An idea I took from George Milauskas takes the "only two points for a correct answer" one step further. George would give his students "magic dots" (= the circles punched out from paper with a 3-hole punch) which they could redeem--in combination with a single point--for any formula required on a test. That is, a student could ask "What's the midpoint formula?" (even though requests for that particular formula make me cringe) and get it, for a mere one point. George's reasoning, which persuaded me instantly, was as follows:
- If a student just writes down the correct formula--but does no other work--he or she will usually get one point of "partial" credit. Most of the problem consists in using or thinking about the formula, not regurgitating it. (That leads to a whole nother conversation, about problems that are just about formulas.)
- Giving a student the formula allows the student to demonstrate what he or she can do with it.
- Leaving the student stranded without the formula means that he or she can't demonstrate anything.
Thus, giving the student the correct formula for a one-point deduction allows me to assess what else he or she knows and can do with it in a fair and reasonable way.
Before you ask how they do on "real" tests outside my class, remember that AP, ACT, SAT all include lists of common formulas. So my students have done just fine.
John, thanks for reminding us how important this work is.