Developing Mathematical Thinking: Changing Teachers’ Knowledge and Instruction

Abstract

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and statistics. We also examined the relation between mathematical knowledge and teaching practices. Across the three domains neither pretest nor posttest mathematical knowledge were related to classroom teaching practices. However, change in knowledge was positively related to six different dimensions of teaching practice for number and operations, and for measurement and geometry; and was positively related to four or six dimensions for probability and statistics. That is, those teachers with greater changes in knowledge demonstrated more effective instruction.

Can teachers accurately predict student performance?

“…Developing Mathematical Thinking (DMT) is an instructional model that hinges on five key dimensions of classroom practice: focusing on students' initial ideas through problem solving, encouraging multiple solution strategies and models, pressing students conceptually, maintaining a focus on the structure of the mathematics, and addressing misconceptions (Brendefur, 2008;Brendefur, Thiede, Strother, Bunning, & Peck, 2013). DMT was chosen for this study because this multidimensional framework for teaching encourages teachers to monitor their students' mathematical ideas and to then modify their instruction based on what they observed from several perspectives.…”

The Importance of Spatial Reasoning in Early Childhood Mathematics

“…The Developing Mathematical Thinking Institute (DMTI) offers a comprehensive curriculum designed to encompass all of these components for students to develop procedural and conceptual understandings. The DMTI curriculum is an alternative to the typical curriculum for teaching mathematics to help teachers develop a different approach to how mathematics is taught [71].…”

The Effects of Professional Development on Elementary Students’ Mathematics Achievement

“…Thus, before building a model for conducting professional development in mathematics, we examined instructional structures that we wanted to observe in teachers' classroom practices. From these structures we then proceeded to build a professional development model to encourage teachers to promote these instructional structures (Brendefur et al, 2013).…”

“…Change in knowledge was determined to be positively related to dimensions of teaching practice for number and operations, measurement and geometry, probability and statistics. That is, those teachers with greater changes in knowledge demonstrated more effective instruction Brendefur et al, 2013).…”