A pre-service teacher’s view on evolving and improving understandings of how children learn mathematics.

Views on teaching maths have changed radically in the last few years. Schools are moving away from a memorisation, process-based mathematics, and towards an understanding of maths based on number sense and an intrinsic understanding of the patterns that define our world. Mathematics, historically, has been a polarising and anxiety-inducing subject. I myself was a victim of maths anxiety for my entire schooling career.

Whenever I was faced with large numbers or required to solve a sum, my heart rate would soar and my mind would cloud as I frantically attempt to decipher the numbers. Even the most basic of sum can cause panic and dismay. The very sight of an algorithm would send me into a state that rendered me incapable of calculating a solution.

This isn’t uncommon, unusual, or extreme. Nearly one in five adults experience maths anxiety (Australian Council for Educational Research, 2011). Maths is a polarising subject — and those who hate it, really hate it.

But where does this issue hail from? I always assumed the numbers themselves were the culprit. I invented several rotating rationalisations to justify my inability to multiply — that I was lazy in primary school, I found large numbers hard to comprehend, I had some form of maths-specific learning disability.

It’s only been this year, when I began the journey to become a primary school teacher, that I learnt how influential teaching and learning was in my relationship with mathematics.

What if instead of teaching and constructing maths as an endless series of memorised processes and formulas, we conceive it as the fluency of number? What if we helped children develop concrete, practical understandings of how numbers and the relationships and patterns between them create the world around us?

What if we taught our primary-aged students to think like mathematicians, not calculators?

Maths, as it was historically taught, involved instructing students in processes they could use to quickly and efficiently solve a problem. Fifty years ago, before the digital age, this ability was invaluable. We needed tricks and mental tools in order to do any form of mathematics. Take, for example, the vertical algorithm.

471528371 +

83168462 =

— — — — — — — -?

The traditional way to solve this algorithm is to work down through the columns, carry the 1s, ect.

But what does this process actually teach us about mathematics? I could google the answer to this question in <4 seconds (<1 if I copy and paste) and have learnt the only thing this process actually gives me — the answer to the questions. Vertical algorithms do not improve our number sense or our mathematical fluency. If anything, they serve as yet another mental block to our conceptualisation of number.

Even the language we use for vertical algorithms is problematic. We say that we are carrying the 1s, when we’re actually referring to a 10. The same issues extend to any vertical algorithm that is solved in columns — by solving problems this way, we are completely forgetting place value, an integral part of anyone’s mathematical understanding. Place value underpins our ability to understand a number, to see a problem and estimate what the answer should look like.

Although literacy and numeracy are considered the bedrock of early learning, the way that they are approached is completely different. Literacy is treated as a fluency, an innate skill that is fluid and dynamic. Numeracy is regarded as the ability to perform certain functions, add, multiply, divide, long divide, solve algebraic equations.

The ‘common core’ approach to mathematics attempts to correct this with fluid and flexible understandings of number. It champions the idea that we can solve a problem and arrive at a solution in many different ways. Common core encourages students to understand the diversity in maths, that processes and functions are a mechanism of solving a mathematical problem, not the maths itself.

There are always going to be people who understand numbers innately, just like some students will be strong readers and some beautiful artists. Their number sense is an intrinsic part of how they make sense of the world. But for students who don’t have that natural understanding, for those who need guidance to learn what numbers actually mean, a new approach is needed.

References:

Australian Council for Educational Research (2011). Deconstructing maths anxiety: Helping students to develop a positive attitude towards learning maths. Camberwell: Australian Council for Educational Research.

Bobis, J., Mulligan, J., & Lowrie, T. (2013). Mathematics for children: Challenging children to think mathematically (4th ed.). Sydney: Pearson Education.