The words curious and curiosity do not appear in the Mathematics Common Core Standards document, yet they are arguably the most important words in mathematics education. If there is any single habit of mind or critical skill I want our students to learn, don’t you agree, it is to be curious, to question, to experiment, to wonder, to imagine what we will do or become. Isn’t this what it means to reason quantitatively?

Curiosity is certainly the most human of traits. It is the reason we explore, the reason we invent, the reason we question, the reason we love mysteries and games. We are naturally curious. And curiosity is at the heart of mathematics as well. We wonder if particular numbers form a pattern, we want to know whether all triangles that fit in a semi-circle are right, whether all right triangles have two sides that when squared are equal to the square of the longest side. We wonder if our business will make money or our budget will enable us to buy that new computer. We are curious big and small, is the universe infinite or finite, is the chance of winning the lottery worth the price of the ticket, is global warming really that bad.

At What if Math we are all about curiosity. How many of the products in a 12 by 12 times table are odd numbers? If we choose any whole number and divide it by 2 if it is even and multiply it by 3 and add 1 of it is odd will repeating that pattern always make a sequence, 4, 2, 1…? What if we make a table using 1 simple rule, add the two cells in the row directly above it? What does the graph of a quadratic equation do if I change the b term? Was Ted Williams or Joe DiMaggio a greater hitter in the 1941 season? Was Napoleon right about using the Great Pyramid to build a wall around France or Moore right about the exponential rate of growth of microprocessors? What does absolute value do to the graphs of polynomials? Is the rate of change of C02 increasing or decreasing? Should I lease or buy that new car?

If curiosity is so central to our lives, then I am curious to know why it doesn’t appear in our math standards or in all too many of our math classrooms. I am curious to know whether students can care about what they are learning in their math classes if they are not curious about the problems we give them or the concepts they are supposed to learn. I am curious to know whether learning math can be fun for kids if they are not curious about it. I am curious to know…