Prospective Elementary Mathematics Teacher Content Knowledge: An Introduction

The first and fundamental requisite for every teacher is that he have thorough command of the subject matter which he teaches; that he have mastered it so well that he speaks with his own authority; only so can he hope to lead the pupil to the corresponding feeling of independent mastery.-j. W.A. Young, 1920This Special Issue on the mathematical content knowledge of prospective elementary teachers (PTs) provides summaries of the extant peer-reviewed research literature from 1978 to 2012 on PTs' content knowledge across several mathematical topics, specifically whole number and operations, fractions, decimals, geometry and measurement, and algebra. Each topic-specific summary of the literature is presented in a self-contained paper, written by a subgroup of a larger Working Group that has collaborated across several years, resulting in this Special Issue sharing the final work. The authors hope this summative look at prospective teacher content knowledge will be of interest to the mathematics education community and will be a useful resource when considering future research as well as designing mathematics content courses for prospective elementary teachers.The following sections in this issue provide background information on our overarching framework for the mathematical content knowledge of prospective elementary teachers as well as our rationale for conducting the summary of research. We briefly describe the intent and history of the Working Group that conducted the summaries, followed by the methods utilized in the summary process. Finally, we provide a description of what follows in each subsequent paper and close with our intentions of how this Special Issue might be used by our readers.BackgroundThe mathematical preparation of K-8 students is a challenge both in the United States and internationally. Studies from many countries report students coming away from their elementary education having memorized facts and procedures with varying degrees of success but not developing robust mathematical conceptions or flexibility in their reasoning (e.g., Reys et al., 1999; Stigler & Hiebert, 1999}. Students who struggle in school mathematics have limited career options. Even those who perform well in mathematics courses are unlikely to enjoy mathematics or take an interest in science, technology, engineering, and mathematics careers if they experience the subject as dry and procedurally focused. Mathematics instruction can emphasize conceptual understanding and the engagement in mathematical practices. In order to positively influence the direction of mathematics teaching and learning, our elementary teachers must be adequately prepared.Research over the last few decades has shown that the work of teaching mathematics requires a different knowledge base than the mathematical knowledge required for other professions (Ball, Hill, & Bass, 2005; Ball, Thames, & Phelps, 2008; Conference Board of the Mathematical Sciences [CBMS], 2012]. Ball and her colleagues identify this knowledge as Mathematical Knowledge for Teaching (MKT], which they define as the "mathematical knowledge needed to perform the recurrent tasks of teaching mathematics to students" (Ball et al., 2008, p. 399]. They developed a framework for MKT consisting of two domains, subject matter knowledge and pedagogical content knowledge (see Figure 1].For these summary papers, we chose to focus primarily on what could be considered prospective teachers' subject matter knowledge, or content knowledge. Included in mathematics content knowledge are Common Content Knowledge (CCK], which is described as the mathematical knowledge that everyone should know; Specialized Content Knowledge (SCK], described as the mathematical knowledge that is special to the work of teaching; and Horizon Content Knowledge, which is an understanding of how mathematical topics fit together and make up a curriculum. In addition to these three types of knowledge, we also include Knowledge of Content and Students (KCS], which involves understanding students' thinking and difficulties with mathematics. …