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Chapter 10

The Impact of Guided Inquiry Materials on Student Representational Level Understanding of Thermodynamics Courtney Stanford,1 Alena Moon,2 Marcy Towns,3 and Renée Cole4,* 1Department

of Chemistry, Virginia Commonwealth University, 1001 West Main Street, Richmond, Virginia 23284-2006, United States 2Department of Chemistry, University of Michigan, 930 N. University Ave., Ann Arbor, Michigan 48109, United States 3Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907-2084, United States 4Department of Chemistry, University of Iowa, W331 Chemistry Building, Iowa City, Iowa 52242-1294, United States *E-mail: [email protected]

Student success has been connected to the ability to translate among three domains: macroscopic, sub-microscopic, and symbolic. Students in active learning classrooms work in groups and engage in productive discourse and interactions that result in meaningful learning. To investigate how guided inquiry materials, specifically POGIL activities, influence students’ use of representational reasoning in their argumentation, data was collected at multiple institutions and over multiple semesters. Analysis of the POGIL materials and classroom discourse helped identify at what level students are prompted to discuss concepts and what connections they make between the levels. It was found that students are often only prompted to examine a concept at one representational level, although they could generally make connections between the macroscopic and symbolic level. Furthermore, few connections to the sub-microscopic reasoning were found in the POGIL materials and this was reflected in student argumentation.

© 2018 American Chemical Society Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Introduction Recent research in physical chemistry education has attempted to better understand the difficulties students have in learning thermodynamics (1–3) as well as faculty beliefs about teaching and learning physical chemistry (4, 5). Tsaparlis (6) examined the history of teaching and learning in physical chemistry, and his work was expanded upon by Bain et al. (2) in a review that examined factors that influence student success, understanding of mathematical concepts and representations, students’ use of the particulate nature of matter, and students’ alternative conceptions in thermodynamics. One aspect of physical chemistry addressed in a special issue of Chemistry Education Research and Practice is the role of textbooks in informing and shaping instructors’ views and philosophies about teaching. It was suggested that more content analysis work should be done in regard to textual features, visual representations, questions, and problems (1). Tsaparlis (7) examined the organization and sequencing of content, and Nyachwaya and Wood (8) examined the representational information presented in commonly used physical chemistry textbooks. The aim of our study was to add to this growing body of knowledge by analyzing the Physical Chemistry Process Oriented Guided Inquiry Learning (POGIL) course materials and investigating how their use in physical chemistry classrooms helps students incorporate concepts at the macroscopic, sub-microscopic, and symbolic levels in the generation of scientific arguments.

Background Analysis of Textbook Materials The use of representations serves two important functions; interpreting representations to help learn chemistry content and how to “talk chemistry” by creating an argument and using representations to support a claim (9). Johnstone (10, 11) promoted the idea that chemistry can be divided into three domains: the macroscopic, sub-microscopic, and the symbolic level. These domains are commonly referred to as Johnstone’s Triangle or the chemistry triplet. The macroscopic level encompasses phenomena that are tangible and visible, the sub-microscopic involves particulate level models of matter, and the symbolic level includes chemical and mathematical signs and their relationships. While there have been different interpretations of Johnstone’s Triangle (10, 12, 13), it is widely accepted that it is critical for students to reason at each level and across levels to have a meaningful understanding of chemistry. At the general chemistry level, there has been a push to incorporate all three representational levels in textbooks to assist students in building connections across concepts. This can be easily seen when comparing the images and figures of today’s textbooks to those of twenty years ago. However, this shift does not appear to have happened in textbooks for upper level courses such as physical chemistry.

142 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Nyachwaya and Wood (8) selected several of the most popular physical chemistry textbooks and analyzed them to determine at what level (symbolic, macroscopic, or sub-microscopic) representations were presented to students in the figures and captions. It was found that many of these textbooks only discuss concepts at the symbolic level (81 to 100% of the representations) and do not included discussions as to how mathematical equations relate to the macroscopic or sub-microscopic levels. Few of the textbooks included information at the sub-microscopic and macroscopic levels, and the use of multiple representations in the figures occurred in less than 1% of figures for all the textbooks analyzed. This creates a situation where students are often expected to understand symbolic information at the sub-micro and macro levels but are rarely provided with information to help them make these connections. Because the students are only experiencing concepts at one level they are likely to end up with fragmented knowledge (14) and not understand how different representations for the same concepts are related. While the high percentage of symbolic representations may not be surprising considering the highly mathematical nature of physical chemistry (1, 6); classroom materials and instruction should support translation among levels of the chemistry triplet. The laboratory is another setting that can support students in translating between levels. Hernandez et al. (15) developed a laboratory activity on adiabatic and isothermal gas expansion to better understand how students struggle to connect macroscopic observations with particulate representations. They found that students typically used symbolic information or macroscopic relationships when making initial predictions, and usually resorted to algorithmic solutions when possible. Furthermore, students did not incorporate sub-microscopic level reasoning into their initial explanations even though the activity prompted students to provide a detailed explanation for their graphs.

Course Materials and Scientific Argumentation One important feature of scientific discourse is the practice of argumentation, which involves generating and considering evidence-based claims (16, 17). Kulatunga et al. (18) examined the connection between the structure of POGIL materials and the generation of student arguments in a general chemistry course. A significant portion of the student arguments came from questions with prompts such as “explain,” “why,” “predict,” and “show”. This indicates that the phrasing and the nature of a question can influence the generation of arguments. While this work begins to help us understand the influence of the structure of materials on student argumentation, additional work is needed to better understand the role the materials have on students’ construction of arguments and use of chemical representations to explain scientific concepts, especially at the physical chemistry level.


