tisdag 6 oktober 2009

The Unreasonable Effectiveness of Mathematics Education

There are different sorts of scepticism: More or less respectable and reasonable in religion, philosophy, science, medicin, evolution theory, and pseudo or false scepticism cin Aids denial and Holocaust denial. Scepticism is a basic principle of science since Descartes.

You take a sceptic attitude if you don't recognize and expect something to make sense unless you find a reason to do so which you can understand.  

The fate of humanity is now decided in a debate between climate alarmists and climate alarmism scepticists, with each side accusing the other for pseudo-science or pseudo-scepticism.

But there is no mathematics scepticism. The big battle took place between the logiscists/formalists and the constructivists in the 1930s, with the constructivists being the scepticists. The scientific game was won by the scepticists, but not the political since they were expelled from the mathematics departments by the logicists/formalists, still in control today as explained in The Losers Take It All and The Hilbert-Brouwer Return Match.

The lack of mathematics scepticism results from a mathematics education making everybody, independent of performance in math classes and use of mathematics in professional life, believe in The Ideology of Mathematics: 
  • mathematics is the most original creation of a free human spirit
  • mathematics is beautiful, difficult and a sign of intelligence
  • mathematics is very useful
  • the unreasonable effectiveness of mathematics in the natural sciences
  • mathematics has universal applicability
  • only few people can properly understand mathematics
  • mathematics is rock solid
  • there is no mathematics scepticism.
This success story does not come out of the blue. A main goal of mathematics education as formulated in the Guiding Principles for Mathematics Curriculum and Assesment of National Council of Teachers of Mathematics NCTM is 
  • By developing ideas, exploring phenomena, justifying results, and using mathematical conjectures in all content areas and at all grade levels, students should recognize and expect that mathematics makes sense. 
Many students learn very little during their many years of math classes,  but all students learn to recognize and expect that mathematics makes sense although it does not make much sense to themselves.  The principles of NCTM thus seems to foster non-sceptic citizens.

This can be expressed as the unreasonble effectiveness of mathematics education: To learn to recognize and expect mathematics to make sense without being able to see it. This explains why there is no mathematics scepticism. It was eliminated in school.

Note that the teaching other subjects including physics, biology, geography, language, history. music et cet, does not involve the explicit goal of teaching students to recognize and expect the subject to make sense. That would be ridiculus. But for mathematics this goal is not ridiculus, or is it?

We may compare with the teaching of Darwin's theory of evolution, which is very effective in a country like Sweden, but much less effective in the US. Climate scepticism is also shared by many in the US, but until recently by very few in Europe. Mathematics scepticism though is very rare in both the US and Europe.

The role of the blogsphere in scientific scepticism is illustrated for example in the recent breathtaking story about UNEPs use of a Wikipedia “hockey Stick” graphic by “Hanno”
with a response in New York Times yesterday. Real time demonstration of what science is and is not. A battle between free sceptic thinking and peer non-sceptic thinking. Between real science and consensus science.

Inga kommentarer:

Skicka en kommentar