The concept of Arithmetic Story Grammar is introduced. Arithmetic Story Grammar maintains that any equation containing a single operand tells, in and of itself, a complete story with a setting, plot, theme, and resolution. Multiple-operand equations differ from their single-operand siblings only in the number of actions undertaken and the number…

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 is the final report for a study whose original purpose was to develop a general theory of the situational constraints imposed by the routines of everyday life on arithmetic skills. Section 1 reviews the goals laid out in the proposal in relation to what was accomplished. Section 2 is the draft of "Everyday Cognition: Its Development in…

This paper reports the results of the second of a series of collaborative studies examining how children acquire the skills to represent and solve verbal addition and subtraction problems. The purpose of this study was to identify the cognitive processing capabilities of a group of Tasmanian (Australian) children. Fifteen cognitive tests were…

The effects of three variables on the difficulty of verbal arithmetic problems were examined. Variables included problem form, sequence of information, and problem verb. A total of 32 problems was generated, four in each of four problem forms and two sequences of information. Vocabulary words were not above second-grade level, and numbers used…

Defines arithmetic, harmonic, and weighted harmonic means, and discusses their properties. Describes the application of these properties in problems involving fuel economy estimates and average rates of motion. Gives example problems and solutions. (CW)

In contrast to the traditional top-down approach, a bottom-up approach is proposed by current reform in mathematics education. According to this alternative proposal, algorithmizing is the activity in which students should be involved. What can we do when we want to enact such an algorithmizing approach in a classroom and our students have already…

This book contains a collection of fraction lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to learn how to: (1) name fractional parts of wholes and sets; (2) represent fractional parts using the standard notation including proper fractions, improper fractions, and mixed numbers, and…

Young children are interested in and capable of building a mathematics foundation at a very early age. Computer software allows children easy access to math. This software consists of seven activities for ages two to five years. These seven activities emphasize numbers, counting, addition, subtraction, patterns, problem solving, size, and…

This book is a collection of teaching strategies and activities for teachers of secondary mathematics. This volume is the product of a workshop that focused on student understanding of directed numbers. Suggested teaching methods include introducing the number concept, using a number line, number strips, monograms, bottle top addition and…

This study examined the effects of a schema-based direct instruction strategy on the addition and subtraction word problem solving performance of three third- and fourth-grade students with learning disabilities. An adapted multiple probe across subjects design was used. The intervention involved training students to distinguish…

Investigates the arithmetical and algebraic problem-solving strategies and skills of preservice primary and secondary school teachers in Flanders, Belgium. Compares aspects of preservice teachers' own problem-solving behavior with the way in which they evaluated students' arithmetical and algebraic solutions to problems. Discusses teachers' use of…

This article provides an overview of the nonverbal learning disabilities (NLD) syndrome and describes appropriate educational strategies. Primary characteristics of NLD and possible indicators are listed. Remedial, compensatory, instructional or therapeutic interventions are listed for psychomotor and perceptual motor deficits, for arithmetic…

Investigates the arithmetic and algebra word problem-solving skills and strategies of future primary and secondary school teachers. Describes the evolution of these skills and strategies from the beginning to the end of teacher education. Indicates that, in the education of preservice primary and secondary school teachers, there is need for an…

Three activities which require a calculator with integer division capabilities are presented. In each activity, procedures and questions for discussion are included. Game boards, samples, and answers are included where appropriate. (CW)