As you can tell, I don't remember the specifics of the conversation very well. But the idea stuck with me. How much physics am I actually asking my students to do on culminating tasks? Of course, there is a lot of applied math in Physics. But when I go back over my tests, sure enough, the majority of the time I am asking my students to perform correct algorithms, not explain the Physics behind the question.
A Lot of MathHere's a typical question from a quiz last year:
I would hope, first and foremost, that students would read the question carefully, and figure out what they need to do and/or which equation to use, based on their knowledge of the subject matter and the information given in the problem.
But I'm not asking them to show this thinking. All I'm asking them to do is predict the height of the diving board. Showing me this, would get them full marks/Level 4+ :
While I would give students credit for being "on the right track," even if mathematical errors prevent them from obtaining the correct answer, this, by and large, is a math question. A common major mistake on this type of question involves students not understanding either what they are given in the question or what they are being asked to do, and as a result, selecting the wrong formula to eventually apply.
Students aren't showing me the reasoning behind choosing that formula/method, because I am not asking them to.
So now I'm re-thinking how I approach testing students on the physics. The math is still important - I don't want to get rid of that completely - but it shouldn't be the only way students can show their thinking for these types of questions.
A New Type of QuestionHere is what I would ideally like students to do:
1) DESCRIBE the procedure they would use to solve a question,
2) ESTIMATE the solution to the question, and then...
3) PREDICT the solution the question.
Along these lines, perhaps, here is how I might rephrase the question next year:
In part a), I'm hoping students give proper thought to how they attack the question. Will having them make their thinking visible help them choose the correct formula or recognize which algorithm to use? Do they understand that the gravitational potential energy of an object depends on three things: its mass, acceleration due to gravity, and height? And will practice communicating this reasoning help them better understand the concepts?
In part b), the multiple choice question might seem obvious, but it amazes me how many students will submit a wildly unfeasible solution (skiers accelerating downhill at 40m/s/s, a piece of metal being dropped in hot water only to end up with a lower temperature, etc.) because they are not thinking about what their answer means.
I'm hoping that a question like this will get the students thinking about what their answer is likely to be, and then recognize if their answer is wildly off. I anticipate that some students might skip over this and come back to it after they have predicted the end result (in order to get the "right" answer), but even this might help students realize if they are in the right ballpark; if their answer actually makes sense.
Part c) is basically the same as the original quiz question, asking the students to "do the math" to determine the height.
In the end, I want students to move away from blindly choosing an equation and then pushing through the math in an attempt to solve the question, thinking it is "all about the math." I also want them to make sure they know why they are choosing one method over the other, and not just because "the variables match."
I'm hoping the focus on math will lessen over time, to be replaced with greater focus on understanding the actual physics behind the problems we solve together.
Do you teach Physics? How do you balance the physics with the math in your classes? How do you present test questions to your students? I'd love to see more ideas!