“There are no coincidences in math.” -A 12-year-old student, reacting to an exercise from James Tanton’s “Guide to Everything Fractions“

This is deep, right? I mean, are there? Or aren’t there?

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“There are no coincidences in math.” -A 12-year-old student, reacting to an exercise from James Tanton’s “Guide to Everything Fractions“

This is deep, right? I mean, are there? Or aren’t there?

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If you believe that mathematics is about looking for patterns, then there shouldn’t be any coincidences.

Not sure I actually

believethis, but it’s one possible answer….Richard Guy’s “Strong Law of Small Numbers” (http://www.math.sjsu.edu/~hsu/courses/126/Law-of-Small-Numbers.pdf) pretty much says the opposite, that math is full of coincidences … I suppose it depends on how you interpret “coincidence”, though.

Given the amount of my students who by some miracle get the right answer by using the wrong method – one that doesn’t translate to other instances – I will disagree with this 12 year old’s analysis.

I teach elementary children who don’t necessarily know what conjecture means, but when someone makes an observation, I often ask “Is that a coincidence or will that always happen?” and I’ve found this question helps younger kids think about generalizations.