Error Analysis
The idea of error analysis is directly connected to theories of meta-cognition as well as validation and a strong understanding of mathematical logic.
In my experience students tend to have weak skills in error analysis. Theoretically, activities like completing the loop gives them the opportunity to
practice finding their mistakes - one has to validate in order to have any sense of whether an error has been made of course. Generally, students will
look for validation from the instructor and then ask for an indication of where the mistake took place. Now, while this is one of the natural functions
of the guide and instructor, I also think that activities ought to be developed where students have the opportunity to specifically practice finding and
correcting mistakes. If not, how do we expect students to learn how to do this. Theoretically, a student with a good sense of how mathematics works would
be able to find errors by just scanning line to line, but sometimes it is hard to divorce yourself from your own work. I have found activities involving
other students work (from different classes) is really useful (and an enjoyable change of pace) activity for students. I am interested in doing more work in
this area and working with other instructors to develop activities that focus on error analysis.
On a related point, I believe error analysis is important as the student that struggles to perform interacts with their work. If we turn from the emotional
response to the intellectual response we have an opportunity to learn from our experiences. Of course, the emotional part of it may in turn serve a purpose
in our learning experience, but my sense is that many students don't get an opportunity to reflect on the mistakes they made, particularly in a performance
and I would assert that any developmental math class where students are not given opportunities to reflect on their errors is doing them a serious
disservice in many ways. Another area of work that would be interesting to me would be talking with instructors about modes of remediation and how that
impacts student learning and beliefs about mathematics.
