Fostering mathematical thinking through a computer algebra system in a differential equation course

Abstract

This study explores the effects of a computer algebra system on students’ mathematical thinking. Mathematical thinking is identified with mathematical thinking powers and structures. We define mathematical thinking as students’ capacity to specialize and generalize their previous knowledge to solve new mathematical problems. The study was conducted in three phases: a preliminary study, a teaching experiment (main study), and task-based interviews (follow-up study). In the first phase, we intended to get to know students’ levels of mathematical thinking; the second phase sought to promote students’ mathematical thinking; and the final phase was designed to help us identify the enhancement of students’ usage of their mathematical thinking powers. A test was conducted at the preliminary study, a teaching experiment was run at the main study, and task-based interviews, like those in the main study, were conducted in the follow up phase. The main study’s participants were part of an undergraduate differential equations class in Malaysia. The worksheets used in the main and follow up studies were designed by the researchers, based on the instrumental genesis, prompts, and questions to be used in the teaching experiment sessions. Qualitative data analyses showed that using a computer algebra system for learning differential equations had a positive impact on the development, identification, and usage of students’ mathematical thinking. Moreover, it was revealed that the students applied specializing powers, imagining, expressing, changing, varying, comparing, sorting, organizing, and checking the calculation in general to make sense of mathematical structures. The findings could be incorporated not only in the mathematics curriculum at the tertiary level but could also be extended to k-12 schools.