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Chapter 11
Reflections on the Effect of the Flipped Classroom on Students’ Difficulties with Homework in Physical Chemistry Lisa M. Goss* Department of Chemistry, Idaho State University, 921 S 8th Ave., Pocatello, Idaho 83209-8023, United States *E-mail:
[email protected] Reflective teaching may be described as the application of Schön’s work on reflective practice to teaching. A brief introduction to reflective practice is given along with examples of the application of reflective practice to the author’s teaching of physical chemistry. Student performance on three homework problems in two different years is qualitatively examined. The observations are interpreted in terms of constructivism and the role of prior knowledge. Repeating the process of making changes, observing the outcome of those changes, and reflecting on that outcome can lead to a deeper understanding of teaching and learning.
Introduction The idea of “reflective practice” originated with Schön’s study of the “distinctive structure of reflection-in-action”. Published in 1983, Schön’s The Reflective Practitioner described a crisis of confidence in professional knowledge. This crisis resulted from events of the time that compromised the confidence of both the public and professionals themselves in the power of professional technical knowledge to solve the problems faced by society. Professionals in a wide variety of fields including doctors, lawyers, and others at that time struggled with the difficulties of applying formal knowledge from professional training to situations of increasing complexity and uncertainty (1). According to Schön, as a result of this increasing uncertainty, the practice of such professionals had at least as much to do with defining the problem as with finding the solution to © 2018 American Chemical Society Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
the problem (1). The process of defining or “setting” the problem did not fit in the prevailing model of professional knowledge, technical rationality, and as a result Schön explored and described the reflection-in-action process used by professionals in dealing with situations of increasing complexity and uncertainty (1). The structure of reflection-in-action that Schön unearthed in careful examination of professional practice situations is what he called a “reflective conversation” (1). This conversation is not with people but with the complex problem that the professional does not initially know how to define, let alone solve (1). As Schön puts it “In this reflective conversation, the practitioner’s effort to solve the reframed problem yields new discoveries which call for new reflection-in-action. The process spirals through stages of appreciation, action, and reappreciation. The unique and uncertain situation comes to be understood through the attempt to change it, and changed through the attempt to understand it.”(132) (1) This reflective conversation may take only minutes or extend over months or longer and the objects of reflection may be as varied as the practice itself (1). This “reflective conversation” can be undertaken by a doctor trying to diagnose a patient who does not fit any of the categories he learned in medical school or an instructor trying to teach students a concept that previous classes of students never quite seemed to understand. The reflective conversation that comprises “reflection-in-action” is therefore an experiment in the sense of trying something and looking at the result. The reflective conversation is not, of course, a controlled experiment in the sense familiar to chemists and other scientists (1). The reflective practitioner evaluates his “experiment” not by the standards of a controlled experiment but by his ability to solve the new problem he has defined and also by his response to the unintended consequences of his actions (1). Schön describes this experiment: [The reflective practitioner] “experiments rigorously when he strives to make the situation conform to his view of it, while at the same time he remains open to the evidence of his failure to do so. He must learn by reflection on the situation’s resistance that his hypothesis is inadequate, and in what way, or that his framing of the problem is inadequate, and in what way. Moreover, he plays his game in relation to a moving target, changing the phenomena as he experiments. Whether he ought to reflectin-action, and how he ought to experiment, will depend on the changes produced by his earlier moves.”(153) (1) If the reflective practitioner maintains this “double vision” of changing the situation while remaining open to evidence of failing to to achieve the desired outcome, he increases the likelihood of reaching a broader and deeper understanding of his craft and its practice (1). 170 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
What does reflection-in-action have to do with engaging students in physical chemistry? The idea of reflective practice is the origin of reflective teaching. As an instructor of physical chemistry, I can reflect on my own teaching of physical chemistry. In my reflective conversation, I can confront my assumptions, make changes as a result of that confrontation, and observe the consequences of those changes. This process can help me improve my teaching and student learning of physical chemistry as a result. One structure that can be used for reflective practice is a variety of “action research.” Action research has been used in many different fields and comes in different varieties (2). Kemmis applies the term “action science” to the variety of action research of interest here (2). Action science aims to develop the reflective practitioner and focuses on the study of practice to acheive new understanding and better practice. In action science, the development of the reflective practitioner involves both the formal knowledge of the profession and the practical knowledge of execution (2). Action science is then a specific form of reflective practice (2). An important component of action science is uncovering the mismatches between what the practitioner believes and what the practitioner actually does (3). These mismatches can explain cases where the reflective practitioner’s attempts to change a situation are unsuccessful and the practitioner must uncover by reflection the source of the situation’s resistance to change. The key feature of action research relevant to my discussion here is the cycle of steps that can be a framework for making changes. The steps include 1) planning a change, 2) implementing that change, 3) observing the consequences of the change, 4) reflecting on the outcome, and then going back to the beginning and making a new or modified plan to repeat the cycle (2). This cycle of steps is then an example of Schön’s reflective conversation occurring on a longer time scale than a spoken conversation between two people. The result of such cycles of change is knowledge unique to the practitioner and specific to his problems and situations. Therefore, as Schön puts it, this knowledge “...is compelling only to members of a community of inquiry who share these commitments (1).” Readers of a book on engaging students in physical chemistry may find my description of reflective teaching interesting not as evidence of changes they should make but as an inspiration to reflect on their own teaching. In that spirit, I offer the following description of a small segment of my own reflective practice.
