I wrote four blog posts for NCTM’s Mathematics in the Middle School blog on using student work to understand and plan around student ideas. Each post is about using student work to make inferences about how they understand mathematical ideas and then using those inferences to help you plan. Note that these posts are actually relevant for mathematics educators at all levels.
- What Knowledge Do You Need to Plan a Unit?
- Categorizing Student Work
- Using Student Work Meaningfully
- The Mathematics of Students
While these posts focus on qualitative information about student learning, this doesn’t mean quantitative information isn’t useful. I have just found that quantitative information abounds while qualitative information seems to be rarely used in systematic ways.