Mathematics Weblog

“Mathematics” vs Mathematics

A link in one of the comments at Mathematics dying on the vine in Australian universities drew my attention to a paper called “Mathematics” vs Mathematics by I. Bokor of the School of Mathematics, Statistics and Computer Science, University of New England, Armidale NSW. This paper attempts to dispel some myths such as:

The view seems to be commonly held, even amongst mathematics and science educationists, that mere passing familiarity with rudimentary facts is more than adequate for teaching these subjects at school. School teachers, and even those who train them, frequently argue that it is actually preferable to know less about mathematics and science in order to teach them better.
There is a confusion of numeracy with mathematics, a fallacy as crude as equating literacy with literature. For while one must be numerate in order to attempt to learn or appreciate mathematics, there is a qualitative difference between mathematics and mere computation, just as a narrative text does not become literature solely because it is free of grammatical errors and spelling mistakes.
Partly as a consequence, there is a pervasive belief, including among those who use and apply mathematics, that any mathematical problem has a unique solution, which can be readily computed numerically if one just had the right computer with the right programme, or, failing that, by being adept enough.

If I had not experienced this myself I wouldn’t have believed that these myths are all too common these days. The author illustrates the difference between mathematics (the reality) and “mathematics” (the myth) by discussing the mathematics involved in answering a supposedly simple problem like .

A paper worth reading.

Mathematics in Crisis

Those of us who live and work in the UK are worried about the crisis in mathematics in this country, both in schools and universities. It appears that there are similar problems in Australia as described in Mathematics dying on the vine in Australian universities. As Alexandre Borovik of Mathematics under the Microscope, who pointed me to the post, says (well almost, I’ve slightly altered what he wrote)

We continue to underestimate the gravity of the crisis of mathematical, and, more generally, scientific education [in] Western civilization.

So the question is What are we going to do about it?

Mathematics is different

Two blog posts have caught my eye. The first is Time Lag in Learning Mathematics which talks about the time it takes for a student to learn mathematics followed by the observation that one cannot be said to understand a topic until one can apply it. This often only occurs in the year after one has learnt the subject which is why I often tell my university students that it will always be true that Last year’s course was easy, this year’s is hard and next year’s is impossible.

A very important point that Mathematics under the Microscope makes is that anyone teaching mathematics should have a qualification at least one level higher than that being taught.

It is so hard to convince non-mathematicians that teaching and learning mathematics is very different from most other subjects. This partly accounts for the appalling state of teacher training and observation in the UK and why I absolutely refused to be judged by unqualified observers.

In the second post the secret life of numbers gives a quote from the book it is discussing which gives a better alternative to a question I often ask Why are people happy to admit to being innumerate but prefer to hide their illiteracy? PS Mathematics under the Microscope has an interesting response to this.