Mathematics Education, (4 Volume Set)

Mathematics education is one of the most publicized and contested fields of endeavour in the area of education more generally. The entrails of international comparative mathematics achievement surveys are pored over by the media, politicians and educators alike; and, while for the last fifty years at least it has been assumed by most everyone in modern societies that mathematics should be a compulsory subject in all schools, parents and scholars alike argue furiously about whether traditional teaching and rote practising of mathematical skills is better or worse for pupils than conceptual teaching based on children’s own constructed ideas. University mathematics professors tend either to deplore the dropping of standards in their students, and thus the dropping of standards in teachers, or heartily embrace the new learning techniques made possible through careful use of the new technologies.

As academic thinking about and around mathematics education continues to flourish and develop, this new title in the Routledge series, Major Themes in Education, meets the need for an authoritative reference work to make sense of the subject’s vast literature and the continuing explosion in research output. Edited by Alan Bishop, a prominent scholar in the field, this Routledge Major Work is a four-volume collection of foundational and cutting-edge contributions that cover all of the major themes in mathematics education.

The first of the four volumes (‘Mathematics, Mathematics Education, and the Curriculum’) brings together key work on the goals of mathematics education, as well as vital material on the relationship of the curriculum with numeracy, assessment, technology, and the place of marginalized students. The second volume (‘Mathematics Teaching and Teachers’) gathers the most important thinking on topics such as pedagogical practices; mathematics teachers’ beliefs, attitudes, and values; professional development; teacher education; and teachers as researchers. The third volume covers the central theories of ‘Mathematics Learning and Learners’. The final volume in the collection (‘The Contexts of Mathematics Education’) gathers vital material from the rich body of literature that explores the social, cultural and political contexts in which mathematics education sits.

With comprehensive introductions to each volume, newly written by the editor, which place the collected material in its historical and intellectual context, this Routledge Major Work is an essential work of reference. It is destined to be valued by specialists in mathematics education and scholars working in related areas - as well as by educational policy-makers and professionals - as a vital one-stop research tool.

Volume I : Mathematics, mathematics education, and the curriculum

Part 1 : Mathematics and Mathematics Education

Section A : Histories of Mathematics
Chapter 1 : Luis Radford, ‘On Psychology, Historical Epistemology and the Teaching of Mathematics : Towards a Socio-Cultural History of Mathematics’, For the Learning of Mathematics, 1997
Chapter 2 : G. G. Joseph, ‘Different Ways of Knowing : Contrasting Styles of Argument in Indian and Greek Mathematical Traditions’, in P. Ernest (ed.), Mathematics, Education and Philosophy : An International Perspective
Chapter 3 : N. Kleiner and N. Movshovitz-Hadar, ‘The Role of Paradoxes in the Evolution of Mathematics’, The American Mathematical Monthly, 1994

Section B : Conceptions of Mathematics from an Educational Standpoint
Chapter 4 : Tommy Dreyfus and Theodore Eisenberg, ‘On the Aesthetics of Mathematical Thought’, For the Learning of Mathematics, 1986
Chapter 5 : Efraim Fischbein, ‘Intuition and Proof’, For the Learning of Mathematics, 1982
Chapter 6 : S. MacLane, ‘Mathematical Models : A Sketch for the Philosophy of Mathematics’, American Mathematical Monthly, 1981
Chapter 7 : S. Restivo, ‘The Social Life of Mathematics’, in S. Restivo, J. P. Van Bendegem, and R. Fischer (eds.), Math Worlds : Philosophical and Social Studies of Mathematics and Mathematics Education

Section C : Culture, Mathematics, and Mathematics Education
Chapter 8 : Ubiratan D’Ambrosio, ‘Ethnomathematics and its Place in the History and Pedagogy of Mathematics’, For the Learning of Mathematics, 1985
Chapter 9 : B. Barton, ‘Making Sense of Ethnomathematics : Ethnomathematics is Making Sense’, ESM, 1996
Chapter 10 : A. J. Bishop, ‘Western Mathematics : The Secret Weapon of Cultural Imperialism’, Race & Class, 1990

Section D : Society, Technology, and Mathematics Education
Chapter 11 : Paulus Gerdes, ‘Conditions and Strategies for Emancipatory Mathematics Education in Underdeveloped Countries’, For the Learning of Mathematics, 1985
Chapter 12 : C. Keitel, ‘Numeracy and Scientific and Technological Literacy’, in E. W. Jenkins (ed.), Innovations in Science and Technology Education, Vol. 6
Chapter 13 : W. Blum and M. Niss, ‘Applied Mathematical Problem Solving, Modelling, Applications, and Links to Other Subjects : State, Trends, and Issues in Mathematics Education’, Educational Studies in Mathematics, 1991

