I just finished teaching Riemann Sums, using the patented Shah Technique. I’ve always had my kids enter a program in their calculator which automatically does Left Handed and Right Handed Riemann Sums (actually it also can do midpoint!). And last year we used this program to estimate how the* number of rectangles *was related to the *error to the true area. *(That came out of me just playing around.)

The program we enter is here:

(If you want to use this, this is what you need to know. If you want the Riemann Sum of 20 left handed rectangles of from [2, 14], you enter A=2, B=14, N=20, and R=0. If you want right handed rectangles, you enter R=1.)

This year I decided to **not **go into the whole error thing like I did last year. This year I wanted students to really and more fully understand how the program worked. I always explained it, but I never really was convinced that they got it. Me up there lecturing how the program worked wasn’t really effective. So I whipped up this worksheet.

I tried to do less talking and them do more thinking (in pairs). I felt like there were a number of students who had this “OMG!” and “this is crazy” moments. Some were awed that the program worked and it gave them the answers we had been calculating by hand. Some had this amazing moment when they figured out what the variable S stood for — and how it actually calculated the Riemann Sum. And my favorite was when a couple students figured out how the R variable worked — and why R=0 gave left handed rectangles, and R=1 gave right handed rectangles.

I really enjoyed this. I think the worksheet could be tweaked to be clearer, but it’s something I see myself doing again. Well, I guess I will be doing it again tomorrow with the *other* calculus class. But I mean: next year.

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Sam,

Have you had the students come up with the program for Riemann sums (or any other subject)? Dubinsky has shown that having the students create the program leads to pretty big conceptual gains in the understanding of the mathematics.

If you have, do you have any tips? I am beginning to incorporate programming (in Python) in my classes, but I have been having a tough time giving all of the students the necessary background.

Bret

I haven’t. If I would, I probably would give them programs at the beginning of the year and analyze them… and have kids keep a running list of the commands we use.

Then I’d ask them for a homework assignment to do something simple, like “program the QF in your calculator” and have them show me that.

Eventually I’d have them play around a lot with for loops. So they could see what they do, and how they work. I’d probably give them a for loop and have them write out what the calculator would do/display at each for loop. And then finally I’d ask them to program something that required a for loop.

But that’s from someone who doesn’t teach students how to program. It’s just from someone IF I taught students how to program.

Very nice!

Great program – and a really good worksheet. I teach a class of three calc students and (along with my algebra 2 class) I keep struggling with the idea of having them start programming now. I searched for a Riemann program that was ready-made for TI’s, but I definitely love having students do more for themselves.

Nice work!