Abstract
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).
Highlights
This paper investigates the nature of mathematical understanding that is needed to teach three foundational early algebra topics
Subject matter knowledge plays a central role in teaching (Buchmann, 1984)
The paradox begs the question: What is the nature of mathematical content understanding that is needed in order to teach middle school and high school mathematics? What does this mathematical content understanding look like? This paper addresses these questions through an empirical study of a sample of undergraduate STEM majors at one of the research universities in the west coast of the United States
Summary
This paper investigates the nature of mathematical understanding that is needed to teach three foundational early algebra topics. Subject matter knowledge plays a central role in teaching (Buchmann, 1984). Shulman (1986) regarded content as “the missing paradigm” in research on teaching. Despite the fact that subject matter knowledge is central to teaching, content knowledge rarely figures prominently in research or teacher preparation programs (Ball, 1990; Harel, 1993). To address this “missing paradigm” on teaching, Shulman proposed several types of knowledge teachers need in order to teach.
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