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Teaching to the Mathematical Point: Knowing and Using Mathematics in Teaching

The ambitious vision of mathematical proficiency for all students demands skillful instruction that is too rarely found in American classrooms. The literature is replete with examples of teaching that fails to engage students in rigorous mathematical work: Teachers who adopt the surface features of new curricula, such as games and manipulatives, but do not use these materials to teach for understanding (Cohen, 1990); efforts to “make math fun” that result in art projects instead of mathematics (Hill et al., 2008); motivating examples and representations that distort the mathematics (Heaton, 1992); and problems intended to engage students in high-level mathematical thinking that deteriorate into lower-level and routine tasks as they are implemented (National Center for Education Statistics, 2003; Stein, Grover, & Henningsen, 1996; Stein, Smith, Henningsen, & Silver, 2000). In each of these examples, teachers seem to miss the mathematical point of the task or materials, or have difficulty maintaining the mathematical focus once the activity is in motion with students.

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