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…

Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. The authors discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment.

Currently, there are more theories of learning in use in mathematics education research than ever before (Lerman & Tsatsaroni, 2004). Although this is a positive sign for the field, it also has brought with it a set of challenges. In this article, I identify some of these challenges and consider how mathematics education researchers might think…

A study of (n=26) prospective elementary teachers' understanding of the area of a rectangular region as a multiplicative relationship between the lengths of the sides resulted in the development of a description of the quantitative reasoning involved. (23 references) (MKR)

Begins with an overview of the constructivist perspective and the pedagogical theory development upon which a constructivist teaching experiment with 20 prospective elementary teachers was based. Derives a theoretical framework for mathematics pedagogy with a focus on decisions about content and mathematical tasks. (49 references) (Author/DDD)

Discusses constructivist teaching, students' prior knowledge, teachers' construction of models of students' mathematics, and the need to make the role of the mathematics teacher problematic. (three references) (MKR)

Used open-response written instruments (n=33) and interviews (n=8) to investigate understanding of connectedness within and between procedural and conceptual knowledge in division and knowledge of units. Found knowledge of symbols and algorithms was good but conceptual knowledge was weak. Concerns about individual differences emerged. (GW)

Articulates methodology for studying mathematics-teacher development in the context of reform. Provides an approach to understanding teachers' current practices and viewing their current practices in the context of development towards envisioned reforms. Applies conceptual frameworks developed within the mathematics-education research community to…

All fields of research need to reconsider, on an ongoing basis, their standards for research quality. At the present time in mathematics education, such discussion is particularly critical to the ongoing growth and strength of the field. Mathematics education research has evolved significantly in the last 20 years. The most sweeping change has…

We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970).…