In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. I examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment.…

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack.…

Quantitative and qualitative analyses of 37 first-graders' solutions to addition problems were conducted to re-examine inconsistencies in children's progress from counting-all to counting-on. The authors applied the constructivist's participatory-anticipatory stage distinction as a tool for fine-grained assessment. Among solutions given by…

In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain "mathematical caring relations" (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to…

Discusses constructivist teaching, students' mathematical knowledge, activating prior knowledge, hypothetical learning trajectory, and reflection in teaching mathematics, all in reaction to Simon's model of constructivist pedagogy. (24 references) (MKR)

The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

Describes generalization activity as an opportunity to learn about seventh graders' understanding of functions. Findings indicate that the modeling efforts of students allowed them to analyze their understanding of representations of quantities, relationships among quantities, and relationships among the representations of quantities in both…

Responds individually to Shoenfeld's objections that Ohlsson, Ernst, and Rees' model is unclear; that the hypotheses about learning are unjustified; that the models have not been tested against extant data; and that it is unclear whom the model models. (MDH)

A method of organizing studies on sequencing problems in mathematics according to a theoretical model based on characteristics of empirical science is explained. The conceptual framework underlying eight studies that follow this article in JRME (SE 508 022 through SE 508 029) is discussed and a brief overview of each study is given. (DT)

An outline of a model that provides a new perspective on the conceptual foundations of mathematics and a new approach for the study of children's acquisition of numerical operations is proposed. Attention is viewed as a pulse-like succession of moments and is supported by recent data from neurophysiology. (MP)

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)

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

Describes a program in second-grade Dutch mathematics classes that emphasizes mental addition and subtraction of two-digit numbers up to 100. Deals with a strategy of counting by 10s from any number. (Contains 56 references.) (RLB)