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HINGES - An Illustration of Gauss-Jordan Reduction - The HINGES Activity - Background

Przemyslaw Bogacki

I have recently class-tested this activity in a section of an Introductory Linear Algebra course with 35 students, most of whom were distance students at remote sites. (The Teletechnet system  operated by Old Dominion University allows for one-way video and two-way audio connection using a satellite broadcast. Additionally, some students participated in this class via video-streaming on their home computers.)

To proceed cautiously the first time around, I chose to make this a very low-stakes extra-credit activity. I promised up to two extra points on a class test for a successful completion of the activity, which was meant to be just a token of appreciation, as it amounted to less than 0.5% of the overall course grade.

I presented these modules after row operations were already covered -- mostly from the algebraic point of view -- so that students were already familiar with terms such as pivot, pivotal column, leading entry and reduced row echelon form . However, in the course of this activity, there was no mention of Gaussian elimination or elementary row operations. It was meant to challenge students to think about this model from a purely geometric point of view at first, subsequently to make the connection to the algebra of row operations.

The activity was deployed in three stages, spaced two days apart from each other, using our Blackboard system. This gave me the opportunity to track access to each of the stages by the individual students. My depiction of the activity on the following pages was modified to make it Web-based (rather than Blackboard-based).

Przemyslaw Bogacki, "HINGES - An Illustration of Gauss-Jordan Reduction - The HINGES Activity - Background," Convergence (June 2005)