5.4. Reflection

"A mathematician is a machine for turning coffee into theorems."--Paul Erdös

This is a topic I looked forward to, and have enjoyed, teaching. Coordinates are something that all students in this class have seen in some form (2-dimensional Cartesian), and the idea of giving directions or specifying a location is also something that any student can relate to. Vectors are a more "advanced" topic that is nevertheless accessible at a pictorial level (as with the head-to-tail graphical addition method). Even better, both topics lead into fairly deep and heady mathematics, and I hope that I can interest students in taking advantage of the multiple paths of understanding open to them.

Unfortunately, as I found the textbook treatment computation- and procedure-oriented, I even now in the process of locating and devising material. I have been loath to create lesson plans in any further detail because every time I try to teach a topic, some interesting student question, confusion or misconception derails the plan. My cooperating teacher is willing to see me try a new approach with these topics, though I'm not sure if any of this can be considered to have worked, let alone well. Then again, this has been true all year, and there's only one reasonable way to find out.

As a unit lesson plan, this still needs considerable work. I can only say that I feel under some pressure to "innovate" in both the Integrated 1 and Integrated 3 classrooms at my placement, which are very different classes in terms of needs, background and curricula. So far, perhaps unsurprisingly, I have had very limited success with the prior (which is more constrained by district testing) and some success with the latter. While I agree with the sentiment, due to my unhappiness with some of the existing material and the students' interests I have been either creating extensive amounts of material or making heavy modifications, and this is true of this unit as well, where I feel the textbook is a good resource but remains lacking in terms of mathematical depth.

The integration of groupwork with somewhat open-ended and "real-life" activities should catch their interest, and perhaps that interest will sustain them through the more computational portions of the unit. The real test of this unit's effectiveness, as always, is the students' interaction with it. Their comments and feedback, glazed expressions and rapt stares, have guided me as they have throughout the year.

Copyright © 2002 Yoon Ha Lee <requiescat@cityofveils.com>
Last updated on 20 May 2002