The study investigated whether 15 children (ages 6-21) with IQs from 31 to 66 could spontaneously invent more efficient calculational procedures and abstract basic arithmetic relationships after individualized tutoring in computation. Experimental subjects were given training that focused on accurate computation but specific relationships and…

This study systematically examined developmental changes in the flexibility of preschool children's counting skills by assessing their use of counting to solve different kinds of quantitative problems at several preschool age levels. Three principal kinds of quantitative problems were considered: (1) quantifying a given set; (2) generating a set…

This book introduces children to the numbers 1 through 16 (and some basic mathematical concepts) using the petals of a variety of flowers. The first part of the book contains 16 full-color photographs, each photograph showing a flower with 1 to 16 petals, with the number printed below the photograph. These pages can be used to introduce or…

The author describes a new graphing algorithm for computing probabilities, and presents problems for these algorithms for use in the classroom. (SD)

Describes the magnetic field of Helmholtz coils qualitatively and then provides the basis for a quantitative expression. Since the mathematical calculations are very involved, a computer program for solving the mathematical expression is presented and explained. (GS)

These materials were developed in response to the Utah State Board of Education's new high school graduation requirements, particularly as they relate to the identification, teaching, and assessment of certain basic functional competencies. The document has been compiled as a guide and aid to mathematics teachers. Thirty competencies have been…

The purpose of this study was to investigate the effects of the use of hand-held calculators on the teaching of decimal arithmetic in seventh and eighth grade pre-science units. In particular, the effects of calculators on pencil and paper computational skills and on conceptual understanding were studied. The study consisted of a pre-unit…

A study designed to serve as an initial step in building a theory of computer literacy was conducted to provide new information concerning how humans think about calculators and to determine how individual differences in students' intuitions affect their understanding and use of the calculator. Thirty-three expert and 33 novice calculator users…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

The report describes the development and accomplishments of the Early Start Preschool Program (Vineland, New Jersey), a project to overcome developmental delays in communication and learning through a structured curriculum, parent training and participation, and a model nutrition program. Six outcome objectives, including objectives of gain in…

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for…

Several examples are given of a variety of nonstandard problems, not ordinarily found in texts or courses, now accessible to students who have programmable calculators. These include: (1) finding limits; (2) evaluating infinite series; (3) calculating finite series; (4) computing variable length products; (5) solving equations; (6) searching for…

In response to an increasing demand for faculty evaluation, focus is on elements of a successful evaluation program. It is suggested that faculty must be consulted in order to arrive at a mutually agreed upon structure, incorporating such areas as which sources should provide the information or data on which the evaluation will be based. Another…

This study was an attempt to provide some evidence on the effects of calculator usage with primary-age children. Specifically, the study compared the performance of children who had access to calculators for an extended period of time, and whose teachers used calculators in specified instructional ways, with children who did not have access to…

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…