K-12 public education system where, in many ways, we are forced to do our best in supporting students in "doing mathematics" through a variety of predetermined concepts to be explored.
It seems to make sense to me that in order to assess mathematical thinking, you would have to 1. determine the habits that comprise mathematical thinking, 2. have some sort of feedback system to assist students in developing those habits, and 3. figure out some way of measuring student progress in each.
At the moment, I have been toying with the idea of having students contribute to a semester/year long portfolio. The portfolio would be based around the habits of a mathematician, with a divider/section for each one. As we progress through the year, students would complete reflections on works of their choice and file them in the appropriate section. At the end of the semester/year, each student would evaluate their portfolio and present or reflect on their growth.
A few questions:
1. Am I even on the right track here?
2. How would this portfolio system correlate to a grade?
3. Does this system support students and give them enough feedback on how they can develop/improve/progress?
P.S. I just had another thought…what does a "unit test" implicitly tell students about what is valued/looked for in class?