Agua

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 fiveweeks, 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 ableto 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 functionalapproach 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, linearfunctions, 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 standard explicit and implicit forms of function rules such as y = mx + c and ax + by = c. Following the textbook sequence, they are taught tograph 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

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things: first, that during the unit of work students repeatedly ask “What are we doing this for?” and second, that when the students start the context based problems (usually wordproblems) they are unable to apply what they have learned. In the study reported in this paper, a group of students were taught algebra through an approach that developed concepts through a series of problems based in a real world context. To assist with this alternative approach, students were given access to graphics calculators in all lessons. From the pre-test, post-test, interviews and observationwe see that students engaged with the context of problems, gained skills in using technology and made important progress in both their understanding of, and facility with, algebra. This paper reports on two different aspects of the impact of the teaching program: first the students’ response to the emphasis on contextbased learning and the use of technology, and second the influence of both thecontent and teaching approach on students’ understanding of, and facility with, algebraic symbols.

T HIS S TUDY The seventeen year 8 students (about 13 years old) who participated in this study were classified by their school as being of above average ability. In the experience of the class teacher, the range of abilities in this group was narrower than that of a standard class but there was...