Background In this chapter, I will describe changes and observations made in the two semester physical chemistry lecture course sequence that I teach at a regional public university. This two semester sequence is taken primarily by junior and senior chemistry majors who are obtaining a B.S. in Chemistry. (Chemistry majors earning a B.A. and most biochemistry majors take a different physical chemistry lecture sequence.) The two classes of this sequence are relatively small with an average enrollment of 9 ± 3 students. Pre-requisites for this two semester sequence include two semesters of general chemistry, two semesters of calculus, 171 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
and two semesters of calculus-based physics. The fall course in the sequence covers the failures of classical physics, introduction to quantum, atomic structure & spectroscopy, symmetry, and molecular structure and spectroscopy. The spring course in the sequence covers classical and statistical thermodynamics, phases & mixtures, chemical equilibria, and chemical kinetics. The textbook used is McQuarrie and Simon’s Physical Chemistry A Molecular Approach (4) and we cover the majority of chapters 1-10, 12, 13, and 16-29. The 2011/2012 academic year is the first year considered here because previous years were different in various ways that are outside the scope of this chapter. A time line is shown in Table 1. As shown in that table, I taught these two courses using a traditional lecture format during the 2011/2012 and 2012/2013 academic years. Class met three times per week with about one-third of those classes being computer lab sessions (analogous to a recitation session) and the rest being lectures. Lectures used a combination of Mathematica slides projected on a screen and additional material written directly on a whiteboard. Computer lab sessions were used to teach students to use Mathematica and then give students time to work on homework in Mathematica with instructor assistance. One homework assignment per chapter was collected and graded and each homework assignment consisted of 3-8 separate problems. Three exams were given on paper.
Table 1. Timeline for changes
a
Changes madea
Academic Year
Class format
2011/2012
lecture
Completed book switch Maple to Mathematica Whiteboard only to whiteboard and Mathematica
2012/2013
lecture
None
2013/2014
flipped
Screencasts prepared and assigned JiTT/warm-up questions written and assigned CLEs prepared and assigned
2014/2015
flipped
Many screencasts divided into multiple smaller ones Many warm-up questions revised Many CLEs revised New CLEs written
2015/2016
flipped
New CLEs written
HW Grades used First set
Second set
CLE stands for “cooperative learning exercise”
As I have taught this two semester physical chemistry lecture sequence repeatedly, I have encountered various challenges to effective teaching and student learning of physical chemistry. The effect of student math preparation on performance in physical chemistry has been discussed and investigated in the literature (5–7). My observations indicated that teaching my students to use a 172 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
symbolic math program such as Mathematica (8), Maple (9), Matlab (10), or Sage (11) can at least partially compensate for lack of student skills in executing algebra and calculus although it does not compensate for lack of student understanding of the fundamental concepts of calculus. During the 2011/2012 and 2012/2013 academic years, there were two particular problems that I thought about repeatedly. One of these was my own frustration with the inefficiency of how I was teaching students to use Mathematica. Through the 2012/2013 academic year, I would demonstrate the use of Mathematica on screen and then check individual student work as they followed along in their own files on individual computers. The other problem was that I wanted to do more cooperative learning in class but could not seem to make time for it. All of class time was taken up providing clear explanations of new concepts in lecture. There were two reasons I wanted to incorporate more cooperative learning. One reason was that students told me that they thought they understood the material covered in lecture but had difficulty when they sat down to do the homework problems at home. The other reason was my experience with the effectiveness of cooperative learning when I did manage to squeeze it into my classes. For the 2013/2014 academic year, I converted this two semester sequence of classes to a flipped format using screencasting, Just-in-Time-Teaching, and cooperative learning (12, 13). The new class format was described in detail in a previous publication (14). A brief summary is given here. Class met on the same schedule and covered the same chapters of the same textbook. The same homework assignments (with minor changes) were collected and graded. I used my existing lecture notes to make screencast videos (“screencasts”). Before class, two to four screencasts of 8-12 minutes length were assigned and an open-ended-question quiz (“warm-ups”) was given online over the material covered in the screencasts (12). During class, the warm-up questions were reviewed, points