[OLPC-GSoC] Dr. Geo Interactive geometry project for SoC

[Hilaire Fernandes]

Hi,

My name is Hilaire Fernandes, I am a Phd student in computer science
at the University of Lille 1, working in learning system
(http://www.istoa.net).

I am also the author of DrGeo interactive geometry software and its
port to XO/EToys architecture.
I have applied as a student to finish major parts of its port to the XO/Etoys.

Interactive geometry is a transposition of the paper-pen based
environment to teach geometry to a numerical environment. As such it
is a tool to construct and manipulate interactively geometric figures.
By itself -- and as Logo or EToys environments -- it does not provide
content, the contents is built by the teachers and the students.

The resulting computerized environment is a kind of micro-world where
learners can create geometric figure and manipulate interactively its
elements in respect with their geometric constraints. Contrary to the
paper-pen environment, in this micro-world the learner can discover
properties (constant behavior) on a geometric figure, verify
experimentally hypothesis. Moreover interactive geometry can be used
to modelised real world phenomena related to euclidean geometry.

All in all, interactive geometry environment are widely acknowledge by
educators to be a big win provided by the computer to teach
mathematics and geometry. First elements of such systems appeared at
the end of the '70 at the Xerox Parc with ThingLab on Smalltalk
system.

Depending on the content, it is usable in teaching situation with
students from primary to secondary schools.

The OLPC initiative is a very unique opportunity to get in the hand of
the children such software they can use at school and at home.
DrGeoII is such a software ported to the the XO laptop
(http://wiki.laptop.org/go/DrGeo).


The major part I am proposing to fix/write are:

- implementation of the macro-construction system. It is a system to
record a set of constructions as a function the user can save and use
repeatably. Such system is used to apply repetitive sequences of
construction. A teacher can also use it to prepare a teaching
situation with a preset of macro-construction. For example,
macro-construction of regular polygons: equilateral triangle, square,
regular pentagon, hexagon, etc. From the feedback I got from teacher
with DrGeo1.1, it is a must to have feature for regular use of the
tool.

- implementation of the script system. A script within DrGeo is code
hooked to an interactive sketch, it is used to perform calculus. The
script language will be Smalltalk based. At first it seems to be not
such a useful feature for primary school, but more useful in higher
class. Because of it programmatic dimension it is used in DrGeo 1.1 to
modelize real world phenomena like optic diffraction
(http://www.ofset.org/it/uploadfiles/129)

- improve the load time, the load time is now unacceptable for the
user and make DrGeo unadapted for the OLPC. This is a limit of the
Etoys loading system I can fix by two mean: improve EToys image itself
and get the fix accepted, or ship DrGeoII in its own EToys image. Of
course another solution (the best) will be to ship DrGeoII in the
Etoys image, but the offer was declined by the Etoys people.

- define a journal type entry to save/load.

- improve the user interface, particularly the access to the
construction tools. Minor usability problems need to be addressed.

- improve the locus sampling, it is by now suboptimal. Locus sampling
is an advanced feature used in many different situation: basically it
is just about collecting the positions of a given point when another
ancestor point cover an entire line. It result in a sampled line (the
locus). As for now the sampling rate of the locus is fixed, it need to
be a sampled at a variable rate.

Hilaire Fernandes