Fwd: inverses

[michel paul]

Just posted the following at mathfuture. 

My principle came in to observe the other day, and this morning we had the followup meeting. He was impressed, and I was glad to see how genuinely impressed he was. What he observed was the students interacting with the Sage Cell. I told him how asking students to code mathematical ideas immediately shows why they've never understood math previously. There are students who have advanced year by year in math just through imitation, and it shows when you ask them to interact with code. There are students in post Alg 2 classes who believe that f(x+h) = f(x) + f(h).

- Michel

---------- Forwarded message ----------
From: michel paul <python...@gmail.com>
Date: Thu, Nov 20, 2014 at 6:09 PM
Subject: inverses
To: mathf...@googlegroups.com

http://sagecell.sagemath.org/?q=nvjnsk

A student can change the function used as well as the start, stop, and step values of the domain.

Everything else takes care of itself.

What's more, the code reads naturally. You don't have to learn anything extra to follow what's going on in the first 4 lines. That stuff is the core curriculum.

I've been finding the Sage Cell amazingly effective. Send a link to students with code and comments. They respond, creating their own code, and then reply sending their own link.

I have found it a very powerful and easy way to do things.

--

​Michel

​

===================================
"What I cannot create, I do not understand."

- Richard Feynman

===================================
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
===================================

--

===================================
"What I cannot create, I do not understand."

- Richard Feynman

===================================
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
===================================

[kcrisman]

Awesome!

Have you done much with interacts?  Try http://sagecell.sagemath.org/?q=ptjeid

But I do see the pedagogical point of NOT doing them to get them to really 'interact' by hand with the code to understand the math better.  Great point, and glad it's so successful.

[michel paul]

Yes, I have done lots of stuff with interacts. But yeah, I also am trying to coax the kids to realize that they can think with this. A lot of these kids are not strong mathematicians, nor do they have much of a background in programming. They are extremely easily intimidated by symbols, so the fewer the better. I start by having them do really simple things like use interval notation to create sequences and then move on to list comprehension. I'm making list comprehension a core standard. Many students find it challenging, but getting them to persist in understanding it really pays off. You can model so much with it, from plotting ordered pairs to articulating sigma expressions. Since it's based on set builder notation, it has a whole lot to do with the mathematics we want them to understand in the first place.

But the fact that you can then add interacts to core code you've created is fantastic. It's actually timely that you mention it right now, because it could be a great thing to do tomorrow : ) 

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