### Re: Inequalities with two variables in answers?

by D. Brian Walton -I agree with what you said. My point was more along the lines that WeBWorK is not very designed to check student's thinking process, which is what I was presuming from your original example regarding the absolute value inequality.

My interpretation of the WeBWorK philosophy is that it is designed to have students submit answers that are well-defined mathematical objects (numbers, formulas, intervals, etc.) and compare that to a pre-calculated (either predetermined or algorithmically generated) and give a student Yes/No answers on the correctness of that answer.

Furthermore, the underlying machinery is designed in a way to allow the student to enter the answer in a much more flexible way than providing a list of approved answers. Any answer that is mathematically correct is supposed to be acceptable. Special contexts were later created to facilitate certain conditions such as requiring simplified polynomials or to exclude the use of various functions.

Your example with the absolute value inequality is problematic because the student's answer is a class of mathematical object that has not yet been implemented (i.e., a logical statement with free variables). However, it is composed of elements that are implemented.

For example, if you were to construct a problem that involved multiple parts, you could ask for the student to fill in the blanks:

[------](expression) >= [---](number) and/or(popup-list) [------](expression) < [---](number)

This allows the student to construct the statement you were desiring, but the structure of the problem imposes the form.

I implemented some similar problems based on rewriting expressions involving absolute value as piecewise formulas, similar to the following form (hopefully the forum reformatting doesn't make this unreadable):

|x^2-5x| = { [-----](formula) if x >= [-----](number)

{ [-----](formula) if x <= [-----](number)

Along the lines of what you were discussing, this could be extended to include an earlier step:

|x^2-5x| = { [-----](formula) if [-----](formula) >= 0

{ [-----](formula) if [-----](formula) < 0

Such problems make it so that you are only checking the formulas, not the inequality itself.

My experience with these problems suggest that students do not pay attention to the structure of the problem as it is presented on WeBWorK. They are only focused on finding the formula/answer that goes in the answer box. I'm not sure that WeBWorK can teach students to practice the metacognition required to think at this higher level.

- Brian