This article reports on models of teaching that developed as outgrowths of a study of middle-grades mathematics classes. Three specific cases are highlighted that represent deductive (associated with univocal), inductive (associated with dialogic), and mixed (a hybrid of deductive and inductive) models of teaching. Teaching practices associated…

The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…

This article explores the complex relationship between language and mathematics education in multilingual settings by presenting an analysis of one lesson from a multilingual primary mathematics classroom in South Africa taught by an appropriately qualified and experienced teacher. English emerged as a dominant language in this classroom, and this…

The transformation to reform mathematics teaching is a daunting task. It is often unclear to teachers what such a classroom would really look like, let alone how to get there. This article addresses this question: How does a teacher, along with her students, go about establishing the sort of classroom community that can enact reform mathematics…

Describes one pattern of reasoning observed in a mathematical activity with students in a grade 5 class and discusses ways in which the pattern is or is not mathematical. Describes patterns of reasoning in terms of ways of reasoning and degree of formulation of the reasoning. Distinguishes between mathematical reasoning and scientific reasoning in…

Contrasts student achievement using commercial curricula (CC) for initial fraction learning with that of using the Rational Number Project (RNP) fraction curriculum. Indicates that students using RNP materials had statistically higher mean scores on concepts, order, transfer, and estimation. Interview data showed differences in the quality of…

Discusses an attempt to promote the development of prospective elementary teachers' own subject-matter knowledge of the division of fractions as well as their awareness of nature and likely sources of related common misconceptions held by children. Indicates that before the described mathematics methods course, most participants knew how to divide…

Studies four preservice elementary teachers during a field-based mathematics methods course to investigate elements of mathematics teaching and learning that teachers found problematic and how they resolved those problems. Concluded that teachers exhibited concerns about classroom context, pedagogy of mathematics, children's mathematical thinking,…

Devises a new curriculum to introduce rational numbers by using developmental theory as a guide. Experiment concluded that students in the treatment group showed a deeper understanding of rational numbers than those in the control group, showed less reliance on whole-number strategies when solving novel problems, and made more frequent references…

Presents and describes a pedagogical framework that supports children's development of conceptual understanding of mathematics. Advancing Children's Thinking (ACT) is synthesized from an in-depth analysis of observed and reported data from one skillful first-grade teacher's use of the "Everyday Mathematics" curriculum. Indicates that teachers…

Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…

Examines mathematics instruction and its intersection with culturally relevant teaching in an elementary/middle school in a Mexican American community. Proposes a model of culturally relevant mathematics instruction with three components: (1) building on students' informal, cultural, and experiential knowledge; (2) developing critical thinking;…

Reports on efforts to produce a multicultural mathematics curriculum for grades K-6 that was socially transformative. Describes the perplexity of issues related to the definition of multicultural and mathematics curricula for social transformation, the complexities of group deliberation, and the demands involved in the teacher-research process.…

Investigates the relationship between a beginning elementary school teacher's beliefs and mathematics-teaching practices. Results indicate that the teacher's practice was more closely related to beliefs about mathematics content rather than beliefs about mathematics pedagogy. Beliefs about mathematics content were highly influenced by personal…

Describes an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop a disposition toward more realistic mathematical modeling in pupils. The learning and transfer effects of an experimental class of 10- and 11-year-old students that were compared to the results of two control groups support this…