Mathematical Knowledge in Teaching

Cumulative research within a number of traditions has shown that effective teaching calls for distinctive, identifiable forms of subject-related knowledge and thinking, yet the significance and complexity of such knowledge is not well represented in professional debate and policymaking. This is a particularly pressing issue within mathematics education, given world-wide aspirations to improve quality of teaching and learning in the face of widespread difficulties in recruiting teachers who are conventionally well-qualified in mathematics and confident in the subject. This book, the outcome of two years of collaborative effort, brings together a team of experts in the field of mathematics teacher knowledge to produce an authoritative, ‘state of the art’ exposition and critical commentary on this important and topical domain, including reports of original research in the field. It offers constructive and helpful ways of conceptualising mathematics teacher knowledge in its cultural context, as well as a range of theorised tools to support its improvement. Introduction: Mathematical Knowledge In Teaching / Tim Rowland And Kenneth Ruthven -- Part I. Conceptualising Mathematical Knowledge In Teaching: Conceptualising Teachers' Mathematical Knowledge In Teaching / Marilena Petrou And Maria Goulding -- Knowing And Identity: A Situated Theory Of Mathematics Knowledge In Teaching / Jeremy Hodgen -- Changed Views On Mathematical Knowledge In The Course Of Didactical Theory Development: Independent Corpus Of Scientific Knowledge Or Result Of Social Constructions? / Heinz Steinbring -- Teaching Mathematics As The Contextual Application Of Mathematical Modes Of Enquiry / Anne Watson And Bill Barton -- Conceptualising Mathematical Knowledge In Teaching / Kenneth Ruthven -- Part Ii. Understanding The Cultural Context Of Mathematical Knowledge In Teaching: The Cultural Location Of Teachers' Mathematical Knowledge: Another Hidden Variable In Mathematics Education Research? / Paul Andrews -- How Educational Systems And Cultures Mediate Teacher Knowledge: 'listening In English, French And German Classrooms / Birgit Pepin -- Modelling Teaching In Mathematics Teacher Education And The Constitution Of Mathematics For Teaching / Jill Adler And Zain Davis -- Audit And Evaluation Of Pedagogy: Towards A Cultural-historical Perspective / Julian Williams -- The Cultural Dimension Of Teachers' Mathematical Knowledge / Andreas J. Stylianides And Seán Delaney -- Part Iii. Building Mathematical Knowledge In Teaching By Means Of Theorised Tools: The Knowledge Quartet As An Organising Framework For Developing And Deepening Teachers' Mathematics Knowledge / Fay Turner And Tim Rowland -- Learning To Teach Mathematics Using Lesson Study / Dolores Corcoran And Sandy Pepperell -- Using Theories To Build Kindergarten Teachers' Mathematical Knowlege For Teaching / Dina Tirosh, Pessia Tsamir, And Esther Levenson -- Teachers' Stories Of Mathematical Subject Knowledge: Accounting For The Unexpected / Julie Ryan And Julian Williams -- Building Mathematical Knowledge In Teaching By Means Of Theorised Tools / José Carrillo -- Conclusion / Kenneth Ruthven And Tim Rowland. Tim Rowland, Kenneth Ruthven, Editors. Includes Bibliographical References And Indexes. Front Matter....Pages i-viii Introduction: Mathematical Knowledge in Teaching....Pages 1-5 Front Matter....Pages 7-7 Conceptualising Teachers’ Mathematical Knowledge in Teaching....Pages 9-25 Knowing and Identity: A Situated Theory of Mathematics Knowledge in Teaching....Pages 27-42 Changed Views on Mathematical Knowledge in the Course of Didactical Theory Development: Independent Corpus of Scientific Knowledge or Result of Social Constructions?....Pages 43-64 Teaching Mathematics as the Contextual Application of Mathematical Modes of Enquiry....Pages 65-82 Conceptualising Mathematical Knowledge in Teaching....Pages 83-96 Front Matter....Pages 97-97 The Cultural Location of Teachers’ Mathematical Knowledge: Another Hidden Variable in Mathematics Education Research?....Pages 99-118 How Educational Systems and Cultures Mediate Teacher Knowledge: ‘Listening’ in English, French and German Classrooms....Pages 119-137 Modelling Teaching in Mathematics Teacher Education and the Constitution of Mathematics for Teaching....Pages 139-160 Audit and Evaluation of Pedagogy: Towards a Cultural-Historical Perspective....Pages 161-178 The Cultural Dimension of Teachers’ Mathematical Knowledge....Pages 179-191 Front Matter....Pages 193-193 The Knowledge Quartet as an Organising Framework for Developing and Deepening Teachers’ Mathematics Knowledge....Pages 195-212 Learning to Teach Mathematics Using Lesson Study....Pages 213-230 Using Theories to Build Kindergarten Teachers’ Mathematical Knowledge for Teaching....Pages 231-250 Teachers’ Stories of Mathematical Subject Knowledge: Accounting for the Unexpected....Pages 251-271 Building Mathematical Knowledge in Teaching by Means of Theorised Tools....Pages 273-287 Conclusion....Pages 289-291 Back Matter....Pages 293-302 The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.