Chapter 8: Research-Design Interactions in Building Function Probe Software

Over the period of 15 years, our research team¹ designed and built Function Probe,² a multirepresentational software for teaching introductory functions to students in Grades 4 to 14. Originally developed to support a precalculus course at Cornell University and the mathematics classes at the Apple Classroom of Tomorrow (ACOT) in Columbus, Ohio, Function Probe was designed to support student thinking about, and exploration and understanding of families of functions, including linear, quadratic, exponential, polynomial, rational, and trigonometric. The software was built to permit students to explore the contrasting and complementary appearance and behavior of these functions using different representations. With research and development support from numerous sources,³ we designed the software to respond to students’ own inclinations to act in applied problem-solving settings and to permit them to explore the results of their actions. Fortunately the design work coincided with a very active research field to produce opportunities to experiment with novel approaches and to assess the results. A group of talented graduate students undertook a variety of studies that made such investigations possible. Function Probe was constructed through multiple rounds of design and research, which served to clarify how students thought about functions, how they can learn about functions in improved ways, and thence to inform subsequent rounds of design of the software’s features. In this chapter, we review some of the more original design innovations in the software and discuss their interactions with the research process.