Re: [Tuxmath-devel] GSoC project on "Personalized, adaptive game-play to improve learning in Tuxmath"

[David B. <dav...@gm...>]

Hi Siddarth,

>> 4. In your section on "modifying the game variables," certainly the speed
>> is
>> an important parameter. But a more interesting---and more conceptually
>> challenging---issue is how to decide which _type_ of problems to pose. Is
>> the
>> kid ready for addition facts up to 10, or should we stick with 0 to 5? How
>> can
>> you tell when the kid is ready for multiplication?
>
> There is an interesting approach Animalwatch (It's a tutor for pre-algebra
> mathematics) uses for this which is described here Using the student model
> to control problem difficulty. I am thinking of using a approach on similar
> lines, will post it shortly.

I don't know how much you've looked at how tuxmath generates math
question lists, but basically a lesson file sets a series of criteria
for questions:

- allowed math operations (addition, subtraction, multiplication, division)
- ranges of allowed numbers for operands
- whether to allow negative numbers
- format of question (i.e. 1 + 1 = ?, 1 + ? = 2, or ? + 1 = 2)

and so forth.  There are also some variables related to how answered
questions are handled - in the "lesson" games, correctly answered
questions are considered "done", and the lesson ends with a win when
all the questions have been handled correctly.  In the "arcade" games,
all questions get reinserted into the list so the game goes on
indefinitely until the player runs out of lives.  In both modes,
questions which are not answered correctly get reinserted so the
player sees them again.  There is an option to reinsert multiple
copies of missed questions so as to give extra practice on those
facts.  Finally, the code contains functions to support the use of the
just the "missed questions" from the previous game as the question
list for the next game, although we've never implemented a way to use
this feature.  So, some of these features might be useful in your
project, but they might not be sufficiently flexible for your needs.

What tuxmath does not currently provide is the reading of a list of
arbitrary functions from a text file.  I think we may want to do
something like that for your project.

I read your blog, and am eager to hear more about specifics, or to
help you work them out.  It seems to me that there are at least two
ways in which this adaptive instruction can be applied:
1. Within the same math game, use the player's initial performance to
adjust the subsequent questions.
2. For subsequent games, adjust the questions based on results from
previous games.


>> 5. Given this tuxmath-as-the-teacher mode of thinking, do we need to think
>> somewhat about creating mechanisms to explicitly teach, rather than just
>> let
>> them practice things they've already been taught?

Yes - I've thought for some time that this was a shortcoming of the
program.  The only "teaching" is when we show the answer when the
igloo gets hit, plus the factoring hints we put in at the start of
each level in factoroids.  But there isn't any illustration of the
concepts of math.  There are plenty of ways that new activities could
be designed for these purposes, e.g. having Tux combine groups of fish
to illustrate addition, or having him build stacks of ice blocks in a
grid layout to illustrate multiplication.

I think the existing games have been shaped a lot by the ages of our
kids at the time when the games were written.  My daughter was a
second-grader when I started trying to make Bill's original comet game
more flexible, and she was a fourth-grader doing a lot of factoring
stuff when I proposed the factoroids game.  Maybe we need someone with
pre-school or kindergarten kids to get interested in coding up a new
activity.

David Bruce