I was sort of thrown into teaching calculus based physics to a bunch of non-physics majors, who have taken one semester of calculus, and are poor with that material. It is only a 50 minute per week class. So I've been stuck in between teaching elements they'd receive in the calc sequence (integration by parts, $i$ and $j$ vector notation, dot product, partial derivatives, etc), and somewhat random integral or derivative versions of stuff they've seen in their normal physics class running in parallel. I also don't like the calc based text I'm using in parallel to their regular non-calc class text. Since it's a 50 minute per week, 1 credit hour class with low expectations, can anyone recommend me some "interesting" activities, or else point me to a nice standard problem set, to do in there?
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$\begingroup$ I would agree that it would be pretty helpful to know a little more about the exact aim of the course. $\endgroup$– kcrismanFeb 11, 2019 at 15:06
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3$\begingroup$ What country is this in? Here in the US, I've never heard of a 50 min/week physics class. This sets off huge alarms for me. So I've been stuck in between teaching elements they'd receive in the calc sequence (integration by parts, i and j vector notation, dot product, partial derivatives, etc) I'm having a hard time making sense of this. Integration by parts, at least at my school, would be in their second-semester course, so you should just not use it. Partial derivatives ditto. The vector stuff, in my school, they are theoretically supposed to learn in the trig prereq, but the trig [...] $\endgroup$– user507Feb 11, 2019 at 20:44
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$\begingroup$ [...] instructors tend to skip it, so students see it for the first time in physics. There is review of vectors in 3rd-semester calculus. In general, I don't really understand what the situation is and what the question is. Does activities mean in-class activities? Homework problems? Could you edit your question to clarify what's going on and what you're asking for? $\endgroup$– user507Feb 11, 2019 at 20:44
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$\begingroup$ Related question: "Mathematics that can be worked into 8th grade engineering course" $\endgroup$– JasperFeb 12, 2019 at 1:32
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$\begingroup$ Allow me to elaborate: I am teaching a standard non-calc physics course. But, some of those students meet with me once (50 mins) per week for what's supposed to be "throw in some calc based examples of what we saw in class." This hasn't been as smooth a process as I anticipated, partly again, because of the need to teach some things that they weren't taught in calc 1: integration by parts, dot product, cross product, partial derivatives (used in studying conservative forces), etc. Easy stuff to teach on the fly, but again, this is a 50 min per week class. Suggestions? $\endgroup$– NightsFeb 16, 2019 at 19:55
2 Answers
I am going to assume that you are teaching a calculus "helper" versus the entire physics class. Your initial statements don't match that. But then all your content described is math, not physics. And also 50 minutes per week sounds rather light for a whole class. [If the converse is the case, I would spend your time on...physics.]
With that in mind, my advice is NOT to look for some interesting activities. Instead use this as an opportunity for you to learn about the math required in stereotypical physics 101 classes. And give the kids a brushup related to that. Look at the homework and see what are the key math steps in them. And give a little help on them. Don't teach the physics of it (no word problems, they get that in real class). But abstract it down just to the math itself.
I would try to parallel whatever is being done in physics class. If vectors are important this week, spend some time on vectors this week. If integrals are important a different week, spend time on that. Now, it may not match perfect match, and some remediation may be needed of issues in previous semester. But let that be a general guide.
In terms of format, I would try to do something interactive, using a handout each week. Some lecture and some practice, using the sheet.
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1$\begingroup$ And lots of calculations for the students to do. $\endgroup$– TommiFeb 11, 2019 at 7:37
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$\begingroup$ Good ideas, and this was what I initially intended. Unfortunately this is the second semester of this physics sequence (and in parallel the second semester of the calc based once-per-week section), and the book I've been using to pull calc based examples from either hasn't had very good accompanying derivations/explanations or, more practically, hasn't had very good calc based examples. So I've jumped around in it, just trying to find any calc-based examples for stuff we've already done in the regular class. So ideally, my question was seeking more specific sources I could pull from. $\endgroup$– NightsFeb 16, 2019 at 20:03
I don't have any specific resources, but I suggest that you might find a little success by finding some physics applications where there really is a difference between the "algebra-based" and "calc-based" physics that use e.g. multivariate calc or integration by parts or something.
As an example, I think that there are some problems involving work (e.g. pumping water out of a conical tank?) that probably aren't exactly solvable without integrals, and which might require even trig substitution or worse. If you have access to a solution manual for the "real" calc-based physics course, you can just browse it for problems where those specific techniques come up, and then just do the problem up to the point where calculus comes in. Give them two minutes to talk to a neighbor to say "now what do I do", and assuming they have no idea, now you review the relevant calc technique.
This is probably not really going to help them internalize new calculus they need, but then again a 1-credit hour class probably is going to have pretty minimal expectations so at least it will connect a bit.
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$\begingroup$ (By the way, this doesn't mean guest's answer might not be useful to you as well; a lot depends on what the culture of the institution expects of this course.) $\endgroup$– kcrismanFeb 11, 2019 at 15:11
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$\begingroup$ This has been my approach. Though it's generally become more frustrating with the text I'm using, as I've gone along. Essentially my question was asking, ideally, for specific sources. At least you've reminded me of the problems that come up in calc 2 involving pumping water, or stuff like center of mass, etc. thanks. $\endgroup$– NightsFeb 16, 2019 at 20:00
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$\begingroup$ Yeah, honestly I'd just check out a "classic" calc-based physics text and look for everything that involves an integral or a non-polynomial derivative. Good luck! $\endgroup$– kcrismanFeb 19, 2019 at 3:35
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$\begingroup$ Also, maybe you can write your own such resource eventually and open-license it - I will plug and recommend the GPL pretextbook.org for use in writing such resources $\endgroup$– kcrismanFeb 19, 2019 at 3:36