In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into…

Number fact knowledge spans far beyond conventional automatic mastery practices involving rote learning. Having the ability to automatically recall number facts fluently does not mean students will have strong conceptual understanding. This article provides suggestions for how number fact thinking and fluency might be developed in primary…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

Our everyday lives have been transformed in 2020. Key features of this transformation have been the significance of COVID-related numeracy in our everyday lives and the realisation of the story it might tell about lives, health and death. In recent years, governments and educators around the world have been advocating for numeracy as an essential…

While focusing on numeracy is essential in preschool classrooms with deaf and hard of hearing (DHH) children, it is also important that concepts of numeracy be taught in a way that incorporates executive functions, introduces computational thinking, and prepares students for life in a 21st-century world. Technology-enhanced teaching resources…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

Research suggests that young children have a complex sense of informal mathematics, including an understanding of more and less, shape, and patterns (Ginsburg, Lee, & Boyd, 2008), and that attention to mathematics in early childhood ensures that children have a strong foundation for later learning. For children with identified disabilities,…

Children's development of foundational mathematics concepts begins long before they enter the kindergarten classroom. Early experiences with color, shape, and pattern recognition as well as the ability to seriate sizes all contribute to a strong beginning to young children's mathematical conceptual development. This article presents how a…

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;…

Children and animals of all kinds are said to develop some degree of number sense. The search for "number neurons" and neural correlates of computational thinking aims to identify biological primitives to explain the emergence of number sense. This work typically looks for the sources of number sense in organisms, but one might extend…

Differentiating instruction can be difficult, however, when higher performing students yearn to be stretched and lower performing students benefit from scaffolded support. One way to meet these students' learning needs and everyone in-between is to embrace the notion of novel exploration in support of critical school mathematics concepts. Novelty…

Quality primary education is one of the 17 UN Sustainable Development Goals (SDGs). Undoubtedly, mathematics plays a key role in overcoming future challenges, and mathematical competence and problem-solving skills could help provide appropriate solutions to current and future social, environmental and economic challenges. The following paper deals…

Secondary teachers and leaders, many of whom are implementing the Common Core State Standards, are seeking guidance about how to implement disciplinary literacy practices. Of the four core subjects taught in secondary schools--English, history, math, and science--the authors have found through their work with secondary teachers that math teachers…

Using a game-based context and concentrating explicitly on language, students in the early years are able to make sense about place value amid the vagaries of the English language in naming numbers. This conceptual approach to understanding place value allows students to further develop number strategies beyond counting by ones.

A Number Talk is a brief activity (10-15 minutes in length) that is designed to support students' mathematical sense making and promote flexible thinking. During a Number Talk, students engage in mental computations. Number Talks help students do the following: (1) Develop number sense focused on making sense of quantity and mathematical…