[Edu-sig] Archived letter to community college prof

[Kirby Urner]

Here's an example of a letter sharing about an aspect of 
CP4E:  math through programming.  

Certainly this isn't the only angle of interest to this 
edu-sig, but I'm posting this here as representative of 
what I put our re the "Urner approach" to numeracy + 
computer literacy i.e. the goals I'm pursuing in my 
own curriculum writing.

The following was to an Associate Professor of Mathematics
at a community college, regarding a paper she'd helped
write, assessing the impact of technology on pedagogy.
Her paper includes the following passages:

      New models of teaching will capitalize on dynamic 
      interactivity to build connections between symbolic, 
      graphic, tabular, and written representations of 
      math using web browsers such as Live Math (See 
      Link 9 and (get plug-in to See Link 10.), Scientific 
      Notebook (See Link 11), and JAVA scripted models 
      on the web (See Link 12 and See Link 13). In these 
      students can animate graphs and models as well 
      as manipulate computational algebra systems to 
      explore mathematical patterns. The classroom of 
      the future will integrate this software into every 
      level even developmental courses. (Link14 to 
      description of a math classroom of the future).[1]

Link14 points to a posting of mine to a listserv archives:

   http://archives.math.utk.edu/hypermail/mathedcc/nov99/0082.html

Unfortunately, this is one of those posts with a lot of =20s 
at the ends of lines.

For a related email, sent to another community college math 
professor last April, see the copy archived at:

   http://www.egroups.com/message/synergeo/555

You'll find a high degree of consistency between the above 
letter and the one copied below, i.e. I'm in the habit of
making a lot of the same points over and over (so what 
else is new?).

Kirby

[1] http://www.tc.cc.va.us/planning/strategi/whitepap/math.PDF

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Hi Marcia --

I've been reading your paper and consider it a valuable 
resource, as it focuses on a real, and some might say
typical, community college, with all its plusses and
minuses.

I'm especially interested in the math section.

I think one respect in which my curriculum writing 
diverges from the mainstream is I have this "math 
through programming" ideal, wherein students learn
math at the same time they're learning a computer
language, with the former providing most of the raw 
material (e.g. series, prime numbers, functions), 
and the latter providing a structured language that 
runs parallel to traditional notations, but also 
adds its own layer of intelligence (i.e. object 
orientation, and all that entails).

For example, students of my approach would appreciate
that polyhedra might be developed in a "class hierarchy",
with generic code for rotation and translation in the
"root class", with specific shapes providing their 
own coordinates, and in some cases "overriding" parent 
methods.

Internally to polyhedra, we make use of vectors, and
here again, there's a class hierarchy, with some 
kinds of vectors defined as subclasses of others.[1]

My underlying assumption driving my approach is 
that computer languages are affecting math concepts
in many subtle ways.  It's not a one-way street 
with math being "pure theory" and computer science
being "applied".  On the contrary, both disciplines
work to inform the other, and the synergies become
most pronounced when we allow them to interpenetrate.[2]

Thanks again for making a link to my posting to 
the Mathedcc archives.

Kirby

[1] example discussion on another list:
    http://www.python.org/pipermail/edu-sig/2000-May/000415.html

[2] This is the thesis I develop in more detail at
    http://www.inetarena.com/~pdx4d/ocn/trends2000.html

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