Knowledge of different forms of complex numbers through quantitative reasoning: The case of teachers
Résumé
This study investigated the development of five secondary mathematics teachers' conceptualizations of different forms of complex numbers through quantitative reasoning in a PD program. We report from the pre and post-written sessions with the post-interview data upon completion of a 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 by mentioning 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. These results suggest that quantitative reasoning might lay a foundation for connecting different forms of complex numbers.
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