The front and back of mathematics aren’t physical locations like dining room and kitchen. They’re its public and private aspects. The front is open to outsiders; the back is restricted to insiders. The front is mathematics in finished form—lectures, textbooks, journals. The back is mathematics among working mathematicians, told in offices or at café tables.
Front mathematics is formal, precise, ordered, and abstract. It’s broken into definitions, theorems, and remarks. Every question either is answered or is labeled: ‘open question.’ At the beginning of each chapter, a goal is stated. At the end of the chapter, it’s attained.
Mathematics in back is fragmentary, informal, intuitive, tentative. We try this or that. We say, ‘maybe,’ or ‘it looks like.’
-Reuben Hersh, Professor Emeritus, Department of Math and Statistics, UNM
Tracy explained at the meeting that restaurants and theaters have a “front” where everything is presented perfectly to the public and a “back” where the chaos happens. This is the metaphor that Hersh is using. Too often our students are only exposed to the “front” of mathematics and none of the “back.”
I recently shared this at a BMTN meeting when a colleague coined the term “math kitchen.” And then she said, “Put on your apron – it’s going to get messy in here.” It made me think about how often my students want to have their math papers be perfect. Every mistake must be erased. Nothing can look messy. Am I alone here?
Another colleague said that she used to make all of her students do math in pen. That way they had to cross out mistakes. They couldn’t erase them. I think this is a brilliant idea.
Too often I hear my students say things like, “I remember doing something like this” or “I’m trying to remember what my teacher told me” or, God forbid, “I never learned this before.” What are we doing to our students that makes them think that they should have memorized or learned before what we are trying to teach them now?
So, in the spirit of exposing students to the “back of math” I say, “Welcome to the math kitchen. Grab a pen and put on your apron. It’s going to get messy in here.”