CAROLINE BARDINI, ROBYN U. PIERCE and KAYE STACEY ⋆ TEACHING LINEAR FUNCTIONS IN CONTEXT WITH GRAPHICS CALCULATORS: STUDENTS’ RESPONSES AND THE IMPACT OF THE APPROACH ON THEIR USE OF ALGEBRAIC SYMBOLS ABSTRACT. This study analyses some of the consequences of adopting a functional/ modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the predominantly graphical approach feasible. Students made considerable progress in describing linear relationships algebraically. They commented favourably on several aspects of learning concepts through problems in real contexts and were able to set up equations to solve contextualised problems. Three features of the program exerted a ‘triple influence’ on students’ use and understanding of algebraic symbols. Students’ concern to express features of the context was evident in some responses, as was the influence of particular contexts selected. Use of graphics calculators affected some students’ choice of letters. The functional approach was evident in the meanings ascribed to letters and rules. Students were very positively disposed to the calculators, and interesting differences were observed between the confidence with which they asked questions about the technology and the diffidence with which they asked mathematical questions. KEY WORDS: algebra, algebraic expressions, functional approach, graphics calculators, linear functions, modelling approach, real world problems, secondary school mathematics, teaching in context I NTRODUCTION A brief overview of Australian school mathematics textbooks shows that linear functions are a key topic. Typically students are introduced to stan- dard explicit and implicit forms of function rules such as y = mx + c and ax + by = c. Following the textbook sequence, they are taught to graph functions, taking consideration of both the x and y intercepts and the gradient of the function. Next students solve simple equations for x graphically and perhaps find the intersection of two functions. Symbolic equation solving may precede or follow graphical work. Finally there is usually a section of context based ‘word problems’ designed to illustrate applications of the theory studied. Class teachers commonly report two ⋆ Author for correspondence. International Journal of Science and Mathematics Education (2004) 2: 353–376 © National Science Council, Taiwan 2004