Tenoch E. Cedillo A.* (Mexico), tcedillo@mail.ajusco.upn.mx

Plotting and Function Graphs as tools to face problem solving: A study with
12-13 year olds using graphing calculators

The graphing calculators offer new forms of mathematical validation that
challenge the conventional algebraic methods.  We used to study Differential
Calculus to approach the behaviour of functions, but, currently we can use
calculators to start exploring graphs of functions visually, before the study
of their algebraic properties and further applications in Calculus.  Thus,
intuition is acquired before formalisation.

This presentation comes from an exploratory study which addressed core issues
of the teaching and learning of algebra.  The study was carried out in a
comprehensive school in Mexico City with a class of twenty five students who
had not had any instruction in algebra.  Preliminary results suggest that 12-13
years olds can successfully approach the study of algebra and efficiently use
functions to face problem solving.  The TI-92 was used to put the students in a
situation where they learn algebra by tackling problems using plotting and
function graphs as cognitive tools.  The strategy consisted of making students
(12-13 year olds) familiar with the relationships between the coefficients and
graphical behaviour of linear and polynomial functions.  Once they were able to
work confidently with such functions and their graphs, they were handed a
series of problems where modelling through functions is a way to negotiate
solutions.