Part 2 : Education and the Mathematics Curriculum

Section E : Goals of Mathematics Education
Chapter 14 : R. B. Davis, ‘The Culture of Mathematics and the Culture of Schools’, Journal of Mathematical Behavior, 1989
Chapter 15 : T. A. Romberg and J. J. Kaput, ‘Mathematics Worth Teaching, Mathematics Worth Understanding’, in E. Fennema and T. A. Romberg (eds.), Mathematics Classrooms that Promote Understanding
Chapter 16 : P. Davis and R. Hersh, ‘The Ideal Mathematician’, The Mathematical Experience

Section F : Mathematics Curricula in Schools
Chapter 17 : D. Robitaille and M. Dirks, ‘Models for the Mathematics Curriculum’, For the Learning of Mathematics, 1982
Chapter 18 : J. Confrey, ‘Conceptual Change Analysis : Implications for Mathematics and Curriculum’, Curriculum Inquiry, 1981
Chapter 19 :  L. Streefland, ‘The Design of a Mathematics Course : A Theoretical Reflection’, Educational Studies in Mathematics, 1993

Section G : Mathematics Curricula at Tertiary and Vocational Levels
Chapter 20 : M. Harris, ‘Looking for the Maths in Work’, in Harris (ed.), Schools, Mathematics and Work
Chapter 21 : D. O. Tall, ‘Comments on the Difficulty and Validity of Various Approaches to the Calculus’, For the Learning of Mathematics, 1981
Chapter 22 : B. Cornu, ‘Limits’, in D. O.Tall (ed.), Advanced Mathematical Thinking

Section H : Assessment, Evaluation, and the Mathematics Curriculum
Chapter 23 : B. Cooper, ‘Authentic Testing in Mathematics? The Boundary Between Everyday and Mathematical Knowledge in National Curriculum Testing in English Schools’, Assessment in Education, 1994
Chapter 24 : J. Kilpatrick, ‘The Chain and the Arrow : From the History of Mathematics Assessment’, in M. Niss (ed.), Investigations in Assessment in Mathematics Education

Volume II : Mathematics teachers and teaching

Part 1 : Mathematics Teachers

Section A : Mathematics Teachers’ Knowledge
Chapter 25 : D. L. Ball, S. T. Lubienski, and D. S. Mewborn, ‘Research on Teaching Mathematics : The Unsolved Problem of Teachers’ Mathematical Knowledge’, in V. Richardson (ed.), Handbook of Research on Teaching (American Educational Research Association, 2001)
Chapter 26 : H. Freudenthal, ‘Should a Mathematics Teacher Know Something about the History of Mathematics?’, For the Learning of Mathematics, 1981

Section B : Mathematics Teachers’ Beliefs, Attitudes, and Values
Chapter 27 : A. G. Thompson, ‘The Relationship of Teacher’s Conceptions of Mathematics Teaching to Instructional Practice’, Educational Studies in Mathematics, 1984
Chapter 28 : C. Chin, Y.-C. Leu, and F.-L. Lin, ‘Pedagogical Values, Mathematics Teaching, and Teacher Education : Case Studies of Two Experienced Teachers’, in F.-L. Lin and Thomas J. Cooney (eds.), Making Sense of Mathematics Teacher Education

Section C : Pre-Service Mathematics Teacher Education
Chapter 29 : T. J. Cooney, B. E. Shealy, and B. Arvold, ‘Conceptualizing Belief Structures of Preservice Secondary Mathematics Teachers’, Journal for Research in Mathematics Education, 1998
Chapter 30 : J. Hiebert, A. K. Morris, and G. Glass, ‘Learning to Learn to Teach : An "Experiment" Model for Teaching and Teacher Preparation in Mathematics’, Journal of Mathematics Teacher Education, 2003

Section D : Mathematics Teachers’ Professional Development
Chapter 31 : D. Clarke, ‘Ten Key Principles from Research for the Professional Development of Mathematics Teachers’, in D. B. Aichele and A. F. Coxford (eds.), Professional Development for Teachers of Mathematics
Chapter 32 : C. Laborde, ‘The Use of New Technologies as a Vehicle for Restructuring Teachers’ Mathematics’, in F.-L. Lin and T. J. Cooney, Making Sense of Mathematics Teacher Education

