Professor Jo Boaler uses the award of the Fields Medal to Maryam Mirzakhani to criticise the teaching of procedures in British maths education. Meanwhile, in The Guardian, the laureate herself cites the problem that was her inspiration - Gauss's quick and accurate reply when asked to add the numbers from 1 to 100. Nishad Karim provided this account:

*The answer is fiendishly simple once you know how. Gauss discovered that on adding the consequential numbers of the highest and lowest values in the sequence you would get 101. So for example, the first pair takes the lowest value, 1, and the highest value, 100, and, when added, give 101. Similarly, for the second pair, the second lowest and highest numbers, 2 and 99, summed give 101, and so forth. In total there are 50 pairs each amounting to 101, so using simple multiplication (50 x 101) the answer is given in seconds, 5050. Or as Mirzakhani puts it, “a beautiful solution”.*

Gauss could not have done this if he had not been fluent in addition facts and able to combine and adapt them to solve the problem. It is indeed a beautiful solution, and reinforces the point made by Professor Peter Bryant that knowledge and reasoning are both important.

To substantiate her argument, Professor Boaler needs to provide evidence of success in mathematics by pupils using her approach under controlled conditions. So far there is none. The case studies on this site, notably the fourteen year old who is now enjoying algebra after developing fluency with numbers, beginning with multiplication and divison facts, indicate that she is wrong, though of course they are no more than case studies, and provide indications for further work rather than definitive answers.