The experience was so challenging, frustrating, and ultimately rewarding, that it didn’t take long to realize it was a perfect exercise for students.
I ended up creating some simpler examples that gently introduce the student to the idea of a self-referential test, a test where questions and answers refer to other questions and answers. By playing around with these easier versions, students develop a sense of how to reason their way through using various problem-solving strategies.
After working through the more challenging versions, the final project for students is to create their own self-referential tests, which we then all enjoy solving. This is the perfect kind of project, in that it allows students to exercise their creativity while pondering substantial and significant mathematical questions like “What constitutes a solution to this test?” and “Are we sure that this puzzle has a solution?”, as well as fundamental mathematical ideas like logical consistency.
Inspired by Dave Cormier's learning contract, and previous work at learn-defined syllabus and assessment, I had though about learner-created project evaluation rubrics. It occurred to me that for advanced learners having them propose their own evaluation criteria for rubrics. In the course of investigating what should be important they are beginning to learn about what is important. The students should create the criteria for success of the project, and consequently the criteria for the evaluation of the project.
The link to the learning contract can be found here: http://davecormier.com/edblog/2012/05/09/ed366-learning-contract-prior-to-student-input/