The purpose of this paper is to propose an effective learning environment for the initial stages of mathematical learning. Basic numerical skills and the objects and actions that trigger those skills are conceptualized as a mathematics-learning environment. We discuss numerical learning mechanism and the basic skills and environments we use to…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

In this meta-analysis of 54 longitudinal studies with over 58,000 students in kindergarten through 12th grade, we examined the predictive nature of early numeracy measured at or before the first year of formal schooling in relation to later mathematics. Results showed that early numeracy significantly predicted mathematics measured after 6 months…

This study aimed to reveal the solutions of pre-service teachers to contextual problems related to number bases other than the base ten. Furthermore, it was intended to investigate which issues pre-service teachers discussed about their learning in the problem-solving process, including context, and about student learning in their future teaching…

Traditionally, various meanings of "10" are systematically ignored in early childhood curriculum and children's understanding of numbers is restricted within the solitary mapping between the symbol "10" and quantity concept of "ten." This may be problematic for other ways that mathematics is used, both in modern life…

We make a "prima facie" case for identifying a single pathway in the learning of Hindu-Arabic numerical symbols and discuss why this ability may be a critical gateway concept in developing mathematical competencies. A representative sample of English and Scottish children was assessed using a number symbol identification paradigm in the…

In this study, a situation-based interactive e-book system was developed for improving children's learning performance of numerical operations. To evaluate the effectiveness of the system, an experiment was conducted in one kindergarten. The results showed that the proposed approach significantly improved the children's learning achievements.…

Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

This action research project looks at what happened when a small group of adult numeracy teachers with widely different experiences of learning and teaching mathematics explored their own informal numeracy practices and undertook a series of collaborative mathematical tasks. Evidence from qualitative data collected during the enquiry suggests that…

"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…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

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,…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

In the renewed "Primary Framework for Mathematics" for England, great emphasis is given to calculation and its prerequisites (DfES, 2006). Expectations are increased for calculations and the recall of number facts, with mental calculation owning a higher profile, while progression in written calculation is clarified. The greater focus on…

Studied number use in language by preschool children and their mothers during cooking experiences. Found that although children used a variety of number words, mothers made greater use of number words than did children. Strong relationship between reciprocal numeracy episodes (between mother and child) and child's number use suggests that adult…