Content area
Full text
In this article we present and describe a pedagogical framework that supports children's development of conceptual understanding of mathematics. The framework for Advancing Children's Thinking (ACT) was synthesized from an in-depth analysis of observed and reported data from I skillful Ist-grade teacher using the Everyday Mathematics (EM) curriculum. The ACT framework comprises 3 components: Eliciting Children's Solution Methods, Supporting Children's Conceptual Understanding, and Extending Children's Mathematical Thinking. The framework guided a cross-teacher analysis over 5 additional EM 1 st-grade teachers. This comparison indicated that teachers often supported children's mathematical thinking but less often elicited or extended children's thinking. The ACT framework can contribute to educational research, teacher education, and the design of mathematics curricula.
Key Words: Pedagogical knowledge; Professional development; Reform in mathematics education; Teaching (role, style, methods); Teaching effectiveness; Teaching practice
A broad-based reform movement focused on teaching and learning within mathematics classrooms and based on curricular and instructional recommendations of the Standards (National Council of Teachers of Mathematics [NCTM], 1989, 1991) is currently underway in the United States. One of the major aspects of this movement is the change from traditional classrooms that focus on students' acquiring proficiency in reproducing existing solution methods to classrooms that support instructional goals of helping students construct personally meaningful conceptions of mathematical topics. In another aspect of the movement, researchers examine the instructional changes required to create classrooms that foster children's development of conceptual understanding of mathematics, specifically, the redefined roles and new instructional strategies of classroom teachers.
Cobb and his colleagues have articulated the social norms teachers need to establish to create mathematics classrooms that focus on the development of children's thinking (Cobb, Wood, Yackel, & McNeal, 1992) and on the changing profiles of teachers' roles (Cobb, Yackel, & Wood, 1989; Yackel, 1995; Yackel, Cobb, & Wood, 1991). They emphasized children's engagement in personally meaningful mathematical activity, children's explanation and justification of personal solution methods, children's willingness and ability to make sense of their peers' solution methods, and children's collaborative work that focuses on challenging their classmates. Important teachers' roles in this type of classroom include establishing and guiding the development of these social norms, facilitating the discourse among students while they engage in collaborative problem solving, and supporting children's developing understanding of adequate...