WeBWorK Problems

Worked correct and incorrect examples

Worked correct and incorrect examples

by Anne Gunn -
Number of replies: 2
I am working on a small planning grant, looking into the idea of producing some supplemental materials for community college developmental math instructors and their students.

I'm specifically interested in authoring problems in the form of worked examples where one step in a multistep problem (adding unlike fractions, say, or factoring polynomials) is highlighted as correct or incorrect and the student is asked to select an 'explanation' for the rightness or wrongness from a list. (I can supply references for scholarly research validating this approach if anyone is interested -- although, to date, it doesn't seem to have been used with young adult / adult learners.)

At first glance, this probably seems like a pretty simple authoring problem: hard-code the example, set up the reasons as multiple choice, and let the students pick. And, certainly, I can probably use some of the existing randomization features to vary the actual numbers displayed.

But, for any step within a standard multistep problem, there is normally a small set of common error types. And what I would really like is to be able to model/vary the error types as well as just the numerical constants.

I don't yet have a webwork installation to use. I've looked through some of the documentation on the wiki and through some of the forum contents. In neither place am I finding any material talking about the use of correct and incorrect worked examples or self-explanation.

I've got two specific questions:
  1. Are there any existing problem sets or templates (for any course level, doesn't have to be intro math) that incorporate worked examples and prompted self-explanation?
  2. Inside or outside of the context of Webwork, can you refer me to any background material on how to model math process errors in an efficient way? Working with math formulas seems like a complicated problem that webwork handles. Intentionally manipulating those formulas to introduce errors seems as if it could get quite hairy quite quickly.
Do, please, feel free to redirect me to another forum or an existing thread if I've misplaced this question. I'm new to the community.


In reply to Anne Gunn

Re: Worked correct and incorrect examples

by John Travis -

Sounds like a great idea.  You might take a peek at some of the problems I have been working on for my "Intro to Proofs" course at http://math.mc.edu/webwork2/301/Ordering_Proof_Statements/ .  You can log in as guest to see how these work and if perhaps you could use something similar for your work.  

I presume that these could be stacked as part of a multi-step problem but am not certain how they might be combined together in a multi-step.

In the same course linked to above, there are also some sets which use the Essay Answer macro.  These allow for (unchecked) open-ended questions which the instructor would grade individually later.  Perhaps that type problem could also help you with your needs.

In reply to John Travis

Re: Worked correct and incorrect examples

by Anne Gunn -
Thanks for the tips. Mike Gage mentioned your work, also. We've submitted a grant proposal for working on this project but won't hear back from the Dept of Ed until 3rd week in June. Meantime, I'm spending time on my ordinary commercial projects, so I'm not sure how much time I'll have to investigate until summer -- at which point I really hope I'm working on our game project pretty much full time for 6 months.

The proposed project includes time to attempt to create a new/modified MathObject for the worked examples. If I start on that, I'll be back to these forums a bunch.