For those who are wondering what future math teachers learn in ed school, here is a concise summary:
Traditional mathematical teaching has never worked and has failed thousands of students.
The standard ed school catechism is that traditional math teaching is based on rote memorization with no understanding, and no connection between concepts. Another is that the conceptual underpinning of math procedures are not explained. According to ed school teaching, procedures are presented as a “bag of tricks” (such as “keep, change, flip” for dividing fractions). The evidence presented is simply that many adults do not remember how to solve certain problems. This stands as proof that the traditional methods are not effective–if they were, they would “stay with us.”
That people do not maintain proficiency in math as they age says less about traditional or reform math than about the way in which a population’s knowledge and skill base…
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