We often hear our learners refer to their peers (or themselves) as someone who is either good at or not good at maths. The ones who classify themselves as not good at math probably wonder how the former group are just ‘good’ at math.
I want to start by saying that mathematics is not a verb – it is not something we do in the same way that we run, jump, sleep, or eat. It is a field of study, a body of knowledge. We do not do math – we learn about math and use our understanding to solve problems. Therefore, I would go so far as to say one cannot be good, or not good, at math. Instead, we can be more or less proficient in using math to help us solve problems in our lives.
So the real question is – what does it mean to be mathematically proficient? To answer this, I draw on the work of Kilpatrick, who described 5 Strands of Mathematics Proficiency (see the link at the end of this article to access his work). These 5 aspects of teaching and learning mathematics are:
1. Conceptual understanding
To be proficient in mathematics, one needs to understand the content and have mastery of the concepts. In teaching mathematics, we need to focus on helping learners understand how different mathematical concepts are linked and why they work the way they do.
2. Procedural fluency
This is the “doing” math part. Procedural fluency is about carrying out the correct steps when using mathematical concepts to solve problems. It is the part of teaching where we focus on how the concepts work.
3. Strategic competence
Mathematical concepts can be presented in various ways. For example, an equation can be represented algebraically, verbally (in words) or graphically. Strategic competence is about helping learners understand the most suitable way to present mathematical information to make it more accessible and ‘usable’ in problem-solving.
4. Adaptive reasoning
This skill development allows one to identify which mathematical tools and concepts help solve problems in various contexts. It is about being able to ransack our mathematical toolbox and identify the combination of concepts and procedures that will help us to make sense of a problem and work towards solving it.
5. Productive disposition
This is a crucial aspect of developing a love for mathematics. We need to instil a productive disposition in our learners. This means that we need to help our learners understand how mathematics can be helpful in their lives so that they become willing to engage with the body of knowledge outside their textbooks and homework. Learners deemed good at math are often also viewed as liking math. However, I believe being good at or proficient in math does not necessarily precede a liking of maths. If we can encourage our learners to explore maths rather than fear it, they can develop a liking for the subject, which is crucial to becoming proficient in it.
For more information on Kilpatrick’s 5 Strands of Mathematical Proficiency, download the PDF from the following link: https://www.mathnic.org/downloads/06_proficiency_guide.pdf