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Topic: In favor of teaching "dot notation"
Replies: 26   Last Post: Oct 20, 2012 12:26 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 3,690 Registered: 11/29/05
Re: In favor of teaching "dot notation"
Posted: Oct 18, 2012 1:42 AM
 att1.html (4.1 K)

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
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

Date Subject Author
10/7/12 kirby urner
10/13/12 Joe Niederberger
10/15/12 kirby urner
10/13/12 Joe Niederberger
10/16/12 Joe Niederberger
10/16/12 kirby urner
10/17/12 Joe Niederberger
10/17/12 Paul A. Tanner III
10/17/12 kirby urner
10/17/12 Joe Niederberger
10/17/12 kirby urner
10/17/12 Paul A. Tanner III
10/17/12 kirby urner
10/17/12 Robert Hansen
10/17/12 Louis Talman
10/17/12 Robert Hansen
10/18/12 Louis Talman
10/18/12 Robert Hansen
10/18/12 kirby urner
10/17/12 Joe Niederberger
10/17/12 kirby urner
10/19/12 Joe Niederberger
10/19/12 Robert Hansen
10/19/12 Joe Niederberger
10/19/12 kirby urner
10/19/12 Joe Niederberger
10/20/12 kirby urner