International Trends in Post-Primary Mathematics ... International Trends in Post-Primary Mathematics

ISSN 1649-3362

© NCCA 2006 National Council for Curriculum and Assessment

24, Merrion Square, Dublin 2.

Research Report No.5

International Trends in Post-Primary

Mathematics Education: Perspectives on Learning, Teaching and Assessment

Paul F. Conway and Finbarr C. Sloane

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International Trends in Post-Primary Mathematics Education: Perspectives on Learning, Teaching and Assessment

Research report commissioned by the

National Council for Curriculum and Assessment

October 2005

Paul F. Conway University College, Cork (UCC)

Finbarr C. Sloane Arizona State University,AZ, USA

National Science Foundation (NSF),Washington, DC, USA

International Trends In Post-Primary Mathematics Education

© NCCA 2006

ISSN 1649-3362

National Council for Curriculum and Assessment

24 Merrion Square, Dublin 2.

www.ncca.ie

Acknowledgements

We are grateful to many people and organisations without whose

timely and generous assistance and/or comments this report would

not have been possible.

Individuals

Prof. Linda Allal, Prof. Sigrid Blömeke, Dr Caroline Brew, Paul

Brady, Dr Stephen Buckley, Prof. David Clarke, Dr Sean Close, Dr

Leland Cogan, Dr Judith Cosgrove, Simon Coury, Lorraine Crossan,

Tom Daly, Claire Dooley, Dr Carol Gibbons, Prof. Jim Greeno,

Tadelle Hagos, Hannah Joyce, Prof.Anthony E. Kelly, Kathrin

Krammer, Dr David Leigh-Lancaster, John MacGabhann, Doreen

McMorris, Barry McSweeney, Dr Kieran Mulchrone, Dr Tom

Mullins, Marie Nash,Veronica O’Brien, Eileen O’Carroll, Elizabeth

Oldham, Prof. Kurt Reusser, Dr Susan Sclafani, Prof. Denis

O’Sullivan, Prof. Jack Schwille, Dr Ciaran Sugrue, Prof. Harm

Tillema, Prof. Maria Teresa Tatto, Peter Tiernan. Prof.Yong Zhao.

We are especially grateful to Dr Sean Close and Elizabeth Oldham

who provided assistance in a variety of ways, particularly in relation

to the historical context of mathematics education in Ireland and the

background to the PISA mathematical literacy framework.

We would like to thank members of the NCCA’s Senior Cycle

Review committee who provided thoughtful feedback on a

presentation of this report’s preliminary findings.

A special thank you is due to Simon Coury whose careful and timely

proofreading of the draft document were important in completing

this report.

International Trends In Post-Primary Mathematics Education

Organisations

Boole Library, UCC; Department of Education and Science;

Education Department, St. Patrick’s College of Education;

Library, Michigan State University; National Council for

Curriculum and Assessment (NCCA); Office of the Chief

Science Advisor to the Government; Printing Office, UCC;

Research Office, UCC; Office of Marketing and

Communications, UCC;Victorian Curriculum and Assessment

Authority,Australia.

We would like to thank our colleagues in the Education

Department at University College Cork (UCC), the

Department of Counseling, Educational Psychology and

Special Education, Michigan State University (MSU), the US

National Science Foundation (NSF), and the College of

Education,Arizona State University (ASU). Finally, we are

grateful to the Executive of the NCCA: Dr Anne Looney,

Chief Executive, John Hammond, Deputy Chief Executive,

and Bill Lynch, Director, Curriculum and Assessment, whose

support as well as detailed comments on a draft document

were important in completing this research report.

Paul F. Conway and Finbarr C. Sloane

22nd October 2005

International Trends In Post-Primary Mathematics Education

International Trends In Post-Primary Mathematics Education

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International Trends In Post-Primary Mathematics Education

Contents

Chapter 1: MATHEMATICS EDUCATION IN AN AGE OF GLOBALISATION: ‘WE ARE ALL COMPARATIVISTS NOW’ . . . . . . . . . .1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .1

1.2 Overview of research report . . . . . . . . . . . . . .5

1.3 What is mathematics? . . . . . . . . . . . . . . . . . . .8

Mathematics as a ‘basic’ skill: three views . . . . .13

1.4 Concerns about mathematics education . . . . . .15

1.5 Why is maths taught the way it is? Curricular cultures, textbooks and examinations/testing traditions . . . . . . . . . . . .23

