Making Mathematics Messy

"Mathematics is popularly conceived of as a pure body of knowledge, independent of its environment, and value-free."

 I agree with Renert, that mathematics today is considered as abstract and separate from reality, with the exceptions of well-posed contrived problems that promote linear and binary thinking; there's very little mess in a mathematics classroom. Students are consumed with getting the right answer, and sadly, the current state of teaching, perpetuates the value of that desire. But rather than "reform" or even "transform" this present state by looking to a more socially responsive future, I believe we should look to our past. I believe the Ancients did not create and develop mathematics to serve as a pure abstraction intended to live in parallel with reality. Mathematics was created from life for life; it arose organically to measure, predict, and understand nature so that they could plant, grow and ultimately sustain their existence. The Ancients would never have to question whether mathematics should concern itself with ecological issues. Therefore, I think Renert's arguments  are compatible with the age old idea of what mathematics truly was.

"It turns mathematics from a collection of objects, or a series of competencies, into an open-ended state of observing the world."

Renert's argument that "our number sense is almost entirely divorced from any quantity sense,"  underlines this chasm between a two-dimensional linear view of mathematics (right and wrong) and a fuller more holistic viewpoint that values process and possibility. Yes, we know what numbers are, and how they relate to one another; but what do they mean to us? When I first learned to swim I remember hearing that now depth didn't matter, because I could presumably swim in it regardless. I think this is what we are imparting to our students through our mathematics education; they learn the rules, apply them to any problem they are given, and make sure you get the right answer. But does depth really not matter? Surely we should know how much water lies below us, what could be swimming next to us, temperature or water composition. And yet, we are taught to focus on the surface, as the answer to such questions shouldn't affect our swimming technique: but they do! When we pull ourselves out of our trained monochromic thinking, we open our minds to messy, and necessary, complications - we open ourselves up to life. Telling a student that they got "42" tells them nothing without them further questioning, "out of what?" or "how did everyone else do?" Numbers need context to be understood, just as mathematics needs to be placed back into life to have relevance and meaning.

"'radial creativity'...shifts the responsibility of knowledge production from the teacher to the entire classroom collective."

I love the idea of making our classrooms a learning community; allowing ideas to flow unlimited in non-linear ways.  I want to make every student feel valued and that their contributions matter as much as anyone else's. I don't believe one correct solution is necessarily better than a hundred incorrect attempts. Indeed, promoting discussion and sparking our thoughts is, to me, what teaching is at its best. I think the ecological issues that face us are bigger than any one of us, and to assume we know more than our students is naiave and unproductive. Telling them what to do will not empower them to experience the problem and it won't initiate their curiosity and concern. I think this problem, like our planet, belongs to all of us and needs to have everyone's buy-in.