The following article gives a brief account of some empirical research done in the 1980s in the UK by the present author with his colleague, Ibrahim Abdel-Ghany of Minia University, Egypt. At the time both researchers were working at the University of East Anglia at Norwich, England. This work is partly based on empirical arguments, and on…

Students sometimes have difficulty in mathematics because they solve problems mechanically, without understanding the ideas represented by their equations. This brief note provides mathematics instructors with ideas for rectifying this fundamental flaw in students' paradigm of problem solving. (Contains 1 footnote.)

In this action research report 4 teachers and 1 teacher educator use the Japanese lesson study model of professional development for 15 months in rural Carlinville, Illinois. In March 2001, 4 teachers identified a goal to improve their students' understanding of two step word problems in 2nd grade elementary mathematics. Teachers completed three…

Pupils need to experience a variety of reading activities in mathematics. For all pupils, the mathematics teacher should identify unknown words from their texts and print these words on the chalkboard clearly for learners to see. Phonics should not generally be emphasized in the mathematics curriculum, but brief "teachable moments" may…

This booklet summarizes findings from data on mathematics achievement gathered on the 1992 National Assessment of Educational Progress (NAEP) for grades 4, 8, and 12. Approximately 26,000 4th, 8th, and 12th graders in 1,500 public and private schools participated in the national assessment. Information included in the report are: trends in…

The majority of research investigating gender-related differences in problem-solving ability has focused on the product of word problem solving--the problem solution. This paper reports an investigation of potential gender-related effects on sixth-graders of an explicitly stated problem-solving plan. Two versions of the test were given: the…

This study, involving 65 undergraduates at the Georgia Institute of Technology (Atlanta); explores a scheme for representing problem-solving knowledge and predicting transfer as a function of problem-solving subgoals acquired from examples. A subgoal is an unknown entity (numerical or conceptual) that needs to be found in order to achieve a higher…

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…