Teachers’ knowledge of different forms of complex numbers through quantitative reasoning

ABSTRACT

This study investigated teachers’ conceptualizations of different forms of complex numbers in a professional development study (PD) conducted with classroom teaching experiments focusing on quantitative reasoning. We report from five secondary school mathematics teachers’ post-interview data and the post-written sessions upon completion of the PD. Results showed that all the participants could relate the formal definition of complex numbers with the roots of quadratic equations both algebraically and geometrically. Participants could also explain the Cartesian and polar form relationship using vectors with connections to the roots of quadratic equations. They further explained the Euler form by pointing out that the polar form of any complex number on a circle determines a function of Θ from R to C. Albeit making connections, results also pointed to some teachers’ difficulties in certain points. Altogether, results suggest that quantitative reasoning might lay a foundation for connecting different forms of complex numbers. We discuss implications for curriculum, teaching, and teacher education.

KEYWORDS:

• Complex numbers
• teacher knowledge
• quantitative reasoning

Acknowledgements

This paper is based on work supported by Boğaziçi University Research Project under Grant No. 19350. Opinions, findings and conclusions in this paper are those of the authors and do not necessarily reflect the views of the funding agencies.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Gülseren Karagöz Akar

Gülseren Karagöz Akar works as an Associate Professor at the Department of Mathematics and Science Education at Boğaziçi University, Turkey. Her research interests focus on the learning of mathematical concepts through quantitative and covariational reasoning, the development and nature of mathematics teacher knowledge mostly at the secondary level.

Mervenur Belin

Mervenur Belin is a research assistant at Boğaziçi University, Department of Mathematics and Science Education. She is also a Ph.D. candidate in Mathematics Education at Middle East Technical University. She studies pre-service and in-service mathematics teachers’ quantitative and covariational reasoning and specifically focuses on how mathematics teachers’ reasoning affect their knowledge of and their teaching practices in algebra.

Nil Arabacı

Nil Arabacı is a Ph.D. Candidate at the Department of Mathematics and Science Education at Boğaziçi University, Turkey. She is interested in task design, teaching functions, interdisciplinary science and mathematics education.

Yeşim İmamoğlu

Yeşim İmamoğlu is an Assistant Professor of Mathematics Education at Boğaziçi University, Turkey. She holds Bs. and MSc. degrees in mathematics. Her research interests include the development of mathematical thinking in students and teachers, processes of constructing and evaluating mathematical proofs, problem solving, mathematical modeling, and interdisciplinary mathematics education.

Kemal Akoğlu

Kemal Akoğlu works as an Assistant Professor at the Department of Mathematics and Science Education at Boğaziçi University, Turkey. His research interests focus on teaching and learning of probabilty and statistics and the role of technology in mathematics education, as well as cognitive processes in mathematocs education.