### National Curriculum issues and opportunities for revitalizing geometry thinking in the classroom

This is a talk I gave to the Independent Schools Heads of Departments of Mathematics meeting at Knox Grammar School, Sydney on August 13, 2012. The aim was to try to address the issue of a new national mathematics curriculum for Australia that ACARA, the Australian Curriculum Assessment and Reporting Authority, have proposed for advanced mathematics for Years 11 and 12. The two courses are called Mathematical Methods and Specialist Mathematics. For those teaching in NSW, these are roughly at the level of Two-unit and Four-unit mathematics.In the talk I summarize the main points of a detailed report prepared by the School of Mathematics and Statistics at UNSW by Mr Peter Brown (Director of First Year Studies), Dr. Daniel Chan (Dept. of Pure mathematics), Assoc. Prof. David Warton (Dept. of Statistics) and myself. We are highly critical of the proposed drafts. I explain our reasons briefly, and refer interested viewers to the report itself, available athttp://www.maths.unsw.edu.au/news/2012-07/schools-response-draft-senior-mathematics-curriculum-acara . To quote: The proposed national curriculum will be, in our opinion, a setback for mathematics education in NSW, and we would support the Federal government having a fresh look at the project.The second part of the talk is an attempt to reposition geometry in the high school curriculum. The construction of a national curriculum is an important opportunity to ask key questions about how we can encourage participation and learning in mathematics, and strengthen school leavers understanding, competence and confidence in the subject. Geometry, I will argue, is a historically vital subject which we need more of today rather than less (ACARA proposes to banish geometry almost entirely from the main advanced mathematics course: Mathematical Methods!!) To make the case, I will briefly introduce a number of topics that are potentially appealing and illuminating for high school students. These include conics and Cartesian geometry, the rational parametrization of a circle, Pappus' and Pascal's theorems in projective geometry, triangle centres and the Euler line, Archimedes' law of the lever and convex combinations, centers of mass and means of probability distributions, Olympic rankings and even a bit of rational trigonometry! This is a smorgasbord of geometric delights that hopefully will encourage the realization that geometry can have broad appeal, is important to the modern world, and underpins other areas of mathematics as well as of course science and engineering.While the curriculum issues are focussed on particular plans afoot here in Australia, the issues no doubt are of interest much further afield.Hopefully anyone with an interest in geometry and mathematics education will find the discussion useful.

Length:
48:49