I like that test where some of the questions are wrong and wonder whether we should have that kind of thing in maths textbooks.
I think people need to be trained to be more confident in what they know, and if we gave them that kind of thing we could maybe train them to become so.
Actually - do they do this in LLM benchmarks? As a measure of overconfidence/confabulation? Seems immediately applicable.
"incomplete information" is a standard concept in word problem curriculum. But usually it's explicitly an option in the test, as a fairness to the student.
Making mistakes in lecture is a standard technique used by good teachers, to promote active listening and critical thinking.
I didn't see that in the document. What page is it on?
I think they mean at the bottom of p216 (pdf page 4), where he says he doesn't know, r+s=80 but there isn't enough information to solve for r and s.
There's two questions that are intended to be wrong (probably to test confidence). One with insufficient information and where the question itself implies falsehoods.
The questions are on page 215 (3/26) and Tao's answers are on the next page.