Given your example, it is a good use case for the Smalltalk DrGeo API to construct programmatically sketches with circle and polygons. See an example: http://blog.ofset.org/hilaire/index.php?post/2010/07/08/Sierpinski-triangle

Compare to other interactive geometry software, DrGeo comes with some user power tools as Smalltalk programmed sketch (bellow) and Smalltalk scripting in live sketch.

Previous C++ version of DrGeo (1.1) was also enjoying these features, with Scheme language, but the Smalltalk version brings an infinite better user experience.

The whole documentation still need to be written.

Regarding use cases, I have seen math teachers using these programming facilities to explore historical examples: http://documentation.ofset.org/drgeo/es/drgenius_88.html But so far, only a few use cases with learner in senior high school were reported to me.

Hilaire

Le 03/08/2010 06:42, karl ramberg a écrit :

You should take a look at DrGeo in the new Etoys image. It's just the right tool for your challenge. It's a fantastic extention to Etoys for geometrical work. It is a litte confusing to begin with. Open a new DrGeo. You can click and get a tool menu to pin down. Or get a button menu from the halo menu to build a interface for your challenge.

Karl

On Mon, Aug 2, 2010 at 5:52 AM, Steve Thomas <sthomas1@gosargon.com mailto:sthomas1@gosargon.com> wrote:

_*Why I think this is possible*_: I created a project in Etoys
(Circle Explorer
<http://www.squeakland.org/showcase/project.jsp?id=10212>) which
allows kids to inscribe and circumscribe a circle with a regular
polygon of N sides.  When I have shown this to kids (as young as
8) they comment (in a number of cases without prompting)  "hey its
filling up the circle".  The regular polygon is made up of
triangles.  I have seen kids can figure out how to determine the
area of triangle using GeoBoards (Here is a sample GeoBoard
project
<http://www.squeakland.org/showcase/project.jsp?id=7744> in Etoys
that uses squares, you can add a triangle by opening the object
catalog,  click on find and type triangle, place it on the
GeoBoard and move around the vertices to create different triangles.).

_*My initial thoughts on how to do this*_*:*

   1. First ask the question:  How can we figure out the area of a
      Circle?
   2. Let them play with the Polygon in a circle tool
   3. Have them record in a table the "# of sides" and "area of
      the Polygon"  This can be done with both inscribed and
      circumscribed polygons (the diameter of the circle can be
      set by them or they can inspect it by looking in the viewer
      for the circle object.
   4. They could try this for different size circles
   5. Then ask the question: What is the ratio of the area of the
      Polygon to the Radius squared (how to lead them to this I
      haven't figured out, suggestions welcome)
   6. Have them plot their results on graph.

The other possibility is to have them determine the circumference
of the circle and then the ratio of that to the Diameter of the
circle.  They could figure out the Circumference using the Ruler
Object within Etoys.

*
*
*Ways in which you can help:*

   1. Provide a set of suggestion on how to use the Circle
      Explorer and a GeoBoard (to help kids figure out how to
      derive Pi
   2. Provide other activities within Etoys (or other similar
      tools) and hands on activities that can help facilitate
      understanding.
   3. Provide sample lessons and/or a set of lesson plans for
      these concepts.
   4. Point me to already created lessons (that I can use as is or
      use to derive lessons that can be freely distributed under a
      Creative Commons or similar license).
   5. Provide a set of "Head Games" they can play in the car to
      help them become more facile in playing with and
      manipulating the ideas in their heads.  An example of a
      simple "Head Game" you can play in the car is "Guess My
      Function" where you ask the kids to give you a number and
      you can make funny "machine" noises then spit out the
      answer.  Once the kids catch on they will come up with
      "trick" functions like "YourNumber + 2 * 20 / 20". This can
      lead to a discussion on equivalent functions, or in kid
      terms ("Hey you cheated its the same thing!!!")



*Screenshots*:
Here is a screenshot of the inscribed circles:


<http://3.bp.blogspot.com/_VzolrwmoPkw/TFYOBY1FUmI/AAAAAAAAABM/g3ByCCeuFSQ/s1600/Inscribed.png>


Here is a graph showing the results the kids would collect:
<http://4.bp.blogspot.com/_VzolrwmoPkw/TFYO_E4XykI/AAAAAAAAABU/sqUmCXyI3r8/s1600/graph.gif>


*Why Etoys?*
Etoys is a free educational software tool for teaching children
powerful ideas in compelling ways. It works on almost all personal
computers and OLPC laptops.  Projects created within Etoys can be
easily modified by people around the world (for translation into
local languages and cultural symbols).  Any kid can create their
own work.  It allows kids (young and old) to make their own
models, stories and games.

This challenge is posted here
<http://etoys4teachers.blogspot.com/2010/08/etoys-challenge-1-help-6th-graders.html> as
well.

Thanks to Carlos Rabassa for his initial Mathematical Challenge
which spawned this idea.

Stephen

_______________________________________________
squeakland mailing list
squeakland@squeakland.org <mailto:squeakland@squeakland.org>
http://lists.squeakland.org/mailman/listinfo/squeakland

---

squeakland mailing list squeakland@squeakland.org http://lists.squeakland.org/mailman/listinfo/squeakland