Functions, Algebra and Geometry for Middle-Level Teachers
Target Audience: This course was designed for teachers of middle level mathematics. The concepts of function, algebra and geometry are developed and therefore prior experience is not a prerequisite.
Graduate Credit Hours: 3
Usual Delivery Format: Two-week, on-site, summer course; taught in partnership with Inquiry into Teaching and Learning or Curriculum Inquiry
Texts: Beem, J. (2006). Geometry Connections.
Papick, I. (2007). Algebra Connections.
Description: This course builds upon Mathematics as a Second Language. Participants will obtain a deep understanding of the concepts of variable and function, utilize functions in problem solving, the theory of measurement (especially length, area, volume), and develop geometric modeling in algebra. Emphasis is placed on the ways in which these concepts develop across the middle level curriculum.
The course includes a number of classroom connections and classroom discussions (activities which teachers might someday use in their middle school classrooms). Both are designed to deepen the connections between the algebra and geometry being studied to the algebra and geometry in the middle school curricula. Excerpts from Standards-based middle school mathematics curricula are included in the texts to also deepen this connection.
Course Goals: The goals of the course are to introduce some basic concepts of number theory, modern algebra and geometry that underlie middle grades arithmetic, algebra and geometry. The primary goal is to help teachers gain a fundamental understanding of the key mathematical ideas that they will be teaching in the areas of functions, algebra, and geometry, so that in turn, they can help their students learn important mathematics. Attention is given to the need to further develop the “habits of mind of a mathematical thinker”.
Topics: include linear equations, functions, graphs of functions, inverse functions, composition of functions, quadratic functions, patterns, divisibility tests, the fundamental theorem of arithmetic, Euclidean geometry, measurement, area and volume, congruence, and similarity. The course will also explore ways to increase students’ visual literacy as a component of learning, understanding, and communicating ideas in mathematics.