Personal Essay

For my dissertation research, I would like to study how high school physics students use metacognition while solving physics problems. Before I start to study physics students’ metacognition while problem solving, it is important for me to understand my own metacognitive strategies while solving a physics problem. Analysis of my own metacognition while problem solving will accomplish three things. First, it will help bring to light any biases I may have about how to solve a physics problem. Second, this gives me an understanding of how an expert uses metacognition while solving a physics problem. And lastly, it allows me to practice the think aloud protocol both as a participant and a researcher.

Method

For this mini think aloud experiment, I printed the 2019 AP Physics 1: Algebra-Based Free-Response Questions (The College Board, 2019). I had not previously seen these problems, so they were new physics problems to me. I chose this source for questions because I had previously taught AP Physics 1, was familiar with the curriculum, and was familiar with past released exam questions. For those reasons, I was comfortable assuming the questions would be appropriate for my use and could be used without looking at the test ahead of time. I worked through three of the five physics problems on the exam. The problems were selected at random while I was engaged in the think aloud. This ensured I did not have time to see or think about the problems prior to the think aloud. The only criteria I had for picking the problems was one of the problems had to involve actual numbers for calculations. As a result, I did problems one, two, and five.

While working through the three problems, I recorded my thought processes, using my phone as a recording device, while solving the problems (van Someren, Barnard, & Sandberg, 1994). Once the think aloud was completed, the recording was transcribed and analyzed for problem solving steps and use of metacognition. Table 1 shows the etic codes used to analyze my process of solving physics problems for both the problem solving and metacognitive processes. While coding, I used hard copies of the transcription and different colored highlighters that corresponded with the colors in Table 1 to code the statements.

Table 1

Etic codes for analysis of metacognitive and problem solving processes.

Findings and Discussion

My Problem Solving Process

When starting a physics problem, the first thing I did was read the question itself. Once I read a problem, I would start to map out the problem by drawing a picture or free body diagram (FBD). If the problem provided a picture of diagram, I would make sure I understood it. While drawing or looking at the picture provided, I would decompose the problem into different parts, label the knowns and unknowns in the problem, and make sure I understood the question itself. Sometimes, this process would require that I reread the problem to ensure I had all information or I was clear as to what the problem was describing and asking.

After mapping out the problem, I would decide on a physics concept or equation that best fit the problem. For some questions, this meant using an existing equation such as v=l*f. In other problems I chose the concept, such as Newton’s Laws, and derive the equation from a diagram or picture. This step was beyond mapping out the problem itself, but not quite calculating the answer.

Once I had decided upon an equation, I would start to solve for the answer. If the equation was not already solved for the unknown, I would use algebra to do so. Next I would plug in my known quantities with correct units. I would use a calculator to solve the problem and write down my correct answer with units. Finally, I would make sure my answer made sense.

For the most part, my problem solving process aligns very well with the process both Phang (2009; 2010) and physic textbooks (Etkina, Gentile, & Van Heuvelen, 2014; Knight, 2013) describe. As shown in Figure 1, my problem solving followed all of the same steps as their processes, but I would diagram my process slightly different than how Phang diagramed the problem solving process of high school students in three ways. First, Phang (2009; 2010) shows the process as a linear process. I found myself going back to reread the problem while mapping the problem or bouncing back and forth between mapping out the problem and choosing the correct concept or equation to answer the question. For that reason, I used a double arrow to show the iterative process. Second, Phang (2009; 2010) includes selecting the correct concept or equation as part of the planning phase of solving the problem. While I agree that during my problem solving, the mapping stage and the selecting a concept or equation phase informed one another, the selection of a concept or equation seemed to be the transition from mapping to calculating and needed to be its own phase. And lastly, Phang (2009; 2010) had checking as part of the calculating phase. I did not check my work or understanding while calculating the answer, so I removed it from my own model.

Figure 1. A model of my own physics problem solving process.

My Use of Metacognition

While working on solving the physics problems, I made statements that reflected regulation of cognition more often than statements about knowledge of cognition. Table 2 shows the number of statements coded for the two metacognitive processes and each of the eight metacognitive subprocess. In terms of knowledge of cognition, declarative statements were the most frequent. For regulation of cognition, information management and comprehension monitoring statements were most likely to occur. Because I did not have knowledge of the problems prior to the think aloud, planning statements were missing. The one planning statement made reference to the fact that I had planned to do a problem with numbers, yet forgot to plan ahead and have a calculator ready to use.

Table 2

Frequency of statements reflecting the metacognitive subprocesses.