Part 2 : Teaching Mathematics

Section E : Issues in Teaching Mathematical Topics
Chapter 33 : J. Boaler, ‘Learning from Teaching : Exploring the Relationship Between Reform Curriculum and Equity’, Journal for Research in Mathematics Education, 2002
Chapter 34 : Z. Markovits, B.-S. Eylon, and M. Bruckheimer, ‘Functions Today and Yesterday’, For the Learning of Mathematics, 1986
Chapter 35 : J. Gregg, ‘The Tensions and Contradictions of the School Mathematics Tradition’, Journal for Research in Mathematics Education, 1995

Section F : Pedagogical Theories and Practices
Chapter 36 : P. Cobb et al., ‘Characteristics of Classroom Mathematics Traditions : An Interactional Analysis’, American Educational Research Journal, 1992
Chapter 37 : S. Crespo, ‘Learning to Pose Mathematical Problems : Exploring Changes in Pre-Service Teachers’ Practices’, Educational Studies in Mathematics, 2003

Section G : Classroom Cultures and Interactions
Chapter 38 : H. Bauersfeld, ‘Hidden Dimensions in the Reality of a Mathematics Classroom’, Educational Studies in Mathematics, 1980
Chapter 39 : I. M. Christiansen, ‘When Negotiation of Meaning is also Negotiation of Task : Analysis of the Communication in an Applied Mathematics High School Course’, Educational Studies in Mathematics, 1997

Section H : Teaching and Assessing
Chapter 40 : D. J. Clarke, ‘The Interactive Monitoring of Children’s Learning of Mathematics’, For the Learning of Mathematics, 1987
Chapter 41 : A. G. Thompson and D. J. Briers, ‘Assessing Students’ Learning to Inform Teaching : The Message in the NCTM Evaluation Standards’, Arithmetic Teacher, 1989
Chapter 42 : P. J. Black and D. Wiliam, ‘Inside the Black Box : Raising Standards through Classroom Assessment’, Phi Delta Kappan, 1998

Section I : Teachers as Researchers
Chapter 43 : S. Lerman, ‘The Role of Research in the Practice of Mathematics Education’, For the Learning of Mathematics, 1990
Chapter 44 : B. Jaworski, ‘Mathematics Teacher Research : Process, Practice and the Development of Teaching’, Journal of Mathematics Teacher Education, 1998
Chapter 45 : B. Clarke, D. Clarke, and P. Sullivan, ‘The Mathematics Teacher and Curriculum Development’, in A. Bishop et al. (eds.), International Handbook of Mathematics Education

Volume III : Mathematics Learners and Learning

Part 1 : Mathematics Learners

Section A : School Learners
Chapter 46 : S. H. Erlwanger, ‘Benny’s Conception of Rules and Answers in IPI Mathematics’, Journal of Children’s Mathematical Behavior, 1973
Chapter 47 : N. Gorgorio, N. Planas, and X. Vilella, ‘The Cultural Conflict in the Mathematics Classroom : Overcoming its "Invisibility"’, in A. Ahmed, H. Williams, and J. M. Kraemer (eds.), Cultural Diversity in Mathematics (Education)

Section B : Adult Learners
Chapter 48 : D. Coben, ‘Mathematics or Common Sense? Researching "Invisible" Mathematics Through Adults’ Mathematics Life Histories’, in D. Coben, J. O’Donaghue, and G. E. FitzSimons (eds.), Perspectives on Adults Learning Mathematics : Research and Practice
Chapter 49 : C. Hoyles, R. Noss, and S. Pozzi, ‘Proportional Reasoning in Nursing Practice’, Journal for Research in Mathematics Education, 2001

Section C : Disadvantaged and Marginalized Learners
Chapter 50 : T. N. Carraher, D. W. Carraher, and A. D. Schliemann, ‘Mathematics in the Streets and in Schools’, British Journal of Developmental Psychology, 1985
Chapter 51 : S. Zeleke, ‘Learning Disabilities in Mathematics : A Review of the Issues and Children’s Performance across Mathematical Texts’, Focus on Learning Problems in Mathematics, 2004

Section D : Gifted Learners
Chapter 52 : K. Tirri, ‘How Finland Meets the Needs of Gifted and Talented Pupils’, High Ability Studies, 1997
Chapter 53 : D. Buerk, ‘An Experience with Some Able Women who Avoid Mathematics’, For the Learning of Mathematics, 1982