of confusion were addressed, and the rest of class time was spent in “Structured Problem Solving” where students worked in groups on cooperative learning exercises (CLEs) (13). Students were assigned to these groups of 3-4 based on math and chemistry background. Roles including “Leader”, “Scribe”, etc. were assigned and rotated among group members. The material taught in the computer lab sessions during prior years was also incorporated into screencast videos. For those screencast videos, students were instructed to email their Mathematica files to the instructor for review before class. The classes continued in the flipped format for the 2014/2015 and 2015/2016 academic years. The conversion to the flipped format allowed me to address the two problems I described earlier. I used screencasts to teach students to use the symbolic math program Mathematica. I moved the introduction of material out of lecture to make room for cooperative learning and students did cooperative learning exercises in class that helped to prepare them for the homework assignments. However, reflection on how the classes were going after the conversion to the flipped format suggested to me that students still had difficulty with some homework problems but did much better than lecture format classes on other homework problems. With this vague sense of differences, I decided to closely examine student performance on a few homework problems to further investigate. 173 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
In order to do this, I looked at records from my homework grading. Because we make extensive use of Mathematica, I do a lot of the homework grading electronically. This means that I open all of the students’ Mathematica homework files on my computer screen next to a spreadsheet file window. If a student does not get full credit on a particular part of a particular problem, I add an explanation in text form about the mistake the student made to the appropriate cell of the spreadsheet. As a result of using this process, I have many brief text comments about student mistakes across many homework assignments. Here I describe what I found in student work on three problems in two different years: the 2011/2012 academic year (lecture format) and the 2015/2016 academic year (flipped format).
Problem #1 The first problem I considered is shown in Figure 1. It is one of the problems from the chapter 7 homework assignment on methods of approximation. In this problem, students must determine the elements of a 2x2 coefficient matrix and then use the secular determinant to find the ground state energy. The Fall 2011 class got an introduction to the multi-parameter variational method in lecture and then worked an example similar to this problem in a computer lab session under instructor supervision. In the Fall 2011 class, 9 of 12 students had the matrix elements wrong in some way but correctly executed the process of finding the ground-state energy in Problem #1.
Figure 1. Problem #1 The Fall 2015 class got both the introduction and the example in screencast form and their Mathematica files with the example were checked before class. Based on discussion with students in prior years, I added a cooperative learning exercise in class on paper on the multi-parameter variational method for the Fall 174 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
2015 class. This cooperative learning exercise is shown in Figure 2. This exercise is worked on paper and does not require any algebra or calculus to be executed. Instead, it focuses on the process of assembling the matrix elements that go into the secular determinant. In the Fall 2015 class, all 5 students completed the homework problem shown in Figure 1 correctly.
Figure 2. Cooperative learning exercises related to Problem #1 The homework problem shown in Figure 1 required students to transfer concepts from the example that they saw in a computer lab session or a screencast to a problem of the same type but with different details. The cooperative learning exercise added for the Fall 2015 class and shown in Figure 2 gave students practice in transferring the overall approach that they were learning to a new problem. The use of Mathematica meant that students did not get bogged down in the linear algebra and could find the ground state energy correctly. One example, in either lecture or screencast form, was not enough, however, for students to understand the general approach to assembling the matrix elements and the cooperative learning exercise seemed to help with this.
Problem #2 The second problem I considered is shown in Figure 3. It is one of the problems from the chapter 20 homework assignment on entropy. In this problem, a heated object was placed in thermal contact with a room temperature object and allowed to come to thermal equilibrium. Students calculated the final temperature 175 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
and entropy changes for the two components of the system. The Spring 2012 class got an introduction to this material in lecture. In that Spring 2012 class, 4 of 7 students had a mistake in the calculation of the final temperature although the calculations of the entropy changes were set up correctly.
