Presented are activities which give practice in making estimates, gathering data, and checking the reasonableness of results. (TG)

In one experiment, subjects from third grade through college relied on memory retrieval rather than on counting to solve multiplication problems. An effect of confusing problems on error rates and reaction times indicated the activation of related information. In a second experiment, subjects demonstrated automaticity of fact retrieval on simple…

Proposes a framework that identifies the components of number sense and the attributes of students who possess it. Discusses various aspects of three areas where number sense plays a key role: number concepts, operations with numbers, and applications of number and operation. (MDH)

Children and adults were tested on six speeded perceptual-motor and cognitive tasks, including a (1) response time task; (2) button tapping task; (3) pegboard task; (4) coding task; (5) picture matching task; and (6) mental addition task. Age-related change in processing time on most of these tasks was described by a single exponential function.…

This material describes two games, Minicomputer Tug-of-War and Minicomputer Golf. The Papy Minicomputer derives its name from George Papy, who invented and introduced it in the 1950's. The Minicomputer is seen as an abacus with the flavor of a computer in its schematic representation of numbers. Its manner of representation combines decimal…

This essay traces the history of two standards--estimation and mental calculation--devised by the National Council of Teachers of Mathematics (NCTM). It is hoped that the history of these standards will illustrate the difficulties encountered by other proposed standards and by the standards movement as a whole. The essay provides an overview of…

Presents a stochastic model for distinguishing mental arithmetic errors according to causes of failure. A series of experiments (1) studied questions of goodness of fit and model validity among four and five year olds and (2) used the model to measure the relative contributions of developmental improvements in short-term memory and arithmetical…

Study of the performance of nearly 2,000 students in grades 2 through 9 on a variety of mental computation tasks using visual and oral presentation found a wide variation in performance within the sample of each country at each grade level. (33 references) (MKR)

Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations;…

Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a…

Describes three activities using dominoes, playing cards, and the calendar to give students mathematical experiences reinforcing basic skills and problem-solving strategies that involve patterns, relationships, and functions. Students discover mathematical relationships underlying the magic tricks used in the activities. (MDH)

In this article, data from a study of the mental computation competence of students in grades 3 to 10 are presented. Students responded to mental computation items, presented orally, that included operations applied to fractions, decimals and percents. The data were analysed using Rasch modelling techniques, and a six-level hierarchy of part-whole…

This paper discusses the central thesis that new research on estimation and mental computation will benefit from more focused attention on the situations in which they are used. In the first section of the paper, a brief discussion of cognitive theory, with special attention to the emerging notion of situated cognition is presented. Three sources…

The Calculators in Primary Mathematics Project was a long-term investigation into the effects of the introduction of calculators on the learning and teaching of primary mathematics. The Australian project commenced with children who were in kindergarten and grade 1 in 1990, moving up through the schools to grade 4 level by 1993. Children were…