CHAPTER 3: Using Children’s Thinking to Develop Mathematical Content Knowledge

Elementary teachers spend a substantial amount of time talking to children and listening to their explanations in order to interpret their mathematical reasoning. As they talk and listen, the teachers have to assess the mathematical understandings of their young students and make instructional decisions in the moment. With years of experience, this listen-assess-teach process becomes more fluid and productive as teachers develop a deeper mathematical understanding, modify their instructional practices, and refine their assessment skills. In other words, teachers develop their mathematical knowledge for teaching, in part, through experience. In mathematics education, mathematical knowledge for teaching is seen as having two domains, pedagogical content knowledge, which teachers acquire primarily in methods courses, and mathematical content knowledge, which teachers primarily acquire in mathematical content courses (Hill, Rowan, & Ball, 2005). A recent summary of research on the mathematical content knowledge of prospective elementary/middle school teachers (Thanheiser et al., 2014) shows that they usually possess procedure-based knowledge for solving mathematics problems without fully understanding the main mathematical ideas behind their strategies. Also, prospective teachers usually take courses of mathematics content and mathematics teaching separately (Silver, Clark, Ghousseini, Charalambous, & Sealy, 2007). Thus, it should come as no surprise that prospective elementary teachers often come to believe that memorizing formulas, following rules, and getting correct answers are the main focus of teaching and learning mathematics, and experience difficulty in making connections between content knowledge and pedagogical knowledge of elementary school mathematics. In this chapter, we focus on the development of mathematical content knowledge through an “applied” perspective for the prospective elementary teacher by examining children’s thinking.