This publication contains reference materials and activities for teachers in a staff development program in New York City, teaching grades 3 and 6. The program combines content and methodology. Sections in the publication include: (1) Student Verbalization Resources; (2) Manipulative Resources; (3) Probability, Statistics, and Graph Resources; (4)…

This longitudinal study investigated the ways in which two groups of eight students used spreadsheets to represent and solve algebra problems and related this to their previous arithmetical experiences and evolving use of symbolic language. The spreadsheet environment supported students to move from specific to general thinking. Includes story…

For nine-week periods during two consecutive years, sixth-grade students at the same school were taught identical mathematics content using two different instructional approaches. Year 1 involved low achievers, whereas Year 2 was mixed ability students. The experimental treatment was a problem-centered approach (PCL) where potentially meaningful…

A qualitative case study was conducted to investigate the understanding of the limiting reagent concept and the strategies used by five Year 11 students when solving four reaction stoichiometry problems. Students' written problem-solving strategies were studied using the think-aloud protocol during problem-solving, and retrospective verbalisations…

This study investigates how a variety of resources mediated collaborative problem solving for a group of preservice teachers. The participants in this study completed mathematical, combinatorial tasks and then watched a video of a sixth grader as he exhibited sophisticated reasoning to recognize the isomorphic structure of these problems. The…

Giving effective instructional explanations requires a special type of pedagogical content knowledge, that is, foreseeing where students could employ different assumptions in building their understanding of a specific content. This paper proposes the importance of rehearsing instructional explanations and fine-tuning the coherence and…

Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3+4+6=3+__) and completed a…

Society's failure to educate proportionate numbers of African American students in mathematics is an ongoing problem. The roots of this problem lie in systemic racism and segregated schools. The overwhelming majority of economically disadvantaged African American high school students at segregated schools receive substandard mathematics education.…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

The Proceedings of PME-XVIII have been published in four separate volumes because of the large number of individual conference papers reported. Volume I contains brief reports for 11 Working Groups and 8 Discussion Groups, 55 "Short Oral Communications," 28 Posters, 5 Plenary Panel reports, and 4 Plenary Session reports. Volume II…

Technological literacy education involves the teaching of basic engineering principles and problem solving, including elementary electrical circuit analysis, to non-engineering students. Learning materials on circuit analysis typically rely on equations and schematic diagrams, which are often unfamiliar to non-engineering students. The goal of…

A grounded theory approach was employed to explore the variation in strategies used by students when solving mental multiplication problems. Metacognitive prompts, externally generated stimuli that activate thoughtful cognition, were automatically generated via computer during the solving of mental multiplication problems to elicit awareness,…

Developed by Dodge (1995), WebQuest is an inquiry-based teaching tool, in which students of all ages and levels participate in an authentic task that use pre-designed, pre-defined internet resources, though other print resources can also be used. Learners will put the focus on gathering, summarizing, synthesizing, and evaluating the information…

This paper discusses a radically different set of assumptions to improve educational outcomes for disadvantaged students. It is argued that disadvantaged children, when exposed to carefully organized thinking-oriented instruction, can acquire the traditional basic skills in the process of reasoning and solving problems. The paper is presented in…

Project AIMS (Activities that Integrate Mathematics and Science) produces a variety of curriculum materials that deal with the integration of learning experiences, problem solving activities, and the use of cooperative learning. This document is a compilation of the AIMS newsletters published during the 1986-87 academic year. Each of the ten…