[math4] an Introduction and on the Math API

[Enimihil]

On Thu, Apr 2, 2009 at 3:22 PM, gabriel <gabrielitodecastero at gmail.com> wrote:
> 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.

Welcome aboard, though I'm also new to the project. :-D

> 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.

These, and the ideas that follow look like good goals, but as
proposed, the quiz/question API wouldn't attempt to be quite so
ambitious, nor restricted to mathematical questions.

> 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 Moodle question formats[1] provide some provision for
explanations/comments along with the answer(s) for questions, so the
work to make those formats importable with the API will suport at
least that much.

[snip example of multiplication = repeated addition hint]

> 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.

The taxonomies for doing this, I don't well understand, not do I see
any simple subset that is more useful than what one might call
"difficulty", "level", or "category".  The categorization and
query/retrieval of appropriate questions is a natural extension of the
(simple) proposed question API.

> 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).

This is something that can't be done for "general" questions, but for
mathematical questions of certain forms it makes a lot of sense.
Perhaps using the API's abstractions to allow asking for generated
questions of a certain class would be appropriate.

[snip importance of distributive rules in early math]

> 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?

I've started work on a basic GIFT[2] format parser and skeleton of the
API here[3], though there's not much more than a few hours of work
done yet.  Very much not working and in early prototype/design stages.
 Still trying to drum up interest (and opinion).

[snip description of Geometry visualization software]

[1] http://docs.moodle.org/en/Import_questions
[2] http://docs.moodle.org/en/GIFT
[3] http://git.sugarlabs.org/projects/question-support-api

Greg S.