On the impact of the first generation of graphing calculators on the mathematics curriculum at the secondary level

Antonio R. Quesada

: Before the second generation of graphing calculators with true symbolic manipulation capabilities start influencing the mathematics classroom, it is important to ponder on the main contributions made by the first generation. In this note we present five of these contributions via a selection of examples that illustrate the impact of numerical and graphical capabilities, multiple representations and methods, and iterative and recursive solutions.

As it is usually the case, the fast pace of technology has brought to the market the second generation of graphing calculators before there has been time to fully analyze the impact of the first generation in the mathematics classroom. The recent introduction of the Texas Instrument TI-92, the first hand-held calculator with true symbolic capabilities, raises new questions on what changes, if any, are needed in the mathematics curriculum, and on how to appropriately integrate its use on the teaching of mathematics. However, the numerical and graphical capabilities of the first generation are kept in the second. Hence, it is appropriate to pause and reflect on some of the important lessons brought forth by the first generation; lessons not fully accepted, and for the most part not implemented yet in the curriculum.

There are many areas of the curriculum where the graphing calculator may have a serious impact on the teaching and learning of mathematics. In this note, five basic areas will be considered representative of this impact. The first area deals with the variety of approaches now available to solve problems, and, in particular, equations and inequalities. Next, the numerical and graphical contributions of these tools will be considered. The examples provided will show how these capabilities make possible the introduction at lower levels, of mathematical concepts and models, as well as problem solving methods, traditionally studied in upper levels by a smaller and more advanced audience. The fourth area considered treats the use of iteration and recursion, mainly in Home Screen.

The ability of displaying data or doing calculations using multiple representations facilitates students understanding (NCTM, 1989). Graphing calculators, in particular the later representatives of the first generation, are equipped with a variety of data structures that can store, manipulate and display data in many different ways. Functions and relations can also be represented using different coordinate systems. The fifth area of consideration investigates this flexibility in representing and manipulating data and relations in multiple ways. It will be illustrated by solving in different ways, using different representations, some of the examples included in the other four areas.

Several examples have been chosen within each of the first four categories. In each category the selection of problems was done so as to give an idea of the variety of applications possible, but by no means to exhaust the category. All the examples should be accessible to high school students. The syntax used in the commands and the screens provided in all the examples correspond to a TI-82. The screens included, sometimes in excess, will hopefully remove any doubts in reproducing the solutions provided.

Antonio R. Quesada

Quesada - 5 OCT 1996

There is a PDF file available for this paper.

Gómez, P. & Waits, B. (Eds.) (1996). Roles of calculators in the classroom.

Mail comments to Pedro Gómez: pgomez@uniandes.edu.co