In a recent tutoring session, I told my student the following riddle:

A father is driving his son to a baseball game when they are involved in a car accident. The man is killed instantly; the boy is badly injured and taken to a nearby hospital for emergency surgery. While reviewing the case before surgery, the surgeon suddenly cries, “I can’t operate on him! That’s my son!” Who is the surgeon?

I used this simple riddle as an example of unexamined assumptions. One of the great contributions that math makes to a liberal arts education is teaching people how to examine assumptions and construct sound logical arguments. Learning how to write proofs can be frustrating at first, because it means learning to break down every hidden assumption, even the ones that seem pretty basic.

We use the commutative and associative properties of addition and multiplication every day; learning that they have names, and that they’re not necessarily a given in some systems, is so counter-intuitive that it’s hard to absorb. They don’t seem like things that need to be stated or counted among our assumptions. It’s hard to imagine that in some systems a times b doesn’t give you the same answer as b times a. It gets easier after you’ve seen a few examples; not necessarily simple, but easier.

Learning to find the hidden assumptions and then imagine alternatives in math prepares people to do the same thing in the world of human interactions. In human interactions, when cherished assumptions are challenged, and alternatives imagined, the assumptions often get defended as “facts of nature,” or “God’s law,” or “just the way it is.” But once people learn that hidden assumptions aren’t necessarily true, and once they see a few counterexamples, those arguments sound weaker and weaker.

That’s why a proposal to ban teachers from talking about homosexuality will ultimately backfire. The legislator sponsoring the bill claims that he’s trying to give teachers more time to teach core subjects, like math. People trying to defend their unexamined and unsupportable assumptions about human relationships would be better off trying to stop teachers from teaching math, because math is what teaches people to examine their assumptions, imagine alternatives, and recognize counterexamples.

This is why teaching keeps my hope alive, especially when my student was able to come up with three different possible answers to the riddle. It makes me hopeful that it will get easier to imagine that a boy has two fathers or that women, even mothers, can be surgeons.

3 thoughts on “What do we teach? Where’s the proof?

  1. Excellent post, and one that reminded me of something. I used to do Enrichment Math workshops for elementary school kids identified as bright and one of the strategies I focused on was “Be aware of unwarranted hidden assumptions”. I used the following to highlight misogynist assumptions:

    Prime Minister Smith (you could use President since you’re in the US) took time out from running the country to visit the funeral home where Michael, the Prime Minister’s brother, was resting after the tragic explosion that killed him the day before. But the Prime Minister was not Michael’s brother. What was Prime Minister Smith’s relationship with Michael?

    One could re-write the story like this to highlight homophobia instead of misogyny:

    David took time out from his work to visit the funeral home where Pat, who David had happily married twenty years earlier, was resting after Pat had died in the tragic explosion of the day before. At the funeral home David encountered Emily, Pat’s grieving sister. However Pat was not Emily’s sister. What was Pat’s relationship with Emily?

    I had to stop using the Prime Minister riddle when Kim Campbell, our first female prime minister, was elected. Incidentally, if I say the word “doctor” what image pops into your head? A male figure? A Caucasian figure? In the Math workshops we used to work through various puzzles involving unwarranted assumptions (as well as eight other strategies) e.g. I told them not to assume every triangle has 180 degrees as an introduction to non-Euclidean geometry via the “what colour was the bear?” puzzle.

  2. Riddles in general are a good way to challenge assumptions. The entire reason they’re riddles is that they exploit some hidden assumption to mislead you into thinking something else. The infamous Sphinx’s riddle? Exploits the assumption that dawn, day, and dusk are segments of a day and not a life, and that a “leg” will be an actually biological leg.

    Incidentally, if I say the word “doctor” what image pops into your head? A male figure? A Caucasian figure?

    White or Asian, and with the sex of the doctor, it depends on where the hospital is located, whether it is a specialized facility, and what kind of doctor. But then, I’m bad with those “what’s the first thing that pops into your head when I say _____,” since the first things that pop into my mind are questions for clarification.

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