Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

Anthropological approaches to studying the contextual specificity of mathematical thought and practice in schools can productively inform descriptions and analyses of mathematical practices within and across different teaching and learning contexts. In this paper I argue for an anthropological methodological orientation that takes into…

Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.

Certain dates stand out in history--October 12, 1492; July 4, 1776; and May 8, 1945, to name a few. Will December 21, 2012, become such a date? The popular media have seized on 12/21/12 to make apocalyptical prognostications, some venturing so far as to predict the end of the world. Scholars reject such predictions. But major archeological finds…

Children are often intrigued by number patterns and games and so it makes sense for teachers to include them in their mathematics lessons. Puzzles encourage the use of critical thinking skills and provide practice in important skills areas. The use of games fosters mathematical learning and encourages the mathematical processes that children use.…

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…

Hypothesizes that exploring the mathematical ideas behind mathematical terms enables children to gain insight into the structure of a number system and provides a basis for powerful playing with this structure. Describes visualizing mathematical ideas for exploring aspects of mathematics. Offers rectangular numbers to link and explore structures…

The numeracy handbook is a practical guide for teachers of numeracy and literacy to learners of English as a Second Language. Focus is on teaching numeracy and integrating numeracy and literacy. It considers issues in defining and teaching numeracy, examines numeracy in the workplace, designing a course and a unit of work, and analyzes numeracy…