Li / Kaiser Expertise in Mathematics Instruction

An International Perspective
2011
ISBN: 978-1-4419-7707-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 372 Seiten

Accumulated research findings in past decades have led to the common knowledge that teachers' professional knowledge is essential to effective classroom instruction. However, there is still very limited understanding about the nature of teachers' expertise in mathematics instruction. Expertise in Mathematics Instruction addresses this need clearly and concisely. In particular, it examines all aspects of emphases employed to characterize the nature of expertise in mathematics instruction from both researchers' and practitioners' perspectives. Moreover, with research contributions from both the East and the West, this book also examines ideas pertinent to fostering and demonstrating expertise in mathematics instruction within different system contexts. This book will raise questions and issues for mathematics education researchers to guide a critical examination of what can be learned from other education systems. Expertise in Mathematics Instruction builds on its theoretical and methodological approach with contributions from international experts in the field. Additionally, a review of related research from mathematics education serves as an introduction to the new research in both Eastern and Western settings. Concluding this resource is a reflection on the benefits of this international collaboration and possible research directions for the future. The final chapter cohesively joins traditional and current research for action. Expertise in Mathematics Instruction is of interest to researchers in mathematics education, mathematics teacher educators, and mathematics educators.

Autoren/Hrsg.

Kaiser, Gabriele

Li, Yeping

Inhaltsverzeichnis

1;Contents;5
2;Contributors;7
3;About the Authors;9
4;Part I Introduction and Research Perspectives;17
4.1;Expertise in Mathematics Instruction: Advancing Research and Practice from an International Perspective;18
4.1.1; Introduction;18
4.1.2; Examining and Understanding Expertise in Mathematics Instruction in an International Context;20
4.1.2.1; The Issue of Identifying and Selecting Teachers with Expertise;21
4.1.2.2; The Issue of Specifying and Analyzing Aspects of Teachers' Expertise in Mathematics Instruction;22
4.1.2.3; The Issue of Understanding Expertise in Mathematics Instruction that is Valued in Different Cultures;23
4.1.3; Overview of the Book;24
4.1.3.1; Part I: Introduction and Related Research Summaries;24
4.1.3.2; Part II: Understanding and Examining Teacher Expertise in a Western Setting;25
4.1.3.3; Part III: Understanding and Examining Teacher Expertise in an Eastern Setting;27
4.1.3.4; Part IV: Researching and Reflecting on Teacher Expertise in an International Context;28
4.1.4; Significance and Limitations;29
4.2;References;29
4.3;Theoretical Perspectives, Methodological Approaches, and Trends in the Study of Expertise;31
4.3.1; Retrospective for the Past Three Decades;31
4.3.1.1; Studying Exceptional Experts;32
4.3.1.2; A Difference in Search Strategies;32
4.3.1.3; A Difference in the Structure of Knowledge;36
4.3.1.4; A Difference in Representation;38
4.3.1.5; Issues of Training;40
4.3.2; The Current Constructs;42
4.3.2.1; Deliberate Practice;42
4.3.2.2; Adaptive Expertise;44
4.3.2.3; Team or Group Expertise;46
4.3.3; Expertise as Perspective Shift;47
4.3.4; Conclusion;50
4.4;References;51
4.5;Images of Expertise in Mathematics Teaching;54
4.5.1; A Vignette of Mathematics Teaching: The Crowd Estimation Problem;56
4.5.2; Research Paradigms in the Study of Mathematics Teaching;57
4.5.2.1; Process-Product Research;57
4.5.2.2; A First Look into the Mind of the Teacher;58
4.5.2.3; A Focus on Subject-Specific Teaching;59
4.5.2.4; A Situative Perspective on Teaching;60
