Teaching Problem Solving in Physics

Papers: When Physics Intuition Fails (Chandralekha Singh), Some Implications from Physics Education Research for Teaching Problem Solving in General Physics (Maloney et al. 2008)

Presenter: Robin Rehagan

What is a problem?

  • something difficult
  • something that needs a solution
  • something that you don't know how to do
  • Maloney: you are presented with a novel situation, and you perform a sequence of steps to arrive at a solution
    • implies that a "problem" can't be something that you've seen before
    • just because it's in the back of a physics book, doesn't make it a "problem"

What skills do students need to solve a problem?

  • Determination/persistence
  • understanding the problem
  • visualization
  • identification of important (vs. unimportant) variables
  • being able to connect with previous knowledge (pattern recognition)
  • be able to make assumptions/estimations about unknown (not given) information
  • Maloney: 2 steps to problem solving
    1. Representation - the mental model of the task that the solver constructs
      • Singh: Most novices (students) do not start a problem by drawing a picture, even when it is merited. Most experts do draw a picture before beginning.
      • How do you convince students to take the time to draw a picture?
        • Maloney: use picture-based ranking tasks that describe the problem using pictures to force students to think about problems visually
        • Maloney: Students have a limited amount of "brain energy" that can be spent on a problem, and they need to learn to use it efficiently
    2. Heuristics - procedures to get from the representation to the answer
      • Polya 1945: "How to Solve it"
        • lists problem solving strategies
        • IDEAL - Identify the problem, Define and represent the problem, Explore possible strategies/solutions, Act on a selected strategy/solution, Look back and evaluate
      • How did we (faculty and graduate students) approach a difficult physics problem?
        • drew a diagram(s)
        • jump to relevant physical laws/principles
        • write down equations relating to relevant variables
        • examine the limiting cases to gain intuition
        • decode the text of the problem to discover relevant laws/equations
        • relate to real-life situation
        • (experts debated about the correct solution to the problem)
      • how did students in Singh paper solve the problem?
        • seldom employed a systematic response to problem-solving
        • most students did not take the time to analyze the situation qualitatively
        • rarely contemplated conservation laws
        • rarely looked at limiting cases
      • Have students been "trained" to solve problems incorrectly?
        • if you are used to the "plug-and-chug" method, why would you try to spend time visualizing the problem?
        • students are often under a time crunch to get problems done and don't believe that stopping to think about the problem before applying equations is worth their time
        • should professors be giving students fewer problems (or more time on tests for problem solving)?
        • inadequate time spent in solving the problem is what prevented most students from solving the problem
        • should professors be testing problem solving strategies individually before asking a single word problem that requires students to apply many strategies all at once?
          • how would you go about grading such a test?
  • Maloney: write problems that forces students to visualize the problem
    • ranking tasks are a good vehicle for testing visualization skills while still including important content
    • benefits of ranking tasks:
      • students get used to visualization
      • students get used to taking ratios and comparing different situations
      • tests students conceptual understanding of the physical principles
      • can use these problems to tease out common misconceptions that need to be addressed in class
      • requires students to explain their reasoning without using equations
    • students in general do not appreciate being given these types of problems, even when it helps them improve their scores
      • professors are hesitant to use these strategies because they can get bad evaluations
      • do teachers need to explain why these types of problems are being given to justify the teaching strategies?
        • Studies have been done showing that students who are taught about problem solving methods and/or the neuroscience behind learning tend to do better on a set of physics problems
      • students get angry when the professors don't "give you the answer"
      • students feel like the professor should be "doing the work"
      • teachers could try asking the students to write their own problem to give them an understanding of the difficulty involved
  • "Means-Ends Analysis"
    • Maloney says that this is the "plug-and-chug" method, and shouldn't be used
      • is this way of problem-solving somewhat mindless?
      • there is no time for reflection and self-evaluation (no place for meta-cognition)
      • no time to stop and think about the big picture

Resources for finding educational papers:

PER Central: http://www.compadre.org/per/

SERC: http://serc.carleton.edu/index.html

Takeaways: Think about the ways that you solve problems before trying to teach students how to solve problems. Take time to make sure that students have a good strategy for problem-solving and understand the procedure that they should employ. Give students enough time to explore possible solutions on homework and exams. Problems should be developed with the problem-solving strategy in mind. Identify the skills you want your students to practice before writing the problem.