The morning bell rings. Students file into my mathematics classroom. The national anthem and morning announcements occur. I start teaching. I’m asking questions. Some students are answering – I wish I had a different question for each of them and time to answer them all. I hand out the practise work. I circulate and answer questions. There will probably be a quiz tomorrow. The next day – same thing. A week later – a review day. The day after that – a test. I may be oversimplifying here and not everyday looks like this in all mathematics classrooms but one question always hovers like a dark cloud over me… how do I know they’re learning?
Is it grades that tells me that? I think that tells me a little bit about learning. In the conditions that I’ve described above, I think it tells me more about how well they’ve figured me out in that one week window or the procedures that I’ve demonstrated. I think about the kinds of questions that I usually answer during practise time. They are almost exclusively procedure questions. What do I do now? How do I do that? Is it the act of assessing the learning that hampers learning itself? Do students see a finish line when we assign a grade so they don’t pursue any learning thereafter? And if we are only assessing procedures and content, that sounds more like a 100 metre dash, not an obstacle course.
Is it observational evidence that tells me if students are learning? If students are sitting quietly at their desks, are they learning? If students are sitting together collaborating, are they learning? I think learning occurs in both situations but 2 things have to happen. There has to be some structure and expectation around each activity and you have to allow for a little bit of both. Productive group conversation is effective for gathering and consolidating various perspectives but individuals need to struggle a little bit on their own to mold their own ideas especially in the case of an introverted student.
I should be mixing up my teaching style from day-to-day as well as within the class period. Students learn in different ways and can quickly disengage if I teach in the same style that feels most comfortable to me. Too often, I assumed that if I taught, they learned. So if they disengaged, that was a choice they made. Yes, that was a choice they made, but some of the reason they made that choice was for the same reason I choose a different channel while I’m watching television.