Friday, July 24, 2015

Physics: It's Not All About the Math

Earlier in the year (or was it last year?), I had a conversation with someone (or was it a Twitter chat?) where the idea came up that when we test students in Physics, 80% (or was it 75%? or 90%?) of what we are actually testing them on is not their ability to do physics, but their ability to do math.

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 Math

Here'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 Question

Here 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!


  1. Ho boy. You do ask big questions! :) I've struggled with the this as well. I've tried a few different things, like making sure that this kind of question isn't the only way for students to show that the conceptually understand something. I like your idea of integrating that into this kind of typical problem. One of the things I always tell my students is that the physics is in the thinking about the problem. The identifying of variables, concepts and ideas. Once they've set if all up, the rest is the math. I'll freely admit that they were intertwined (as I think they have to be, math is a language used to describe science), but if a student can demonstrate that they understand concepts, but maybe make math errors, that's got to count for a lot.

    1. Hi Colin! I like the idea of physics being in the thinking through the problem - I'll try and lean on that a bit more this year. We do talk about "physics intuition" (knowing that a skier accelerating at 40 m/s/s is unrealistic), but that thinking often falls to the wayside on tests, I think, because of the stress to get through some of the math. Some really struggle with units too - if they solve for the correct height, but then list the final unit as m/s, what does that tell me about their understanding of the problem? I'm hoping to focus the students less on the math, but still keep it prominent... if that's possible? :)

    2. Part of it is to carefully consider the thought process during the marking process. The final mathematical answer is not the only goal, I was them to communicate their thoughts. That is the emphasis. Plus I always include theory questions and application.

  2. Very interesting indeed. It's really difficult to separate the math from the physics in a physics course. I do like putting more emphasis on getting the students to explain the physics concepts, rather than showing they remember a procedure (almost always "the math").

    1. Hi Al :) I try to have some non-math questions on unit tests because of this, but because it's so hard to separate math from physics sometimes, I'm wondering if it's better to combine the different ways of thinking in most questions (as opposed to having just "math questions" and "non-math questions"). I have to think how I'd like to apply this to the pre-existing eLearning material, too, since that's what my grade 12s will be accessing primarily. What's a good balance?

  3. Great write-up and great questions! I've started to learn more about more about Modeling ( and I really, really want to go to a workshop on it. I've tried to do some (I was told not to try without going to the workshop... oh well) and I think it gets at what you want. Every unit starts with an experiment and quickly moves into qualitative, conceptual tasks. Only later, once they've built an understanding with diagrams, charts, & graphs, do they tackle the tricky math problems. There are times where the math has tripped the students up (I recognize this because I have students in calculus, precal, alg II, and sometimes even geometry in my physics class), but it's much better than it was before I tried modeling

    If you haven't yet, I would highly recommend reading Kelly O'Shea's stuff on it:

    1. Hi Jon! I'm interested in this approach especially as I usually get 1 or 2 grade 10s taking SPH3U... BEFORE they have taken grade 10 math! Nothing like a crash course in trig and the quadratic formula to really drive things home :) I'll be sure to take a good look at it. I've moved away from whole-class direct instruction lately... I wonder if this type of modelling still works when everyone is going at their own pace? I'd be interested in hearing more about how you do it in your classes (even if you do it illicitly!).

  4. Hey Heather!
    Love this. I often talk about ways to get students to focus on the concepts instead of the math. This is a great idea. I wonder if it would be most useful as a form of practice instead of on formal assessment. Use things like this to create the habits that they need to use??
    Just a thought :)

    1. Hi Heather! I'd LOVE to be able to have this kind of thinking become routine for the students, and I do hope to add it where I can to the learning resources. With everyone learning at a difference pace, I wonder how well I'll be able to sustain it through the semester? I was thinking of formal assessment primarily because that tends to be when students forget all their "training" and push themselves to go quickly through the test (to stay within time constraints? because "tests are worth more? because of extra stress? For whatever reason.). Here's hoping we can develop the habits and have them stick!

    2. Maybe there is a more generalized way to create the 3-part question, and it could be a requirement for any problem that they solve during the semester? And could be part of any formative thing you assign (i.e. quiz, etc)?

      I am trying to work more and more toward "Big Ideas" in assessment. I would love a partner-in-crime for this if you are interested in collaborating on creating these ideas for SPH3U? The plan would be to then base the whole courses assessment & evaluation on those big ideas which would lead to having shorter evaluations (i.e. if there are 5 big ideas then there might only be 5 questions on a test, which would potentially lead to less rushing on students parts? - this is the kind of thing one of m colleagues has been trying in Bio and I am hoping to move toward in various areas).

      [Ideally I hope to eventually stop having the traditional "test" altogether as things become more authentic, but I am not there yet!!!!]

    3. WOW! In short, YES! Let's collaborate!


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