Abstract

From the theoretical framework of Realistic Mathematics Education, action research was conducted at a public high school. Three sections of precalculus started a unit of trigonometry by modeling the motion of an animated Ferris wheel in The Geometer's Sketchpad. A fourth section followed the design of the course textbook. Student reflections were collected periodically throughout the unit. In addition, interviews were conducted with students from the experimental and comparison classes. From the data analysis, common themes emerged. Students routinely commented concerning the benefits of the unit being linked to a real life, the process of developing the mathematics, and the specific benefits afforded for graphing trigonometric functions and use of the unit circle.

In addressing the questions of the study, the evidence shows the potential power of a contextual realistic problem solving scenario as the instructional starting point for a trigonometry unit of instruction. The Ferris wheel supported the concepts of amplitude, period, and the general behavior of the graph increasing or decreasing through various angles. The data reveal that the students more than simply recognized these connections while looking at the Ferris wheel. Even though not all students availed themselves to the contextual footholds, many took advantage of the context to support their thinking concerning the unit circle and the graphing of trigonometric functions.

Since the context was the starting point, the Ferris wheel supported the developing understanding of the students by allowing many students to shift from considering the animation as a model of trigonometric functions to a model for trigonometric functions. With the rich initial experience, students built upon this foundation to generate connected and flexible understanding of graphing trigonometric functions and effectively using the construct of the unit circle.