Exploring Geometry

A workshop for high-school and middle-school teachers

10AM-3PM          26-27 June 2008

Directed by Kelly Gaddis, Bard College

Hosted by the

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.



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.