The Instructor’s Role in Building Connections across Representations Kozma et al. (9) noted the importance of the role of the instructor in active learning environments, including modeling the discourse and representational use that is desired of students. Instructors must demonstrate how to use representations to ask questions, interpret findings, and draw conclusions. This in turn will allow students to create an understanding of content that is grounded in representations. Becker et al. (19) investigated how an instructor can encourage the use of particulate level reasoning to explain thermodynamic phenomenon so that it becomes part of the classroom socio-chemical norms. The use of questioning, repeating, and expanding discursive moves has also been shown to promote the generation of student arguments and encourage students to translate between the macroscopic, sub-microscopic, and symbolic levels of chemistry (20). To help instructors better understand the type of support they are providing to students in building these connections, Philipp et al. (21) developed an observation protocol known as the Representations in Chemistry Instruction (RICI) protocol to measure the use of representations in inquiry-based classrooms. The RICI looks at aspects of instruction specific to chemistry classes that are not found in other observation protocols such as the use of particulate level reasoning, students’ ability to translate between representations depending on conceptual views (22), and the use of principle concepts about the representations in discourse (23).

The Role of Social Interactions in Learning POGIL and other active learning pedagogies encourage students to engage in meaningful discourse to construct knowledge to master content (24, 25). When instructors promote social interactions through group work and whole class disucssions, they help encourage the development of a classroom community. Roth and McGinn (26) suggested that the use of representations should be a fundamental part of any community of practice in order to help support students understanding of symbolic representations and the concepts that they represent. This is further supported by a study that found the use of representations and tools in communities confirms membership in a community of practice (9). It was postulated that environments could be designed to provide students with the representational tools needed to support their ability to use the language of chemistry, increase their understanding of chemistry content, and assist in becoming a member of a chemistry knowledge-building community. POGIL classrooms incorporate many of the practices suggested by Kozma et al. (9) and encourage representational competency by emphasizing analysis of representations to make sense of data and models, use of representations to explain chemical phenomena, and the use of language in a social context to communicate chemical understanding.


Rationale and Research Question Many instructors use published POGIL materials, but little research has been done to investigate how the materials support students in developing process skills such as argumentation and support reasoning about concepts across multiple levels. One way to understand how students make sense of thermodynamics concepts is to look at their use of the macroscopic, sub-microscopic, and symbolic levels in their arguments. Our study examined at what representational levels the POGIL materials addressed thermodynamics concepts for students to internalize and construct an understanding of the content. The aim of this study was to examine POGIL materials in thermodynamics as well as their implementation to determine: 1.

2. 3.

What macroscopic, sub-microscopic, and symbolic level information is provided by the thermodynamic POGIL materials and expected in student responses? To what extent do students incorporate macroscopic, sub-microscopic, and symbolic level information in their arguments? To what extent does the instructor mediate student interactions with the written materials?

Methods Participants and Setting The data for this project was drawn from three case studies of upper–division undergraduate physical chemistry courses at two mid-western institutions in the United States. All three courses used the Physical Chemistry: A Guided Inquiry – Thermodynamics POGIL Materials by Spencer, Moog & Farrell (27). A summary of each case study can be found in Table 1. The instructors, Dr. Black and Dr. Green, were both experienced using the POGIL curriculum, had attended POGIL workshops, and were active in the POGIL community. The student participants in each course consisted predominately of a mixture of 3rd and 4th year students. The backgrounds of the students varied, but in general the participants had completed two semesters of general chemistry, two semesters of organic chemistry, other upper-division chemistry courses, at least one semester of physics, and one or more calculus courses. In every course, the students were divided into small groups of three to five, in which individuals were assigned roles, although these roles were not always enforced in Dr. Green’s class. For this study, the research team selected one group from each iteration to observe during the small group work (SGW) portion of the class and observed the entire class during the whole class discussion (WCD) and lecture portions of the courses.


Table 1. Comparative Overview of Classroom Demographics for Case Studies B1, B2, and G1 2009

2010

2013 Instructor: Dr. Green

Instructor: Dr. Black Instructor Experience

9 years of implementing POGIL



Medium Mid-Western University

Small Mid-Western College

Thermodynamics

Physical Chemistry

Setting

Spencer, Moog & Farrell POGIL Materials (27) Number of Participants

15 Students

10 Females 5 Males

18 Students

146

3rd and 4th years

5 Females 13 Males

3rd and 4th years

10 Students

3 Females 7 Males

2nd, 3rd and 4th years

Participant Demographics Chemistry Majors Class Time

1/3 to 1/2 class small group work, rest whole class discussion

1/3 to 1/2 class small group work, rest whole class discussion

Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Science Majors 2/3 time small group work and 1/3 lecture

