Structured Problem Solving for Physics Word Problems

As I have mentioned in my previous blogs, solving problems (particularly Physics word problems) have always interested me. In this blog, I would like to share about a problem-solving technique or strategy that I read from Estelle Gaigher’s “The Effect of Structured Problem Solving Strategy on Performance and Conceptual Understanding in Physics: A Study in Disadvantaged South African Schools”. Although her paper was written in 2004 and parts of it were published in 2006 and 2007, I was very grateful I was able to read it because it made me affirmed some of the points that I believed in. It also explained some of the things that I felt worked for me. In this blog, I would like to point out two of these things.

    The first of these points is on the hierarchical knowledge structure. I could remember when I was in high school, my mom would wonder why I would keep re-writing my notes. My reason then was that I do not want to bring lots of papers/notes when I study while I travel (the trip from home to school is approximately 1 hour so I used to study on the way. My parents would make us sleep at 8:30 pm. The latest you can bargain with is 10:30 pm.) So, I used to re-write my notes such that when I read a phrase or a word, I would remember concepts/ideas related to it. I would keep re-writing my notes until my notes would fit into a few pieces of paper the size of calling cards (I used to use the back of raffle tickets for my notes.) This way of studying became a habit for me that I would sometime catch myself asking myself or my teacher how a new concept that we are learning in class would fit into my notes. I have not heard of concept maps or mind maps at that time, but I would ask whether the new concept is a sub-concept of what we have learned in class, or is it a different category, etc.? Although I often share this experience with my students, I do not suggest that they follow it because I cannot provide any theoretical or research-based explanation for it. I just knew it worked for me. Reading Gaigher’s paper made me stood up because it says there that according to researchers, expert problem solvers tend to have hierarchical knowledge structures and that we, teachers, could help our students attain a more organized knowledge structure to make them better problem solvers. So there goes my explanation! 😊 I am not saying I am an expert problem solver, but this help explains why it was relatively easier for me to relate one concept to another. I made conscious efforts to organize what I have learned in my mind. 😊

              Another hunch that somehow got affirmed by Gaigher’s paper is my belief that students’ ability to solve word problems is related to their ability to make translations. My idea about “translation” then is limited to understanding the problem and expressing the word problem into mathematical statements. However, I think of “understanding” as linking certain words or ideas to relevant Physical concepts that are necessary to solve the problem. In her discussion on a strategy called structured problem solving, Gaigher presented Greeno’s Model in Scientific Problem Solving. In this model, Greeno states that there are four domains of knowledge (concrete, model, abstract, and symbolic) and that each domain consists of two layers (layer a which consists of independent components that when put together becomes the concept in layer b). In her paper, Gaigher explains that the steps involved in structured problem facilitate multiple translations between domains. This process of multiple translations enhances true conceptual understanding which in turn helps learners become better problem solvers. The link between multiple translations and problem-solving is something that I believe in between but I didn’t know how to articulate, and I have not thought about the various domains of learning, so it was really exciting for me to read an article which expressed my tentative thoughts so well.

Structured Problem-Solving Steps 1. Draw a simple diagram to represent the system. 2. Indicate the data on the diagram. 3. Identify the unknown variable. 4. Analyze the problems in terms of Physics principles. 5. Write the relevant equation/s. 6. Substitute and solve. 7. Interpret the numerical answer.

         As you might have guessed, I am excited to teach the strategy to my students then see how it impacts their problem-solving performance. However, I would like to make a few adjustments. The first one is a minor step – to underline important words/quantities in the problem. I think advanced problem solvers can skip this step, but I believe it would be very helpful for novice problem solvers. I believe that this step forces them to think about why they think what they underlined is important. Through this process, I hope to encourage the students to become aware of their own schema or knowledge structures. I have done this procedure in my class and I have observed that those who do this step were more mindful about how terms that are seemingly unrelated to Physics provide clues to the physical principles that are the keys in solving the problems.

        I am on study leave so I won’t be able to implement this sooner than I want to but if any of you have taught this strategy in your class, maybe you can share some of your observations in the comments section below. Looking forward to hearing from you.