Online Small Group Discussions In Geometry

 

Matthew J. Haines, Augsburg College

 

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.