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Explaining why a step-by-step process works, not just the steps
Students in my class can execute the steps of procedure_or_algorithm correctly but don't understand WHY it works, which means they can't adapt it when a problem doesn't fit the standard form. Help me build an explanation of the underlying reasoning.
The procedure as normally taught (steps): procedure_steps
Do this:
1. For each major step, explain the actual mathematical/logical reason it works, not just what to do, connect it to a concept students already understand rather than presenting it as a new rule to memorize.
2. Identify which step is usually taught as 'just do this' with no reasoning given, that's typically where the real understanding gap lives.
3. Give me one example problem that's slightly non-standard (doesn't fit the exact form the procedure is usually taught with) where a student who only memorized steps would get stuck, but a student who understands the reasoning could adapt.
4. Write out how a student WITH real understanding would think through that non-standard problem, showing the reasoning transfer explicitly.
5. Suggest one question I could ask during normal instruction (not a separate lesson, just a question inserted into the regular flow) that would push students toward the 'why' without turning every lesson into an extended proof.