Section E : Gender Issues
Chapter 54 : M. Walshaw, ‘A Foucauldian Gaze on Gender Research : What Do You Do When Confronted with the Tunnel at the End of the Light?’, Journal for Research in Mathematics Education, 2001
Chapter 55 : G. C. Leder and H. J. Forgasz, ‘Single-Sex Classes in a Co-Educational High School : Highlighting Parents’ Perspectives’, Mathematics Education Research Journal, 1997

Section F : Cultural Issues
Chapter 56 : A. Chronaki, ‘Researching the School Mathematics Culture of "Others"’, in P. Valero and R. Zevenbergen (eds.), Researching the Socio-Political Dimensions of Mathematics Education : Issues of Power in Theory and Methodology
Chapter 57 : G. De Abreu, ‘Understanding How Children Experience the Relationship Between Home and School Mathematics’, Mind, Culture and Activity, 1995

Part 2 : Learning Mathematics

Section G : Issues in Learning Mathematical Topics
Chapter 58 : C. Kieran, ‘Concepts Associated with the Equality Symbol’, Educational Studies in Mathematics, 1981
Chapter 59 : N. Movshovitz-Hadar, ‘The False Coin Problem, Mathematical Induction and Knowledge Fragility’, Journal of Mathematical Behaviour, 1993
Chapter 60 : G. Vergnaud, ‘Multiplicative Conceptual Field : What and Why?’, in G. Harel and J. Confrey (eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics
Chapter 61 : J. Adler, ‘A Language of Teaching Dilemmas : Unlocking the Complex Multilingual Secondary Mathematics Classroom’, For the Learning of Mathematics, 1998

Section H : Theories of Learning Mathematics
Chapter 62 : S. Pirie and T. Kieren, ‘A Recursive Theory of Mathematical Understanding’, For the Learning of Mathematics, 1989
Chapter 63 : A. Sfard, ‘On Two Metaphors for Learning and the Dangers of Choosing Just One’, Educational Researcher, 1998
Chapter 64 : R. Skemp, ‘Relational and Instrumental Understanding’, Mathematics Teaching, 1976
Chapter 65 : L. P. Steffe and T. E. Kieren, ‘Radical Constructivism and Mathematics Education’, Journal for Research in Mathematics Education, 1994

Section I : Language, Visualization, and Mathematics Learning
Chapter 66 : N. Presmeg, ‘Visualisation in High School Mathematics’, For the Learning of Mathematics, 1986
Chapter 67 : M. Setati et al., ‘Incomplete Journeys : Code-Switching and Other Language Practices in Mathematics, Science and English Language Classrooms in South Africa’, Language and Education, 2002

Section J : Beliefs and Affective Aspects of Learning Mathematics
Chapter 68 : M. Lampert, ‘When the Problem is Not the Question and the Solution is not the Answer : Mathematical Knowing and Teaching’, American Educational Research Journal, 2001
Chapter 69 : G. A. Goldin, ‘Affect, Meta-Affect, and Mathematical Belief Structures’, in G. C. Leder, E. Pehkonen, and G. Törner (eds.), Beliefs : A Hidden Variable in Mathematics Education
Chapter 70 : D. B. McLeod, ‘Affective Issues in Mathematical Problem Solving : Some Theoretical Considerations’, Journal for Research in Mathematics Education, 1988
Chapter 71 : D. Moreira, ‘Facing Exclusion : The Student as Person’, in P. Gates and T. Cotton (eds.), First International Mathematics Education and Society Conference 6th–11th September

Volume IV : The Contexts of Mathematics Education

Part 1 : Societal and Cultural Contexts

Section A : Parental and Community Aspects
Chapter 72 : R. Merttens, ‘Teaching Not Learning : Listening to Parents and Empowering Students’, For the Learning of Mathematics, 1995
Chapter 73 : M. Civil, ‘Culture and Mathematics : A Community Approach’, Journal of Intercultural Studies, 2002

Section B : Numeracies and Mathematics Education
Chapter 74 : R. Noss, ‘New Numeracies for a Technological Culture’, For the Learning of Mathematics, 1998
Chapter 75 : R. Zevenbergen, ‘Technologizing Numeracy : Intergenerational Differences in Working Mathematically in New Times’, Educational Studies in Mathematics, 2004

