Date: Oct 18, 2012 1:42 AM
Author: kirby urner
Subject: Re: In favor of teaching "dot notation"
On Wed, Oct 17, 2012 at 4:49 PM, Robert Hansen <bob@rsccore.com> 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