4.5.2.5; Design Research: Teaching as Curriculum Adaptation;61
4.5.3; Current Research on Mathematics Teaching: Four Images of Expertise;62
4.5.3.1; Mathematics Teacher as Diagnostician;62
4.5.3.1.1; Looking at Data;63
4.5.3.1.2; Studying Teacher Expertise;63
4.5.3.1.3; The Crowd Estimation Lesson;64
4.5.3.2; Mathematics Teacher as Conductor;64
4.5.3.2.1; Looking at Data;65
4.5.3.2.2; Studying Teacher Expertise;65
4.5.3.2.3; The Crowd Estimation Lesson;66
4.5.3.3; Mathematics Teacher as Architect;66
4.5.3.3.1; Looking at Data;66
4.5.3.3.2; Studying Teacher Expertise;67
4.5.3.3.3; The Crowd Estimation Lesson;67
4.5.3.4; Mathematics Teachers as River Guide;68
4.5.3.4.1; Looking at Data;68
4.5.3.4.2; Studying Teacher Expertise;68
4.5.3.4.3; The Crowd Estimation Lesson;69
4.5.4; Discussion;70
4.6;References;71
5;Part II Expertise in Mathematics Instruction in a Western Setting;74
5.1;Coordinating Characterizations of High Quality Mathematics Teaching: Probing the Intersection;75
5.1.1; Characterizations of High Quality Mathematics Teaching;76
5.1.1.1; Highly Accomplished Teaching: NBPTS Certification;76
5.1.1.2; Effective Use of Cognitively Demanding Mathematics Tasks;78
5.1.1.3; Innovative Pedagogy;80
5.1.2; Study Methods;82
5.1.2.1; Sample;82
5.1.2.2; Data;82
5.1.2.3; Data Analysis;83
5.1.2.3.1; Cognitive Demand of Mathematical Tasks in NBPTS Portfolio Submissions;83
5.1.2.3.2; Pedagogical Features of NBPTS Portfolio Submissions;84
5.1.2.3.3; Relating Mathematical and Pedagogical Features of the Portfolio Entries;86
5.1.2.3.4; Relating NBPTS Certification Status to Mathematical and Pedagogical Features;86
5.1.3; Findings;87
5.1.3.1; NBPTS Status and Cognitive Demand;87
5.1.3.2; NBPTS Status and Innovative Pedagogy;88
5.1.3.3; Cognitive Demand and Innovative Pedagogy;89
5.1.3.4; NBPTS Status, Cognitive Demand and Innovative Pedagogy;90
5.1.4; Discussion;91
5.2;References;94
5.3;Expertise in Swiss Mathematics Instruction;97
5.3.1; Data Sources;99
5.3.2; Characteristics of Swiss Mathematics Instruction in International Comparison;100
5.3.3; Student and Expert Judgments of the Instructional Quality of Swiss Mathematics Teaching;103
5.3.4; The Role of Instructional Reform;106
5.3.5; Conclusion;111
5.4;References;115
5.5;Responding to Students: Enabling a Significant Role for Students in the Class Discourse;120
5.5.1; Introduction;120
5.5.2; Methodology;122
5.5.3; Responsiveness to Students in the Lessons;123
5.5.3.1; Work on the Main Topic;124
5.5.3.1.1; Opposition During Work on the Main Topic;124
5.5.3.1.2; Elaborating Talk During Work on the Main Topic;125
5.5.3.1.3; Accompanying Talk During Work on the Main Topic;128
5.5.3.1.4; Puzzlement During Work on the Main Topic;129
5.5.3.2; Reviewing Content Introduced Previously;130
5.5.3.2.1; Elaborating Talk During Reviewing Content Introduced Previously;130
5.5.3.2.2; Accompanying Talk During Reviewing Content Introduced Previously;132
5.5.3.3; Extending Beyond the Main Topic;133
5.5.3.3.1; Elaborating Talk During Extending Beyond the Main Topic;133
5.5.3.3.2; Accompanying Talk During Extending Beyond the Main Topic;135
5.5.3.3.3; Puzzlement During Extending Beyond the Main Topic;135
5.5.4; Conclusion;136
5.6;References;138
5.7;Effects of a Research-Based Learning Approach in Teacher Professional Development;141
5.7.1; Introduction;141
5.7.2; The Philosophy of the PFL Programme;144
5.7.3; Examples of Competences the PFL Courses Aim at;145
5.7.3.1; Pedagogical Content Knowledge;145
5.7.3.2; Pedagogical Knowledge;145
5.7.3.3; Attitudes and Beliefs;145
5.7.3.4; Self-Related Cognitions;145
5.7.3.5; Reflection and Networking Competences;145
5.7.4; Research Design;146
5.7.4.1; Theoretical Background;146
5.7.4.2; Research Plan and Questions;146
5.7.4.3; Instruments;147
5.7.4.3.1; Questionnaires;147
5.7.4.3.2; Video Task;148
5.7.4.4; Sample of the Study;149
5.7.5; Results;149
5.7.5.1; Questionnaire Analysis;149
