An Activity Structure for Supporting Students’ Coordination of Computer Algebra Systems and Paper-and-Pencil Across Phases of Curriculum
By Nicole L. Fonger
Abstract: In this study I examine the issue of how to support students’ coordination of computer algebra systems (CAS) and paper and-pencil in solving mathematics problems. Together with a classroom teacher I designed and conducted a collaborative teaching experiment in a ninth-grade algebra classroom to understand how to support students’ coordination of tools. I introduce a predict-act-reflect-reconcile activity structure for coordinating CAS and paper-and-pencil in solving problems involving linear expressions and equations and adopt this as an analytic lens to examine the role of curriculum materials on impacting students’ learning. Findings suggest the activity structure of predict-act-reflect-reconcile is a potentially fruitful starting point for coordinating CAS and paper-and pencil in classroom activity, but not sufficient on its own as a task design principle without focused classroom discussion and support during the enacted curriculum. This research points to the importance of teaching students how to communicate about their process of using multiple tools while solving problems, especially the mathematical thinking that students engage in while reconciling differences across tool based representations.
Indicators of CAS use: Determining CAS use through analysis of written solutions
By Lynda Ball
Abstract: This paper provides a set of five indicators of CAS use, which provide a means to analyse a student’s written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra information by students about CAS use for solving problems.
Polynomial interpolation of functions: Introducing Chebyshev polynomials in a CAS laboratory
By Ivy Kidron
Abstract: In this paper I analyze students’ conceptual understanding of the quality of polynomial approximation. In particular, I analyze to what extent the interactive play with various methods of interpolation enables the students to build visual pictures that help understanding the formal mathematical statements. The role of the Mathematica software in enabling the students to visualize the theory is investigated as well as the importance of accompanying visual intuitions with the formal statement of the theory.
Teaching with Virtual Reality: Crafting a Lesson and Student Response
By Geoff Goehle
Abstract: This paper presents a “virtual reality” based lesson for a common Calculus topic, including a description of how the lecture was implemented in both a virtual reality and an augmented reality hardware system. This lesson was delivered to a number of calculus classes and we describe the student response to the lesson via a quiz and a survey. We conclude with some general impressions on this emerging technology.