The Mathematical Association of America (MAA) and other organizations frequently stress the value of connecting and developing algebraic and geometric reasoning in K-16 mathematics.
For example, in the most recent Committee on the Undergraduate Program in Mathematics (CUPM) Curriculum Guide, the authors emphasize that “geometry and visualization are different ways of thinking and provide an equally important perspective … [which] complement[s] algebraic thinking … [and] remain[s] important in more advanced courses” (MAA, 2015, p. 12). Although complex analysis originated through formal extensions of real-valued algebra and analysis, discoveries of rich geometric interpretations revolutionized and extended the field. However, unlike other courses such as calculus, real analysis, and linear algebra these geometric connections are rarely highlighted in complex analysis textbooks.
In this presentation, I will share research related to the teaching and learning of complex analysis that that my colleagues and I have conducted over the past 10 years. Much of this research centers on how research participants can discover and develop geometric foundations of complex analysis, beginning with the product of two complex numbers and extending to differentiation and integration. Research participants include high school students, pre- and in-service teachers, undergraduate mathematics and physics majors, and mathematicians. As part of my presentation, I will offer some teaching implications.
Series: Mathematics Colloquium
Presenter: Hortensia Soto, Colorado State University