Section C : Technologies and Mathematics Education
Chapter 76 : S. Schuck and G. Foley, ‘Viewing Mathematics in New Ways : Can Electronic Learning Communities Assist?’, Mathematics Teacher Education and Development, 1999
Chapter 77 : W. Dörfler, ‘Computer Use and Views of the Mind’, in C. Keitel and K. Ruthven (eds.), Learning from Computers : Mathematics Education and Technology

Section D : International Comparisons of Mathematics Achievement
Chapter 78 : C. Keitel and J. Kilpatrick, ‘The Rationality and Irrationality of International Comparative Studies’, in G. Kaiser, E. Luna, and I. Huntley (eds.), International Comparisons in Mathematics Education
Chapter 79 : F. K. S. Leung, ‘The Mathematics Classroom in Beijing, Hong Kong and London’, Educational Studies in Mathematics, 1995
Chapter 80 : D. Zhang, S. Li, and R. Tang, ‘The "Two Basics" : Mathematics Teaching and Learning in Mainland China’, in L. Fanet al., How Chinese Learn Mathematics

Part 2 : Research and Theoretical Contexts

Section E : Developments in Research Approaches
Chapter 81 : H. Ginsburg, ‘The Clinical Interview in Psychological Research on Mathematical Thinking : Aims, Rationales, Techniques’, For the Learning of Mathematics, 1981
Chapter 82 : M. A. Eisenhart, ‘The Ethnographic Research Tradition and Mathematics Education Research’, Journal for Research in Mathematics Education, 1988

Section F : Histories of Mathematics Education
Chapter 83 : G. M. A. Stanic, ‘The Growing Crisis in Mathematics Education in the Early Twentieth Century’, Journal for Research in Mathematics Education, 1986
Chapter 84 : A. G. Howson, ‘Seventy-Five Years of the International Commission on Mathematics Instruction’, Educational Studies in Mathematics, 1984

Section G : Philosophies of Mathematics Education
Chapter 85 : P. Ernest, ‘The Dialogical Nature of Mathematics’, in Ernest (ed.), Mathematics, Education and Philosophy
Chapter 86 : E. Wittmann, ‘Mathematics Education as a "Design Science"’, Educational Studies in Mathematics, 1995

Section H : Theories in Mathematics Education
Chapter 87 : P. Cobb, ‘Experiential, Cognitive and Anthropological Perspectives in Mathematics Education’, For the Learning of Mathematics, 1989
Chapter 88 : E. Fennema, H. Walberg, and C. Marrett, ‘Explaining Sex-Related Differences in Mathematics : Theoretical Models’, Educational Studies in Mathematics, 1985
Chapter 89 : G. Leder, ‘Sex-Related Differences in Mathematics : An Overview’, Educational Studies in Mathematics, 1985
Chapter 90 : E. Fennema and P. L. Peterson, ‘Autonomous Learning Behavior : A Possible Explanation of Sex-Related Differences in Mathematics’, Educational Studies in Mathematics, 1985
Chapter 91 : J. Eccles, ‘Model of Students’ Mathematics Enrollment Decisions’, Educational Studies in Mathematics, 1985
Chapter 92 : D. R. Maines, ‘Preliminary Notes on a Theory of Informal Barriers for Women in Mathematics’, Educational Studies in Mathematics, 1985
Chapter 93 : A. Sfard, ‘Reification as the Birth of Metaphor’, For the Learning of Mathematics, 1994

Section I : International Cooperation in Mathematics Education Research
Chapter 94 : J. Cai, ‘Why do US and Chinese Students Think Differently in Mathematical Problem-Solving? Exploring the Impact of Early Algebra Learning and Teachers’ Beliefs’, Journal of Mathematical Behavior, 2004
Chapter 95 : B. Nebres, ‘International Benchmarking as a Way to Improve School Mathematics Achievement in the Era of Globalization’, in G. Kaiser, E. Luna, and I. Huntley (eds.), International Comparisons in Mathematics Education

Section J : Globalization, Post-Colonialism, and Critical Perspectives
Chapter 96 : B. Atweh and P. Clarkson, ‘Internationalisation and Globalization of Mathematics Education : Towards an Agenda for Research/Action’, in B. Atweh, H. Forgasz, and B. Nebres (eds.), Sociocultural Research on Mathematics Education
Chapter 97 : R. Vithal and O. Skovsmose, ‘The End of Innocence : A Critique of "Ethnomathematics"’, Educational Studies in Mathematics, 1997