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Coordinates & Vectors Unit
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Summary Reflection
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"A mathematician is a machine for turning coffee into theorems."--Paul Erdös Introduction
The teaching event was based on the first three lessons of my Curriculum Unit: Coordinate Systems & Vectors. These lessons attempted to introduce the necessity and utility of coordinates in a gentle manner by having students give directions from point to point in the confines of the classroom, then devise their own coordinate systems for board games. This motivated the introduction of polar coordinates as an example of an alternate to Cartesian coordinates, leading into conversions between the two to illustrate their description of the same underlying space.
Later in the unit, with those lessons and subsequent ones as a foundation, students wrote LETTER TO ZAP #1 to explain either a polar-to-Cartesian or Cartesian-to-polar conversion. Afterward, based on a set of criteria [link], students graded each other's letters and gave feedback [link] on the grade writeups.
The mathematical goal was for students to demonstrate their understanding of both sets of coordinates and their ability to articulate it in a written form, and check others' letters for accuracy. In addition, I wanted (perhaps selfishly) to give students the opportunity to grapple with the issues of assessment, as they had to decide what was important in assigning a grade. While I did give them the basic criteria, students had the freedom to allocate points (even extra credit) as they saw fit. Finally, students gave feedback on the grad sheets they received for their letters, so they were involved in all parts of the process.
The following relevant materials come from the Curriculum Unit, referenced here for easy viewing:
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