Numeracy Strategy Research Articles

EVIDENCE INFORMED POLICY AND PRACTICE: METHODOLOGICAL ISSUES INVOLVED IN CONDUCTING A SYSTEMATIC REVIEW IN MATHEMATICS EDUCATION

This paper focuses on a systematic review of studies on the impact of the pedagogy of the National Numeracy Strategy (England) on primary school pupils’ confidence and competence. Findings from the review are that gains in competence may be a result of the specification of the curriculum rather than changes in pedagogy, that interactive whole class teaching as envisioned has not been fully realised, and that low attaining pupils may be disadvantaged by the way in which whole class teaching is being interpreted. In conducting the review there were some tensions involved in judging the reliability, validity and generalisability of the findings of the included papers, and in judging the weight of evidence in terms of the review question. This paper will address these tensions, describe this particular review process and discuss the findings.

MATHEMATICS IS NOT EASY: THE IMPORTANCE OF TEACHING CHILDREN TO STRUGGLE

This paper describes aspects of an 11-week teaching project with low achieving children. The children's prior experience of mathematics was one of failure to complete tasks successfully. They had made negative comparisons between themselves and their peers and had low self-esteem. The paper focuses on how I developed affective strategies to use alongside cognitive strategies as I tried to improve the children's mathematics. Six critical incidents, which illustrate the progression of the work, are described and analysed. Significant changes in how the children tackled mathematical work are discussed in terms of other research. Finally the outcomes of the project are considered in the context of the National Numeracy Strategy. I propose that the conscious use of affective strategies needs to be introduced alongside cognitive strategies if low achieving pupils are to make progress in learning mathematics.

Word, Definitions and Concepts in Discourses of Mathematics, Teaching and Learning

National Numeracy Strategy (NNS) guidance appears to characterise mathematical language as a set of specialist words with unambiguous definitions, yet analysis of the classroom transcript suggests that at least some mathematical concepts cannot be captured by such definitions. This paper explores the notion of definition within mathematics, considering both school mathematics and the field of academic mathematics research. Extracts of texts from these domains are analysed using tools drawn from systemic functional linguistics. The more advanced texts show definitions to be constructed and used in creative and purposeful ways. This contrasts with the one-to-one word-concept relationship apparent in the NNS guidance and in a text for ‘Intermediate Level’ secondary students. This finding raises the question of the extent to which the linguistic models implicit in the texts for less advanced school students and their teachers allow students to learn more powerful aspects of mathematics.

Ambiguity in the Mathematics Classroom

Mathematics is commonly seen as a discipline with no place for linguistic ambiguity. In this paper, the treatment of ambiguity in two data extracts is critically examined. Analysis draws on two contrasting models of the nature of mathematics and mathematical language. The formal model sees meaning as fixed and relating to language relatively unproblematically. The discursive model sees meaning as situated in and by interaction, and so as shifting and changing as interaction unfolds. Analysis of the extract from the National Numeracy Strategy suggests that it is based on the formal model. This analysis is contrasted with analysis of classroom interaction which reveals how, from a discursive perspective, ambiguity can be seen as a resource for doing mathematics and for learning the language of mathematics.

Implementing the foundation stage in reception classes1

This article draws upon a Department for Education and Skills (DfES) commissioned telephone survey of a nationally representative sample of schools to investigate the challenges faced by those seeking the successful implementation of the Foundation Stage (FS) (for 3–5‐year‐olds) in reception classes. Its focuses on head teachers' and reception teachers' own reported knowledge, perspectives, experiences, attitudes and views about reception practice, as well as background information on provision and teacher characteristics. A vast and rich amount of data was gathered providing a snapshot of practices and opinions related to the second year of implementing the FS. The majority of head teachers and reception teachers had a positive view of the FS and progress made in implementing it. In general, implementation of the National Literacy and Numeracy Strategies, transition to Key Stage 1 and planning opportunities for children to engage in activities they had planned and initiated themselves was not regarded as a problem. The survey highlighted the importance of staff training and the need to extend this. Greatest concerns were expressed in schools with mixed‐age classes, teaching two curricula with distinct pedagogies. It is concluded that schools in both urban and rural/mainly rural areas have distinct, though similarly diverse teaching groups. A wide range of teaching strategies, based on children's diverse needs, will be required to motivate, support and extend them appropriately. The results are interrogated from the perspective of relevant research carried out during the same period.

