There still seem to be a lot of problems in the teaching of basic maths. This is suprising given that the core task is, to a first approximation, independent of culture and natural language. Of course the conditions of education do vary widely and there is also some general variation in the way natural language designates the numbers (for example the counting scheme in Welsh is more consistent than English and most of the European languages) - but most of the conceptual challenges lies in the mathematical structure and are shared by the billions that pass through the education system. Yes, billions! The world population is approximately 7 billion and about 90% of children attend at least primary school.
Given the scale of the endeavour one would think the human race would have the teaching methods pretty well sorted by now, but it seems not.
I am continually encountering intelligent children who are almost innumerate at the age of 15. Huge problems exist in basic work, even for students doing A level maths. In many cases these problems are more serious than pure ignorance and reflect genuine blocks in learning. For example I had a student who had attained an A in a year 12 maths exam but couldn't tell me a quarter of twelve. Such problems are actually common even in years 11-13.
Similar conditions hold in science teaching, but here there is far more excuse. The subject matter has deep aspects and requires maturity to understand. But again I find some excessive basic ignorance - for example students in years 11 to 13 that do not understand the rotation of the Earth and it's relation to night and day. Many also believe that the big bang refers to the birth of the solar system!
These extraordinary failures are, I feel, due to a lack of quality control at the level of the individual learner. Performance in exams is not picking up failure at the right time.
In my opinion, students need to be measured more not less! However, not by formal one off key stage exams but by continuing assessment of each micro task. This needs to be built in to the teaching process so it is painless - this can surely be achieved with todays information technology. The mangement of these micro records needs integrating into the personal teaching profile of each student. In this way weak areas can be identified, monitored and readdressed.
Given the scale of the mathematical education problem it would seem well worthwhile for society to undertake the design and implementation a flexible, self-correcting, computerised scheme for teaching at least the basics of maths. Teachers would be freed to illustrate the application of the mathematics, to create and inspire.
I am hoping these sentiments will strike a chord with educators or developers who are thinking along the same lines and require detailed input on the teaching structure.
Bill Stewart (12 July 2009).