Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

Supporting students of all levels to move beyond empirical arguments, which employ example based reasoning to endorse universal truths and are thus mathematically invalid, remains a challenging goal in mathematics education. Arguments that make use of generic examples are both mathematically valid and accessible for even young learners. However,…

Through the historical analysis of Dienes' works and through the suggestions of activities, the objective of this text is to understand the movement of systematization of knowledge for teaching and to teach classification, ranking, and ordination through the use of logical blocks during the Modern Mathematics Movement (1960-1980), a time of…

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD,…

In the number to position task, several studies have shown that typically developing children shift from a biased (logarithmic) to an accurate (linear) mapping of symbolic digits onto a spatial position on a line. The initial pattern of overestimation of small numbers and the underestimation of larger numbers is compensated by means of age and…

In this study we set out to investigate the errors made by students in logarithms. A test with 16 items was administered to 89 Secondary three students (Year 9). The errors made by the students were categorized using four categories from a framework by Movshovitz-Hadar, Zaslavsky, and Inbar (1987). It was found that students in the top third were…

Task-cuing experiments are usually intended to explore control of task set. But when small stimulus sets are used, they plausibly afford learning of the response associated with a combination of cue and stimulus, without reference to tasks. In 3 experiments we presented the typical trials of a task-cuing experiment: a cue (colored shape) followed,…

A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…

While numbers, data and statistics have been part of the bureaucracy since the emergence of the nation state, the paper argues that the governance turn has seen the enhancement of the significance of numbers in policy. The policy as numbers phenomenon is exemplified through two Australian cases in education policy, linked to the national schooling…

Compared children's cognitive abilities at four years and their prenatal amniotic fluid testosterone levels. For girls, prenatal testosterone levels were related in a curvilinear manner to language comprehension and classification abilities, and inversely related to counting and knowledge of number facts. For boys, no relationships were found. (BC)

A theoretical discussion of categorization, unit structures and structured units, and fractions as operators was introduced. The thinking of grade-three students (n=3) with regard to the meaning of fractions was investigated in two teaching episodes using the computer environments of SuperPaint and CopyCat. (Contains 14 references.) (MKR)

Describes longitudinal study of the development of understanding of two logical properties of number by 36 children during the first three years of primary school in Glasgow. Piagetian tests and number skills tests were administered to explore the acquisition of number as class and number as order concepts. (Author/LRW)

Written for a variety of audiences, this volume describes the University of Western Ontario Preschool Project in sufficient detail to permit its replication; findings of formative and summative program evaluations are reported along with research developing new criterion measures of social competence. Begun in 1973, the program was primarily…