Let us take the example of the four operations: addition, subtraction, multiplication and division. Their teaching has been considerably retarded and neglected in recent decades, to where the majority of middle school children do not know the multiplication tables and many high school students are unable to add two fractions. These operations have been neglected because of the emergence of calculators, and the belief that an operation carried out by a machine can be the same thing as an operation carried out by a human spirit. It is the same thing as to result – supposing that one has calculated correctly and not made an error of fingering, and with the reservation that there are, just the same, many occasions where the calculator doesn’t replace a mental calculation: I recently received a letter from a grandfather whose granddaughter had been fired after several hours as a salesgirl in a market because she was unable to make change. But above all, a calculator which one has programmed to perform certain operations knows only those operations for which it has been programmed. Whereas those same operations acquired and mastered by a student becomes nourishment for his spirit, empowers him, is digested by him, is made his own, enlarges and awakens his mathematical faculties and power. A familiarity with numbers, and similarly as to geometric objects, that permits the life that has been given him to enter, little by little, into the world of mathematics.

http://www-history.mcs.st-and.ac.uk/Biographies/Lafforgue.html

Plymouth University helps teachers with maths

Professor Burghes, who is still an active mathematics teacher, and will be working as the teaching expert in East London, added: “This project gives a real opportunity to change things for the better in the UK, and break the reliance on the traditional ‘transmission model’ of education. We only have to look at the example of Finland to see how it is possible to turn around teaching, and they are acknowledged now as world leaders in creating a more relaxed, and enjoyable style of lesson where children of all ability groups are not afraid to play a role in class, and are encouraged to problem-solve together.

“We need to help teachers not only to extend their mathematical knowledge but also to find an enthusiasm for the subject – and the enthusiasm for teaching itself – so that they in turn can inspire their pupils.”

One might think that if calculation and solving equations were absent from a mathematics course, then there would be nothing left to teach. But that is quite wrong: there are plenty of things one could teach, many of them entertaining, important and useful in later life. Here are some examples.

http://www.spectator.co.uk/features/8744071/should-alice-marry-bob/

Timothy Gowers visits Watford Grammar School.

Rethinking maths for the 21st century – Research – University of Cambridge.

The emphasis will be on simple underlying mathematical ideas, helping students to explore connections between different areas of mathematics, and supporting the development of key mathematical skills and clarity of thought. The impetus for the programme comes from a belief in the importance of dialogue between schools, higher education and research