workshop for high-school and middle-school teachers
by Kelly Gaddis, Bard College
Long Beach Project in Geometry and Symmetry
Mathematics Department, CSULB
a series of open-ended problems through construction and
learning that builds upon intuitive conjectures, allows for diverse
ideas, and uses physical models and small group discussions to
investigate and convey ideas.
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?
spheres and crocheted hyperbolic planes.
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.
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.
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.