Thinking about returning to the classroom -- how do you make sense of student reasoning in algebra?
I taught high school math for a year, stepped away, and I’m seriously considering returning. One thing I never felt fully confident about was interpreting student reasoning in multi‑step algebra problems.
When you’re looking at a student’s work -- especially when the steps are messy, incomplete, or go in an unexpected direction -- what’s your process for figuring out why they made a particular error?
Do you look for familiar patterns?
Do you reconstruct their thinking step by step?
Do you start with the misconception or the structure of the work?
I’d love to hear how more experienced teachers approach this. And if anyone is open to talking through their workflow in a bit more detail (even briefly), I’d really appreciate it. Even a quick comment here would help a lot.