Dr. Black’s POGIL physical chemistry class was an upper level thermodynamics/kinetics course that could be taken before or after the quantum mechanics/spectroscopy course. Usually Dr. Black’s class spent one-half to one-third of each class period engaged in small group discussion, and the remaining time the class was engaged in whole class discussion. In both iterations of Dr. Black’s course, the membership of the groups remained the same throughout the observation period. Typically, Dr. Black introduced a new topic, after which students would work on activity questions from the POGIL thermodynamics workbook. During SGW, Dr. Black generally monitored student groups, assisting as needed. Students would work in their small groups on the assigned questions for a designated amount of time (typically five to ten minutes) and then the instructor would bring the groups together for a whole class discussion. In WCD, the instructor often initiated discussion of critical thinking questions (CTQs) by asking the spokesperson from one of the groups to report on their groups’ reasoning and solution to a question. The class would then engage in more general discussion of the concepts and models related to the questions. Dr. Black would present mini-lectures as needed to clear up any confusion the students were having. Dr. Green’s physical chemistry class was a course in which thermodynamics, quantum mechanics, spectroscopy, and kinetics were all covered. Core concepts were introduced in Physical Chemistry I, and the concepts were revisited and discussed in further detail in Physical Chemistry II. Data were collected in both the Physical Chemistry I and II courses, but for the purposes of this study, only the thermodynamic concepts that match the activities used in Dr. Black’s course were analyzed. In general, Dr. Green’s classes would spend approximately one-half to two-thirds of the class time working on the POGIL activities in small groups and the remaining time in lecture reviewing the concepts from the previously completed POGIL activity. The students would complete the CTQs from a given ChemActivity before Dr. Green began his lecture on the material covered in the activity. In this implementation, the membership of the groups changed throughout the observation period. During small group work, Dr. Green would walk around to the different groups, answering questions and providing assistance as needed. During lecture, Dr. Green would write on the board to review the content from the POGIL activities and supply additional content to help link the thermodynamic concepts to kinetics and quantum mechanics concepts. During the lectures, students would copy the information provided and ask questions to clarify concepts. To ensure the students had the correct solutions to the POGIL activities, the instructor would collect the recorder’s copy of the activity, write comments, and then return it to the student. It was then up to the other students to get the information from the recorder. Data Collection The topics covered in this study included work, heat, enthalpy, heat capacity, entropy, and Gibbs Energy. These topics were chosen because the content involves a significant interplay between mathematical symbolism and physical chemistry concepts. For this study video recording data was collected from three different 147 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

classrooms that were using the same POGIL materials. Table 2 indicates the activities for which data were collected for each case study.

Table 2. Data collected for ChemActivities for each case study ChemActivity

Topic

B1

B2

G1

T1

Work

x

x

T2

The First Law of Thermodynamics

x

x

x

T3

Enthalpy

x

x

x

T3a

Enthalpy

x

x

T4

Heat Capacity

x

x

x

T5

Temperature Dependence of Enthalpy of Reaction

x

x

x

T6

Entropy

x

x

x

T7

Entropy Changes as a Function of Temperature

x

x

x

T8

The Third Law of Thermodynamics

x

x

T9

Gibbs and Helmholtz Energy

x

x

T10

Gibbs Energy as a Function of Temperature and Pressure

x

x

x

Both the whole class and small group portions of the POGIL classrooms were recorded. To capture the small group portion of the class, one group was selected from each class and video recorded using an additional camera. Video recordings were transcribed verbatim and then analyzed, however due to some technical difficulties some portions of the small group work was not audible and could not be transcribed. The students and instructors were provided pseudonyms to protect their identities.

Data Analysis In order to gain insight into the role POGIL materials have on the degree to which students’ coordinate between the macroscopic, symbolic, and sub-microscopic levels, multiple lenses were used to investigate different facets of classroom discourse and materials, as shown in Figure 1. By characterizing the materials and instructor discourse we could determine at what levels concepts were presented to the students and at what levels students were asked to address and explain concepts. Student arguments provide a means to determine what information students were drawing from the materials and instructor and the ways in which they reasoned about the concepts. 148 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Figure 1. Summarization of the data analysis process for the classroom discourse and POGIL course materials

Video recordings were transcribed verbatim, and then analyzed to examine student arguments and instructor discursive moves used to encourage student discourse.

Johnstone’s Triangle The initial conceptualizations of what constituted macroscopic, submicroscopic, and symbolic levels was informed by research literature (10–13). These were refined to identify the specific types of macroscopic, sub-microscopic, and symbolic ideas used in classroom discussions. The macroscopic level addressed tangible and visible properties and included concepts like density, volume, temperature, and heat. The symbolic level encompassed representations such as chemical equations, mathematical expressions and manipulations, and graphical and tabular data. The sub-microscopic level involved the structure and behavior of atoms, molecules, and ions. A complete description of the coding scheme is given in Becker et al. (20).

Materials Analysis The models/information and questions in the POGIL materials were analyzed in terms of the components of Johnstone’s Triangle, similar to work done by Nyachwaya and Wood (8), to see what information was provided to students. The workbook analysis included multiple components for each ChemActivity: provided information (Models and Information), focus questions (FQ) and critical thinking questions (CTQ), and the author’s solutions to the questions. When examining the author’s solutions, the research team acknowledges that the given answers are for use by the instructor and were not intended to be the complete answers. If a component contained multiple representational levels it was coded accordingly. Two team members independently coded the given information and author solutions for all eleven ChemActivities (T1-T10). Initial percent agreement between the raters was 88% and all discrepancies between the raters were reconciled through discussion.


Instructor Discourse The instructor discourse was analyzed using the Inquiry Oriented Discursive Moves (IODM) framework to look at the discursive moves used by the instructor to create and sustain an inquiry-oriented classroom (20, 28). This analysis allows for comparison of different classroom interactions, facilitation, and environments to better distinguish between the role of the materials and the instructor implementation of those materials. The IODM framework consists of four distinct discursive moves—revoicing, questioning, telling, and managing. In this analysis IODM was used to identify instances in which the instructor provided information to the students. To establish reliability, the B2 dataset was coded collaboratively by the research team to establish a consistent use of the coding scheme. One team member coded all of the B1 and G1 transcripts, while a second team member coded approximately 25%. The percent agreement between the two raters was 80% for B1 and 88% for G1, and all discrepancies between the raters were reconciled through discussion. Instructor discursive moves that provided information to students (rephrasing, expanding, initiating, facilitating, responding, and summarizing) were then coded in terms of the components of Johnstone’s Triangle to identify the representation level(s) used. One team member coded all of the B1, B2 and G1 transcripts, while a second team member coded at least 25%. The percent agreement between the two raters was 89% for B1, 84% for B2, and 86% for G1 and all discrepancies between the raters were reconciled through discussion.

