One evening at the dinner table, when my oldest daughter was 3 or 4, I was in a teasing mood, and I called her a goose. She didn't want to be a goose, so she refuted the claim, "I am not a goose!" Then I told her to prove me wrong. After some back and forth, she realized that her cause would benefit from some distinguishing feature: "A goose has feathers, but I don't have feathers, so I'm not a goose." I was impressed, so I chose not to continue the teasing by concluding she was a plucked goose.

So began our game "Prove me wrong," in which I make wild claims for her to refute. In the modern version of the game, I will respond to her "proofs" with more refined claims. As a mathematician, it is quite the guilty pleasure to construct these logically sound but apparently absurd refinements. For the child, the game presents a fun way to navigate silly ideas. In the end, she's refining her ability to apply basic logic.

On a good day, I will bring "Prove me wrong" into the classroom. When I introduce matrix multiplication in linear algebra, everyone has seen it before, and so I inject some "fun" by claiming that multiplication is commutative. The more outspoken students read my smile and speak up with an emphatic "No, it isn't!" I then proceed to make my case by multiplying $1\times 1$ matrices and $2\times 2$ matrices that happen to commute. Eventually, a student suggests that I put variables in the entries of my $2\times 2$ matrices.