Saturday, October 6, 2007

CCTM- Proportional Reasoning

presented by Jimmy Frickey and Russ Rendon, Eagle Rock School based on chapter of John Van deWalle's book Elementary and Middle School Mathematics, teaching developmentally.
Even if the title suggests otherwise, I think this may be one of the most important books I should read to be a better high school math teacher--as judged by student success. I'd like to see if we have any copies available through the district and if anyone else is interested in doing a PL book study--all contents included.
Takeaways:
  • Proportional reasoning is the cornerstone of Algebra*
  • A key developmental milestone is the ability of a student to begin to think of a ratio as a distinct entity, different from the two measures that made it up.*
  • Elementary focuses on relationships resulting from adding and subtracting whereas proportions involve multiplicative relationships.
  • Proportional thinking is not "cross multiply and divide"
  • Proportional thinking is recognizing direct and indirect correlations, quantitatively and qualitatively.
  • Proportional thinking is evident in fractions, similarity, indirect measurement, data graphs, probability, percents, rates, linear relationships, trig and many more math concepts as well as other contents. Proportional thinking is in many science topics, including biology and chemistry, art such as mixing colors on a color wheel in different proportions to determine the desired color, health since there are so many rates involved, economics, including unemployment rates and interest rates, social studies, such as currency exchange rates, bad press vs number of votes, allocation of resources-is it proportional? etc...
  • Incorporating Proportional reasoning in other subjects can enhance most other contents.
  • It is estimated that more than half of the adult populations cannot be viewed as proportional thinkers.* It might be interesting to have the students "quiz" other teachers and staff so and start a community initiative, so they students feel not so alone in the endeavor and appreciate its importance in seeing other adults make efforts to learn it.
  • Premature use of rules encourages students to apply rules without thinking and, thus, the ability to reason proportionally often does not develop.*

*Taken directly from copy of John Van deWalle's book.

What do you think? Anyone interested in a PL book study? How can we get this message across to the whole school or community?

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