Friday, January 20, 2006

School Geometry

We are short-changing our students on geometry in Ireland. A recent OECD comparative study showed that our 15-year-olds perform well in general, but are below par in handling problems that involve spatial ideas. We need to get them thinking geometrically. Apart from giving it the necessary time and attention, we need good books, of two kinds:

(1) Texts and extra reading for secondary students that will be mathematically sound, interesting, and challenging. Most of our students hate geometry. If they were exposed to the right stuff, they would learn to love it. see
a typical good geometry resources page.

I recommend the posters on Math in X (where X is a country), if you can still get them.
There are excellent books available, tailored for US school practice. An outstanding example is Harold Jacobs, Geometry: Seeing, Doing, Understanding, 3rd edition, Freeman 2003. Let's have something like this in use here.

(2) University texts for prospective maths teachers. Most younger teachers also seem to hate geometry. The universities should do things to fix this, at least with the new entrants to the profession. Most US universities have courses that aim to meet this need, and there are many texts, at varying levels of sophistication. A sample course is that at Clark University Some examples of texts:


P.D. Barry. Geometry with Trigonometry. Horwood. Suitable for a one-semester course, with modest prerequisites.


H.S.M. Coxeter. Introduction to Geometry. Wiley. A vast panorama. Could be used over three or four courses, over several years.


D. Pedoe. Geometry. A Comprehensive Course. Dover.


D.A. Brannan, M.F. Esplen and J.J. Gray. Geometry.
Cambridge UP. Designed for Open University work; works up from the basics.

J.N. Cederberg. A Course in Modern Geometries. Springer. 1995. Needs mathematical sophistication in the student, to begin with.

At Maynooth, we've used Greenberg. Euclidean and Non-Euclidean Geometries: Development and History. 3rd edition. Freeman. 1994. This has worked reasonably well with 3rd year students of Mathematical Studies.

2 comments:

Tony said...

See the talk by V.I. Arnold
at this site. There is a lot of sense in what he says. However, our problem here in Ireland is not just a manifestation of a global trend; it's our particular problem.

Tony said...

Further examination of Jacobs reduced my enthusiasm. He has some circular arguments. I discovered this when I was composing proofs for the foundation document for new geometry programme for schools. However, It's still a very engaging book.