Using an advanced graphing calculator in the teaching and learning of calculus

摘要

The purpose of this study was to investigate how the use of TI-Nspire~(TM) could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire™ for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire™, and the learning tasks, and how they lead to the learning of calculus. A design experiment was conducted in a class of 35 students from a secondary school in Singapore. Use of TI-Nspire~(TM) was integrated into the teaching and learning of calculus concepts in the classroom with the aid of TI-Nspire~(TM) Navigator, a wireless classroom network system that enables instant and active interaction between students and teachers. It was found that the appropriate use of graphical, numerical and algebraic representations of calculus concepts using TI-Nspire~(TM) enabled students to better visualize the concepts and make generalizations about relevant mathematical properties. In addition, the students were able to link multiple representations, especially algebraic and graphical representations, to improve their conceptual understanding and problem-solving skills. Six roles of TI-Nspire™ in classroom mathematical practice were identified from the findings of the experiment; TI-Nspire™ was used as an exploratory tool, graphing tool, confirmatory tool, problem-solving tool, visualization tool and calculation tool. This suggests that TI-Nspir~(TM) is a multi-dimensional tool that supports mathematics learning. Overall, the findings of the study indicate that TI-Nspire~(TM) is an effective tool to develop mathematical concepts and promote learning and problem solving.