Hortensia Soto-Johnson

Assessing Multiple Abstract Algebra Assessments

Abstract In this qualitative study, we initiate a discussion as to why instructors should implement numerous assessments into their mathematics courses. We describe the purpose and structure of formative and summative assessments implemented in an undergraduate two-semester sequence of abstract algebra. The evaluations included homework, exams, projects, oral assessments, worksheets, and presentations. We discuss students’ reactions to these assessments and summarize how the students believed the assessments contributed to their learning. We describe students’ perceptions of how the assessments measured their abstract algebra knowledge and helped them learn the material in an interactive environment. Through the students’ voices, we illustrate how the assessments promoted interaction among the students and modeled potential alternative assessments for preservice teachers.

Research to practice: Developing the amplitwist concept

Abstract Although students may develop extensive geometric intuition about derivatives during calculus, many complex analysis texts avoid geometric connections between the real and complex derivative. In this report, we discuss our implementation of, and student responses to, a Geometer’s Sketchpad lab that was informed by mathematics education research. This lab served to guide students towards discovering a geometric description of the complex derivative known as the amplitwist, and connecting this interpretation to the derivative of a real-valued function. We hope that instructors adopt aspects of this lab to promote a more dynamic, geometric perception of complex differentiation.

Game Building with Complex-Valued Functions

Abstract In this paper, we describe how we integrated complex analysis into the second semester of a geometry course designed for preservice secondary mathematics teachers. As part of this inquiry-based course, the preservice teachers incorporated their geometric understanding of the arithmetic of complex numbers and complex-valued functions to create a game using Geometer’s Sketchpad. We detail a game created by a pair of preservice teachers that exemplifies their creativity and knowledge of complex-valued functions. Given inquiry-based courses have inherent challenges we also present projects that were not as exemplary.

Assessing Proofs via Oral Interviews.

Abstract In this qualitative study, we explored how oral interviews can inform instructors about students’ understanding of abstract algebra and their ability to construct a proof in this setting. Our findings indicate that some students had a good understanding of the ideas needed for a subgroup proof, but could not write a coherent proof. One the other hand, these same students provided fairly sound verbal proofs. We discuss the implications of these results for teaching and future research.