[Edu-sig] creating an interface vs. using one (Michel Paul)
mpaul at bhusd.k12.ca.us
Sat Sep 23 17:34:21 CEST 2006
> I don't quite understand where OO fits into math education
Fractions can be an example. A fraction is not "really" a decimal. Students treat fractions as though they were unfinished division problems, but a fraction is a two-part data structure, just like complex numbers. In terms of data structures, fractions and complex numbers are similar kinds of things. Students already study how to algebraically represent the behaviors of fractions and complex numbers. With a little tweaking, they could be creating classes. Complex numbers already exist in Python, of course, but I think it would be a very good thing for math students to create their own complex number class. Kirby has great examples of what you can do with a rational number class.
There could also be line classes, parabola classes, etc. The typical stuff that we have kids learn in the Algebras could be put into OO terms. A line object could tell you its x an y intercepts, could tell you if it contained a given point, could tell you its point of intersection with another line object, etc.
>Let me ... ask if Python has a way to plot a function
>that's as easy as on the TI. Without that I think
>it's going to be a very tough sale, unfortunately.
Yeah, that's the main wall I run into. If there was an EASY way - something as easy as turtle - that would be excellent. Does anyone on the list know of a simple to use Python function plotter? Something you could just hand over to beginners?
I know Kirby has done stuff with ray tracing - but I still have to learn about that. The kinds of things you CAN graph with Python are amazing, 3-d and so on, but it requires a bit of effort.
Something I saw at the SciPy conference was SAGE - Symbolic Algebra Geometry Explorer. It was really amazing. It's something I'd like to explore more, but using it requires a little knowledge of Unix. You can't just hand it over to a typical student or teacher and have them run with it - requires some tinkering.
From: edu-sig-bounces+mpaul=bhusd.k12.ca.us at python.org on behalf of Andy Judkis
Sent: Sat 09/23/06 04:20 AM
To: edu-sig at python.org
Subject: Re: [Edu-sig] creating an interface vs. using one (Michel Paul)
My daughter is a senior, taking AB Calc and struggling with it somewhat.
I'm becoming alarmed as I realize how little mathematical intuition she has
developed. She used to be good at it, but now she really needs the
calculator to tell her how numbers and functions behave. Very frustrating
to both of us -- she's come to hate math, and I haven't been able to get her
to consider that it is worthwhile, builds strong mental muscles, etc. And
she's an intellectual kid, well above average in math (if SATs are any
guide) and in a pretty good school system. So what are most kids getting?
I think all the points you make are very thoughtful and interesting to me,
but I doubt many HS math teachers are going to have any sense -at all- of
what OO means, let alone why it matters. I'm a tech guy, not a math guy,
and I don't quite understand where OO fits into math education, but I
believe you when you say it does. A few concrete examples would help me
understand, and might help make your case.
Let me reveal my ignorance (there's a lot of it!) and ask if Python has a
way to plot a function that's as easy as on the TI. Without that I think
it's going to be a very tough sale, unfortunately.
Finally, let me say that I really appreciate the tone of your message. Your
sincerity and humility really comes through. I'm sure you're going to
continue to encounter plenty of frustration with the math faculty but I
think you will make some headway, and inspire a lot of kids too.
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