Guided Discovery in a Discrete Mathematics Course for Middle School Teachers

Abstract

We describe a discrete mathematics course for in-service middle school teachers taught exclusively using guided discovery. The article describes the structure and facilitation of the course itself and the set of notes used as a textbook. We discuss the benefits of using guided discovery with middle school teachers and student reaction to the experience. Introduction The Master in Teaching Middle School Mathematics (MSM) program at Salem State University is designed for middle school teachers who already have an initial license to teach grades 5–8 math in Massachusetts (or equivalent certification) and who wish to be eligible for professional licensure with certification in middle school mathematics. The program was established in the spring of 2004 under a Title II-B: Massachusetts Mathematics and Science partnership grant. We discuss the use of guided discovery in the MSM course in discrete mathematics, one of nine mathematics courses required for the degree. The courses provide the students with a deeper understanding of the mathematical content in or related to the middle school curriculum. In each course there is a emphasis on problem solving as well as some discussion of logical reasoning and proof writing. Most students in the MSM program have not majored in mathematics and their background in formal mathematics is limited. In the spring of 2008 the MSM discrete mathematics course was taught by Reva Kasman. In the class were twelve middle school teachers and one high school teacher. Only one middle school teacher had been an undergraduate math major and the high school teacher had minored in math. She chose a guided discovery approach for the course, with students using course notes written by Ken Bogart [2] and adapted by Mary Flahive [3] as a textbook.We describe the logistics of the class and reflect on the experience of teaching the course in this manner.