On Wed, Oct 17, 2012 at 4:49 PM, Robert Hansen wrote:

On Oct 17, 2012, at 5:38 PM, kirby urner <kirby.urner@gmail.com> wrote:

For example, if you're "2", a member of the set Z (integers) then your blueprint / template includes circuitry / a recipe for "adding".

And the sum of 12, 63.4, 10 and 56 would be?

>>> 12 + 63.4 + 10 + 56
141.4

These numbers are objects though.

>>>12 .imag
0

means the imaginary component is 0.

How about 3 * (4 + 2) - 16 / (7 + 1)?

>>> 3 * (4 + 2) - 16 / (7 + 1)
16.0

4 + 2 is equivalently 4 .__add__(2) i.e. the __add__ method is triggered by +.

Why is this important?  Because when a math student designs her own objects, she can define __add__ and then use +.

"AB" + "CD" gives "ABCD" i.e. the __add__ method works differently with string type objects, versus integer type objects, as one would expect.

Good to get string type in the mix.  1900s math was way too number-centric, unsuitable for 21st century STEM.

How do you handle units? Like 12 miles or 14 hours?

Good question.  math.radians( ) and math.degrees( ) convert one into the other, for trig purposes.

http://packages.python.org/quantities/

How do you show a rational function between polynomials, such that a student can see it and simplify it or factor it?

Bob Hansen

Stuff like this:

http://4dsolutions.net/ocn/python/simppoly.py

I'm just giving answers like you'd find in 'Mathematics for a Digital Age...'   Other languages using dot notation might do it differently.

Note that including dot notation in math teaching is not to the exclusion of other notations.  You can keep the usual notations as well, and indeed they reinforce each other as it's easy to go:

>>> def f(x):  return x * x

... to get a function, but then with dot notation you can annotate it like this:

>>> f.note = """some people say 'squaring a number' reflexively -- without really thinking about it --
when they see n * n, but a triangle would work, as you will learn in this course"""

See how the function object now has an attribute called "note".  Consistent.

Anyway, this is about expanding the notations to which we give consideration, not replacing.

Bringing back more focus on music notation, in a mathematical context, linking to concepts of frequency and time could easily be a part of this same initiative.

Kirby