This semester I am teaching a transition level Modern
Geometry course. The prerequisite is Calculus I. The roster
includes mathematics majors, math majors seeking secondary education teaching
license, and non-major students seeking K-8 teaching licensure with a
concentration in mathematics. There both "traditional aged"
students and adult students in the course. The mix provides a wide level
of mathematical abilities, perspectives, and attitudes. Most of the
students do not have any formal learning experiences outside of Euclidean
geometry.
The course meets in 3-hour class sessions once per
week. I have designed the course to include small group discussions,
large group discussions, and writing. The purpose of these
discussion/writing assignments is to improve the students' ability to
communicate mathematics effectively and gain a deeper understanding of the
mathematics while increasing their ability to think more abstractly.
Each week, the students are given a question to discuss
on-line in small groups formed on Blackboard. The students participate in
their group's discussion for the week. During the subsequent class
period, the small groups organize their thoughts and then a representative
presents their thoughts to the entire class. A large group discussion
ensues. The topic of the question either leads into new material or covers a
topic that had been explored in the previous class period. For example,
the first discussion question was "As geometers, how do we want to
interpret the term "straight line?" (The idea for this question came
from Henderson's Exploring Geometry textbook).
In discussing the weekly questions, the students have to
write and talk about mathematics so that their peers can understand them.
I monitor the discussions and interject only if need be - namely, if there is
an incorrect idea that no one else corrects. This is not formal
writing or discussion, but it may build the students' confidence in discussing
mathematical ideas.
Formal writing will be evaluated in a project that the
students must submit by the end of the term. The project will consist of
several small assignments that lead up to either a research paper or the
creation of a teaching module. The students have the option to work
in pairs or alone on the project.
During the class hour, students pair up and explore
concepts using Geometer's Sketchpad. In this pairing, the students
discuss creating constructions and properties of given constructions.
Some lessons ask the students to derive conjectures and provide either informal
support or a proof for their conjecture.
Writing and discussion assignments are not unique to my
class, however, the use of Blackboard to get students to discuss ideas is
relatively new. In presenting at the joint meetings, I can share my
insights into using Blackboard for group discussion and perhaps create contacts
with people who have additional experiences and insights.