“How do you assess this?”
This is the question I eventually field during every opportunity I get to share pieces of my classroom with other stakeholders in education–be it teachers, administrators, or pre-service teachers. I don’t mind fielding it; it is a good question, one teeming with complexities and littered with implicit values.
There seems to be three sacred cows in mathematics education:
It is not surprising that these three feed off one another, and make up the bulk of assessment in the typical mathematics classroom (including my own).
Here’s my disclaimer:
While I have been known to slaughter a few of the sacred cows of the instructional process, I have lagged severely behind in my attention to assessment. I value the complexities of learning that occur when student ideas encounter perturbations, curiosities, and other conceptualizations. The type of assessment that comes out of these mathematical encounters is rich, connected, and constantly evolving.
This semester, I’ve been attempting to infuse my courses with more opportunities for students to collaborate while solving problems. This post is designed to examine the shift in student disposition throughout the process.
I have noticed an increased conceptual understanding almost across the board and this is reflected in the differing solutions on summative assessments. It is also nice to see their marks grow on these unit tests. I do not believe that paper-and-pencil tests are the best venues for displaying conceptual understanding, but it is awesome when the two intertwine.
This year my department decided to make using whiteboards as formative assessment tools our department focus. This was nice because I had already began to experiment with the process. It just meant that:
I have been playing around with several ways to get students to realize why they make mistakes. I am fed up with the traditional grading process where the student completes a task and then is handed dead feedback–stuff to do the next time. In my opinion, the student needs to be the one seeing the diagnosis.
I guess you could call it “active assessment” or “confidence assessment”. My goal is to get students looking into the patterns of their mistakes and isolating skills that they need to practice.