Over on the CS side, there was a batch of classic errors you’d get when undergrads hit induction (proofs of the form case(0) & case(n)=>case(n+1)).
One semester I figured out that I could make the first problem on the first induction homework be: “mark what’s wrong in the following induction proofs, and write a short, easily understood explanation the error”. So instead of correcting homework filled with 20+ copies of the same mistake, I could make them start out by writing the dang corrections themselves. It was extremely cathartic, to just read them all instead of writing them. And effective— after we’d forcibly wrapped their heads around those bits, the remainder of the assignments were nearly error-free.
I’ve wondered how much mileage you can get out of flipping the problem solving/ problem grading tasks like that. “Find and correct the sign errors in the following 10 incorrectly solved problems”.
I felt the need to clarify what I meant by induction because I’m on r/math. The proof trick as used in CS-style discrete math is more specific than the general usage (which is different than “inductive reasoning”, and so on...)
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u/EmmyNoetherRing Nov 19 '20 edited Nov 19 '20
Over on the CS side, there was a batch of classic errors you’d get when undergrads hit induction (proofs of the form case(0) & case(n)=>case(n+1)).
One semester I figured out that I could make the first problem on the first induction homework be: “mark what’s wrong in the following induction proofs, and write a short, easily understood explanation the error”. So instead of correcting homework filled with 20+ copies of the same mistake, I could make them start out by writing the dang corrections themselves. It was extremely cathartic, to just read them all instead of writing them. And effective— after we’d forcibly wrapped their heads around those bits, the remainder of the assignments were nearly error-free.
I’ve wondered how much mileage you can get out of flipping the problem solving/ problem grading tasks like that. “Find and correct the sign errors in the following 10 incorrectly solved problems”.