Enhancing Conceptual Understanding in Mathematics Through Lab Modules via Computer Algebra

Abstract

In recent years, Computer Algebra Systems (CAS) have revolutionized Mathematics teaching and learning through their powerful symbolic, graphic and numeric features. The last two decades have witnessed extensive research, which focus on the impact of CAS on mathematics instruction.

This paper describes a research study that examines the impact of integrating computer algebra (Mathematica) in a traditional teaching environment where using technology is not a common practice and where the prescribed curriculum emphasizes on developing ‘by-hand’ skills. The research focused on helping students visualize concepts, discover patterns and generalize results through Mathematica while developing ‘by hand’ skills thus maintaining a balance between the use of technology and paper-pencil techniques. This paper describes two exploratory lab modules. The first one deals with visualizing solutions of linear equations in three variables and was conducted with 40 students of year 11 while the second deals with exploring the application of fourier series to radio tuning and was conducted with 32 students of year 12. The activities were conducted in a lab were students were given access to Mathematica and were provided with specially designed worksheets which enabled them to explore the concepts in a step-by-step manner.

A structured feedback from the students at the end of each module revealed that Mathematica was instrumental in enabling them to obtain a deeper insight into the concepts. More importantly, the students’ eagerness to attend similar lab sessions for other topics provided encouragement for larger scale integration of CAS into traditional mathematics teaching.