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Developing Effective Mathematics Teaching: Assessing Content and Pedagogical Knowledge, Student-Centered Teaching, and Student Engagement

Abstract: The Mathematics Teacher Transformation Institutes (MTTI] program attempts to develop math teacher leaders in part by providing content, inquiry and leadership courses aimed at making them more effective teachers. We assessed progress by observing teacher leaders' teaching practices, and encouraging them to introduce or extend studentcentered pedagogy in their classrooms. We found there was little relationship between our measures of mathematics content knowledge and student-centered pedagogy. But teachers who employed student-centered pedagogy tended to have more highly-engaged math students in their classrooms.Keywords: effective mathematics teaching; math content knowledge; student-centered teaching; student engagement.Improving student achievement in mathematics and science has been a concern in the United States of America since the early 1980s when international tests began showing U. S. students falling behind most developed countries in mathematics and science skills. Many U. S. students do not obtain the knowledge and skills, particularly in science, technology, engineering, and mathematics (STEM), which are required for success in the global marketplace of the 21st century (National Academy of Sciences, 2006}.Educators, educational researchers, and policy makers have not always agreed about the reasons for the failure of U. S. students to perform. Some argue many mathematics teachers have inadequate mathematical content knowledge themselves, and thus are unable to teach their students to the highest level (Ahuja, 2006; Ginsburg, Cooke, Leinwand, Noell & Pollock, 2005]. Others (Darling-Hammond, 2007; National Council of Supervisors of Mathematics [NCSM], 2008; National Council of Teachers of Mathematics, 2000; Office of Science and Technology Policy, 2006; U.S. Department of Education, 2004; National Science Board, 2006), in part, relate such an educational failure not only to the lack of qualified teachers with solid content knowledge in STEM, but also to a profound lack of understanding of teaching and learning in grades K-12, which may lead to the use of ineffective teaching practices. For Brown and Borko (1992), and Ball and Bass (2000), understanding content knowledge and methods of inquiry in mathematics are at the core of effective teaching and learning. The use of inquiry-based approaches to instruction, in which students have opportunities to construct their own understanding of basic concepts, is thought by many educational theorists to be most appropriate in developing students' understanding of mathematics and science concepts. Such approaches call for teachers to be able to engage students in critical, in-depth, higher-order thinking through use of manipulatives, technology, cooperative learning and other pedagogical approaches that enable students to construct mathematics concepts on their own through reasoning, verifying, comparing, synthesizing, interpreting, investigating or solving problems, making connections, communicating ideas and constructing arguments (Grouws & Shultz, 1996; National Council of Teachers of Mathematics [NCTM], 2000). These approaches are characteristic of what is often called student-centered teaching as opposed to the so-called "traditional" approaches in which the predominant view is that mathematics teaching is a show-and-tell as well as a supervision of drills and practice (Davis, 1988). In this view, it is assumed that learning occurs passively when students absorb received knowledge from an all-knowing teacher or expert. This approach is often referred to as "teacher-centered." The Mathematics Association of America (MAA, 2008) argues that in order to prepare students for the increasingly complex mathematics of this century, a student-centered approach to teaching is more appropriate than the traditional teacher-centered approach. The MAA (2008) asserts the need to develop pedagogies that could be used effectively to facilitate students' mathematical abilities. …