Tales from Camppp, V.2 or Mathematicus Mortis
“Most of us teach mathematics as if it were a dead language.” Catherine Twomey Fosnot
What is ‘important mathematics’ for you? Is this question easy for you to answer, or is the asking of it so anxiety-prompting that you need to take deep breaths and sit down, or run to the wine rack? Are you one of those educators who are certain that you know all you need to know about the teaching of mathematics, or are you one of the many who slink down in your chair, hoping you won’t be called upon?
It should not be a surprise that research has provided a fairly robust and clear vision of the most effective approaches for teaching mathematics in elementary and secondary school for teachers to draw upon. After all, mathematics as a discipline has been with us for thousands of years, it’s not like it is ‘new’. It is impossible to think, view, act or speak without using mathematics. And, unlike language, it is based upon a consistent, concrete set of principles that hold true everywhere in the know universe. How’s that for an unlimited, juicy context for learning?
Why is then that most school math instruction is so…limited? Why is it that we focus so much on the memorization of tricks and short cuts to apply the algorithms for computation? Why is it that most of our mathematics instruction is focused on drill or simple, contrived ‘ number situations? Why is it that we look at school mathematics as a series of subjects, or strands, to be covered, rather than as a way of discerning and describing patterns and relationships in the world around us?
For most of us, the answer is simple, we teach math the way we were taught. And we were taught by teachers who did the same…and so on. Leaving aside the issue that no pedagogy should stand unchallenged for even one generation, let alone several, let’s consider the world that demanded the mathematical understandings that underpinned this instruction. A world where calculations were carried out by clerks, not computers, where measures and financial matters generally involved face to face interactions and where opinions where formed based upon conversations and community cultural norms and values. An analog world formed the basis of this mathematics.
The digital world we live in now demands that we focus our mathematics teaching to develop each student’s understanding of important mathematics ideas so they may learn to solve authentic meaningful problems, in context, and, with purpose and creativity. This is the mathematics that has been with humans for thousands of years, long before the shop clerks of the 19th century co-opted it. This is the mathematics we spent the week talking about at MathCamppp.
Sounds great…how do we do this? Deborah Loewenburg Ball’s research suggests that we need both mathematics content knowledge as well as pedagogical content knowledge to pull this off. In other words we need to know that math our students need to know, as well as how to develop lessons that push students to develop this knowledge. Processes such as Lesson Study (an action research model developed in Japan), when grounded in research-based resources, can develop both of these areas when used by teachers. As does co-teaching with a knowledgeable coach. These are the processes we are implementing this year at our school to support our teachers as learners. Among the key insights I gained from my time at MathCamppp was the understanding that we have lots of people willing and qualified to support this process.
The question I have is what is stopping us? To paraphrase Simon Sinek, perhaps it is not what, but why? We focus so much on the what of mathematics; the rules, the labels, the stuff, that we forget the importance is in the why. We have only four operations in math (+,-,x,/) yet we have an infinite quantity of numbers, the why, my friends, is in the numbers, the patterns and the relationships. Why do we need to teach so that students may learn ‘important mathematics’ to solve real problems, in context and with creativity and purpose? Because they will need to be able to do this to make a life, because mathematics shouldn’t be the sole property of the elite, because a digital world means a mathematical world, because mathematics is not a dead language.