Mathematical thinking in multivariable calculus through blended learning

Abstract

Blended learning is proposed as a sufficient environment in supporting students’ mathematical learning based on mathematical thinking. This research explores a blended learning model for teaching and learning of multivariable calculus in fostering students’ mathematical thinking based on the data gained through the preliminary investigation, the existing model, and integrating creative problem solving. The main purpose of this research is to identify the effectiveness of the blended learning in developing and supporting students’ thinking powers in the construction of mathematical knowledge, problem solving, and in reducing their difficulties in multivariable calculus course. The theoretical foundation of the three worlds of symbolic, embodied, and formal mathematics was adopted to develop strategies for mathematical knowledge construction and to enhance students’ mathematical thinking. Sixty two first year engineering students participated in this study. Data were collected via think-aloud verbal protocols, students’ written solutions to assessments, semi-structured interview, students’ web comments, and semi-structured questionnaire. The findings revealed that the students’ mathematical knowledge construction and problem solving had improved. They could overcome their difficulties in the learning of multivariable calculus. The data collected also showed that students used mathematical thinking activities and multiple representations of mathematics worlds, especially the symbolic and the embodied worlds, when solving the problems.