Obstacles in the Learning of Two-variable Functions through Mathematical Thinking Approach

Function of several variables is one of the most important concepts in mathematics and its applications. The lack of its understanding will cause certain obstacles in the learning of next concepts or even subjects. The researchers at Universiti Teknologi Malaysia (UTM) tend to support students to overcome their deficiencies in the learning of two-variable functions by promoting mathematical thinking. The purpose of this study is to demonstrate how this method can help students in the learning of two-variable functions when they encounter non-routine problems in face-to-face Engineering Mathematics (Multivariable Calculus) course through this method. The data collection for this study was collected from a Multivariable Calculus class at UTM during semester II 2009-2010. Data collection for the study was carried out through written assessments and structured questionnaires. The data analysis reveals that students still display difficulties in their learning. Specifically, students’ common difficulties are: students’ met-before (previous experience), selecting appropriate representation of the three worlds of mathematical thinking, the transition from one world to another world of mathematical thinking, lack of understanding two different embodiments, and lack of understanding two different symbolic for a concept. The findings reveal that the sketching the graph of two-variable functions in 3-dimensions is the greatest difficulty for majority of students in this method. Additionally, the quite entrenching of students in their learning behaviour and styles is the most important reason for the lack of using prompts and questions as guides by students and then no enough effectively of this method.