Curricular cultures in mathematics education: ‘new/modern’ maths and ‘real world’ maths . . .23

‘It’s in the book’: textbooks’ role in shaping mathematics education . . . . . . . . . . . . . . . . .26

Testing and examinations . . . . . . . . . . . . . . . .31

1.6 Mathematics education as policy priority . . . . .33

1.7 Trans-national alliances in mathematics education policy . . . . . . . . . . . . . . . . . . . . . .36

National initiatives in mathematics education policy . . . . . . . . . . . . . . . . . . . . . .38

Mathematical literacy, computing and algebra in Australia . . . . . . . . . . . . . . . . . . . .41

Post-primary mathematics education in Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45

Creativity in mathematics problem solving in Singapore . . . . . . . . . . . . . . . . . . . . . . . . .49

High stakes testing in the US: driving the bull by the tail . . . . . . . . . . . . . . . . . . . .51

United Kingdom: making maths count and counting maths teachers . . . . . . . . . . . . .53

International Trends In Post-Primary Mathematics Education

Ireland: slow emergence of concern about mathematics education . . . . . . . . . . . . . . . . .55

1.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .56

Chapter 2: UNDERSTANDING AND IMPROVING TEACHING:VIDEO STUDIES AND LESSON STUDY . . . . . . . . . . . . . . . . . . . .59

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .60

2.2 Understanding classroom practice: the critical role of video . . . . . . . . . . . . . . . .60

2.3 Many types of video studies: from video surveys to video cases . . . . . . . . . .61

TIMSS video studies . . . . . . . . . . . . . . . . . . .64

2.4 Understanding classroom practice: Japanese lesson study . . . . . . . . . . . . . . . . . . .68

Lesson study re-situated: The wider context of schooling in Japan . . . . .75

What do lesson study and the context of learning in Japan mean for mathematics teaching and learning in Ireland? . . . . . . . . . .80

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . .83

Chapter 3: CULTURES OF LEARNING IN MATHEMATICS EDUCATION: RETHINKING TEACHING AND ASSESSMENT . . . . . . . . .85

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .86

3.2 Different approaches to learning in mathematics education . . . . . . . . . . . . . . . . .89

Three perspectives on learning and assessment in mathematics education . . . . . . . .92

Behaviourism: direct teaching followed by controlled practice . . . . . . . . . . . . . . . . . .94

Cognitive: promoting active learning and problem solving . . . . . . . . . . . . . . . . . . . . . .98

Socio-cultural perspectives: engaged participation . . . . . . . . . . . . . . . . .104

International Trends In Post-Primary Mathematics Education

Three views of assessment . . . . . . . . . . . . . .109

Changing views of assessment: A three-part learning-based model . . . . . . . .112

3.3 Realistic Mathematics Education (RME) and learning . . . . . . . . . . . . . . . . . . . . . . . .124

3.4 Situated cognition in mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . .134

3.5 The PISA mathematics literacy framework: situated cognition and RME . . . . . . . . . . . .138

The components in the PISA mathematical domain . . . . . . . . . . . . . . . . . . . . . . . . . . .141

3.6 Neuroscience as a basis for mathematics education: is it a bridge too far? . . . . . . . . . .144

3.7 Fostering ownership of learning: learning to learn . . . . . . . . . . . . . . . . . . . . .147

3.8 Conclusion: rapid changes in approaches to learning . . . . . . . . . . . . . . . . . . . . . . . . .153

Chapter 4: FIVE INITIATIVES IN MATHEMATICS EDUCATION . . . . . . . . . . . . . . . . . . . . .159

Paul F. Conway, Finbarr C. Sloane,Anne Rath and Michael Delargey

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .160

4.2 Case 1: Mathematics in Context (MiC) . . . . .161

Rationale . . . . . . . . . . . . . . . . . . . . . . . . . .161

Background . . . . . . . . . . . . . . . . . . . . . . . .162

Key features . . . . . . . . . . . . . . . . . . . . . . . .163

Impact and outcomes . . . . . . . . . . . . . . . . .165

Issues and implications . . . . . . . . . . . . . . . . .166

4.3 Case 2: coaching as a case of subject-specific mentoring: a professional development model for teachers of math