are best described by Adam Smith’s famous words displayed on a £20 banknote:

*“The division of** labour** in pin manufacturing*

(and the great increase in the quanitity of work that results)”

The ever deepening division of labour has reached a unique point in history when 99% of people have not even a vaguest idea about the workings of 99% of technology in their immediate vicinity. The schism is profound: only engineering students are taught some elements of mathematics built-in in a mobile phone or MP3 player—but *without proofs*. Moreover, the *proofs* involved are beyond the reach of most British mathematics graduates.

It is no longer an issue whether we change mathematical education: the change is being forced on us by Adam Smith’s “invisible hand”.

Changing economic imperatives lead to the collapse of the traditional pyramid of mathematics education.

On the left is how it looked in the mid 20th century, with pupils / students / graduate students at every level of education being selected from a larger pool of students at the previous level, and when every year invested in mathematical education was bringing a student an immediate economic return. On the right is what we should expect in the future. Returns are becoming postponed and less certain, destroying economic motivation for study.

We have to accept that the majority of the population do not need “practical” mathematics beyond use of calculator. We have to re-brand mathematics with emphasis on its human component, as a tool of personal development and empowerment more efficient than music or religion.

However, this makes even more challenging the problem of motivating and educating the minority stream of students who are to become professional users of mathematics in science, engineering, finance, defence.

[I imported that post from an earlier version of my blog]

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