Attitudes, inclusion and widening participation: a model of interactive teaching and leadership

Interactive whole‐class teaching is championed by the English National Curriculum and the accompanying National Literacy and National Numeracy Strategies. Inspection of the related literature, however, reveals no corresponding pedagogy, which is also lacking in earlier ‘interactive’ initiatives. The paper considers how traditional ‘hierarchical’ perceptions have undermined the ‘practical’ prescriptions given and neglected attitudinal influences. It argues that this practical deficit, aspects of teacher education and institutional leadership/culture have historically made it difficult for teachers to fully ‘unlearn’ authoritarian ‘transmission’ practices which the UK Government recognizes work against inclusion and performance at all education levels. Research undertaken in the 1970s provides a practical model of inclusive interactive teaching, training and leadership and this is considered to be one of three related requirements necessary to overcome the reported implementation failure of an interactive approach. Finally, the paper considers the example of a headteacher whose collaborative ‘interactive’ attitudes enabled an inclusive learning ethos, increasing accessibility and pioneering routes to widen participation for the traditionally excluded.

Implementing a required curriculum reform: teachers at the core, teaching assistants on the periphery?

This paper considers the part played by teaching assistants in the implementation of the National Literacy and National Numeracy Strategies, two widespread UK government reforms. Evidence from two sources of evaluation (the Ontario Institute in Canada and OfSTED, the school inspectorate for England) indicates that assistants are providing ‘remedial’ support for up to 25% of children in English primary schools. However, although the evaluators note this, they fail to truly acknowledge the important contribution of assistants to the functioning of the Strategies. The paper argues that the lack of acknowledgement arises from the evaluators’ view of teaching assistants as ‘peripheral’ and teachers as ‘core’. This does assistants a great disservice, but also masks the shortcomings of the Strategies, particularly with regard to the way in which a required pedagogy, linked to targets and tests, has created an exclusionary pressure leading to the separation of teaching by teachers and assistants, respectively.

Teacher–Pupil Talk in Whole-class Discussions and Processes of Social Positioning within the Primary School Classroom

The shape and form of effective teacher–pupil talk has recently become the focus of attention within policy guidelines such as the National Numeracy and Literacy Strategies. Prior to this, research on classroom discourse has established that social context plays an important role in determining the quality of teacher–pupil talk since it directs teachers' and pupils' interpretations of what is said. This paper presents a multi-layered approach to the analysis of whole-class discussions which highlights the impact of wider, institutional and historical aspects of the classroom context on the meanings relayed within interactions. Video and audio data, collected over a five-month period of participant observation in a primary school mathematics classroom, highlights how issues such as teacher expectations and time pressure influence the quality of interactions pupils experience. The paper concludes that teacher–pupil interactions play an instrumental role in determining the social positioning of pupils within the classroom and this has a profound effect on the pupil's access to the learning process. In light of such findings, the potential limitations of establishing and implementing guidelines on effective teacher–pupil talk within policy are discussed.

National numeracy initiatives in England and Wales: parallel attempts at achieving large‐scale reform

The introduction of the National Numeracy Strategy (NNS) in England in September 1999 represented a very significant attempt to change the way mathematics was taught in primary schools. In Wales, where the NNS does not apply, an alternative strategy required Local Education Authorities (LEAs), in consultation with their schools, to develop locally based numeracy initiatives. This article presents and discusses results from a comparative study of the way in which headteachers viewed these contrasting attempts to raise standards of numeracy and their perception of the way in which the initiatives impacted upon pupils, teachers and teaching approaches. Whilst the data presented within the article may be of particular interest to policy makers and practitioners in England and Wales there would also appear to be some messages for those who may be concerned with similar large‐scale reform efforts, elsewhere.

