urban teaching
urban teaching
This is a point of entry to several papers I wrote in the course of teaching.
Geometry Patterns
Creating this paper was a one-year project that required another year to refine, and it is still a work in process. I wrote it for two distinct reasons.
1.Our one-size-fits-all Geometry textbook weighed five pounds. This was not so different from the weights of the textbooks for other courses my students were taking. Many of my students were not taking the books home to do homework and were not bringing them to class, or they would simply leave them in the classroom. Although some of my colleagues built courses around the assumption that students would take their books home to do homework and bring them to class each day, only a few of my exceptionally motivated students were doing this. (One enterprising student submitted a formal request--with an ostensible medical basis--for a second book to keep at home; it was granted.) I felt compelled to create a course around handouts reproduced from the worksheet masters provided with the textbook plus materials I originated. "Geometry Patterns" became my 21-page version of "CliffsNotes"(R) for the course, containing all the principles for which the students were to be held responsible, (For the usual end-of-year reasons the chapters on measurement did not make it into the document.)
2.In mathematics in general, and particularly so in Geometry, solving a problem starts with recognizing a pattern that leads you to a principle you have learned and that you can then apply. There seem to be three distinct pattern-recognition skills required for Geometry, and I could not assume that any given student was strong in all three skills: 1)the English description of the principle, 2)a picture illustrating the principle, and 3)an algebraic or other formal expression of the principle. The Pythagorean Theorem offers an example. 1:”The Pythagorean Theorem: The measure of the hypotenuse of a right triangle is equal to the sum of the squares of the measures of the two legs of the triangle.” 2:a picture of a right triangle with the sides labeled, perhaps with the classic three squares one of whose sides coincides with a side of the triangle. 3:“c squared = a squared + b squared.” I felt it would be useful to organize the three patterns for each principle so that the student could use any of the three recognition skills as a point of entry to find a principle. This led to the three-column form of the document in which each row describes one principle.
The latest version of the Geometry Patterns document is a 1.6 MByte pdf file. You can obtain it by clicking here.
I have licensed this and other documents referenced here under a Creative Commons Attribution-Share Alike license. You the reader are therefore invited to copy, distribute, and improve upon them subject to the provisions of the license. This is an "open source" license in the sense that I am willing to cooperate with educators intent on improving this work under the license by providing, for example, the original source materials used to create the pdf file. There is no restriction to non-commercial use. My attribution specification: any copy or derivative work must accurately display the document’s copyright notice.
Linear Function Worksheet
Use of this worksheet succeeded in engaging several of my most discouraged students. It teaches that three mathematical forms: linear graph, linear table, and linear equation are just three views of the same underlying object: a linear function. (I have a chimp-in-the-box lecture explaining what a function is that I have not yet written up.) After a little practice I could give a minimum amount of information in any of the three forms and the students would fill in the whole sheet. There is a natural segue from this activity to understanding how slope and intercept look in all three forms. The pdf file is here.
Units in Measurements
I have felt that there must be a way to convey to my students the ease in calculating with physical units I had developed as an undergraduate Physics student. This ease can be creative; for example, it makes unit conversions and rate problems trivial. Most students acquire this ease by osmosis if they acquire it at all; I was looking for a way to teach it explicitly. I wrote this paper when I realized that a “measurement” is not a number but is something more inclusive than a number, and that the additional thing, the unit word, can be treated exactly like a prime factor of a number. The pdf file is here.
© Copyright 2008 Mel Conway PhD
Some Resources
Tuesday, February 26, 2008