P.S. Here's an example of an interval testing function I might discuss that
would be simple enough for general discussion:
def interval_test(x, a, b, braces):
if braces == '[]': return a <= x and x <= b
if braces == '(]': return a < x and x <= b
if braces == '[)': return a <= x and x < b
if braces == '()': return a < x and x < b
It works for the kind of stuff presented in our text, and I think it should
be no more difficult than the ordinary algebra.
Please let me know of alternatives.
Plus, since SAGE can handle infinity, it allows for this:
interval_test(oo + 1, -oo, oo, '()')
I think it might be a fun discussion to ask them what they think will get
returned before actually executing.
SAGE does return True.
- Michel
On Sun, Sep 20, 2009 at 9:03 AM, michel paul <[email protected]> wrote:
> Hi,
>
> I'm a high school math teacher experimenting with getting kids to use
> SAGE. My situation - high school math in a department that rigidly believes
> either that
>
> 1. graphing calculators provide sufficient technology for contemporary
> math classrooms or that
> 2. technology is something secondary to the mathematics itself - it might
> be 'useful', but it's not what mathematics itself is about.
>
> It has been extremely frustrating trying to communicate in this
> environment. Ideally my vision would be to create a computational analysis
> kind of course where the kids would first learn how to articulate basic math
> concepts in pure Python. Things like the Euclidean Algorithm. Simple
> enough but important enough to focus on for good computational ways to
> think. Important - the point wouldn't be Python per se. The point would be
> computational thinking. How can we analyze tasks or concepts? Then show
> them what they have access to in SAGE. Wow. There's absolutely no rational
> reason at all why a course like that shouldn't be promoted.
>
> Well, anyway, at the moment I've opted for a strategy to weave SAGE into
> the curriculum as unobtrusively as possible. I have been successful in
> getting all my kids to open up SAGE notebook accounts. I've decided to
> weave in the use of SAGE as we work through our standard text. I'm going to
> use SAGE as my blackboard as often as possible, and I'm posting SAGE
> notebook worksheets paralleling the examples in our text for the kids to
> experiment with. It's a weird balance - trying to introduce using Python or
> SAGE to kids who have never associated that with 'math'. Funny, their
> attitudes actually parallel 1 and 2 above. It's such a weird culture. But
> other kids are seeing that, yeah, this really is pretty cool. So I hope to
> build momentum from that.
>
> So we are about to study interval notation. I'm going to show them how
> interval notation means something different in SAGE than it does in their
> texts. However, there's lots of ways they are related.
>
> My question - the text expects them to express things like (1, 4) intersect
> [2, 8] on a number line to produce the graph of [2, 4). That kind of
> stuff. It will also ask them to solve and graph typical linear
> inequalities, absolute value inequalties, etc. Is there a way to easily
> illustrate this in SAGE?
>
> I was contemplating discussing something like an interval testing
> function. But I also notice that testing something like
>
> 2.3 in [1 .. 3, step = .1]
>
> produces False. Issues like this can be a booby trap with already
> reluctant learners.
>
> Thanks for any advice,
>
> Michel Paul
>
>
>
> --
> "Computer science is the new mathematics."
>
> -- Dr. Christos Papadimitriou
>
--
"Computer science is the new mathematics."
-- Dr. Christos Papadimitriou
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