Exploring Geometry

A workshop for high-school and middle-school teachers

Directed by Kelly Gaddis, Bard College

Long Beach Project in Geometry and Symmetry

Mathematics Department, CSULB

Explore a series of open-ended problems through construction and experimentation.

Experience learning that builds upon intuitive conjectures, allows for diverse ideas, and uses physical models and small group discussions to investigate and convey ideas.

Investigate the geometry of surfaces. What's straight? What’s an angle? What’s the sum of the angles of a triangle on the Euclidean and hyperbolic planes, a sphere, a cylinder, a cone?

Use physical models--Lenart spheres and crocheted hyperbolic planes.

Engage in small group collaborative inquiry.

Develop visual and spatial thinking.

Rationale  Mathematical investigation starts with a problem situation and an intuitive sense or conjecture about how to proceed. Studies of mathematical thinking have found that the essence of understanding can often be found in reasoning and justifying. The challenge to justify a claim can trigger reflection about reasoning. In many mathematical contexts, reasoning and proving are simply ways of making sense out of an experimental result, either by convincing oneself or convincing others. However, reasoning through problem situations and convincing others of one’s findings are not common or central learning goals in schools.

Goals

• Provide teachers with an opportunity to be learners of mathematics who reason and prove as a primary mode of mathematical inquiry.

• Acquaint or reacquaint teachers with these mathematical practices while learning new geometry.

• Use those experiences to consider how reasoning and convincing can in turn be central to their own students’ experiences of mathematics.

Specifics

Enrollment limited to fifteen. Preference given to high-school or middle school teacher (in-service or pre-service) with an expressed interest in exploratory learning.

Stipends available--$100 per day.