Student Arguments Toulmin’s Model of Argumentation (16, 29) was used as an analytical framework to identify student arguments. In this framework, the components of arguments consist of claims, data, and warrants, and may include qualifiers, rebuttals, or backings. This framework acknowledges the use of argumentation as a way to build explanations, models, and theories, which parallels how scientists use warrants and backings to connect the data they collect to their claims (16, 30). For the analysis of the transcripts using Toulmin’s model, a portion of the transcripts were coded collaboratively by the research team to establish consistent use of our coding scheme. After the initial collaborative coding, the remaining transcripts were coded independently by team members. The team would discuss all identified arguments until a consensus was reached, these agreed upon arguments were then used to develop the argumentation logs. Each component of the argument was then coded using Johnstone’s triangle to identify how students were using the different representational levels to answer the question prompts and reason about physical chemistry. To establish reliability of the representational analysis for the argumentation logs, one team member coded all of the argumentation logs and additional team members independently coded ~25% of each dataset. Initial percent agreement between the raters was 75% for the B1 data, all discrepancies between the raters were reconciled through discussion 150 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

of coding approaches. The other two data sets were coded after this discussion and had inter-rater agreements of 89% for B2 and 88% for G1. Limitations This study observed physical chemistry classrooms of two instructors from two different institutions who were experienced using POGIL materials and pedagogy. The findings from this study represent only two instructors’ implementation of the thermodynamic POGIL materials and their students’ argumentation and coordination between representational levels in the classroom. It is not to be taken as a generalization for how all instructors or all POGIL materials affect student reasoning.

Results and Discussion Use of Representations in the POGIL Physical Chemistry Materials The POGIL materials were analyzed in two distinct sections: the information provided to students in the activities and the author provided solutions to the critical thinking questions (CTQ)s. In this discussion when referring to the “author”, we are referring to the author of the POGIL materials. The given information consists of the information provided by the POGIL materials including the models, figures, information, tables, and question prompts. Both the questions and the solutions were analyzed to examine the representations presented in the materials and the minimum expectations for students when answering questions. Figure 2 illustrates the differences in representational levels between the given information (N=280) and the author solutions (N=233). As expected, a significant portion of the given information addressed thermodynamics concepts strictly at the symbolic level. This was usually in the form of numerical tables, chemical equations, mathematical formulas, and question prompts that addressed this information. There were a similar number of instances in which the macroscopic and symbolic levels were presented together, which should help students translate between the two levels. In these cases, information was typically presented as chemical equations with piston models, as chemical equations with conceptual explanations of enthalpy for chemical reactions, or as mathematical equations under specific conditions. Typically, if information was provided at one level, such as the symbolic level, the author solution to the prompt would be at the same level. However, when the information provided by the POGIL materials connected macroscopic and symbolic concepts, it was found that the minimum expected solutions were more likely to be only at the symbolic or the macroscopic level. For example, students were presented with symbolic equations that are valid under certain conditions. Students were then asked a series of questions to derive a new expression. In these instances, students were only concerned with the mathematical process, not how the expressions they derived were related to the macroscopic level or why the expressions are only valid under certain conditions. Many activities included symbolic representations of piston models labeled with 151 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

variables. In these activities, questions encouraged translation between levels by asking students to interpret the symbolic representation and explain macroscopic processes under different conditions for the system. In general, very little information was presented to students that addressed the sub-microscopic level. The analysis was also organized in terms of the activities to see which concepts were presented at which representational levels. Figure 3 shows the distribution of representations provided in the activities and the author solutions, respectively. Symbolic information could be found in every activity, although the proportion varied. When examining both the given information and the author solutions, some activities, such as T3, T7, T9, and T10 (enthalpy, entropy, Gibbs energy), were predominately at the symbolic level. These activities emphasized derivation of mathematical models. Activities such as T1, T2, T3A, T6, and T8 (work, 1st law, enthalpy, entropy, 3rd law) focused more on macroscopic aspects of thermodynamics. In these activities, there were explicit connections to physical models and to measured quantities. Students were also prompted to consider scenarios and predict outcomes for processes. The POGIL materials approached concepts such as enthalpy (T3, T3A) and entropy (T6, T7) from both the macroscopic and symbolic view, ensuring students were more likely to be able to make connections between levels. However, more abstract concepts like Gibbs energy (T9 and T10) were predominately addressed at the symbolic level. T9 and T10 focused on deriving Gibbs energy expressions under different conditions, but did not connect the equations back to their meaning at the macroscopic level.

Figure 2. Macroscopic, symbolic, and sub-microscopic representations for the given information and the author solutions to the critical thinking questions from the POGIL materials. (N= 280 for given information (n= 47 for models and information, and n=233 for questions) N=233 for author solutions)


Figure 3. Representational analysis for each activity indicating at what level information was presented in the materials as models and questions and at what level the author solution addressed the questions Use of Representations in Arguments Classroom argumentation provided a means to analyze student reasoning as students completed the activities. Figure 4 shows the use of representations in the generated arguments for B1 (N = 283), B2 (N = 336), and G1 (N = 103). When comparing these arguments to the minimum expected author solutions, shown in Figure 5, there was more diversity in the representations used in the classroom arguments than the solutions.

