Student Understanding of Complex Numbers

The purpose of this preliminary report is to (1) describe shifts in student conceptions of complex number over the course of a two and a half week instructional unit, and (2) discuss data that challenge some of our assumptions about how student conceptions develop around the complex plane. Our initial motivation for this study arose as a direct consequence of our experience teaching prospective high school mathematics teachers. Although these students are exposed to complex numbers as early as intermediate high school algebra, and continue to encounter them sporadically throughout their undergraduate education, student conception of complex number often fails to extend much past i = –1. This is particularly unfortunate in light of the fact that many of these students will become the teachers who will be introducing complex numbers to the next generation of students. An additional motivation for this study was the fact that a literature review did not reveal any empirical studies about student learning of complex number. Background Literature Although we did not find any empirical studies, we did find several sources that addressed the historical development of complex number, and hypothesized some of th