a/k/a Great Moments in Digital Networked Math Curricula
You Should Check Out
Math Caching and Immediately Useful Teaching Data from Evan Weinberg.
What It Is
Evan has his students working on some practice exercises. As they complete their exercises, they use their Macbooks to submit a) an answer (which is nothing new in a world driven by quantitative machine-graded data) but also b) a photo of their work.
The images are titled with their answers and then start populating a folder on Evan's computer.
Why It's Important
Mistakes are valuable. Student work is valuable. This collects both quickly.
Mistakes are valuable for starting conversations, for prompting to students to construct and justify arguments, for asking students, "What different question does this work correctly answer?"
Most machine-graded systems hold back students with wrong answers and let them advance once they've corrected their errors. But this essentially sweeps clear the brambly trail that led to that correct answer when there's so much value in the brambles. Those systems don't tell you why the student had those incorrect answers. They don't allow the teacher to sequence and select incorrect student work for productive discussions later. Math Cache does.
I didn’t need to throw out the tragically predictable ‘who wants to share their work’ to a class of students that don’t tend to want to share for all sorts of valid reasons. I didn’t have to cold call a student to reluctantly show what he or she did for the problem. I had their work and could hand pick what I wanted to share with the class while maintaining their anonymity. We could quickly look at multiple students’ work and talk about the positive aspects of each one, while highlighting ways to make it even better.
A main assumption that I work with when doing these [student] interviews is that children do what makes sense to them even if it seems like nonsense to me. My job is to figure out what makes sense to them and why.
2013 Oct 2. Pearson's research blog picks up this post and argues that I'm too pessimistic about machine-graded data.