Teaching Complex Numbers in High School

Abstract

One of the mathematics standards for high schools stated in the Common Core State Standards Initiative (CCSS, 2010 Appendix A, p. 60) is the understanding of the Complex Number system, performing arithmetic operations with complex numbers, representing complex numbers and their operations on the complex plane, and using complex numbers in polynomial identities and equations. In this thesis, we trace back the history of complex numbers and formulate a set of problems based on the history. The thesis gives a description of the Common Core standards and goals. The exercises based on the history of complex numbers are shown to be in accordance with the Common Core standards. The different approaches to teaching complex numbers are described with examples. Their merits and shortfalls are discussed from a teacher’s mathematical perspective. A list of Guidelines on teaching complex numbers for high school teachers is given in the last chapter of this thesis.