Figure 4. Representational levels for the B1, B2, and G1 arguments In all three case studies there were frequent connections made between the macroscopic and symbolic levels. Explicit connections to the sub-microscopic levels were also observed, particularly for B1 and B2, which were not present in the author solutions. Since the materials themselves do not highlight the connection to the sub-microscopic level or the translation between levels, this may indicate that these connections being made by the students are a result of the influence of instructor facilitation of the POGIL materials (19). 153 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Activities in which students made more connections between the macroscopic and symbolic level include T2 (first law of thermodynamics), T3 (enthalpy), and T4 (heat capacity). In these activities the author solutions used a very mathematical approach while the students tended to spend more time connecting the concepts to previous experience and knowledge of molecular behavior. The largest percentage of sub-microscopic arguments were found in topics on heat capacity (T4) and the third law of thermodynamics (T8). In these cases, students made explicit connections between thermal energy and the motions of particles.

Figure 5. Representational analysis for the author solutions vs the generated arguments in B1, B2, and G1. Note: The author solutions contain the analysis for all 233 questions while each iteration only contains the analysis for the questions that generated arguments. Furthermore, G1 did not use T3a and due to technical difficulties T1 for B2, and T8 and T10 for G1 data were not useable. These years are represented by an empty column. Role of Question Prompts in Encouraging Coordination between Levels If an aim of course materials is to have students understand a concept at the macroscopic, sub-microscopic, and symbolic levels, then questions in the materials should also encourage students to build connections between levels. When examining question prompts that encourage argumentation, Kulatunga et al. (18) found that prompts using terms such as “explain,” “why,” “predict,” and “show” helped promote argumentation. This study found that students would still generate arguments for questions that did not explicitly prompt students to support their claim. However, these arguments did not always include students translating between levels.

Questions that Do Not Encourage Students to Coordinate Levels While the the questions in the POGIL materials are designed to encourage students to engage in critical thinking, problem solving, and interpretation of figures and equations, we found that the wording of many of the questions did not indicate that there was an explicit expectation that students provide justification or 154 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

support for their answers. Because the materials did not prompt for explanations, there were many questions in which students did not provide explanations to their solution, resulting in a lack of coordination between levels. Arguments of this nature could be found in all three case studies. One example from ChemActivity T7, shown in Figure 6, prompts students to derive an expression relating dS to Cp, T, and P for an ideal gas. Analysis of the question and solution indicates that students are expected to examine this question at the symbolic level to see how entropy is related to heat capacity in terms of temperature and pressure. The author’s solution shows the mathematical procedure used to arrive at the desired equation.

Figure 6. ChemActivity T7: Entropy Changes as a Function of Temperature, Critical Thinking Question 7 and author provided solution. Reproduced with permission from reference (27). Copyright (2004) Houghton Mifflin. As expected, the students also treated this problem as simply requiring mathematical manipulation as shown in the example from the small group work in case study G1. (Note that in the arguments illustrating examples of classroom discourse, italicized text indicates a direct quotation from the transcript.) SGW G1 ChemActivity T7: Temperature, CTQ 7

Entropy Changes as a Function of

Claim: (Qi) Data: dH = dU +VdP + PdV (Qi) Data: dH = pdT (Qi) Data: dU = TdS - PdV (Qi) Warrant: So you just rearrange…It’s just doing algebra with all the d stuff. (Qi) Qi explained to his group that you arrive at the final equation, , by taking the formulas and doing algebra to rearrange the equations. This example shows that even though students were able to arrive at the correct 155 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

answer, they took a very superficial approach to the problem, resulting in a weak warrant. While it is not expected that students would make connections across levels for every mathematical manipulation, the data from all three case-studies suggests that the students not only struggled with manipulating equations, which has been well-documented (2, 31–33), but also in understanding what the mathematical expressions represent in terms of chemical concepts at the macroscopic and sub-microscopic levels. It was very common for students to talk about mathematical processes without articulating any explanations, and, as is common in many physical chemistry materials, students were often not prompted to make conceptual connections through later questions in the activity.

Questions that Encourage Translation As indicated in Figure 4, students did make connections between representational levels. Arguments of this nature could be found in all three case studies. Often these connections were provided in the warrant of the argument. Figure 7 is an example from ChemActivity T3a in which students were provided a piston model under constant temperature and were asked a series of questions. These questions required students to interpret the model, extract information from it, and then make connections between symbolic representations and macroscopic concepts. However, the question prompts were often not designed to elicit explanations from students to demonstrate these connections. For example, question 12 requires students to determine the sign for work for the process shown in Model 2. This question does not prompt for explanation, and the authors did not indicate a justification as to why work is negative in their solution. However, the students frequently did provide a reasoning to claims for these types of question. WCD B2 ChemActivity T3A: Enthalpy, CTQ 12 Claim: w is negative for this process. (Class) Data: Model 2, page 73 (POGIL Materials) Warrant: The piston moves up, the system probably did work, which means it’s negative, loss of ability to do further work. (Francis) Here the students claimed that the sign for work is negative, a symbolic level statement. Francis then states this is because the piston rises, meaning the system did work, which is a macroscopic interpretation of the process symbolically represented as a piston model and chemical equation in Model 2. This indicates that Francis connected the symbolic representations to a process at the macroscopic level.


Figure 7. Model 2 from ChemActivity T3A: Enthalpy and Critical Thinking Question 12 with the author provided solutions. Reproduced with permission from reference (27). Copyright (2004) Houghton Mifflin.

