Reflection

Elizabeth Broder

Our goal in creating this project was to design a set of enrichment activities to enhance a typical unit on matrices.  We chose matrices because of the abstract nature of linear algebra.  During my student teaching, I taught matrices to my algebra II class, and it was the hardest unit I taught all year.  The textbook I used went through algorithms and rules for manipulating matrices, but provided few applications for the concept.  As a result, my students had a hard time understanding and conceptualizing the material.  Our hope is that these activities provide some concrete uses for matrices and matrix operations, both in mathematical contexts and in applications.

We developed three lessons for this unit.  The first connects matrices to geometry.  We developed this activity with the new Georgia Performance Standards in mind.  We hoped this activity would provide an interconnected approach to our topic.  The second lesson uses matrices in a more applied way.  My undergraduate degree is in economics, and I've always wanted to incorporate economic ideas into a lesson.  This project provided a wonderful opportunity for me to develop a lesson linking these two topics.  We also thought the island economy problem uses a skill many students struggle with - interpreting word problems.  We also feel this problem helps students make sense of a problem with infinite solutions in a very real way.  The third lesson in an extension of an activity Laura did during her student teaching.  It takes real world problems and develops them algebraically and graphically.

Before this class, I was less than enthused at the idea of using technology in my classroom.  I felt that technology was difficult to implement and that students would be too distracted by the mechanics of a program to make any useful connections.  Looking back, I felt this way because I'd never really used technology in my own learning.  In deveoping these lessons, I was able to make new connections about an already familar subject.  The key to technology is involving the students.  By that I mean, students need to actively participate in the activity and not just watch a demonstration.  I feel that the activities we've devoped will truly enrich a typical matrix unit and help students make connections.

The only potential problem I see with using these types of activities regularly in the classroom is the amount of time they take to develop.  Alot of time and thought went into creating these lessons and deciding exactly what connections we wanted to emphacize.  With as much time as these took, they only provide one weeks worth of instruction.  As a first year teacher, I feel that a good goal for me is to use at least one exploration of this type in every unit I teach.