Discusses the differences between mathematical problem solving typically used in the classroom and problem solving that is a part of everyday situations out of school. Suggests some teaching methods to align classroom instruction with the real world. Seventeen references are listed. (YP)

Describes basic problem-solving skills and presents a protocol of a student solving a problem. Discusses some of the difficulties in obtaining a correct solution. Lists basic prompts for problem solving. (YP)

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)

This is a teaching note on a proposed approach that will correct a common flaw in the way the return-generating process within the APT framework is illustrated in textbooks. The problem can be resolved by dichotomizing the risk factors into two kinds. Based on this approach, the author eliminated the main source of confusion and developed an…

This research provides an analysis of the relationship between a student's beliefs and mathematical behaviors over a seventeen-year period. Romina, the student of focus in this case study, was among the original participants in a longitudinal study which explored how students build mathematical ideas when working collaboratively on problem-solving…

Preschoolers' conceptual understanding and procedural skills were examined so as to explore the role of number-words and concept-procedure interactions in their additional knowledge. Eighteen three- to four-year-olds and 24 four- to five-year-olds judged commutativity and associativity principles and solved two-term problems involving number words…

Middle school teachers realize the value of students playing games in mathematics classes if those games emphasize problem-solving strategies, algebraic reasoning, or spatial sense. This article describes various versions of the traditional game of nim and shows how working backward can be used to find a winning strategy. The link is then made…

Background: Studies on rewording word problems can be grouped into two main groups: situational rewording, in which the situation denoted by the text is described more richly, and conceptual rewording, in which the underlying semantic relations are highlighted. Aims: Our aims are to define and distinguish these two kinds of rewording and to test…

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…

The relationships between heuristic literacy development and mathematical achievements of middle school students were explored during a 5-month classroom experiment in two 8th grade classes (N = 37). By heuristic literacy we refer to an individual's capacity to use heuristic vocabulary in problem-solving discourse and to approach scholastic…

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

This study examines the effects of representational movement on long-term retention and recollection of academic content. The researcher hypothesized that students who used representational movement to elaborate on their understanding of chemical equations would demonstrate improved long-term ability to solve chemical equations. The study…

This article discusses the "BASICS" or "Building Accuracy and Speed In Core Skills" Mathematics Intervention Program which has been designed to enable students who are either low-achievers or have some form of learning disability, to attain real improvement and make the successful transition to core mathematics. The "BASICS" Intervention Program…

This report attempts to discover how students think about and use mathematics in open-ended questions. Part I, "Open-ended Questions in Mathematics," describes the rationale for adding open-ended questions to the grade 12 mathematics test of the California Assessment Program (CAP). Part II describes the findings from students' responses…

This document outlines the 1985-86 Chapter I Corrective Mathematics Program in New York City. The program served 8,825 eligible students in 186 nonpublic schools. The major goals of the program were to alleviate students' diagnosed deficiencies in mathematical concepts, computation and problem solving and to assist students in applying these…