Benefits of Coordinating between Levels Encouraging students to translate between levels can help them develop a stronger foundational understanding of chemical concepts. In one example from ChemActivity T8, shown in Figure 8, the students were prompted to explain why there was an abrupt change in the graph describing entropy versus temperature for a typical pure substance. This question was considered to have symbolic information because it presented information in graphical form that students had to interpret. This question also provided information at the macroscopic level because the question provides a description that entropy changes gradually with increasing temperature. The author’s solution, “The solid warms then abruptly changes to a liquid, which has a higher entropy than a solid.” only acknowledges the macroscopic reasoning for the abrupt changes that are shown in the graph.


Figure 8. ChemActivity T8: The Third Law of Thermodynamics, Critical Thinking Question 4 and author provided solution. Reproduced with permission from reference (27). Copyright (2004) Houghton Mifflin.

When examining the student arguments, the justification also connected to the sub-microscopic level. In B1 and B2 connections were made to the sub-microscopic in the warrant portion of the argument, as shown below. Each argument began with the macroscopic claim that the abrupt changes in the graph indicate a phase change as the result of increasing temperature, based on the data given in the problem. In both iterations of Dr. Black’s class, a student made the connection to the sub-microscopic level to explain what this meant for the actual molecules: there is an increase in molecular movement allowing for more ways to distribute the energy. SGW B1 ChemActivity T8: The Third Law of Thermodynamics, CTQ 4 Claim: An abrupt change in entropy indicates a phase change. (Adam) Data: The entropy changes gradually from 0 K then undergoes an abrupt change as shown in the Figure [Figure 8 in this manuscript], page 108. (POGIL Materials, CTQ 4) Warrant: Temperature increases as the phase changed, so it makes more movement and distribution of energy. (Melissa) SGW B2 ChemActivity T8: The Third Law of Thermodynamics, CTQ 4 Claim: Entropy changes gradually, then abruptly at phase change because of temperature. (Group/Question) Data: Graph page 108 (POGIL Materials) Warrant: Because temperature increases, there is more molecular movement. (Thaddeus)


Another benefit of having students translate between levels is that it provides feedback to the instructor as to how students are thinking about chemical concepts. In Figure 9, the materials prompted students to determine if a piston will be raised, lowered, or stay the same based on the given chemical reaction: 2C2H6(g) + 7O2(g) ↔ 4CO2(g) + 6H2O(g). In this example, students were provided information at all three representational levels. This question gives a macroscopic view of the piston system at constant temperature, provides a sub-microscopic view of what the molecules look like in the piston, and gives a symbolic representation of the chemical reaction taking place in the system. The author’s solution addressed the macroscopic and symbolic levels in the statement that since the weight on the piston will be raised (macroscopic) while at constant temperature and pressure, there is in increase in the number of moles (symbolic). While the concept of a mole can also include the macroscopic and sub-microscopic levels, it is clear in the transcripts that students infer this information by simply interpreting the coefficients in the chemical equation for the reaction rather than thinking about the particulate level.

Figure 9. ChemActivity T3A: Enthalpy, Focus Question and author provided solution. Reproduced with permission from reference (7). Copyright (2004) Houghton Mifflin.

When looking at the arguments generated in case study B2, the initial argument presented by one group was that the weight would be raised, because more moles are produced. This example shows that Jerome was able to make the connections between the macroscopic and symbolic levels evident in the author solutions, but Jerome took the opportunity to expand upon the answer, saying that in cases like this the reaction is exothermic and the work is done by the system. Here Jerome was able to connect the question back to information discussed in ChemActivity T1: Work.


WCD B2 ChemActivity T3A: Enthalpy, FQ Claim: The weight would be raised. (Class) Data: More moles of gas are produced then reacted. (Jerome) Data: Diagram, page 71 (POGIL Materials) Warrant: When this (data) happens, the system is exothermic. The energy that is lost tends to do work. (Jerome) Alternate Claim: The weight will be lowered. (Caprice/Aiden) Rebuttal: More moles of product results in increased volume. (Dr. Black) Alternate Data: Hydrogen bonding is a stronger intermolecular force. (Aiden) Alternate Warrant: Stronger intermolecular forces, lowering the pressure, lowers the piston. (Aiden)

However, the discussion about this system continues when Aiden and Caprice disagree with the original argument. They believed that the weight would be lowered due to the presence of stronger intermolecular forces in the products. Even though the instructor interjects to refute their position, Aiden defended his point of view by stating that, due to the hydrogen bonding occurring in the system, the pressure inside the cylinder decreases, thus lowering the piston. This extended explanation allows the instructor to identify that the student did not have an appropriate sense of the relative magnitudes of non-ideal gas behavior compared to increasing the number of particles.

Variations in Facilitation of POGIL Materials

In all three case studies students made more connections between the macroscopic and symbolic level than were present in the author solutions, and students in case studies B1 and B2 made more connections to the sub-microscopic level. Because students in all three case studies used the same course materials, this indicates that the learning environment was shaped by the instructor and influenced students’ use of representations in their responses to the questions. Figure 10 compares the use of the representations in instructor discourse across all three case studies. Both instructors discussed thermodynamics strictly at the symbolic level approximately one-third to one-half of the time. Another third of the discourse dealt with concepts strictly at the macroscopic level, and less than one-third makes connections between these levels. This distribution is different than the given information and author solutions of the materials (Figure 2) and student arguments (Figure 4), except for B1 in which the student arguments and instructor discourse use similar representations. These differences indicate that the instructors are supplementing their class discussions and lectures with additional macroscopic and sub-microscopic level concepts not present in the materials. 160 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

