Abstract:

In this presentation I will share how I have created an active learning unit for preservice elementary education majors and for non- mathematics majors in a liberal education course to develop a conceptual understanding of the Jordan Curve Theorem.

Many undergraduate universities in the United States require preservice elementary education majors to take between 6 and 9 semester credits of mathematics applicable to teaching state required mathematics content, and most college and universities require all students to take a variety of courses which fall under the category of general education or liberal arts categorized for example as mathematical/logical reasoning, quantitative reasoning, quantitative literacy, quantitative or formal reasoning and various cognate category titles. A typical mathematical reasoning course offered in these various categories explores general topics that are accessible to non-mathematics majors include problem solving, logical reasoning, naive graph theory, descriptive statistics, introduction to sets, finance, geometry, and introduction to algebraic thinking.

In this paper, a pedagogical approach to introducing preservice elementary education majors and non-mathematics majors to the basic concept of the Jordan Curve Theorem. Although approaches to this topic via the winding number and the crossing number are readily available from a variety of both scholarly and popular sources through a web-search, none of the available resources outline pedagogical approaches that lead students to a conceptual understanding of this topic, nor lead these particular students to making conjectures based on observation and analysis of data through diagrams. This presentation fills that gap in the scholarly and popular literature with an approach taken in the context of both of these populations of students in the United States.

Keywords:

Pedagogy, active learning, mathematics, preservice teachers, liberal arts mathematics.