Most of the metacognitive statements occurred during the mapping out problem part of my problem solving process. For each problem, I referenced using an existing diagram or creating my own diagram to help with information management. It was also during this time that I had a tendency to monitor my comprehension of both what the problem was asking and decided on which physics concepts were appropriate to use for the problem. Although I did not find gaps or misalignment with my prior knowledge form working on any of these three problems, I believe this is where I would have found dissatisfaction with my prior knowledge given a problem outside of my expertise.

Once I started the process of answering the question, there were fewer metacognitive statements made. I did not evaluate my work at the end of the problem as often as I thought I would. Additionally, I did not use debugging as often as I thought I may. For the most part, I was able to work though the problems with no issues. On the last problem I worked on, I made a mistake and later figured out I made the mistake and was able to figure out where I went wrong and correct it. It is possible that if I had more difficult problems, I would have used debugging and evaluation more often.

Use of a Think Aloud Protocol

This was my first experience with a think aloud protocol as both a researcher and a participant. The use of a think aloud protocol was a more natural process for me because I tend to talk to myself while doing work. But, after doing the think aloud, I can see where this process may be uncomfortable for others. There was a point in the problem when I realized I had done the previous part incorrectly and went back to fix it. I could see how it may not be comfortable for a high school student to admit a mistake to a researcher whom they do not have a close relationship with. I was comfortable admitting my mistake, but I realize I was just admitting it to myself.

If the physics student is comfortable sharing all of their thought processes, I can see how this will be a very valuable tool to study metacognition during problem solving. When analyzing my thoughts, I was able to see, or hear, ways in which I was metacognitive that I would not have thought of if I was asked to list ways in which I use metacognition during problem solving. Additionally, I was interested to hear myself work through mapping out a problem. I spent so many years teaching the individual steps of solving a physics problem, that I did not realize how intertwined many of the steps are in my own problems solving process.

Questions before Future Research

Since this was my first time working with a think aloud protocol, I have a few questions to seek answers to. First, when I did my think aloud, I read the questions aloud. I feel like I may have missed an opportunity to gain more insight to my thinking. If I would have read silently and shared my thoughts from while I was reading instead, I may have gained more useful information. Should I ask students to read silently or should I let them decide that on their own?

To go along with the first question, I need to get a better feel for when to probe students to continue to elaborate on their thinking. When using a think aloud, a researcher should start by giving short instructions such as “Please solve the following problems and while you do so, try to say everything that goes through your mind” (van Someren, Barnard, & Sandberg, 1994, p. 43) and only interrupt the participant when they stop talking. As a researcher-participant, I knew to catch myself when I was being quiet, usually when rereading a question, to note what I was doing. When is it appropriate to ask a student to keep talking? How long can a quiet moment be? I will need to decide on this prior to starting my study so I am consistent throughout. After working through the think aloud myself, I think it would be very valuable to demonstrate a think aloud and have the students do a non-physics related practice think aloud before they work on the physics problems.

While transcribing my think aloud, I went back and forth between transcribing the equations I was talking out loud in sentence form and mathematical equation form. For example, I could type an equation as “v=l*f” or “velocity equals wavelength times frequency”. I think when I do this with the students, I want to compare the think aloud to the work on their paper and make sure the think aloud reflects the work they did. I think this will also depend on the type of physics problems I decide to use for my research. A problem that uses numbers and algebra manipulation will look differently when transcribed than a purely conceptual problem. I need to decide on a system of transcribing that is consistent for numbers, constants, variables, equations, and units.

References

Etkina, E., Gentile, M., & Van Heuvelen, A. (2014). College physics. Pearson Education, Inc.

Knight, R. D. (2013). Physics for scientists and engineers. Pearson Education, Inc.

Phang, F. A. (2009). The pattern of physics problem solving from the perspective of metacognition (Unpublished doctoral dissertation). University of Cambridge, Cambridge, UK.

Phang, F. A. (2010). Patterns of physics problem solving and metacognition among secondary school students: A comparative study between the UK and Malaysian cases. International Journal of Interdisciplinary Social Sciences, 5(8). doi: 10.18848/1833-1882/cgp/v05i08/51816

The College Board. (2019). AP Physics 1: Algebra-Based: The Exam. Retrieved from https://apcentral.collegeboard.org/courses/ap-physics-1/exam

van Someren, M. W., Barnard, Y. F., & Sandberg, J. A. C. (1994). A practical guide to modelling cognitive processes. London: Academic Press.