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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.
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  and adapted by Mary Flahive  as a textbook.We describe the logistics of the class and reflect on the experience of teaching the course in this manner.
In this article we discuss the use of guided group discovery in Oregon State University's discrete mathematics course for math majors. Since Fall 2003 this course has been taught at Oregon State using an ongoingmodification of Kenneth P. Bogart's successful group discovery method and notes , “Teaching Introductory Combinatorics by Guided Group Discovery.” Section 2 summarizes Ken's notes and method, and Sections 3 and 4 respectively contain the adaptation of his notes and the implementation of his method at Oregon State.
Ken's prototype was a small elective course in which the average entering student was very motivated to learn the material. In our department the course is required, and it is financially unrealistic for us to expect either very small classes or in-class assistance from a senior student. We think our modification is sufficiently general that it can be successfully used by other mathematics departments with similar student demographics. Since the adaptation is an ongoing project, the interested reader is referred to  for current information on its status.
Ken generously served as a consultant for our adaptation of his method, both informally in Fall 2003 and during the first year of the grant. We are grateful for his help.
A Short Overview of the Bogart Course
The goal of Ken's project was to design notes and a method for teaching enumerative combinatorics in which “a large majority of the students would learn a large majority of the material of beginning combinatorics.”
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