Figure 10. Representational levels for the B1, B2, and G1 instructor discourse

Use of the Symbolic and Macroscopic Level Reasoning Dr. Black and Dr. Green had different facilitation strategies that influenced how they used the materials in their classroom, interacted with students, and how they presented information. Most of the information presented by Dr. Black was in response to student comments about specific questions from the materials or that summarized a concept. This differed from Dr. Green who used lectures to review the concepts covered in the POGIL activities and connect the information to previous lectures. The analysis of Dr. Black’s use of the macroscopic level showed she would provide students with additional information that was not present in the materials to help students connect the symbolic mathematical representations to something more tangible. Dr. Black also used statements at the symbolic level, primarily when critiquing explanations and addressing questions about mathematical processes. In the example below Dr. Black and the students are discussing an expression the students derived. Here Dr. Black is critiquing students on how they verbalize and explain mathematical processes by encouraging them to go beyond just stating the variables. While the materials guide students through the calculations, they cannot easily inform students on the normative ways to verbalize these expressions. WCD B2 ChemActivity T4: Heat Capacity Dr. Black: So this expression actually represents functions and ideas. So you need to, when you look at these equations, get beyond the alphabet soup and derivatives, that what does this partial derivative mean? What is a partial derivative? Quentin: It’s a term with respect to one different (inaudible). Dr. Black: I don’t want the derivative, that’s just mathematically. What is a partial derivative? Quentin: The change with respect to one variable. Dr. Black: Yes, it’s the change, so when I look at a derivative, what I’m looking at is the change in one variable with respect to another variable, or to changes in another variable. So here, I’m looking at the change in one variable with respect to changes in another variable, while keeping 161 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

all the other variables constant (points to board). So partial, all you do is add in the fact that I’ve got more than one variable, so I have to deal with one at a time. So when you think about the derivatives, when you say them, I want the ‘change in’ kind of phrases, that’s what you’re looking at, how does this function change when I change a variable? Make sense? Yes, no, maybe? From the transcripts we found evidence that the instructor can help students improve their abilities to explain the mathematical processes used in thermodynamics. In Dr. Black’s courses she modeled and encouraged students to articulate what variables represent and not just say the symbol itself in order to help students to better understand what an equation “means”. For example, early in the transcripts students would say an equation like dw = -PdV as a series of letters. With assistance from the instructor, students shifted their language to say “the change in work is equal to minus the pressure times the change in volume.” While this could still be improved, it was seen to be particularly helpful in clearing up student’s confusion about the differences among symbols such as d, Δ, and ∂. When comparing Dr. Green’s use of the symbolic level, it mostly involved deriving mathematical expressions or working through example problems using the mathematical expressions students derived in the POGIL activities. Dr. Green would connect the derived expressions to the macroscopic concepts, similar to the types of connections Dr. Black would make. In the following example Dr. Green reviewed the derivation for work that students derived with guidance from the materials. Following this review he provided the students with an explanation of when this expression is valid, and what it means in terms of a piston cylinder model. G1 Lecture after ChemActivity T1: Work and ChemActivity T2: The First Law of Thermodynamics Dr. Green: … (writing derivation on the board) So if we want to … integrate that, we integrate both sides and we get So this equation is general and we use that equation [it] varies [for] situations so for expansion and contraction work. If there’s no change in volume there is no expansion or contraction work. ... And remember this is defined as the external pressure of the system. The system has to be whatever is pushing back against the piston cylinder arrangement. This explanation by Dr. Green gets at both the macroscopic and symbolic level of work, but it does not really integrate the two in order to be considered translating between levels. This type of explanation is similar to many of the prompts in the POGIL materials that examine one representational level at a time. He explains work at the symbolic level by deriving work in terms of the mathematical expression used to define it, then he explains work macroscopically. This type of explanation makes the assumption that students will make the connections between the macroscopic and symbolic levels because they have 162 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

discussed a concept at multiple levels. If Dr. Green integrated the symbolic derivation with what the equations represent in terms of the macroscopic system during different point of the derivation, this would be more likely to bridge the two levels. In these examples both instructors are using symbolic and macroscopic reasoning to go beyond the information presented in the materials to help students better connect what the mathematical expressions represent both symbolically and macroscopically. Making these connections can also help student begin to understand why they need to derive different mathematical expressions under different macroscopic conditions, which is not always made explicit in instructional materials.

Use of Sub-Microscopic Level Reasoning In addition to the symbolic and macroscopic levels, both instructors provided students with a small amount of sub-microscopic level information that was not often present in the published materials to help students make connections to the atomic/molecular level. In the example below Dr. Green continues his description of work at both the macroscopic and sub-microscopic levels. This example is considered to translate between the two levels because it is an integrated explanation of what work and heat at the macroscopic level means with respect to the movement of individual atoms at the molecular level. Unlike the thermodynamic POGIL materials, Dr. Green’s class is an integrated physical chemistry course in which students discuss thermodynamics, quantum mechanics, and kinetics, and he tries to relate many of the thermodynamic topics back to previous lectures. G1 Lecture after ChemActivity T1: Work and ChemActivity T2: The First Law of Thermodynamics Dr. Green: So we are defining these things from the surroundings point of view, so the way to think about work is if there is an orderly change in the surroundings then that’s work. A typical example is a weight falling or something else and that’s orderly molecular motion because all the atoms in the weight are moving in the same direction. The atoms are individually vibrating around each other in the solid, but overall they are all moving in the same direction. … So if the transfer of energy had a change that was a result of something that was orderly molecular motion in the surroundings something in the surroundings changed in an orderly way the net transfer of energy that we call work. If it’s disorderly then there must have been a difference in temperature that’s what we call a transfer of energy of heat. Even though both instructors provide sub-microscopic level reasoning, the students in Dr. Black’s class incorporated this information into their arguments more frequently. We believed this is due to how the instructor facilitated the classroom. As previously discussed Dr. Green provided the connection to the sub163 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

