The Number Sense Quotes

“If storing arithmetic tables in memory is so difficult, how does our brain eventually catch up? A classic strategy consists in recording arithmetic facts in verbal memory “Three times seven, twenty-one” can be stored word for word alongside “Twinkle twinkle little star” or “Our Father who art in Heaven.” This solution is not unreasonable, because verbal memory is vast and durable. Indeed, who does not still have a head full of slogans and songs heard years earlier? Educators have long realized the huge potential of verbal memory.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition

“Mental arithmetic poses serious problems for the human brain. Nothing ever prepared it for the task of memorizing dozens of intermingled multiplication facts, or of flawlessly executing the ten or fifteen steps of a two-digit subtraction. An innate sense of approximate numerical quantities may well be embedded in our genes; but when faced with exact symbolic calculation, we lack the proper resources. Our brain has to tinker with alternate circuits in order to make up for the lack of a cerebral organ specifically designed for calculation. This tinkering takes a heavy toll. Loss of speed, increased concentration, and frequent errors illuminate the smallness of the mechanisms that our brain contrives in order to "incorporate" arithmetic.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics

“Young children reinvent arithmetic. Spontaneously or by imitating their peers, they imagine new strategies for calculation. They also learn to select the best strategy for each problem. The majority of their strategies are based on counting, with or without words, with or without fingers. Children often discover them by themselves, even before they are taught to calculate.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics

“Any student executes tens of elementary calculations daily. Over a lifetime, we
must solve more than ten thousand multiplication problems. And yet, our arithmetic memory is at best mediocre. It takes a well-trained young adult considerable time, often more than 1 second, to solve a multiplication such as 3 × 7. Error rates average 10 to 15 percent. On the most difficult problems, such as 8 × 7 or 7 × 9, failure occurs at least once in every four attempts, often following more than 2 seconds of intense reflection.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics

“progressive enrichment of children’s intuitions, leaning heavily on their precocious understanding of quantitative manipulations and of counting. One should first arouse their curiosity with some amusing numerical puzzles and problems. Then, little by little, one may introduce them to the power of symbolic mathematical notation and the shortcuts it provides — but at this stage, great care should be taken never to divorce such symbolic knowledge from the child’s quantitative intuitions. Eventually, formal axiomatic systems may be introduced. Even then, they should never be imposed on the child, but rather they should always be justified by a demand for greater simplicity and effectiveness. Ideally, each pupil should mentally, in condensed form, retrace the history of mathematics and its motivations.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition