Continuing reflections inspired by my rush of ACT tutoring last week…one of my students encountered the following problem in the math section of a practice test.
If the statement “If a cat is tricolor, then it is female” were true, which of the following statements would also have to be true?
If a cat is a female, then it is tricolor.
If a cat is not a female, then it is tricolor.
If a cat is not a famale, then it is not tricolor.
If a cat is not tricolor then it is a female
If a cat is not tricolor then it is not a female
Child’s play (for grown-up mathematicians)! Just look for the contrapositive. But more interesting was my tutee’s question.
“Is this math?”
My response: “Sort of.”
I then went on to explain, using a metaphor I’ve long considered, that math is a language just like English or Spanish or French. Just like English has rules that we call grammar, math has rules called logic; the rules themselves are not “math” in the same way that grammar is not “English,” but they’re part of the whole edifice.
If there was one concept I could get across to students studying math at any level, it would be this understanding of math as language. Yes, most math classes are equation and rule laden bootcamps, and maybe they need to be, in the same way that language classes drill grammar, vocabulary, and listening/speaking skills. (Is this the best way to learn language? Food for thought…) But if students could see that the end goal of all this symbolic manipulation is a means of communicating (and understanding) important ideas, in the same way that media bombards us with words and images, that would satisfy me.