microscopic level during lecture, after students completed the POGIL activities. Dr. Black discussed the concepts with the students in a whole class discussion format, which resulted in student-generated arguments. The WCD occurs after students complete a few questions in the POGIL materials rather than the entire activity, and the sub-microscopic concepts are addressed in a more interactive way. One example of this is when Dr. Black posed a question to the class asking them to explain how they think about entropy. Andrea responded with the commonly used metaphor of a messy room. Dr. Black reframed the example by providing a more scientifically acceptable way to thinking about entropy at the sub-microscopic level and prompts students to reassess the messy room analogy. WCD B1 ChemActivity T6: Entropy Dr. Black: So, second law gives us the idea of entropy. What do you use to think about entropy? Andrea: Messy office? Dr. Black: That’s a common way people talk about entropy is disorder. Um, that’s not technically true, it’s kind of a way to think about it but it’s not really disorder. What entropy really is, is the way that we can distribute the energy among particles. So we’re looking at how many possibilities we have. And this is where people sometimes will use the example of an office, that how many ways can I have my office completely organized, everything filed, alphabetized? How many ways can I do that? Carrie: One? Dr. Black: Well maybe not infinite, but a whole lot, I can do a whole ton of ways to do that. And so it’s easier for people to envision disorder than it is to think about number of states. Those of you who’ve had quantum, we’ve talked about looking at distribution of particles in different energy states. In case studies B1 and B2, connections to the sub-microscopic level were made in both the SGW and WCD portions of the class, even though the materials do not provide any sub-microscopic level information for many questions. This in turn indicates that making these connections to the sub-microscopic was likely an influence of the instructor rather than the design of materials.

Conclusions Instructors want students to understand both the conceptual and mathematical concepts in thermodynamics (4). One way to help achieve this goal is by using materials that support students in making connections across levels. While the concepts in thermodynamics are inherently macroscopic, it is often taught entirely at the symbolic level, and published resources often miss opportunities to prompt students to build connections between representational levels. This analysis of the published thermodynamic POGIL materials found that the materials frequently present information at the symbolic level, or the macroscopic and symbolic level. However, the question prompts tend to call attention to either the symbolic or 164 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

the macroscopic level; they usually do not encourage students to focus on both levels at the same time. In addition, the materials place very little emphasis on sub-microscopic level concepts, even though this is the level at which chemical processes occur. When the materials were compared to student arguments, we found two main commonalities concerning student argumentation and translation. First, in all three case studies arguments for derivation questions focused strictly on the symbolic interpretation and manipulation of the mathematical equations. Rarely were connections made to other levels and students generally did not reflect on why it was important to derive certain equations and what the equations represented in terms of macroscopic and sub-microscopic phenomena. This is a missed opportunity to encourage students to build connections between levels and consider what the mathematical equations represent conceptually. The second commonality found was thought to be a result of instructor facilitation. In each case study there were more connections made between the macroscopic and symbolic level in the student arguments compared to the minimum expectations in the author solutions. This is thought to be an instructor influence because both instructors would discuss and connect concepts at the macroscopic and symbolic levels. Generally, students stated a claim at one level and then provided data or warrant at another level to build a connection between the symbolic and macroscopic levels. This is further supported as an instructor influence because many of the POGIL questions did not explicitly prompt students to provide the reasoning behind their answer. Lastly one difference between the instructors in terms of representational use in student arguments was the sub-microscopic level in case studies B1 and B2. This difference is thought to be due to Dr. Black’s facilitation style where she assisted students in incorporating more sub-microscopic level reasoning into their arguments through the use of whole class discussion. While this analysis showed that both instructors used a variety of representations in their discourse, further analysis must be done to better determine what specific aspects of instructor discourse encourages students to integrate different representational levels into their arguments.

Implications As the analysis of many published physical chemistry materials have shown, it is currently up to the instructor to help students make connections across representational levels. If a goal of physical chemistry is to have students think critically and build connections between the mathematical equations and the chemical processes and concepts they model, then the materials and instruction should prompt students to reflect on these connections. This in turn can help students develop a more complete understanding of the content and practices common to physical chemistry. By understanding the limitations of the course materials being used in any classroom, the instructor can be better prepared to address gaps in the materials and support student reasoning. Furthermore, encouraging students to explain the reasoning behind how they arrived at the 165 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.

solution can help the instructor better understand the connections students are making (or are not making) between different concepts and representations. Based on these findings it is suggested that materials using in teaching physical chemistry should be revised to focus more on building connections between the symbolic, sub-microscopic, and macroscopic level to help students understand what the mathematical equations represent in terms of thermodynamic processes. Furthermore, this study also provides an approach to analyze course materials with respect to the chemistry triplet, as well as the influences the materials and the instructor’s facilitation have in student argumentation. This analysis could be extended to examine materials for other chemistry active learning environments to better understand students’ representational understanding of chemistry and how students’ use of representations varies by course.

Acknowledgments Initial work on Case Study B1 was supported by the National Science Foundation under grants #0816792, #0817467, and #0816948. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We also acknowledge the contributions of Nicole Becker in coding and analyzing data from Case Study B1. We are grateful for the contributions of Chris Rasmussen, Megan Wawro, and George Sweeney, who played key roles in the development of the methodologies and in inter-rater reliability analysis for our work with Toulmin’s model of argumentation. We thank Jacob Byers and Marc Muniz for their assistance with inter-rater reliability analyses. We also wish to thank the physical chemistry students and instructors who took part in this study.

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