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Topic: Tutorial software for high school algebra

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Subject:   Tutorial software for high school algebra
Author: SGB
Date: Jul 11 2007
We have used various math teaching packages.  The best of the lot so far has
been "The Learning Equation" but we've found that it lacks depth.

In terms of doing well in math related subjects in university, the feed back we
get from our grads says that they value proficiency in algebraic manipulation.
If this is second nature, then Calculus I is easy.  The best way I've found to
develop proficiency is to do LOTS of problems.  Two things interfere:  1.  As a
teacher I have to mark lots of problems.  2.  A student who doesn't understand
the current work will spend his homework time practicing the skill incorrectly.

I'm looking for a package that has sufficient smarts that it can work as
* Picks a problem at random from a specified set of problem generators.
* Presents the problem to the student.
* Student enters a step in the solution. Initially a step consists
of a statement of what he is trying to do, followed by a new statement of the
* Program evaluates that step, to see if it is an acceptable step.
If yes, then the next prompt is given, if no, the student's answer is redrawn in
red, and the most recent correct line is repeated.
* Program can give hints if the student is persistently stuck.
* Program can solve a problem in parallel with the student.
* Program uses the mistakes made on this problem to guide the next problem.
* Program can record the mistakes.

So, for example, if the problem was:
2(x-3) = 4(x+2) -9
The student could legitimately do the following:
CB (for clear brackets) 2x-6 = 4x + 8 -9
For the next step, there are several possibilities:
A6, A9, or CLT for add 6, add 9 or collect like terms.
CLT      2x -6 = 4x -1
A6       2x -6 +6 = 4x -1 +6
CLT      2x   = 4x +5
S4x,CLT  -2x  = 5
D-2      -2x/-2 = 5/-2
S        x = -2.5

Note that the program permitted multiple actions at one point.
Note that the program should be able to accept any valid step.
It would be nice if it could comment on ones that were steps in the
wrong direction, or if it could analyze the error for misconceptions, and launch
an appropriate tutorial.

I don't want Mathematica:  That is, I don't want a program that will solve the
problem for the student.  I want one that acts as a patient tutor, checking each
step of the solution process.

If the program can save incorrect streams, then the teacher can review them to
see if there is a pattern to the student's mistakes.

Problem generators.  One of my complaints about much math tutoring software is
that they have a very restrictive set of problems, and the kids either can
memorize the set, or John next row over says that "The answers are 6, 10, and
-3"  I would like problems to be stored as paramertized generators instead of
as problems themselves.  Successful answers increase the scope of the generators
to create more difficult problems, bad answers or lengthly waits for input
result in easier problems.  The idea is that students should have enough success
to feel good about math, but to be challenged at the edge of their ability.

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