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…

The principle of inversion--that a + b - b must equal a--requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the…

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most…

This article summarizes research on how students who are bilingual or learning English use two languages and examines how this research is relevant to mathematics classrooms. It is easy to notice that bilingual students sometimes use two languages. It is more difficult to know whether this practice might be significant to learning mathematics.…

This study examines the communication between pre-service teachers and sixth grade students in a project in which email was used for communication as students learned about fractions and were supported by the pre-service teachers. Specifically, the study investigated how the pre-service teachers applied their mathematical knowledge to understand…

Two developments have contributed to the convergence of views about the benefits of real-life and inquiry-based pedagogies in mathematics learning. First, the mathematics teaching community is increasingly focused on the learning of mathematics that involves the transfer of prior knowledge to novel problem-solving situations, a key element in…

This study sought to examine the effects of Tier 2 intervention in a multitiered model on the performance of first- and second-grade students who were identified as having mathematics difficulties. A regression discontinuity design was utilized. Participants included 126 (Tier 2, n = 26) first graders and 140 (Tier 2, n = 25) second graders. Tier…

To date, few studies have investigated the evolution of problem solving and general numeracy abilities during adulthood: skills that have obvious social importance. In this research, evolutions in adults' mental arithmetic skills were investigated using data from the IVQ 2004 French national survey, which tested 9,185 adults aged between 18 and…

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 - 9 yields…

This article shares investigation possibilities that lie within familiar concepts of greatest common factor and least common multiple.

This textbook provides not only a mathematical basis, but also a scientific structure. Blackboard exercises are included, and great facility in comprehending the combinations and divisions of numbers will be acquired by this method.

This textbook is a second-grade course in arithmetic. While it contains a review of the work of Grade I, pupils who have not had the benefit of a kindergarten training or of Grade I drill will need to have certain principles and definitions more carefully explained. Starting with this knowledge, which is usually given in all Kindergartens, the…

This textbook is a third-grade course in arithmetic. It contains a review of the preceding book, a continuation and extension of the work in the fundamental processes and in fractions, and the introduction of several new principles in their simplest form, as percentage. The exercises are divided into lessons for convenience. Better results will…

This textbook is a fourth-grade course in arithmetic. It contains a review of the principles taught in Book III, with their extension to problems of greater difficulty. A few new principles are introduced from time to time, the aim being to introduce the new thought side by side with the review of those already taught. Realizing that the highest…