Fractions remain a challenging area of school mathematics at every stage of education, with impacts that extend far beyond the school years. For this study, researchers engaged in classroom-based design research over a 6-year period to investigate effective strategies for teaching fractions with Canadian students. Participants included 86 teachers…

"Embodied trainings" allowing children to move their whole body in space have recently been shown to foster the acquisition of basic numerical competencies (e.g. magnitude understanding, addition performance). Following a brief summary of recent embodied training studies, we integrate the different results into a unified model framework…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

Using both child-guided and adult-guided learning, Intentional Teaching in the early years can be a powerful tool for enhancing young children's numeracy skills. As Epstein (2009) notes, this can include providing "opportunities for children to represent things by drawing, building and moving" (p. 47). This paper investigates how…

"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard…

In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child's level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning,…

School gardening has become increasingly popular as a context for learning in which children construct new knowledge, learn cultural and societal values related to ecological awareness, and develop and practice authentic or real-world skills (Blair, 2009; Bowker & Tearle, 2007). The present research was a longitudinal case study of children's…

One of the greatest challenges for middle school Earth science teachers is helping our students get a feel for the magnitude of the long spans that make up Earth's history. The intent of the strategy presented here is to help middle school students get a feel for the real sizes of powers of 10, and then help them use that understanding by…

This is a book about teaching maths to pupils with learning differences, not learning difficulties. Teaching and learning in schools is, and always has been, print based. Other ways of thinking--visual, kinaesthetic, practical--are discounted in the classroom. To become teachers, students must jump over a long series of hurdles, formal and…

The paper describes an approach for identifying intervention strategies, techniques, procedures, and activities designed to enhance the developmental competencies of handicapped, mentally retarded, developmentally disabled, and at risk children (birth to 4 years of age). Curriculum procedures are classified according to domains of intervention and…

Shows how a manipulative device for taking attendance can be used to exercise mathematical thinking processes in a variety of contexts at different elementary school grade levels. Suggests activities using a magnetic attendance board for gathering classroom information; developing number, estimation, and graphing concepts; forming and verifying…

Offers 3 teaching designs developed for 12- to 16-year-old pupils taking into account personal differences in gender, culture, knowledge, and use of calculators. The designs concern the representation of three-dimensional objects in the plane, directions and great circles on the sphere, and exploration of the integrating calculator. (Contains 31…

This guide describes 47 number and numeration learning activities that can be used with elementary school students. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in developing further…

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…