Mike Askew

Mike Askew
University of the Witwatersrand | wits · Marang Centre for Mathematics and Science Education

About

71
Publications
40,812
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,397
Citations
Citations since 2016
23 Research Items
583 Citations
2016201720182019202020212022020406080
2016201720182019202020212022020406080
2016201720182019202020212022020406080
2016201720182019202020212022020406080
Additional affiliations
January 1990 - August 2010
King's College London
Position
  • Chair Professor Mathematics Education

Publications

Publications (71)
Conference Paper
Full-text available
This paper shares results from a national ‘familiarisation trial’ of a mental mathematics intervention focused on assessing and encouraging strategic calculation methods with Grade 3 students in South Africa. Successful smaller pilots refined the intervention into 6 foci and this paper draws on assessment results from the four provinces that triall...
Article
Full-text available
Background: The co-establishment of social and sociomathematical norms in the microculture of South African classrooms and its possible effects on early number learning has largely been unexplored. Social norms are considered to be general classroom norms that are relevant in any teaching and learning space, whilst sociomathematical norms are speci...
Article
Full-text available
In this paper, we share details of a South African early grades’ number intervention informed by aspects of Davydov’s writing on early number teaching and learning. A key part of Davydov’s approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number Starters...
Article
This paper focuses, empirically, on the developments seen in a group of South African early grades’ mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consi...
Article
This paper argues that there is a gap in the research on teaching and learning mathematics, and thus a need for research into effective teaching practices. From a selective review of literature, reasons are examined as to why less emphasis appears to have been placed on generating knowledge about teaching and effective mathematical teaching practic...
Article
The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also addit...
Article
Full-text available
The Primary Teacher Education (PrimTEd) project was established in response to concerns about the pre-service preparation of primary teachers in South Africa. In order to inform the development of appropriate pre-service mathematics courses, an initial need in the PrimTEd project was to establish the nature of the mathematical knowledge of pre-serv...
Article
Full-text available
Background: Given the context of low attainment in primary mathematics in South Africa, improving learners’ understanding of multiplicative reasoning is important as it underpins much of later mathematics. Aim: Within a broader research programme aiming to improve Foundation Phase (Grades 1–3, 7–9-year-olds) learners’ mathematical performance, the...
Article
In this paper, we provide an elaboration of the notion of mathematical structure – a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and connects...
Article
This paper is centred around a framework for studying teaching—Mediating Primary Mathematics (MPM)—developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the meditation...
Article
This paper is centred around a framework for studying teaching—Mediating Primary Mathematics (MPM)—developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the meditation...
Chapter
Full-text available
This chapter focusses on the diverse theoretical and methodical frameworks that capture the complex relationship between whole number arithmetic (WNA) learning, teaching and assessment. Its aim is to bring these diverse perspectives into conversation. It comprises seven sections. The introduction is followed by a narrative of a Macao primary school...
Chapter
Full-text available
The goal of the chapter is to explore and discuss teacher education in different parts of the world and to emphasize the commonalities and differences not only in the panellists’ countries, but in a broad perspective. By looking at differences in the parts and processes of different educational systems, we can learn from each other and develop a mo...
Article
Full-text available
In this article, we present aspects of teaching that draw attention to connections – both within and between examples – in order to explore the potential objects of learning that are brought into being in the classroom space and thus what is made available to learn. Our focus is on exploring differences in teaching over time, in the context of lear...
Article
This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of repea...
Chapter
The teaching of division is a complex task: division is difficult to teach in a connected and coherent way, given the diversity of models of division, and differences in their associated actions and utterances. This chapter focuses on the signs produced by teachers in their attempts to explain division. The signs produced follow from unifications b...
Article
Full-text available
[Link to article: http://link.springer.com/article/10.1007/s10649-017-9776-1]. In this paper, we present and discuss a framework for considering the quality of primary teachers’ mediating of primary mathematics within instruction. The 'mediating primary mathematics' framework is located in a sociocultural view of instruction as mediational with ma...
Chapter
The I Hate Maths (IHM) project was set up to acknowledge and address the fear, anxiety, and dislike that primary teachers, like so many people, express in relation to mathematics. The project works on transforming these emotions through annual workshops where primary teachers come together to do mathematics in a safe, collective, and enjoyable envi...
Chapter
A breadth of literature argues that mathematics is a human activity arising from the practices of mathematising real-world experiences. From this perspective, teaching needs to present situations that learners can make sense of and through which they can be guided to re-invent more formal mathematics. Based on principles and resources arising from...
