A Rethink
on the Teaching of Graphs and Functions in the Cartesian Plane
Jim CLAFFEY
jimclaffey@graduate.uwa.edu.au
Australia
Abstract
At
a time when technology is available to help in the teaching, learning
and understanding of mathematics I express some concern that the
technologies are being used to reinforce traditional methods in
ways that are often inconsistent and illogical. Graphic calculators
in current use appear to perpetuate this problem. This seeming inconsistency
pervades much of the mathematics taught in secondary school and
results in confusion. Because of this, many students see mathematics
as a series of rules and procedures to be memorised. The end result
is that students dislike mathematics and are often turned off the
subject.
One area of major concern is the current approach to the teaching
of functions and graphs. Much of the structure and nature of the
mathematics taught in secondary schools relies upon a clear understanding
of the nature of graphs in the Cartesian plane. So why is it that
students have so much difficulty with this work? One explanation
is that many of us teach as we ourselves were taught and we only
use that technology which enhances and supports our approach. What
I am proposing, though not new, will require a radical rethink
of the approach to functions and their graphs. The approach suggested
unifies concepts such as Coordinate Geometry, Geometric Transformations,
Transformation of functions, Matrix transformations and the Multiplication
of Matrices, Vectors etc.
By way of an example: How do you view and teach y = 2(x6)^{2}
+ 9? What is the distinction between this and
?
