This book describes how parents can develop a mathematical environment for children in the home. Four major areas are emphasized: whole numbers, fractions, decimals, and basic geometry. Section 1 "'Shoebox' Activities," provides activities to teach specific concepts within a manageable time period. Materials are listed and diagrams…

The comprehension processes of adult students solving two-step problems of comparison were studied using eye-movement experiments based on the assumption that eye fixations are synchronous with internal cognitive processes. Twenty university students each solved 24 two-step mathematical word problems of three sentences each with consistent…

An understanding-based approach to teaching arithmetic word problems is used in the Training Arithmetic Problem Solving Skills (TAPS) research project, for which four semantic schemas or problem representations have been revised and adopted: Combine, Compare, Change, and Vary. It is hypothesized that a good problem solver identifies the schema of…

Open-ended individually administered questions can ascertain whether students can reason about arithmetic problems. Free response test items are useful in assessing students' thought processes as they solve mathematics story problems. Since story problems do not state explicitly which arithmetic operations are required for solution, students must…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

The purpose of this study was to determine the effects of two types of teacher inservice education programs upon fourth-grade students' achievement in solving mathematics story problems. Participating teachers attended two types of teacher inservice education programs; a traditional program, and a brief, narrowly focused special program (2.5 hours…

This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

A review of literature on selected relationships among metacognition, quantitative problem-solving, and learning disabilities focuses on three types of problem-solving activities: word problems; knowledge-based problems; and decision and argument problems. Techniques for teaching problem-solving and integrating metacognition principles into…

It is generally considered that diagram use aids efficacy of math word problem solving. While understanding diagrams is considered important in both New Zealand and Japanese secondary schools, there is an additional emphasis in New Zealand schools for students to appreciate their use as tools for problem solving and communication. This study…

Building on previous research on the tendency in students of diverse ages to overrely on proportionality in different domains of mathematics (e.g., geometry, probability), this study shows that--when confronted with missing-value word problems--Flemish primary school pupils strongly tend to apply proportional solution strategies, also in cases…

The various difficulties and cognitive obstacles that students face when they are introduced to algebra are well documented and described in the relevant bibliography. If it is possible, in order to avoid these difficulties, we have adopted the functional approach widening the meaning of algebraic thinking. In this paper, which is part of wider…

Measure Up is a research and development project that uses findings from Davydov (1975) and others to introduce mathematics through measurement and algebra in grades 1-3. This paper illustrates the use of generalized diagrams and symbols in solving word problems for a group of 10 children selected from a grade 3 Measure Up classroom. Students use…

This report describes a program for improving students' comprehension of the language of mathematical problems. The targeted population consists of 5th and 6th grade multi-age students and multi-age learners with special needs at a middle school located outside a major city in a Midwestern community. Evidence for the existence of this problem…

This study investigated cognitive constructs to be measured by word problems in algebra. One performance-based assessment was administered to 290 high school students. Students' responses were scored by three scoring systems: the correct/incorrect criterion (0/1); a holistic scoring rubric (0-4); and an analytical scoring rubric for measuring…

This study examined the role of dynamic assessment involving specific and general instructional strategies on expert and novice third graders' error patterns in solving part-whole mathematics word problems. The assessment showed that novices in general required more prompts than did experts. Experts in the specific strategy group had decreased…