Wolfram Problem Generator
There’s a joke in here somewhere along the lines of the Java ProblemFactory joke, but I digress.
Wolfram, the folks who make Mathematica, Wolfram Alpha, and various oddities, have come up with a Problem Generator for certain branches of mathematics. If you don’t want to sign up for a trial of Alpha Pro to try it out, I’m going to give you a quick overview here.
The short version is that they’ve created a random problem generator that takes a template, fills it with random numbers, and asks a straightforward procedural problem similar to back-of-the-textbook practice problems. No word problems, just “find where this is discontinuous” or “find the median of this list of numbers” or “factor this expression.” You can ask it for easy, medium, or advanced problems. Advanced problems involve doing a little more of the work yourself (unfactored expressions in rational functions, for example) and more intimidating numbers with square roots and such. They provide step-by-step solutions that use the exact random values given to you.
In terms of drilling exercises, this is fairly handy. Some of it is higher-level material, so that’s nice. There’s arithmetic, number theory (very basic – factor this, LCM of that), high-school algebra, single-variable calc, linalg (add, subtract, cross, determinant), and super-basic statistics (avg, mean, mode, and range).
The lack of educational sophistication, however, is what makes this less than impressive to me. It’s more of an aid to textbook manufacturers than it is to students or teachers. You can practice doing integrals until your hands fall off, and lord knows people need practice with their skills, but as we all know at this point, Students do not overcome conceptual difficulties after solving 1000 traditional problems. (Yes, that’s in italics because it’s the title of a paper.) You won’t know what an integral is any better afterwards than you did before.
It’s also not extensible. Where’s the tool that allows us to make our own problems? How do we create our own templates? Will this list ever get expanded, or is this just something that someone came up with on their 10% time?
This might be a good product for textbook manufacturers, so they can create books faster and more accurately. It might be good for math teachers as a way to get quick problems for their tests, things they can wrap words around to make real problems and not just exercises. It’s good for drill-and-kill practice, to the extent that such things are necessary. If you’re saying “But we already have all of that stuff in thousands of books and practice sheets…” then you’re hitting on the exact reason I don’t think this is very useful.
We should be working to figure out good ways to use tools like Alpha in the classroom. Right now I just have this bizarre image of someone just sitting there with the Problem Generator open on one page, and Wolfram Alpha open on another page, plugging questions from one into the other and returning the answers.