ERLCMATH20-2: To prove or not to prove

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To prove or not to prove

Wednesday, 30 November 2011, 10:50 PM

Hello,

I have more of a general question: I am wondering whether you prove every formula that you introduce to the class?

I think that in theory it is good form to prove formulas, because that way students can understand the relationship to its application.

However I'm wondering if anyone finds that it actually benefits students, when you could have used that classtime for additional practice? I'm thinking especially with a group that is not in the academic stream (such as Math 20-2).

Thoughts? Experiences?

Thursday, 1 December 2011, 05:40 AM

I only proved sine and cosine laws.

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Thursday, 1 December 2011, 08:20 AM

I did the same as Chris. I just proved the sine and cosine law. But Melissa, I don't see any harm in what you are doing. I actually think that if you have the time, those types of questions further more discussion, which I feel is the most important part of math. More important than doing 80 questions.

I am curious as to which formulas you proved and how your students responded.

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Thursday, 1 December 2011, 01:46 PM

Ugh. I just wrote a really long reply and then my computer had a hiccup and lost it. I will summarize!

I have my students write proofs for their work on mathematical reasoning using angles in triangles and between parallel lines. We make a chart with the work shown on the left and the laws that we use to justify our work on the right.

As a class we prove sine and cosine laws in the same way as with angles, but I do not make them prove it on their own. The kids (should) have a foundation in right angle ratios from math 10-c so they can follow the logic. About half of my class found this useful.

The only other equation I can think of that I will use is the quadratic equation and I would rather not prove that with my class...

Chris

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Thursday, 1 December 2011, 03:55 PM

I agree. The quadratic formula proof would be beyond them. Maybe a high end student.

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Thursday, 1 December 2011, 09:13 PM

We proved the sine and cosine laws, and the class did ok with explaining the proofs (through a lot of repetition!). And we did something pretty similar with the charts for proving the properties of angles and parallel lines.

At the beginning of the year, I did take them through the proof of the volume and surface area formulas for scale factor, and they did ok with it. I'm not sure many students understood the proof but most gave an honest effort. I didn't take them through the proof for the quadratic equation, because I figured the time would be better spent with them practicing its application.

I don't really like just introducing a formula though, because it seems like it's a magic solution and the relationship is lost. But I also I remember when I was in math class in the academic stream, and proofs were lost on the majority of that class. This is my first year teaching, so I am thinking a lot about things like whether to prove or not.

Thanks for the feedback!

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