We examine the role of tasks that have the intended effect of teachers re-conceiving the mathematics they teach as comprising a coherent body of meaningful ideas. We ground our discussion in ideas of trigonometry and modular functions and draw from a professional development research project to illustrate our approach. In this project, many…

There are two different conceptions of the innate basis for numerical abilities. On the one hand, it is claimed that infants possess a "number module" that enables them to construct concepts of the exact numerosities of sets upon which arithmetic develops (e.g. Butterworth, 1999 ; Gelman & Gallistel, 1978). On the other hand, it has been proposed…

Meta-analyses are presented of sex differences in (1) the (mental) arithmetic subtest of the Wechsler intelligence tests for children and adolescents (the WISC and WPPSI tests), showing that boys obtained a mean advantage of 0.11d; (2) the (mental) arithmetic subtest of the Wechsler intelligence tests for adults (the WAIS tests) showing a mean…

There is evidence for both semantic and asemantic routes for naming Arabic digits, but neuropsychological dissociations suggest that number-fact retrieval (2x3=6) can inhibit the semantic route for digit naming. Here, we tested the hypothesis that such inhibition should slow digit naming, based on the principle that reduced access to multiple…

Elapsed-time problems are notoriously difficult for children. Instruction on techniques for teaching and learning elapsed time is not emphasized in current mathematics education literature. Nor is it addressed in "Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence" (NCTM 2006). This absence of…

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this…

People remember information better if they generate the information while studying rather than read the information. However, prior research has not investigated whether this generation effect extends to related but unstudied items and has not been conducted in classroom settings. We compared third graders' success on studied and unstudied…

This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

Number sense has been recognised as central to young children's development of mathematics for a number of decades. A student with a "good" sense of number normally has a thorough understanding of relationships among numbers and operations--being able flexibly to partition and combine numbers in convenient ways to allow appropriate…

The present study was carried out to examine physiological arousal modulation (heart activity and skin conductance), across baseline and cognitive tasks, in females with fragile X or Turner syndrome and a comparison group of females with neither syndrome. Relative to the comparison group, for whom a greater increase in skin conductance was…

This book is intended for students who know the numbers from one to thirty thoroughly, who can count to one thousand, who know something of the multiplication tables of two, three, four, five, six, ten, and twelve, and who understand the simplest facts about ratio and fractions. The purpose of the textbook is to conform numbers in their facts and…

This textbook is for arithmetic students who can use numbers into the thousands in addition and subtraction, who know what ratio is and understand something about fractions, who know some facts of measures, and who have studied the multiplication tables. The book contains about a year's work, mostly in practice, partly in extension of knowledge.…

This textbook presents the divisions of arithmetic in their natural order. The fundamental operations upon integers, common fractions, decimals, denominate numbers, and numbers expressed by letters, are followed by their applications to business and to various employments. The pupil is taught to develop observation and thought power, rather than…

This arithmetic textbook for common schools and academies presents lessons arranged from least complex to most complex to prepare students for algebra study. Lessons include practical business applications, and the book has been adapted to serve the business community's needs while respecting the science of numbers.

The meaning of International Standard Book Numbers (ISBN) and the mathematics involved in the use of a check digit to catch errors in number transcription are discussed. (JM)