Discussed is research which shows, in contrast to the dominant impression given by Piaget's work, that before the onset of schooling the young child possesses several kinds of fundamental "intuitions" concerning numbers. (Author/TG)

The performance of 76 students (ages 10 to 15) with learning disabilities on four tasks of arithmetic computation within each of the four basic operations was examined. Tasks varied in difficulty level and number of strokes needed to complete all items. Intercorrelations between task sets and operations were examined as was the use of…

Described is a study in which three instructional approaches were applied in second grade classes. Discussed are proportional materials, nonproportional materials, nonproportional materials with pictorial models. Findings, results, and recommendations are presented. (CW)

Interviewed 59 2nd- and 44 3rd-year elementary school students concerning their solutions to arithmetic problems commensurate with their age and ability. The results indicate that as children progress through school, they continue to use counting as an important part of their problem-solving repertoire, combining counting skills in idiosyncratic…

Discusses three methods to teach the order of operations to middle school students: (1) asking students to fill in operations in a statement to obtain a given answer; (2) using mnemonics to remember operation order; and (3) having students discover the logic system used by their calculators. (MDH)

A 14-year-old Brazilian boy in the fourth grade was given 170 problems orally, each asking for the sum of 2 2-digit numbers. Responses indicated he had invented his own algorithm for addition, similar to the school one, based largely on his experiences with money. (Contains 13 references.) (JAF)

Examines how parents and teachers influence the development of gender differences in mathematics strategy use in the first grade. Conducts interviews with children about their strategy use and uses questionnaires with parents and teachers. Reports that boys correctly used retrieval during the first grade more than girls; girls correctly used overt…

Describes the way in which 12 primary-grade teachers responded to reform-minded teaching of multidigit addition and subtraction. Discusses the nature of effective teacher-development programs. Contains 21 references. (ASK)

Tested effects of a structured intervention in teaching children to represent addition and subtraction. Found significant differences between two study groups in terms of affecting the addition and subtraction operations and ability to determine which operation was appropriate. Results suggest children's exploration of real world situations should…

Two experiments examined developmental changes in reasoning about intensive quantities--predicting mixture intensity of pairs of liquids with different intensities of red color. Results showed that cognitive averaging in this domain developed late and slowly. Predominating up to 12 years was an extensivity bias, a strong tendency to use rules that…

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 paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…

This booklet offers teacher instructions and student worksheets on number activities for gifted primary grade students. Three sections are included: (1) "moving numbers" which asks students to supply the missing member or members of addition and subtraction equations; (2) "number trails," which involve the completion of number…

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

This set of papers was selected from presentations made at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics because of their pertinence to classroom teachers. The papers concern: (1) "Research and Development Related to Learning about Numerals for Whole Numbers: Implications for…