The O?THO exhibit, situated within the LivingLab at Copernicus Science Centre (CSC) in Warsaw, Poland, introduces visitors to the Cartesian principles of representing numerical data as points in a two-dimensional space--the coordinate system. This interactive tabletop digital exhibit takes the form of a collaborative two-player game where…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…

Young children naturally engage in mathematics as they play and explore. Although many early childhood educators are aware that children are frequently interacting with mathematical ideas, a certain level of knowledge and awareness is required to identify and highlight the mathematics that children are engaging in and to create opportunities for…

The collection of studies in this special issue make an important contribution to our understanding and measurement of the core cognitive and noncognitive factors that influence children's emerging quantitative competencies. The studies also illustrate how the field has matured, from a time when the quantitative competencies of infants and young…

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…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

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…

This paper discusses the critical situations I have been asked to "improve" by providing professional development for teams of adult numeracy and functional mathematics teachers in the post-16 sector in London. These situations have not been identified through any research process, but arise from internal management reviews of course…

An essential part of understanding number words (e.g., "eight") is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words…

In August 2010, ACER held its annual conference in Melbourne. The theme of the 2010 conference--"Teaching Mathematics? Make It Count"--was chosen to highlight that mathematics education is an area of high priority in Australia. In the author's own presentation to the conference, he outlined research into an area that he believes is very…

Now in a second edition, the award-winning "The Trouble with Maths" offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, this book offers a complete overview of the…

Within increasing pressure on young people to perform successfully in work, there is a growing concern regarding their levels of numeracy (and literacy). Whether such concerns are founded is the basis of this paper. This paper reports on the numeracy practices undertaken by three young boatbuilders who were nearing the completion of their 4-year…

Governments and other stakeholders have become increasingly interested in assessing the skills of their adult populations in order to monitor how well prepared they are to meet the challenges of the new information world. The current paper provides an overview of the conceptual framework for the assessment of numeracy developed for the OECD's…

Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…