John Caranci, Ontario Institute for Studies in Education/U. of T., CTL Lecturer Intermediate/Senior Physics, Chemistry, Science
john.caranci@utoronto.ca

A while ago when I taught high school my grade 10 Science class came into my classroom after my grade 11 physics class had left. I had just done a lesson on the development of the kinematic formulae using graphing. One of my grade 10 students seemed mesmerized by the boards covered in figures and diagrams. They turned to me and asked what was on the board. I said kinematics, which is part of the grade 11 physics course. Their response was “I guess it will be biology next year for me.” What makes kinematics like this? Is it the mathematics? Is it the lack of relationship to the real world (ignoring friction)?

I began playing with alternatives to present the topic. I recognized it was not the authentic or real-world connections, it appeared to be the arithmetic. Notice, I did not say the mathematics or physics. Many times, a simple arithmetical mistake (even to the point of a miss-written minus sign), might cause them to believe that their whole solution, and therefore their understanding of kinematics, is wrong.

When a student approaches a kinematics problem, they usually draw the sketches and list what’s given and what’s required. Then they choose the formula. That is where the physics ends, and the arithmetic starts. As physics teachers, do we assess physics or arithmetic?

My pre-service candidates and I adapted other problem-solving methods. What would happen if we only asked students to get to the equation step? Give the students twenty plus problems, never asking for a final answer. The final answer you would look for is simply the initial equation. Doing this, grade 11 kinematics students gained a confidence to do kinematics problems.

I once visited a candidate in their practicum. They asked me to look at a calculus derivatives test’s marking scheme. Only fifteen percent of the marks were on calculus. All the rest of the assessment was on completing the algebra and arithmetic. It begs the question, what are we assessing?

Why does a student have to complete a question? If we accept that problem solving is a process, that would mean we could deliberately isolate the exact steps in physics, from the arithmetic steps. As a challenge, go back to a paper and pencil test you have implemented to see how you distributed the percentage of marks on physics (or calculus) rather than algebra or arithmetic.

A process: In the kinematics unit (or derivative unit in calculus), try this process in class. It is a not a homework exercise.

1. Prepare or choose twenty to thirty problems.
2. Do the sketch of each and every problem (but not more).
3. When 2. is complete for all problems, then list the given and required quantities of each and every problem (but not more).
4. When 3. is complete for all problems, then choose the equation for each and every problem (but not more).
5. When 4. is complete for all problems then end the process. A comparison sheet can be prepared for the list of answers.
6. Gather data on how confident the students feel they are with kinematics.
   

As teachers, we sometimes do things by seeing the end of a problem-solving process as the answer rather than the process. Pedagogically, we teach processes in many tasks in our lesson plans for example: use of apparatus, safety, and observing. We should not set that aside in problem solving.

Please send comments to me at john.caranci@utoronto.ca.

Tags: Assessment, Kinematics, Math, Pedagogy