This workshop is designed for secondary mathematics teachers and leaders who want to take a broader look at conceptual difficulties facing their students. The sessions will be interactive and participants will be expected to work on problems so that their thinking will provide the basis for discussion. In order to help participants consider new approaches, the program will include in-depth examination of several instructional sequences in algebra and geometry. This collaboration with Bill Jacob will prove to be a model for effective development of mathematical ideas aligned with the California Standards for mathematics.
The first day of the workshop will survey ideas that students struggle with when first learning algebra and functions. The workshop will examine the use of representations to help students make sense of these ideas and will illustrate how the use of context can help students develop mathematical ideas, including how context can be incorporated into an instructional sequence to raise concepts. These same ideas will be extended to the two-variable setting where they continue to be critical in secondary and college mathematics.
The ideas developed on day one will be extended to topics beyond first year algebra. To provide context for the discussion two instructional sequences will be examined; one on constrained linear optimization, and a second on transformational geometry. There is a growing library of online materials (many with Creative Commons License) and the goal for the day will be to help participants think through how to use these materials effectively.