Promoting an understanding of multiplication of fractions has proved difficult for mathematics educators. I discuss a research study aimed at developing a concept of multiplication that supports both multiplication of whole numbers and multiplication of fractions. The study demonstrates how domain-specific theories grounded in two major…

In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

We examine a 4th grade teacher's development of a constructivist-based, adaptive pedagogy (AP) approach--and its contribution to student multiplicative reasoning and outcomes, mixing qualitative analysis of segments from her interviews with quantitative analysis of her student outcomes on the state-mandated test. Her reflections indicate a shift…

Discusses the development of multiplicative and divisional schemes within a constructivist framework. Illustrates child thinking and child methods relative to the meanings of these operations using interviews with children. Compares the constructivist perspective on the development of meanings of multiplication and division to what is found in…