[math4] an Introduction and on the Math API

[gabriel]

Hello all,

I'm gabe, a prospective GSoCer, and I just found/read through the last month
of this list. When I first read about Sugar, this was exactly the kind of
thing I had hoped was happening--in particular the API quiz/math problem
collection.

A bit about me:
I'm a graduating math major at the university of chicago; I've been teaching
to highschool and junior-high students through the university for the past
four years. I started programming relatively intensively last September, and
am new to (and excited about) the open source world.
___________________

My thoughts on the math API:
I think another really positive aspect to the development of a library of
math problems which can be imported to games or quizes, etc. is that it
enables us to focus in on the pedagogical aspects of the project.  While
there's something uniquely great about 'hands-on' building blocks (to show
e.g. how to add numbers in a specific base), a SUGAR math program could make
visualizations possible in a routine way that isn't possible in a book--the
API could flesh out these possibilities.

Concretely, there could be hints/pictures associated to math problems in the
API so that, for instance, later in the actual games/quizes, the student
will be able to ask for hints / be given hints if they're incorrect.  Hints
can be text/pictures/animations, etc.  What do people think about including
this kind of functionality in the API?  Also: there could be multiple types
of hints/pictures for each question.  The hints themselves could be grouped,
so that we might get a feel for what kind of thinking works to explain the
concept to the individual student.

The example in my head is e.g. from this list already: if the question is a
simple multiplication problem (3*4), hints could be (what is 3+3+3+3?) or a
picture of a 3 by 4 rectangle of balls or an animation of three balls
replicating themselves 4 times.

Of course, grouping problems together is essential.  The game/quiz would
ideally want to know what the student does and doesn't understand, and be
able to respond accordingly.

I don't remember reading this in the list, but I think this must be what
everyone is thinking: Many/most of the problems in the API should be
generalizable (e.g. with random() quantities associated).

A last note on pedagogy: besides learning addition/multiplication tables by
wrote, *the* important thing to learn in grade school (and even in
highschool) is the distributive property.  The interplay of addition and
multiplication is maybe the initial big idea of arithmetic.  As an
afterthought, prime numbers are fun, too.

While I know there are tons of math problems that are on people's minds, I
haven't gotten a sense that the API development is actually in progress.  Is
it? How can I help?
_____________________

Other ideas to improve the math educational possibilities:
Is anyone familiar with Geogebra? This is open-source program is a great
tool for high-school geometry (which might fall outside the scope of this
list? ...or not?) (In its barest form) the program allows students to draw
lines and circles (i.e. to use a straight edge and compass) to do more
complicated constructions.  The beauty of the software is that Euclidean
geometry becomes a dynamic process: one can fix midpoints, fix circles,
lines, etc. and then drag the picture around.  This software is ideal for
observing/experiencing geometric invariants.  It is the best way to learn
about similarity that I know of--projections become simple and beautiful and
can actually be experienced.  This is one piece of software which I feel
really utilizes the possibilities of technology in the classroom: it allows
students not to get bogged down in drawing and to actually see and get a
sense of geometric properties which can otherwise be overly abstract.  I'm
not as familiar with Geogebra as I am with its proprietary cousin Geometer's
Sketchpad; but I think it would be an awesome addition to SUGAR.  Is it
already on SUGAR? What would it take to put it on?

____________________

Those are my thoughts at the moment, I'd be interested in what people think
of the possibilities of turning any of the above ideas into a GSoC project
proposal.  Was anyone on this project thinking of being a mentor?

cheers.
gabe
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