Chapter
The chapters in this volume are written largely by early career researchers, many of whom draw on studies carried out toward the award of a PhD. Encouraging is the evidence provided here of these researchers not being content merely to build on research conducted in other parts of the world, much of such research coming from contexts that resemble...
Conference Paper
Full-text available
In this paper we discuss findings from data drawn from a broader PhD study. The data was collected in an intervention in a South African grade 2 isiZulu language of instruction classroom. The intervention consisted of 13 lessons based around word problems, conducted twice a week across one term, with the purpose of investigating how the principles...
Chapter
Many responses to issues of diversity in mathematics classrooms result from a discourse of classroom diversity as a difficulty, something at best as to be reduced, at worst, as a problem to be ‘managed’ in some way. Such discourses of reducing or managing diversity arise, in part, through talk about diversity being framed around the causes of the ‘...
Article
Many of the papers in this special issue draw on the fundamental model of numeracy developed by Goos et al. (Transforming mathematics instruction: multiple approaches and practices. 81–102, 2014). Four elements in that model—contexts, tools, dispositions, and mathematical knowledge—are embedded within a critical orientation, and being, or becoming...
Article
Full-text available
p>I cringe at the fashion of reducing everything to a set of discrete points – ‘the five keys to eternal happiness’, ‘twenty-seven ways to beat procrastination’ – yet find myself attracted to the 4 E’s model of cognition: that cognition is embodied, embedded, enactive, and extended. Far yet from being a coherent model in the sense of general agreem...
Article
Full-text available
Globally, mathematics and science education faces three crucial challenges: an increasing need for mathematics and science graduates; a declining enrolment of school graduates into university studies in these disciplines; and the varying quality of school teaching in these areas. Alongside these challenges, internationally more and more non-special...
Article
Full-text available
The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers respo...
Article
Full-text available
Children’s learning of early number bonds is a significant issue in South African schools because evidence shows that flexible and efficient (fluent and reasoned) knowledge of number bonds to 20 correlates with success at the end of primary schooling, yet the evidence is that many South African students are over-reliant on inefficient counting meth...
Chapter
Creativity is increasingly highlighted on education agendas and, internationally, mandated curricula explicitly include calls for creativity. For example, the recently introduced Australian National Curriculum is typical with one of three overall aims being the development of confident and creative individuals (Australian Curriculum Assessment and...
Article
This article is located within the literature arguing for attention to Big Ideas in teaching and learning mathematics for understanding. The focus is on surveying the literature of Big Ideas and clarifying what might constitute Big Ideas in the primary Mathematics Curriculum based on both theoretical and pragmatic considerations. This is complement...
Article
Mike Askew explains why maths and drama can go hand-in-hand and suggests a few improvisation games to get you started.
Article
‘Lively and thought provoking…at a key time in the development of primary mathematics teaching and learning. It offers a very much richer model of mathematics learning than is available to many young learners and has the potential to have a real impact on the way mathematics is taught.’ - Jan Winter, Bristol University, UK
Article
Full-text available
Also available as an electronic publication at: www.nuffieldfoundation.org Database of sources available at: www.kcl.ac.uk/education/research/mechma Copyright © Nuffield Foundation 2010 Extracts from this document may be reproduced for non-commercial purposes on the condition that the source is ackno wledged. www.nuffieldfoundation.org 3 Foreword T...
Article
This chapter reports on aspects of the work of the Leverhulme Numeracy Research Program, a 5-year study funded in the UK during 1997-2002 by the Leverhulme Trust. It focuses on only one aspect of the Leverhulme Program, that of progression in learning. Its objective is to report on a progression model in relation to both items and children and to r...
Chapter
In this chapter, the spotlight is on that part of our model that includes the person within their immediate professional community responding to an external intervention, and has links mainly with the external professional and policy. The policy in this case emanates from the National Numeracy Strategy in the form of a Five-day course covering aspe...
Chapter
Case-studies conducted as part of a longitudinal study of mathematics teaching and learning in primary (elementary) classrooms were originally intended to shed light on children’s mathematical understandings. It became clear, however, that mathematical understanding and attainment were inseparable from the social identities as learners of mathemati...
Article
Teacher change in mathematics education is recognised to be a difficult and at times painful process. This is particularly so in countries such as England where primary mathematics is taught by non‐specialist teachers, who have often had negative experiences of their own school mathematics. In this paper we explore primary teachers' emotional relat...
Chapter
In this last chapter we reflect on our reporting of change from the different perspectives within the Leverhulme Numeracy Research Programme. We consider whether and where in the course of our research we have encountered “deep” change (Earl et al., 2000, p. 39) and how this might be characterised. We develop the notion of zone of enactment by iden...
Article
Full-text available