Figure 3. Problem #2
The Spring 2016 class got the same introduction to this material in screencast form. Based on discussion with students in prior years, I added a cooperative learning exercise for the Spring 2016 class on this material which is shown in Figure 4. This cooperative learning exercise was the same type of algorithmic problem as the homework problem but also required students to report intermediate results. In the Spring 2016 class, 1 of 5 students forgot to use absolute temperature in the entropy calculations and the rest of the students completed the the homework problem shown in Figure 3 correctly. This second problem is one which students did not see an example of in either lecture or a screencast. It also required students to recall from their general chemistry course how to calculate the heat transferred and the final temperature. The calculation of the entropy changes builds on the calculation of the heat transferred. Students who did not learn or do not remember those calculations had difficulty with the homework problem shown in Figure 3.
Problem #3 The third problem I considered is shown in Figure 5. It is one of the problems from the chapter 4 homework assignment on introductory quantum material. In this problem, students calculated the mean and standard deviation for the x and y components of the linear momentum for the particle in a 2D box model system. This model is not covered in the introductory chapters on quantum in our textbook. The Fall 2011 class got an introduction to this material in lecture. In the Fall 2011 class, 8 of 11 students had mistakes on this problem, mostly with the second moment incorrect or trying to do the x and y components in one calculation. 176 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
Figure 4. Cooperative learning exercise related to Problem #2
Figure 5. Problem #3 177 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
I added the cooperative learning exercises shown in Figures 6 and 7 for the Fall 2013 class and the one in Figure 8 for the Fall 2014 class. The Fall 2015 class got the same introduction as the Fall 2011 class to this material in screencast form. The Fall 2015 class completed these three cooperative learning exercises during class. These cooperative learning exercises address the significance of the eigenfunction as well as the calculation of the mean and standard deviation of an observable but are all specific to the particle in a 1D box model. Students also completed a cooperative learning exercise on the degeneracy of the energies of a cubic 3D box. In the Fall 2015 class, all 5 students made mistakes in this problem, either with the terms of the variance reversed or the operator(s) wrong. Unlike Problems 1 and 2, students in the flipped format Fall 2015 class still could not do this homework problem correctly.
Figure 6. Cooperative learning exercise related to Problem #3
178 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
Figure 7. Second cooperative learning exercise related to Problem #3
Figure 8. Third cooperative learning exercise related to Problem #3 179 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
Why did students still have difficulty with problem #3? This third problem required students to apply concepts introduced using the particle-in-1D-box model to a two-dimensional version of that model that they do not encounter before the homework problem. The mistakes made by students in both the lecture format class and the flipped format class seem to originate in an incomplete understanding of the vector nature of linear momentum. The cooperative learning exercises completed in class addressed the concepts of the mean and standard deviation of observables but only using the 1-D box model. Successful transfer of those concepts from a 1D box to a 2D box required that students understand the vector nature of linear momentum from their physics pre-requisite courses. The cooperative learning exercises that I used in this chapter did not provide an opportunity to check students’ understanding of that material. That may explain students’ continued difficulty with this homework problem. Addition of such a cooperative learning exercise will allow me to test this explanation.
Conclusions Reflections on my interactions with my students during cooperative learning sessions and my observations on homework assignments have led me to interpret these mostly in terms of constructivism (15, 16). The idea that “knowledge is constructed in the mind of the learner”, as Bodner puts it, seems obvious to me now (15). My early years as an instructor of physical chemistry, however, were based on the unexamined assumption that “knowledge is transferred intact from the mind of the teacher to the mind of the student” (15) via clear explanation by the teacher and I put a lot of effort into providing clear explanations. In addition, the role of prior knowledge is critically important in physical chemistry where there is more than one pre-requisite course. It appears that understanding of material from multiple pre-requisite courses is a necessary foundation on which to construct the new knowledge of the physical chemistry course. In this chapter, I have given a snapshot of my reflective conversation with my teaching of physical chemistry. Discussions with students during cooperative learning sessions have led me to more fully appreciate the difficulties that students face when they sit down to do homework for my classes. I have taken action to change that by introducing new cooperative learning exercises and refining existing exercises. The reflection on three homework problems described here has led me to more fully appreciate the role of prior knowledge and the importance of the knowledge construction process.
Acknowledgments The author thanks Renée S. Cole and Courtney Stanford for invaluable feedback on a draft of this chapter.
180 Teague and Gardner; Engaging Students in Physical Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 2018.
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