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Concepts
Our project is aiming to understand the mathematical knowledge that is useful in teaching algebra, especially, knowledge that seems related to successful algebra teaching. We hypothesize that there are three broad domains of mathematical knowledge that are important, knowledge of school algebra, of advanced mathematics related to algebra, and a third, harder to define kind of knowledge we are calling "teaching knowledge." We hypothesize a universe of knowledge shown in the diagram below, and our research seeks to pin downmore definitively the relative positions of the elements of knowledge.
To understand the idea of "Advanced Mathematical Knowledge" for teaching algebra, we use the "funnel" shown below. Advanced knowledge includes both ideas that come after what is learned in algebra, and ideas that are foundational to algebra but may not be taught in middle or high school.
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