On Sep 20, 3:46 pm, michel paul <[email protected]> wrote:
> Also so does this:
>
> sage: 2.3 in [1 .. 3, step = 1/10]
> True
>
> That's interesting.
>
Here's why:
sage: [1..3, step=.1]
[1.00000000000000,
1.10000000000000,
1.20000000000000,
1.30000000000000,
1.40000000000000,
1.50000000000000,
1.60000000000000,
1.70000000000000,
1.80000000000000,
1.90000000000000,
2.00000000000000,
2.10000000000000,
2.20000000000000,
2.30000000000000,
2.40000000000000,
2.50000000000000,
2.60000000000000,
2.70000000000000,
2.80000000000000,
2.90000000000000,
3.00000000000000]
even though
sage: RR(2.3) in [1..3, step = .1]
False
What's up with that??
but
sage: [1..3, step=1/10]
[1,
11/10,
6/5,
13/10,
7/5,
3/2,
8/5,
17/10,
9/5,
19/10,
2,
21/10,
11/5,
23/10,
12/5,
5/2,
13/5,
27/10,
14/5,
29/10,
3]
sage: 2.3 is 23/10
False
sage: 2.3 in [23/10]
True
Anyway, in some sense that part of the discussion belongs on sage-
support :) and I encourage you to forward it, because I don't quite
understand why this is happening.
Welcome to sage-edu, Michel. You will also find a variety of opinions
among us as to what the "right" thing to do is with technology in the
classroom.
One idea you may want to consider is using Sage strictly *without* any
programming per se for a significant time. This allows students to
get used to the idea that (for instance) forgetting an "obvious"
argument yields an error, or that caps matter, or that parentheses
matter. Obviously this would depend on what material you are working
on and how well supported it is in Sage. But this gives them time to
get used to a computer environment that is not as forgiving as the GUI/
txt world they usually live in. (Unless your students are already
computer mavens and choosing your course as an elective, in which case
go for it!)
Actually, I like your interval_test function, as long as you don't
show them the code first thing - maybe a few weeks later? Because it
shows something very important:
sage: oo
+Infinity
sage: oo +1
+Infinity
sage: interval_test(oo + 1, -oo, oo, '()')
False
sage: interval_test(oo + 1, -oo, oo, '(]')
True
Namely, Sage consider infinity +1 to be infinity, but that infinity
itself is not in the *open* interval with endpoint infinity! This is
mathematically true, because the real line does not contain infinity -
you have to add that point if you want to use it, which turns out to
actually be useful in various contexts.
And now you can get into a discussion of what the heck infinity IS, if
it exists, and what the Greeks thought, and what the developers of
calculus thought, and what Gauss thought, and what contemporary
mathematicians think or thought, and how that impacts the math one
might or might not do. Well, maybe not all that the first day - but
it provides a way in for a different kind of discussion, especially if
they are already familiar with using oo from some other piece and you
tell them to try a lot of different kinds of intervals. And I hope
that would be at least related to your goals of getting them thinking
of math in a different way - not computational analysis this time, but
as something different from rote memorization of formulas to be
applied at thus and such a time.
Incidentally, it might help with the other teachers with your items 1.
and 2. to try to think about what common ground you may have with each
party. Perhaps there are things Sage cannot do (at least with one
keystroke) that a calculator can, or there are things which are really
hard to get the calculator to do but group 1 would like which Sage can
assist with - not take over, just help out. I suspect that there is
some similar common ground with group 2. - because after all,
mathematicians and computer scientists still provide proofs with their
papers, especially since it will often be the case that the n=7 case
maxes out your memory (as happened to me Friday doing some research),
and n=1 to 6 isn't even enough to get the pattern!
Please keep us posted as to your experiences. There are a fair number
of people at the college level using Sage in teaching, but we would be
very interested in more people at the secondary level letting us know
what is good and what is irksome, particularly functionality which TI
or Geogebra might have that we would be able to implement fairly
easily. But truthfully, there are many things at the secondary level
that Sage is not appropriate for, or even really able to do, so there
is room for more than one solution. The right tool for the right job,
right?
Good luck,
- kcrisman
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