Three experiments investigated the roles of resource-sharing and intrinsic memory demands in complex working memory span performance in 7- and 9-year-olds. In Experiment 1, the processing complexity of arithmetic operations was varied under conditions in which processing times were equivalent. Memory span did not differ as a function of processing…

To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

In this article, the author argues that there is a big conceptual difference between number lines and number strips and that number lines should be consistently used as early as Y1. Her interest in the use of the number line as a powerful image of the real numbers, and how this is introduced in the early years, comes from her own experience as a…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…

This arithmetic textbook aims to teach the reading of figures so as to train the mind to instantly catch the idea that any combination of figures is intended to express. This is to be done by "the simple process of reading;" and the method consists: (1) in teaching the alphabet; and (2) in teaching the combinations of the alphabet, which…

Over the last 20 years, the use of calculators and digital measuring equipment has to some extent replaced mathematical mental/written activity and also the use of analogue measuring equipment. This paper explores some aspects of number concept, reading the number line, and estimation from scales. The students being considered are mainly part of a…

This textbook's goal is to train and develop the mind by means of the science of numbers. This work is designed both for primary and advanced classes. The first part is adapted to beginners, while the latter part is peculiarly fitted to give to the more advanced student that thorough mental drilling in the analysis of numbers, which furnishes the…

Two experiments investigated extent to which English- and German-speaking childrens' mental arithmetic was constrained by working memory. Found higher mental addition spans when numbers were visible throughout calculation than when not. Variation in addition span with age and arithmetical operation difficulty approximated to a linear function of…

Compares the results of a whole-class test on mental computation problems given to fifth graders who had been in a reform-based mathematics curriculum with those of students in a traditional mathematics curriculum. Reports that the students in the reform-based program performed much higher than the comparison group on all but one problem. (16…

This study provides an in-depth analysis of children's use of a taught mental calculation strategy. Three children (aged eight to nine years) who demonstrated contrasting spontaneous calculation approaches, were interviewed following the direct instruction of a calculation strategy. Their responses are explored in relation to constructivist and…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

A teacher in a large suburban elementary school in East Tennessee found that her fourth grade students had poor number sense and relied almost solely upon algorithmic procedure to solve math problems. Therefore, mental math was difficult for these students, so the daily number talks method was employed to strengthen number sense. However, no…

Mental arithmetic problems were presented in one of five modes to 14 fifth-grade classrooms. Results showed no significant gains in ability to use mental arithmetic or in performance on a standardized arithmetic achievement test, but gains on a problem-solving retention test and in positive attitudes. (DT)

Investigated the development of informal addition in Dioula (A Moslem ethnic group from West Africa) from childhood to adulthood and the effect of schooling on mental arithmetic. Compares these data with results from a study of children from the United States. (MK)