Much more than a toy.
Graphing calculators in secondary school calculus

Thomas P. Dick

Graphing calculators are too often dismissed as mere "toys" compared to powerful computers. However, their accessibility in terms of portability, user-friendliness, and cost have resulted in an influence and impact on mathematics education that has far exceeded that of computers. This paper discusses the profound impact that graphing calculators have had in secondary school calculus instruction. We draw on the experiences of the Calculus Connections Project involving over 400 secondary school teachers in the U.S.A. using graphing calculators to teach calculus from a "multi-representational" viewpoint. We also note ways in which graphing calculators can be used for visualization in more advanced mathematics instruction and how the latest generation of hand-held devices has evolved to become true mathematics learning machines.

The Advanced Placement (AP) program provides opportunities for secondary school students to earn college credit or advanced placement in college courses at many colleges and universities in the United States. While there is not a "national curriculum" for calculus in the USA, the AP course description could almost lay claim to that title. Of the approximately 600,000 students who enroll in calculus courses in the USA each year, approximately 120,000 are high school students who take the Advanced Placement examinations in calculus.

The Advanced Placement program is in a unique position in the current era of curriculum reform in calculus. On the one hand, the program's credibility depends heavily on having a course description (and an examination assessing student performance on the course) that reflects a solid college-level calculus course. However, the variation in college calculus courses is probably at an all-time high with several different reform projects being undertaken around the country. Hence, to attempt to keep pace with reform, the AP program has had to implement its most profound changes in thirty years, including the requirement of graphing calculators on its examinations and substantial changes in the philosophy and direction of its course description.

In this paper, I will concentrate on the changes in secondary school calculus for which I feel the graphing calculator has been a catalyst. These include the manipulation of the viewing window of a graph as a basic instrument of investigation of function behavior. In particular, the notion of local linearity, a common theme of many calculus reform projects, has profoundly changed the basic approach to differentiation. Exploitation of this simple yet powerful idea has also motivated an earlier introduction of slope fields and Euler's method to the calculus course (topics formerly postponed until more advanced differential equations and/or numerical analysis courses). Numerical computational power has enabled a new emphasis on modeling to emerge. I will argue that these changes reflect much more than the mere addition or replacement of topics in a syllabus---they change the dynamics of the classroom and give us new eyes with which to see the fundamental power of calculus.

Thomas P. Dick

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