949-6823 Marcy H. Towns: 0000-0002-8422-4874 Present Address †

J.-M.G.R.: Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States Notes



The authors declare no competing financial interest.



SUMMARY Reflecting on the paper we previously published, implications were provided for instruction, but we could improve on our specificity. For example, we discussed how our research could inform assessment and instruction, but we did not take it a step further and provide suggestions for possible exam questions. Reflecting on the process of translating our research into specific assessment items was a challenging process; nevertheless, we often leave it to instructors to accomplish this nontrivial task. Going an extra step and modeling assessment design for instructors has the potential to lower barriers to adoption. Translating research into practice can be daunting and challenging, so the more specific we are in our discussions, the more likely instructors will be to incorporate evidencebased practices into their teaching. The PCK framework and the discussion provided herein is one way of being more intentional about the instructional implications of research.

ACKNOWLEDGMENTS We wish to thank Kinsey Bain, Katherine Lazenby, and the Towns Research Group for their support and feedback on this paper.



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CONCLUSION One of the useful tenets of PCK is the way it shifts the focus away from a student-deficit model, emphasizing the role of the instructor and reframing the conversation around how an instructor can facilitate student learning. This emphasis on practical implementation allows the framework to be used to help reflect on the implications for research and practice, implications that should be both accessible and practical for instructors. As an additional note, from a practical standpoint, one professional knowledge base, assessment knowledge, plays a particularly critical role for both instructors and students. Through assessments, instructors communicate to students what is important; thus, instructors need to develop assessments that reflect learning objectives and require meaningful F

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DOI: 10.1021/acs.jchemed.9b00415 J. Chem. Educ. XXXX, XXX, XXX−XXX