The Models and Modeling Working Group at PME-NA has provided a forum for discussing and collaborating on projects fundamental to research on mathematical modeling since the first PME-NA conference in 1978. We propose to convene this Working Group at PME-NA 41 with a dual purpose: (1) to build on a theme begun in Greenville, holding a focused…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

This dissertation reports the research methodology and findings of three studies focused on mathematical modeling as a structured problem-solving process where the student translates relevant details from a situation, event, or phenomena in daily life into mathematical language with mathematically-defined structures and operations, which form the…

This study aims to obtain a description of the application of Realistic Mathematic Education (RME) that can improve students' mathematical communication ability. The type of research used is a classroom action research that refers to the design of Kemmis and Mc.Taggart research they are planning, action, observation, and reflection. The results…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students' work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in…

Demonstrates how teachers can move their students from the novice into the expert range of problem-solving strategies. Utilizes a problem-solving model that follows how such skills develop. (DDR)

Math-education reformers encourage the incorporation of mathematical modeling activities into K-12 curricula. Many of the purported educational benefits derive from the authenticity of the activities-how well they reflect the everyday and occupational mathematical practices of adults. But a paucity in the literature of observational descriptions…

Examines early retirement plans (ERPs) for public school teachers, compares them with private-sector ERPs, and notes legal considerations involving ERPs' impact on regular retirement systems. Discusses methods for cost analyses of ERPs and proposes a model for assessing an ERP's fiscal impact on a school district. (RW)

Discusses findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. Reveals four sources of mismatches that were significant in bringing about the occurrence of shifts in students' thinking. (Contains 16…

Results from numerous school- and teacher-effectiveness studies suggest that variation between classes is more significant than variation between schools, though evidence often seems contradictory. This article considers why different studies generate different findings, identifies key study design issues, and relates these observations to…

Reports on the results of a project that involved experienced K-12 teachers in mathematical modeling, using variables and functions in a fundamental and intuitive context, while investigating the appropriateness of spreadsheet solution methods across a broad range of grade levels. (14 references) (LZ)

Discusses diagrams and problem solvers' constructions of a problem situation, how the way of drawing changes during the problem-solving process, and the meaning and sense of diagrams. (Contains 15 references.) (MKR)

A restrictive form of equality limits African Americans' ability to benefit equally from public schooling. The "Brown" decision represents the Supreme Court's attempt to apply a mathematical solution to a social problem and left schools free to develop responses that failed to address African-American students' needs. A more expansive…