Numeracy Education

by

Mike Askew

• LAST REVIEWED: 25 November 2014
• LAST MODIFIED: 25 November 2014
• DOI: 10.1093/obo/9780199756810-0118

Introduction

Numeracy has become an integral part of mathematics education. But the precise nature and implications of teaching for numeracy in primary/elementary and secondary schooling are still being worked through by the academic, practitioner, and policy communities. Although numeracy is generally accepted as recognizing the importance of schooling that ensures students will learn mathematics that can be applied in their adult lives (as opposed to say, the mathematics required for further study of the discipline or for specialist professions), there is yet to be agreement on what this should look like in practice. At one extreme, numeracy is interpreted as equipping school leavers with the basic skills of arithmetic in that numeracy is regarded as a subset of mathematics. At the other extreme, arguments are made for numeracy teaching needing to address the political dimensions of mathematics and its uses in society and thus help learners become critical citizens. Sections of this bibliography present key texts for each side of this debate. A common assumption to both positions is that learning about number and arithmetic has to go beyond being taught procedures and needs to help learners develop “number sense.” Many scholars have theorized and researched what the components of number sense might comprise, and others have examined the sorts of pedagogies that might promote such learning: key texts in teaching and learning for number sense are presented. If it is the case that current schooling is not succeeding in helping learners develop the numeracy skills that they need for life outside of school, then this raises questions about the nature and content of the school curriculum. One approach to accounting for the shortcomings of school-taught numeracy is that learning is highly “situated”: what is learned is heavily influenced by the contexts in which it is learned. Hence, different levels of numerate behavior are demonstrated by learners in different contexts; and the argument goes that it may be only a select few learners who have the wherewithal to transfer their mathematical knowledge out of the classroom. Other researchers are more optimistic that the school curriculum can promote numeracy, particularly by engaging learners in authentic problem solving, although what is authentic for one learner may not be for another, which raises issues about equity. Finally, with the increased use of international comparisons to compare nations, policymakers are increasingly concerned to raise standards of numeracy and so a section examines some policy initiatives and outcomes. Readers should note that although there is an increasing literature base about college-level numeracy, and wide research into adult numeracy, the scope of this review mainly addresses numeracy in primary and secondary schools.

Defining Numeracy

Although the term “numeracy” has become widely adopted within education, and particularly by policymakers, there is no agreement over the precise meaning of the term or clarity over its relationship to mathematics. As a verb, numerate as meaning “to count or calculate” dates back at least to the 17th century, but the Crowther Report (Department of Education and Science 1959) turned the term into a noun, with emphasis on high levels of understanding of scientific ideas. By the 1990s numeracy, particularly in the UK and Australia, had become more associated with developing the skills of mathematics in everyday life and basic “number sense” (Cockcroft 1982 and Willis 1990). Thus one generally accepted view of numeracy might be summed up as “functional,” as a subset of mathematics, largely about number and appealing to those in favor of “back to basics.” Girling 1997 argues that the increasing availability of calculators changed the nature of what number sense might be, with less emphasis on performing actual calculations: this debate is still to be resolved, particularly in relation to adults’ needs (Neill 2001 and Kaye 2003). The United States was a late adopter of the term “numeracy,” with US writers preferring the term “qualitative literacy,” seen as distinct from being a subset of mathematics. So whereas mathematics might be characterized as dealing with the abstract and general, qualitative literacy requires the development of critical engagement with particular instances of mathematics in use (Steen 2001 and Mayes, et al. 2013). The growth in attention that international testing has garnered, in particular the Organization for Economic Cooperation and Development’s Programme for International Student Assessment (PISA: Programme for International Student Assessment) and its definition of mathematical literacy has to an extent brought more global unity to the definition of numeracy, particularly as more nations join this program of assessment.

• Cockcroft, W. H. 1982. Mathematics counts: Report of the committee of inquiry into the teaching of mathematics in schools. London: Her Majesty’s Stationery Office.

  Sets the tone for many of the later interpretations of numeracy by defining it as having an “at homeness” with numbers and an ability to cope with the mathematics of everyday life.

• Department of Education and Science. 1959. A report of the central advisory council for education (the Crowther report). London: Her Majesty’s Stationery Office.

  Generally considered to be the first time both “numerate” as an adjective (as opposed to a verb) and the noun “numeracy” were used in the broad sense of “scientific literacy” (a term that is itself now widely contested) and thus mirror the term “literacy.”

• Girling, M. 1997. Towards a definition of basic numeracy. Mathematics Teaching 81:1–4.

  This classic paper, originally written for a meeting of the Schools Calculators Working Party, was one of the first to argue for the sensible use of calculators to replace teaching standard algorithms: the debate around this still continues.

• Kaye, D. 2003. Defining numeracy: Concepts, meaning and words. In Learning mathematics to live and work in our world. Proceedings of the 10th international conference on adults learning mathematics. Edited by J. Maasz and W. Schloeglmann, 194–199. Strobl, Austria: Rudulf Trauner Univ.

  Summarizes a range of definitions presented at the Adults Learning Mathematics conferences. Many of these are relevant to school numeracy, and there are links to papers and other resources.

• Mayes, R. L., F. Peterson, and R. Bonilla. 2013. Quantitative reasoning learning progressions for environmental science: Developing a framework. Numeracy 6.1: Article 4.

  DOI: 10.5038/1936-4660.6.1.4

  Although the primary focus on the numeracy (quantitative reasoning) this paper has a good overview of the literature and various definitions of numeracy.

• Neill, A. W. 2001. The Essentials of Numeracy. Paper prepared for New Zealand Council for Educational Research. Christchurch, 6th–9th December.

  Presents various definitions of numeracy and identifies common themes, particularly in terms of numeracy as an essential skill. The idea of “street-wise maths” is briefly examined.

• PISA: Programme for International Student Assessment.

  Portal to the wide range of PISA reports, many of which focus on mathematical literacy.

• Steen, L. A., ed. 2001. Mathematics and democracy: The case for quantitative literacy. Washington, DC: National Council on Education and the Disciplines (NCED).

  Numeracy is a less frequently used term in the US literature, with Steen consistently working to include quantitative literacy (QL) in public education. This strong collection of papers argues for why QL should be included in education: what it is, what it is not, and in particular how QL is more than just applied arithmetic.

• Willis, S., ed. 1990. Being Numerate: What counts? Hawthorn: Australian Council for Educational Research.

  An early but significant set of papers focusing on numeracy in the context of daily life and on the importance of teaching numeracy skills. Defining numeracy is considered in terms of implications for teaching and assessment.