Twenty-six monolingual and 46 bilingual college students were assigned to 2 groups on the basis of their performance on a complex relational task, an empirical model of instructional control (O'Hora, Barnes-Holmes, Roche, & Smeets, 2004). The subjects were then exposed to the vocabulary, arithmetic, and digit-symbol encoding subtests of the…

This study examined whether knowledge of arithmetic contributes to difficulties with equations. In Experiment 1, children (ages 7-11) completed tasks to assess their adherence to 3 operational patterns prevalent in arithmetic: (a) the strategy of performing all given operations on all given numbers, (b) the "operations=answer" problem structure,…

Some procedures are developed for testing divisibility by prime numbers composed of two or more digits. Accelerating the tests is also considered. (Contains 2 tables.)

This article illustrates how the arithmetic series 1 + 2 + 3 + ... + n is pervasive in mathematical contexts as a powerful problem-solving tool.

A paucity of research has directly compared empirically supported interventions to examine their effectiveness among students with different mathematics fluency skills. The purpose of this study was to compare the effects of two empirically supported interventions and a control condition on the mathematics fluency of 98 second and third grade…

The juxtaposition of articles by Ian Thompson and Ian Sugarman in "MT202" on addition and subtraction respectively engendered some bemused thoughts in this author, who for some years has been sheltered from controversy by retirement. In this article, Fielker shares some thoughts on addition and subtraction raised by Thompson and Sugarman in their…

Everyday, people face situations that call for adding, subtracting, multiplying, or dividing, and at least half of the time, these calculations are accomplished without the use of pen, paper, or calculators. Because figuring "in your head" is such an important life skill, it should have a regular role in classroom math teaching. This article…

We discuss mathematical tasks used in a first mathematics content course for elementary teachers at our university to foster a deep conceptual understanding of early arithmetic, including basic concepts of number, number relationships and strategies, and coordinating units of different rank. Our approach is to immerse our students in a base 8…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

In recent years there has been an increasing international interest in fine-grained diagnostic inferences on multiple skills for formative purposes. A successful provision of such inferences that support meaningful instructional decision-making requires (a) careful diagnostic assessment design coupled with (b) empirical support for the structure…

The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic instruction time. Twenty-two children with CNSd…

The Williams Review (Dept. for Children, Schools and Families, 2008) is significantly important to all early years and primary educationalists, including those who are involved in teaching mathematics to the next generation of primary school teachers. The report, compiled as a result of this review, sets out the ways that children in primary…

In this article we analyse a didactical situation centred on the creation and use of a symbolic play environment in a class of pupils aged five and six years-old. The main source of data for this paper comes from an experimentation planned in relation to the following research question: does symbolic play in simulated contexts help pupils to…

Source memory has consistently been associated with prefrontal function in both normal and clinical populations. Nevertheless, the exact contribution of this brain region to source memory remains uncertain, and evidence suggests that processes used by young and older adults may differ. The authors explored the extent to which scores on composite…

Background: In preschool and primary education, pupils differ in many abilities and competences (giftedness). Yet mainstream educational practice seems rather homogeneous in providing age-based or grade-class subject matter approaches. Aims: To clarify whether pupils scoring initially at high ability level do develop and attain differently at…