# Two Mathematics

Take an equilateral triangle and cut it into three similar parts, just two of which are congruent (Photo credit: fdecomite)

Yesterday, I was sitting in a talk at the Joint Math Meetings, and someone made the comment that the Common Core State Standards to not support quantitative literacy. The comment hooked something in me. Was it true? How might the CCSS fail to support quantitative literacy? What is quantitative literacy anyway? And what does the CCSS support, if not quantitative literacy. I actually haven’t yet gotten familiar enough with the CCSS to answer most of those questions, but I have an answer congealing in my mind anyway. There are two worlds of mathematics.

On the one hand, mathematics is about a love of figuring out problems, and puzzles. It’s about thinking abstractly, putting things together, and taking them about. Mathematics is an abstract intellectual exercise that is a joyful romp through problems, exploration, and mind-bending puzzles. This is the mathematics that mathematicians love. It’s the mathematics of Martin Gardner and the Museum of Mathematics.

On the other hand, mathematics is about understanding and being able to use the quantitative and geometric information that infuses our lives. It’s about being able to interpret basic statistics, make predictions, and pin down relationships between variables. Its about understanding risk, stripping complex information down to basics, and making comparisons. This is the mathematics of quantitative literacy and the mathematics of science.

Mathematicians want people to learn to love the first kind of mathematics. We see the fun, the beauty, and the power of mathematics for mathematics sake, and we want to share it with the world. We also believe that understanding this kind of mathematics will lead naturally to quantitative literacy, without any additional effort needed. But many people want the second kind of mathematics, and are not interested in the first. People want mathematics to be concrete and useful, to serve the world — otherwise what is the point? It is the first kind of mathematics that people see as irrelevant an obtuse. Do I need to convince them that it is not, that it is, in fact, wonderfully fun and beautiful? Or can I be convinced that their experience is authentic, and that they may not actually need that first kind of mathematics at all?

So I wonder — does the CCSS privilege the first kind of mathematics over the other? What kind of math does more traditional K-12 schooling privilege? Does learning the first kind of mathematics lead to understanding the second? Are they inextricably linked?