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Archive for the ‘debate’ Category

Derivative Clicker

I was looking for a derivative-based game to play in Calculus as we were just closing out our first unit on derivatives and the semester was ending. That’s when I found Derivative Clicker:

https://gzgreg.github.io/DerivativeClicker/

It hit the spot with my students. I explained the game and had them all start playing simultaneously, and then saw who had earned the most money in 20-25 minutes. Yes, it’s a little addictive and “brain rot” (as one student said, but, like, it was a positive review) but they had a lot of fun.

The thing about math games, though, is that the real power is not in the game itself but in the debrief. Just the lesson before this was my students’ first exposure to the idea of higher order derivatives. They asked “But what does a second derivative actually tell us about the function” and I explained, but it still felt ungrounded to them. So I thought this would help them feel the power of derivatives viscerally.

Then we filled out some tables: what if I just had a single 1st derivative (or, in other words, f'(t) = 1), how much money would I have after time? What if instead f”(t) = 1? f”'(t) = 1? This helped build up the idea of increasing rate and how the rates grew polynomially.

They also had debate question about strategy – in the game, with $500, you can buy 1 second derivative or 65 1st derivatives. Which is better? (There’s no a clear answer here – if you were to buy the second derivative and then walk away, it’ll probably be better for you by the time you get back. But if you buy the 65 1st derivatives, you’ll have enough money to buy a second derivative way before buying a second derivative will get you 65 1sts.)

Below is the debrief sheet we did today.

2.X – Derivative Clicker DebriefDownload

Category:

Calculus, debate, games, lessons

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Grading Talking Points

Two main things I wound up talking about at MfA Summer Think were talking in math class and grades. One thing we talked about in regards to grades is that students (and parents) often flip out when introduced to a new grading system that is different from what they are used to, even if by the end of the semester they come around and say that they are glad it was done that way.

I thought, then, instead of just springing my grading/SBG system on them, that we could reflect on what grading systems really mean and what they should do first, to prime the transition. So I created a grading Talking Points (with help from my Twitter mentions for some statements).

Category:

conference, debate, MFA Summer Think, Uncategorized

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The Lottery Choice

The other day I read Carl Oliver’s post about the safe and the piggy bank. I was reminded of a lesson I did last year in my exponential unit after taking Chris Luzniak’s wonderful course on debate in math and science classrooms. I wanted to make the typical doubling penny problem more debatable. It actually only really required a small change.

 

“Would you rather…

a) Win $100,000 a month for 30 months, or

b) Win a penny the first month and have your total doubled every subsequent month, for 30 months.”

 

This seems like the same problem as the typical formulation, on the surface, but it’s not. The key difference is in the length of time. Usually, the time frame is over a month with daily payments. This is because the number 30 lends itself well to the problem. In that case is pretty unreasonable to not just wait for the full month to get more money by using the penny.

But now though the penny option gets you more money in the long run, you have to wait a really long time before you get anything of value. It takes two years just to get the same amount of money as option A gets you in one month. For some students, that’s just too long to wait. When you need money, you might gladly choose option one for more immediate relief, even if option B gets you more in the end. So it’s a nice debate and would you rather question.

Category:

debate, math