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This paper investigates the nature of mathematical understanding that is needed to teach three foundational early algebra topics. These three topics include dividing fractions, linear equation in two variables and its graph, and quadratic function and its graph. Data from a sample of undergraduate STEM majors in a major research university affirm the importance of developing what Shulman (1999) calls "far more effective mathematics courses in U.S. undergraduate program" in order to equip future mathematics teachers with profound mathematical content understanding for teaching fundamental mathematics (Ma, 1999).

Chew on why 13/7 = 13 ÷ 7 as we explore two classroom lessons that develop conceptual understanding by building on children's knowledge of whole-number division.