The metaphor of 'scaffolding' is popular in mathematics education, particularly in accounts purporting to examine the mediated nature of learning. Drawing on Holtzman and Newman's interpretation of Vygotsky I argue that scaffolding rests on a dualistic view that separates the knower from the known. In line with their work, I being to explore what a...
Article
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 te...
Article
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 th...
Article
Drawing on the data from the study outlined in Chapter 5, Teachers’ Knowledge, Conceptions and Practices, this chapter includes case studies of teachers in order to examine more closely the ‘space’ between the pupil, the person and the policy within the classroom, hence the core of teachers’ classroom practice. Teachers’ choice of tasks and modes o...
Book
This introduction sets the scene for the remainder of the book by considering first the international context of widespread concern about the improvement of numeracy skills. This is related to reform movements in the United Kingdom, the United States and other countries aimed at modernising primary (elementary) school mathematics curricula. A detai...
Article
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 Pro...
Article
This article examines models of entitlement that are being encouraged through the implementation of the English National Numeracy Strategy in relation to models presented in earlier policy documents. The argument is developed that the rhetoric has moved from entitlement as access to an appropriate curriculum, through entitlement to equality of teac...
Article
This paper describes a theoretical framework being developed as an analytical tool for part of the Leverhulme Numeracy Research Programme. The framework is expected to help our understanding of pupil progress over five years for children in each of two cohorts, as they each move up the school. Building on models developed to examine street mathemat...
Article
The British Government has recently agreed proposals for a National Numeracy Strategy which claims to be based on evidence concerning ‘hat works’. This article reviews the literature in each key area in which recommendations are made, and makes a judgement of whether the claim is justified. In some areas (e.g. calculators) the recommendations run c...
Article
This paper reports on part of a study examining the links between teachers' practices, beliefs and knowledge and pupil learning outcomes in the development of numeracy with pupils aged five to eleven. From a sample of 90 teachers and 2000 pupils, we developed detailed case studies of 18 teachers. As part of these case studies we explored the teache...
Article
Full-text available
This article reports on a study of ‘Effective Teachers of Numeracy’ funded by the Teacher Training Agency, examining the links between learning gains in numeracy with primary pupils and teachers' knowledge, beliefs and practices. From an overall sample of 90 teachers, 18 teachers were selected for detailed case study. Three types of belief orientat...
Article
Full-text available
Education has taken on board the concepts of ‘scaffolding’ and ‘Zone of Proximal Development’ because embedded within them is a psycho‐social model of teaching and learning. In this paper these concepts are examined in schooling contexts rather than those of everyday life. A first section outlines the ideas of the American socio‐cultural school, fo...
Article
Full-text available
A range of data was collectedfrom the 73 Y4 classes which participate~i in thejirst year of the Leverhulme study (1997-1998). This included teacher questionnaire, pupil data, classroom observation and teacher interview. These data are being matched to the mean class gains which pupils made between October an{l June in an assessment of numeracy. In...
Article
Introduction Introduced almost ten years apart, the National Cur riculum and the National Numeracy Strategy each were intended to improve the teaching and learning of primary mathematics in England. Although these initi atives have many things in common, there are also some key differences. The National Curriculum set out the content to be taught a...
Article
Full-text available
This paper describes the innovative methods used for monitoring progression in learning in a longitudinal study which combines large-scale survey and a linked small- scale case-study. The results include a generic model of progression and reasons for departures from this model with reference to data for specific groups of items and to specific chil...
Article
Full-text available
This paper describes a theoretical model for examining teaching and learning in primary mathematics classrooms. The model in intended to be both analytical - to provide insights into classroom incidents - and heuristic - to inform planning and practice. This paper reports on the elements of the model, which are based on Vygotskian theory and encomp...
Article
Full-text available
Longitudinal case study data are informing the different ways that pupils engage and manage their participation within the lesson. Drawing on observations of two children in the "mental and oral" starter of the Numeracy Lesson we develop the argument that, within the whole class sessions, pupils appear engaged with the mathematics in the way the te...
Article
Full-text available
The Leverhulme Numeracy Research Programme was a five year longitudinal study of children's learning and the factors which affect it. In addition to five case-study projects, it included a longitudinal survey of two cohorts of children in 40 primary schools. The research design included assessment, lesson observation and teacher interviews in Year...

Network

Cited By

Projects

Projects (3)
Project
The Wits Maths Connect-Primary project is a research and development project focused on primary mathematics. Based at Wits University, the project has worked, since 2011, on the design, development, implementation and study of a range of initiatives directed at improving teaching and learning. The project includes work by affiliate academics and postgraduate student studies.