D. G. Wells, Can mathematicians help? The De Morgan Journal 2 no. 4 (2012) 1–4.

Abstract:

Professional mathematicians have not made the contributions to the teaching of mathematics in schools that might have been expected, in part, at least, because of their failure to appreciate the processes of conceptualisation and reconceptualisation that lie behind good maths teaching and lead young children from naïve concepts, objectionable perhaps to the professional, in time to more sophisticated and professionally acceptable interpretations. Illustrated

by the idea that ‘Multiplication is repeated addition.’