Interactive whole class teaching in the National Literacy and Numercy Strategies

The study set out to investigate the impact of the official endorsement of ‘interactive whole class teaching’ on the interaction and discourse styles of primary teachers while teaching the National Literacy and Numeracy Strategies. In both strategies, interactive whole class teaching is seen as an ‘active teaching’ model promoting high quality dialogue and discussion between teachers and pupils. Pupils are expected to play an active part in discussion by asking questions, contributing ideas and explaining and demonstrating their thinking to the class. Using computerized systematic classroom observation, discourse analysis of transcripts and a questionnaire, the project looked specifically at the discourse strategies currently used by a national sample of primary teachers when teaching the literacy and numeracy strategies and their perceptions of current practices. The findings suggest that traditional patterns of whole class interaction have not been dramatically transformed by the strategies. The implications of the findings for classroom pedagogy, teachers' professional development and future research priorities are considered.

Nationalising primary mathematics: Mixed messages and conflicting methods?

This paper examines how mathematics education policy at the national level affects practice at the local level, using a policy trajectory model that attempts to trace policy through the contexts of influence, policy text production and practice (Bowe and Ball, 1992). It focuses on the development of calculation in the National Numeracy Strategy (1999), drawing on elite interviews, document analysis and studies carried out over the period in question. It concludes that policy text inevitably incorporates contrasting values, competing ideas, as well as differing vested interests. This creates some inconsistency in guidance for teachers and, hence, the potential for confusion at the level of practice

THE IMPACT OF THE NATIONAL NUMERACY STRATEGY IN YEAR 4 (II): TEACHING

The Nuffield Year 4 project set out to examine selected aspects of the impact of the National Numeracy Strategy (NNS) in primary schools by using comparable data on Year 4 pupil attainment and teaching collected in 1997/98 and 2001/02, two years before and two years after the introduction of the Numeracy Strategy. In this second paper we address the following questions: • How and to what extent has numeracy teaching in Year 4 changed? • Why have these changes occurred? • How can we improve future implementation of reforms? • How can we inform continuing professional development?

THE IMPACT OF THE NATIONAL NUMERACY STRATEGY IN YEAR 4 (I): ATTAINMENTAND LEARNING

The Nuffield Year 4 project set out to examine selected aspects of the impact of the National Numeracy Strategy (NNS) in primary schools by using comparable data collected from 35 schools in 1997/98 and 2001/02 as part of the Leverhulme Numeracy Research Programme. In this first paper we report on changes in attainment using a specially designed test of numeracy administered in October and June. While numeracy attainment rose during the period of the introduction of the NNS, the effect was small and it varied in relation to different aspects of the curriculum. The results of low attainers fell on average, as did results in over a third of schools. The amount of progress made over Year 4 was similar in 2001/02 and in 1997/98. Reasons for these changes are explored.

Oranges aren't the only fruit. Ask a Gardner

The introduction of the National Literacy and Numeracy strategies in U.K. schools is discussed in the light of Howard Gardner's theory of multiple intelligences. Although the core curriculum is evidently important, it is argued that the introduction of the national strategies has created a possible over-emphasis in these subjects at the expense of the foundation curriculum, creating a situation in schools which appears to fly in the face of Gardner's research. As a result children with intelligence profiles outside those demanded by the core curriculum may be disadvantaged. Further implications of the national strategies on children's wider development are discussed.

Giving All/Reaping Rewards

A number of remote Indigenous communities in Western Australia and the Northern Territory runtheir own independent schools. The communities are faced with a constant battle to recruit qualityteachers to their schools and to attain a high level of literacy in their students. The 1996 National School English Survey reported thot less than 20% of Year 3 Indigenous students met the reading standards with similar findings for Year 5 (Department of Education Science and Training, 1997). There is strong evidence that student achievement is significantly linked to committed and wellqualified teachers (Darling-Hammond, 2000). The Commonwealth Government National Indigenous English Literacy and Numeracy Strategy (NIELNS) Report 2000 stated that recruiting 'good teachers' who are culturally aware and who can implement 'best teaching methods' are key elements in raising the literacy standard of Indigenous students (Department of Education Science and Training, 2000).

