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A Four-Stage Model of Mathematical Learning

A Four-Stage Model of Mathematical Learning

By Jeff Knisley of East Tennessee State University, this 2002 article outlines Knisley's own model of mathematical learning based on his own research and observation in hopes that it will be used "to guide the development of curricular and instructional reform." Knisley believes that each of us passes through four stages of understanding as we acquire new knowledge: Allegorization, Integration, Analysis, and Synthesis. Each stage is discussed, with examples, in detail. In addition, Knisley delves into the roles of both teachers and technology in these stages. The article is rounded out by a thorough bibliography for further investigation. This is a helpful resource for mathematics educators to understand how their students process and make meaning out of new material in the classroom.


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