zlacker

I think your example is a curious one, because obviously we want the student to know 10 * 10 by rote. Indeed, arithmetic is one area where (almost) everyone favors rote.

To be more general: if you're giving an 8th-9th grade kinematics test, there's two or three families of easy inclined plane problems, and hopefully your students have seen a few of all types. They shouldn't know the answer is "3.5 m/s", but they should be able to select a procedure they've used before and employ it.

>>mlyle+(OP)
> obviously we want the student to know 10 * 10 by rote

Let's clear that up, make it: 1289 * 689

> they should be able to select a procedure they've used before and employ it.

And if they've already seen the question they know which procedure to use, and you're no longer testing "should be able to select".

>>Walter+CA
> Let's clear that up, make it: 1289 * 689

And if my goal is to figure out if a student has mastery of standard multiplication algorithms, I can take that 1289 * 689 question and flip the digits around have have an equivalent question -- 1688 * 986 will serve just fine. The algorithms aren't secret, and multiplication being on the test shouldn't be a secret.

> And if they've already seen the question they know which procedure to use, and you're no longer testing "should be able to select".

If you teach 8th grade physics, you pretty quickly build a library of all the standard inclined plane problems. If you need to give someone a make-up or repeat test, you grab some from tests that you've given in past years that have not been problematic, and switch a number or two.