Strategic leadership for large‐scale reform: the case of England's national literacy and numeracy strategy

Both ‘strategic’ and ‘distributed’ forms of leadership are considered promising responses to the demands placed on school systems by large‐scale reform initiatives. Using observation, interview and survey data collected as part of a larger evaluation of England's National Literacy and Numeracy Strategies, this study inquired about sources of leadership, the distribution of leadership functions across roles and how such distribution could also provide the strategic coordination necessary for successful implementation of such an ambitious reform agenda

Numeracy Coordinators: ‘Brokering’ Change Within and Between Communities of Practice?

ABSTRACT: This paper draws on a study of numeracy coordinators in primary schools in the UK in the second year of the implementation of the National Numeracy Strategy (NNS). It identifies them as working between three main tasks: embedding the Strategy, sustaining teacher collegiality and auditing accountability. We identify tensions in ‘being a coordinator’ in relation to these tasks, especially for discourse and identity. We assess the usefulness of the metaphor of ‘brokering’ in ‘communities of practice’ (Wenger, 1998) to theorise such tensions. We conclude with some reservations about the metaphor, especially in the way the tensions are discursively performed in relation to the rate of change, complexity of notions of professional identity, and the problematic ‘community’ status of audit in the educational context.

The key role of educational research in the development and evaluation of the national numeracy strategy

Abstract The authors contest a politician's claim that the National Numeracy Strategy (NNS) in English primary schools has been an undisputed success with no contribution from educational researchers. First, the key role of researchers and research in the development of the NNS is outlined. Then there is a description of the Leverhulme Numeracy Research Programme, a linked set of research studies combining a large‐scale longitudinal survey and qualitative case studies. Results suggest that the NNS had a positive but small effect on numeracy standards, but that there are many schools, children and areas of mathematics for whom the effect has been negligible or negative. The discussion of reasons for this relates to evidence from the Leverhulme Programme and elsewhere about the effects of different factors on attainment. Finally, there is some question of whether government and government agencies are being completely open about the evidence of effectiveness of the NNS.

A THEORETICAL COMPARISON OF THE TEACHING OF MENTAL CALCULATION STRATEGIES IN ENGLAND AND THE NETHERLANDS

This comparative study aims to identify the philosophical underpinnings of the principles of two approaches to the teaching of primary mathematics, the English Numeracy Strategy and the Dutch Realistic Mathematics Education and to discuss pedagogical implications. Philosophical views of knowledge as personal'subjective' and culturally'constructed' are considered in relation to inter subjectivity as a state of shared knowledge within a community of mathematicians. The didactics of the teaching of mental calculation strategies from the two approaches are used to illustrate a key epistemological difference in the mathematics that is presented to children.

National Curriculum Mathematics Tests in England at Key Stage 2: Weights and measures?

This paper reports on a series of statistical analyses carried out on some of the National Curriculum tests in mathematics for 11-year-olds in England. In England all 7-, 11- and 14-year-olds are tested in English, mathematics and science (11- and 14-year-olds only). The tests for 11-year-olds are very high stakes, in that the results are published in a school-by-school basis in newspapers etc. The analyses were prompted by the suggestion (from governmental organisations) that the balance of the curriculum content in the mathematics tests should be changed to accommodate better the require ments of the government-initiated National Numeracy Strategy. The analyses were carried out on two datasets, involving nationally representative samples of 11-year-old pupils. The analyses reveal some interesting patterns of change in the overall outcomes when Handling Data questions were statistically replaced by Number items of various kinds and also some interesting changes at the individual level, which could potentially affect the Level outcomes of a significant number of children nationally. However, the final conclusion reached is that, given an appropriately sized and structured pool of items across the curriculum content areas, tests can be constructed which are of an appropriate level of difficulty and discrimination power and which still allow year-on-year calibration of the national standards in mathematics.