The nature of preservice mathematics teachers' knowledge of students

Teachers need to be equipped with various knowledge and skills to establish and maintain effective teaching environments that enable them to enhance students' understanding and learning. Knowledge of students is one of the components of teachers' professional knowledge and it is defined as teachers' knowledge of what mathematical concepts are difficult for students to grasp, which concepts students typically have misconceptions about, possible sources of students' errors, and how to eliminate those difficulties and misconceptions. The purpose of the study was to investigate the nature of preservice mathematics teachers' knowledge of students. Six preservice teachers participated in the study and the data were collected in the forms of observations, interviews and written documents. The findings revealed that preservice teachers had difficulty in both identifying the source of students' misconceptions, and errors and generating effective ways to eliminate such misconceptions. They frequently failed to recognize what conceptual knowledge the students were lacking and they inclined to address students' errors by telling how to carry out the procedure or apply the rule to solve the given problem correctly. Therefore, preservice teachers should be given opportunities 1) to take content-specific courses that they have opportunity to discuss fundamental high school mathematics concepts in detail to gain a solid understanding of how mathematical concepts are related and why mathematical rules and procedures work and 2) to analyze an act of teaching by watching videos of classrooms or discussing a student work and classroom cases to determine how to address students' errors and misconceptions. (C) 2010 Published by Elsevier Ltd.