During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

The efficacy of a research-based number-sense intervention for low-achieving kindergartners was examined. Children (N = 126) were randomly assigned to 1 of 3 conditions: a number-sense intervention followed by a number-fact practice session, an identical number-sense intervention followed by a number-list practice session, or a business-as-usual…

Children can sometimes appear to understand a concept such as place value without really having a deep understanding. Judy Bailey stresses the importance of listening carefully to children to identify their current understandings and then building on them systematically, using a range of materials, to promote a deep conceptual understanding. This…

Introduction: In this paper, Spanish future primary teachers' pedagogical knowledge of numbers and operation, as revealed through their results in the TEDS-M ("Teacher Education and Development Study in Mathematics"), is compared with that of two other groups. The first group are the future primary teachers of other OECD countries that…

This study proposes a framework for examining ways in which prospective teachers integrate mathematical knowledge acquired in advanced topics courses into explanatory knowledge for school teaching. Participants, all of whom had recently completed coursework in abstract algebra, were asked to explain concepts connected to the school mathematics…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue will focus on Number in the Number and Algebra strand. In this article Derek Hurrell provides a few tried and proven activities to develop place value understanding. These activities are provided for…

Children's understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this…

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

This article begins with an exploration of the origins of the Gregorian Calendar. Next it describes the function of school inspector Christian Zeller (1822-1899) used to determine the number of the elapsed days of a year up to and including a specified date and how Zeller's function can be used to determine the number of days that have elapsed in…

This study used a multiple probe across participants design, replicated across two interventions and counterbalanced across participant groups to examine the effects of number sense intervention and extensive practice intervention on strategy transformation when students with mathematics learning disabilities (MLD) solved basic fact problems. In…

The aim of this study was to model the most crucial numerical factors to the development of mathematical skills among children aged five to eight years (i.e. kindergarten, preschool, first and second graders). We categorised numerical skills into four main groups based on the results of longitudinal studies. A series of analyses of test batteries…

Number sense and self-regulation are considered foundational skills for later school learning. This study aimed to investigate the predictive power of kindergarten children's number sense and self-regulation scores on their mathematics and Turkish language examination scores in the 5th and 6th grades. The participants in this study were 5th grade…

Peer play provides ample opportunities for the use and development of self-regulatory and mathematical skills. This study aimed at examining whether children's engagement in solitary low-level play, interactive play and competent play influences their self-regulatory and number sense skills. The effect of demographic variables and children's…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…