A common reaction I get upon telling someone that I am a mathematics teacher, is “I used to hate the subject at school.” The reason would be something like “I’m not good with numbers” or “I could never get the hang of long multiplication and long division.” I am often given the impression that people tend to associate mathematics with numbers and calculations. This, I am afraid, is a gross misconception as mathematics is much more than simply memo­rising the multiplication tables and doing lengthy calculations in one’s head or on paper.

Conrad Wolfram, a physicist, mathematician, technologist, strategic director and European co-founder/CEO of the Wolfram group of companies, is very clear about distinguishing between mathematics and cal­cu­lating. In a TED lecture (https://youtu.be/60OVlfAUPJg) he says mathematics consists of four pro­cesses: posing the right ques­­­tion, transforming the real-world question into a mathematical format, computing, and transforming back to the real world for verification. He believes that in education we tend to dedicate most of the time to calculation, which can be carried out by a computer. We should, he proposes, “stop teaching calculating and start teaching math”.

Some teachers may be shocked to come across students who cannot recite their multiplication tables or have to resort to a calculator to add, subtract, multiply or divide two two-digit numbers. But is this, in itself, a sign of lack of mathematical knowledge?

Some years ago, one of my students needed to multiply 8 by 8. Probably because she did not know the multiplication tables by heart, she multiplied 8 by 10 and subtracted 8. Could I doubt whether she knew her math? Similarly, I think all of us need to develop number sense: place value, mental estimation, sensing whether a computer answer makes sense or not, etc. However, I think we ought to put more emphasis on the other aspects of math that Wolfram refers to.

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