This article presents essential principles for mathematics instruction for students with disabilities and those who are at risk for school failure. These students have great difficulty in applying algorithmic knowledge to solve problems and even greater difficulty with abstract problem solving associated with higher level mathematics. A procedural…

This paper describes a limited longitudinal study of young children's early numeracy development within three testing cycles, at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-of-age), located within the broader context of progress through to Key Stage 1 SAT…

During 3 field experience visits, 23 elementary preservice teachers implemented mathematical problem-solving tasks with grade 3-6 gifted students. Researchers investigated what the teachers learned about gifted students regarding student characteristics, mathematical problem-solving tasks, and pedagogy. Each teacher completed a pre- and…

The National Science Foundation funded Calculators and Mathematics Project, Los Angeles (CAMP-LA) developed curriculum materials focused solely on the use of calculators. The project was developed in three stages. The first stage studied the mathematics curriculums from different states and identified topics that are not included but should be if…

Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

This resource book contains 18 magic number tricks that spark the interest and imagination of students as they are led through a variety of mathematical computations and discoveries. Following each activity, students are asked to write about their discoveries and create their own magic tricks. A matrix of skills for all the activities and lists of…

This paper reviews the current theory and research on algebra/mathematics word problems. First, the major research findings are identified and summarized along with the theoretical perspectives that produced the research. The findings are then interpreted from the perspectives of traditional and wholetheme approaches. Also, a sample methodology of…

This brochure explains a number of aspects of the standards established by the National Council of Teachers of Mathematics for mathematics education. The three sets of standards are: (1) Curriculum and Evaluation Standards; (2) Professional Standards for Teaching Mathematics; and (3) Assessment Standards for School Mathematics. Contained in the…

It has been hypothesized that differences in mathematical word problems are the result of differences in spatial skill. Why complex spatial abilities are needed for an individual to represent the relatively simple spatial relations in word problems is not clear. It is possible that a third variable, cognitive strategy preferences, may partially…

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

This set of papers was originally developed for a conference on Issues and Directions in Mathematics Problem Solving Research held at Indiana University in May 1981. The purpose is to contribute to the clear formulation of the key issues in mathematical problem-solving research by presenting the ideas of actively involved researchers. An…

Describes the use of a scientific phenomenon related to the concept of surface tension as an intriguing vehicle to direct attention to useful problem solving techniques. The need for a definite building process in attempts to solve mathematical problems is stressed. (EB)

Drawing the prisoner's cell after reading the Poe classic, and redrawing it after each of several passages are read, students develop problem-solving strategies. (SD)

A problem solving approach to the teaching of the Pythagorean Theorem is described. (SD)

A unit on problems involving large numbers can begin with calculating the amounts of ingredients needed to produce several thousand hamburgers. Other sources of computational problems are described. (SD)