Illustrates flexible grouping configurations, discussing how different perspectives and theories of peer learning are required to account for their intended effects. A classroom example is provided to illustrate each context discussed. The article also presents examples of an instructional strategy in one multiage classroom where the teachers…

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

During the preliminary stages of classroom-based research, this author conducted a sequence of interviews with six seventh graders regarding their understanding of fractions, decimals, ratios, and proportions. The students represented a variety of ability levels and were all in their first semester of prealgebra. The interviews began with notions…

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient…

In this paper, I explore two beliefs about learning and teaching that I argue are prevalent among educators. The first is the belief that subject matter expertise is sufficient for success in teaching. The second belief is that to learn a specific content area, one needs to begin with an understanding of the formal structure and abstract…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)

In spite of the continued focus on problem solving, American elementary and middle grades schoolchildren are perceived to be ineffective problem solvers. This paper reports the results of a survey of (n=744) kindergarten through eighth grade teachers and interviews and observations of a primary and an intermediate master teacher designed to answer…

This document contains the proceedings of the annual meeting of the Canadian Mathematics Education Study Group. Papers include: (1) "What Does It Really Mean To Teach Mathematics through Inquiry?" (Raffaella Borasi); (2) "The High School Math Curriculum" (Peter Taylor); (3) "Triple Embodiment: Studies of Mathematical…

A secondary mathematics curriculum of open-ended non-routine problems developed by a teacher of high school math over 10 years is described. An open-ended non-routine problem is one that requires problem recognition and orientation, effort, and persistence. It is open-ended in that it allows for various solutions, and requires the student to…

The importance accorded mathematical connections in the professional literature is not properly reflected in the relatively small number of empirical investigations of students' mathematical connections. The purpose of this study was to investigate the mathematical connections that students form and use in solving nonroutine problems. Two main…

This document consists of three workbooks, one each for grades 6, 7, and 8. The workbooks are designed as review and refresher materials for mathematics. The emphasis is on word problems, all of which are written in German. The workbooks are part of a German language immersion program. (JC)

Two task were developed to assess second and fourth grade girls' ability to generate quantitative inferences and estimate answers to math word problems. The generation of quantitative inferences is thought to constitute problem representation, and the ability to estimate answers to word problems is facilitated by the presence of an accurate…

Underlying the research reported in this paper is a theoretical framework which defines the self-regulation of learning as the number and kinds of teaching tasks students perform themselves. Three studies are presented on individual differences in regulation-processes emerging from thinking aloud protocols. Protocols of good and weaker performing…

In this project, a plan for solving word problems based on the students' level of development was developed. A 10-week implementation of a plan for solving word problems at the concrete level of development included the use of a flow chart or plan to map out and solve word problems. Students then used the flow chart and manipulatives to develop…

In recognition of the fact that young children develop informal number concepts and strategies for solving several basic types of verbal addition and subtraction problems before entering school, but lose this ability after a few years of schooling, the study created and tested an intervention designed to build on the children's early insights. A…