WHAT’S THE PROBLEM? by Jack Garb*
An important question regarding the teaching and learning of Maths, is whether we should emphasise problem-solving or the ability to calculate. Many traditional teaching models train teachers to teach as they were taught, and that invariably means an emphasis on calculation ability and rote-learning. Maths experts worldwide agree that it is time we stop teaching “tricks” in Maths, including mnemonics like BODMAS ( to teach the order of operations) Many of us remember “Daddy-Mommy -Sister-Brother” as an aid to recalling the steps of long division.
While tips and gimmicks are intended to make Maths easy and fun, the reality is very different: mathematical ability becomes almost magical, maths anxiety remains rife and phobic attitudes continue. Titles such as “Fear of Mathematics”, “Math Anxiety Resources” and “Conquering Math Phobia” abound. There is apparently no History or Geography phobia, why only Mathematics? Professor Ron Aharoni - a Professor of Mathematics– suggests that the reason for such anxiety lies in the layered structure of Maths. Many of the layers of mathematical knowledge are so elementary that they are often easy to miss. And when this happens and an attempt is made to establish a new layer on top of the missing one, neither the teacher nor the student can discern the origin of the problem. Anxiety is born.
Traditionally, the type of Maths learner that has been valued is the one who can memorize well and calculate quickly. Yet, data from 13 000 students who took PISA tests in 2013 show that the lowest achieving students worldwide were in fact those who used a memorisation strategy. The highest achievers were those who thought of Maths as a set of connected big ideas. Jo Boaler , Professor of Mathematical Education at Stanford University, explains: “We don’t need students to calculate quickly in Math. We need students who can ask good questions, map out pathways, reason about complex solutions” and “…set-up models and communicate in different forms.”
Children who struggle with Maths are often the ones who are ultimately confused by the very “tricks” that are supposed to help them. All children should experience Maths in a concrete form, initially, using relevant manipulatives, before moving to pictorial representations, and finally ,the abstract. Children need to be given time to discuss and investigate problems presented by the teacher.
Computational ability and “calculations” are merely tools to promote fluency in Maths, they are not what Maths is really about. Maths is about thinking, reasoning and solving problems. All of these attributes are needed by the child in the 21st century if s/he is to be employable and able to contribute to a technological society. The learner, who when presented with a sheet of addition sums, asks “Do we “carry” on this page?” clearly reflects a worrying shallowness of understanding.
Merely learning a “method that works” is an impoverished kind of learning which leads to a weak understanding of the nature of Mathematics. The ability to perform calculations does not mean that children will know which skills to use in different problem situations.
To realise the objectives of teaching for understanding, it is important for teachers to increase their own mathematical knowledge. Teachers should be encouraged to bring a sense of curiosity to these opportunities and to pursue ideas with which they may be unfamiliar.
The results will be infinitely rewarding to themselves and their students.
*Jack Garb is a former school principal. He introduced Singapore Maths into South Africa in 2007.