The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

This paper argues that the introduction of the scientific method in the very rich environments of the natural sciences or human sciences may disguise the process and create difficulties for students because of the multiplicity of variables involved, whereas the variables present in a mathematical context can be readily manipulated and their…

This document consists of three papers. The first, "A Parallel Model of (Sequential) Problem Solving," describes a parallel model designed to solve a class of relatively simple problems from elementary physics and discusses implications for models of problem-solving in general. It is shown that one of the most salient features of problem…

Explores the role of spatial orientation skill in the solution of mathematics problems. Reports the role of estimating the approximate magnitude of a figure; demonstrating the flexibility to change; adding marks to show relationships; moving or assessing the size and shape of figure; and getting the correct answer. (YP)

Three gifted and three learning-disabled gifted students (ages 13-15) viewed themselves on videotape solving mathematical problems and responded to questions pertaining to their problem-solving strategies. The non-learning-disabled students applied substantially more cognitive and metacognitive knowledge to the problem-solving task. (Author/DB)

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

The papers in this document follow the order of the meeting and consist of two guest lecturers and reports from four working groups; two topic group presentations are noted but not included. One lecture, delivered by Peter Hilton, discusses the nature of mathematics today and implications for mathematics teaching, while, in the other paper,…

Selects five critical elements for success in problem solving in mathematics and in computer programing: general strategy; planning; logical thinking; variables; and debugging. Describes the role of the five elements based on a literature review. Forty-one references are listed. (YP)

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…

Previous studies were conducted with 14- to 15-year-old students on the nature of the processes they used to solve tasks given the incorrect/buggy/mal-rules. The computer-based Leeds Modelling System (LMS) was implemented and a database of examples, correct and incorrect, or mal-rules had been established which was sufficient to diagnose the…

A study of 12- to 14-year-olds was conducted to investigate which components of spatial ability may be dependent on general cognitive functioning level and to compare possible differences in carrying out certain spatial operations in children of equal intelligence, but who are not specifically gifted for mathematics or visual arts. (MBR)

This is a narrative review of research in mathematics education reported during 1987. The purpose of this review is to extract from research reports ideas that may prove useful to school practitioners. Major sections are: (1) "Planning for Instruction" (relating historical developments, aides and grades, teaching approaches, problem…

Lists references of 16 research summaries, 152 articles, and 220 dissertations alphabetically by author within each category. Provides the grade or age level for each reference. A brief abstract is presented for most of the references. Journals searched and author index by content are included. (YP)

This study explored fourth-grade teachers' understanding of mathematical problem solving, an aspect of the Vermont portfolio assessment program that has been largely ignored. Teachers' conceptions of problem solving, their knowledge of problem-solving strategies, their selection and evaluation of problem-solving tasks, and their instructional…