Much of what we think of as mathematics, from the arithmetic we learned in elementary school to the way we write numbers, the way we draw graphs, the way we write equations, all this and more has been passed down to us. When doing mathematics, we partake in a large and rich cultural conversation, whether we realize it or not, whether we appreciate it or not.
As children, we face schools who put a lot of resources into passing this cultural heritage on to us,with varying degrees of success. This heritage is not passed on genetically, nor can it be dispensed by pill, nor is it made available by implant. It takes years for children to build up their mathematical thinking, to hone and test their mathematical ideas, to partake in the cultural conversation called mathematics, to the point where society considers them ‘done’.
This has been going on for many, many generations. Mathematics hasn’t stood still, hasn’t been static, hasn’t been fixed; instead, it has seen vital, massive, and rich development over the centuries – much of it during the last fifty years. For a single child, and a single teacher, however, mathematics has often seemed to be and has been treated as a fixed thing, massive, static, and complete. Such an approach, though natural and forgivable, is completely ahistorical. There is surprising richness in approaching mathematics as an unfinished, organic, deep way of looking at the world, a gift but not a straitjacket.
In this blog we will explore what’s available from approaching math as something rich, deep, and alive.