[math4] FourthGradeMath Digest, Vol 3, Issue 3

[Edward Cherlin]

2009/4/2 gabriel <eulerian at uchicago.edu>:
> There seem to be different philosophies behind educational software.  There
> are games where the educational content is tangentially related in an effort
> to make the content itself more appealing, and there are quizes or programs
> which try to explain and test understanding of material.

Generically known as shovelware. I first wrote about the problem in 1981.

> What I've found most useful/enjoyable as a student, however, were computer
> programs that were integrated into a lesson in a way that allowed the
> teacher to guide students in their own exploration.

Exactly.

> My favorite examples of
> computers coming into the classroom have been:
>
> 1. Using graphing calculators to get a sense of what polynomials look like,
> to get a sense of what happens when you transform a polynomial (i.e.
> pre-composition vs post-composition), asymptotics etc.
> 2. Using sketchpad to get a sense of Euclidean geometry, invariants, areas,
> etc.
> 3. Using mathematica to program a Fibbonacci number generator.

I'm programming Turtle Art to illustrate topics in plane geometry,
analytic geometry, group theory, set theory, logic, and computer
science. I finally got the current version working under Ubuntu Linux,
so I can provide the equivalent Logo programs plus pictures on any
topic.

> These lesson-types involved a specific tool on the computer used by the
> student to explore and compute.  I understand Sugar already has such a
> calculator.  The question is, what kinds of lessons for the 4th grade
> classroom could really benefit from using a computer.

Yes, a graphing calculator.

> What about a lesson that involves cryptography?  It would have to be able to
> be significantly pared down to a 4th grade level--

Not at all. Secret codes were a favorite topic in the Cub Scout and
Boy Scout type magazines when I was that age. You start with the
simplest of Caesar ciphers, mjlf uijt, where you replace each letter
by the next one in the alphabet, wrapping z to a. You can add
complexity to the systems under study year by year right up through
graduate school, where they are working on elliptic function
cryptography, Zeta functions, and lots more.

I have a book, Babbage's Secret, which explains a sequence of more
complex systems using examples that Charles Babbage solved from the
newspaper "agony" columns. For each, the author provides executable
and understandable code for encryption, decryption, and cryptanalysis.

> but I know of a friend (in
> elementary ed) who's working on such a program at UIC.  The point is the
> program would be a modified calculator that allows one to encrypt/decrypt,
> or gives instructions to do so, etc.  Such a program is written with many
> possible lessons in mind: the program itself becomes a tool for the
> student's own learning/discovery.
>
> It would also be great, as Stephen suggested, for us to highlight different
> kinds of lessons that can be given with the tools that already exist on
> Sugar.  Wouldn't it be cool to have a wiki devoted to lessons ideally suited
> to Sugar? Teachers, students could update and give feedback and their own
> ideas.  Does this exist already?

No, but it will. Go for it.

> gabe
>
> On Thu, Apr 2, 2009 at 9:29 PM, Stephen Jacobs <itprofjacobs at gmail.com>
> wrote:
>>
>> Some good resources and references on the Concord page...
>> http://www.concord.org/publications/detail/
>>
>> 1.  The article on the "Broken Calculator" on this page, with web links to
>> a
>> flash version
>>
>> 2.  The Third White paper "1:1 Computing In Support of Science and
>> Mathematics Education ‹ Recommendations for Large-Scale Implementations"
>>
>> References the need to provide support materials for teachers, not just
>> software.  An "obvious" point that is often overlooked.
>>
>>
>> Stephen Jacobs
>> Associate Professor
>> Game Design and Development
>> Rochester Institute of Technology
>> Building 70
>> 102 Lomb Memorial Drive
>> Rochester NY, 14623
>> 0ffice: 585-475-7803
>>
>>
>>
>>
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>> http://lists.sugarlabs.org/listinfo/fourthgrademath
>
>
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-- 
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And Children are my nation.
The Cosmos is my dwelling place, The Truth my destination.
http://earthtreasury.net/ (Edward Mokurai Cherlin)