5.7.5.2; Video Task;153
5.7.6; Summary and Discussion of Findings;156
5.7.7; Outlook;157
5.8;References;157
5.9;Teacher Expertise Explored as Mathematics for Teaching;161
5.9.1; Mathematics for Teaching;163
5.9.2; Investigating Teachers Mathematics;164
5.9.3; Research Design;165
5.9.4; An Illustration of the Emergence of MFT;166
5.9.5; Opportunities Missed and Made for Enhancing MFT: Developing Expertise;170
5.9.6; Concluding Remarks;172
5.10;References;173
6;Part III Expertise in Mathematics Instruction in an Eastern Setting;175
6.1;Characterizing Expert Teaching in School Mathematics in China A Prototype of Expertise in Teaching Mathematics;176
6.1.1; Introduction;176
6.1.2; Chinese Expert Teaching in School Mathematics: Background and Theoretical Considerations;178
6.1.2.1; Mathematics Teacher as a Profession in China;178
6.1.2.2; Theoretical Considerations;179
6.1.3; The Current Study;181
6.1.4; Method;182
6.1.4.1; Data Sources;182
6.1.4.2; Data Analysis;183
6.1.5; Characterizing Expert Teachers Instruction: Results and Discussion;184
6.1.5.1; Central Tendencies of These Experts' Mathematics Teaching;185
6.1.5.2; Characterizing Expert Teaching: A Case Analysis;194
6.1.5.2.1; Overall Description of the Lesson;194
6.1.5.2.2; The Treatment of Important and Difficult Content Points;195
6.1.5.2.3; Problems Used or Posed During the Lesson;196
6.1.5.2.4; Student Engagement in Learning and Instructional Strategies;197
6.1.5.2.5; Summary of the Case of Expert Teaching;198
6.1.6; Discussion and Conclusion;199
6.1.6.1; Appendix 1: The Categories and Examples of Teachers' Comments and Reflections;201
6.1.6.2; Appendix 2: Frequencies of the Codes Appeared in the Five Teachers0 Comments and Reflections ;202
6.2;References;202
6.3;The Japanese Approach to Developing Expertise in Using the Textbook to Teach Mathematics;205
6.3.1; Introduction;205
6.3.2; The Japanese View of Good Mathematics Teaching;206
6.3.2.1; The Japanese Problem Solving Approach;206
6.3.2.2; Neriage (Extensive Discussion);207
6.3.2.3; Knowledge and Expertise Required for Using the Textbook to Teach Mathematics;209
6.3.2.4; What This Distinction Among Level 1, Level 2, and Level 3 Teachers Means in Terms of Teacher Knowledge and Expertise;210
6.3.3; How do Level 1, Level 2, and Level 3 Teachers Plan a Lesson Differently;212
6.3.3.1; The Subjects of the Study;212
6.3.3.2; Method;213
6.3.3.3; Results;214
6.3.3.4; Discussion;218
6.3.3.4.1; Expertise in Structured Problem Solving;218
6.3.3.4.2; Expertise in Anticipating Students' Responses;220
6.3.4; Helping Practicing Teachers Increase their Knowledge and Expertise;220
6.3.4.1; Two Major Types of Professional Development;220
6.3.4.2; The Japanese Lesson Study Model;221
6.3.5; A Framework for Designing Programs for Prospective and Practicing Teachers;222
6.3.5.1; Phase 1 for Level 1;222
6.3.5.2; Phase 1 and Phase 2 for Level 2;222
6.3.5.3; Phase 1 and Phase 2 for Level 3;224
6.3.6; Conclusion;224
6.3.7; Appendix;225
6.4;References;226
6.5;Perceptions of School Mathematics Department Heads on Effective Practices for Learning Mathematics;228
6.5.1; Introduction;228
6.5.2; Rationale for Study;229
6.5.3; The Study;232
6.5.3.1; Context;232
6.5.3.2; Procedure;233
6.5.3.3; The Instrument;234
6.5.3.4; Analysis of Data;235
6.5.4; Findings;237
6.5.4.1; Quantitative Analysis of Survey Items;237
6.5.4.2; Results from Open-Ended Questions;239
6.5.4.3; Qualitative Analysis;240
6.5.4.3.1; Appraisal Procedures;241
6.5.4.3.2; Practices that Are Valued Highly by the HODs;241
6.5.4.3.3; Practices that Are Less Valued by HODs;243
6.5.4.3.4; Practices that Are Considered as Having an Impact on Pupils' Mathematical Development;244
6.5.5; Implications and Conclusion;245
6.6;References;247
6.7;Exploring Korean Teacher Classroom Expertise in Sociomathematical Norms;249
6.7.1; Introduction;249
6.7.2; Theoretical Background;251
6.7.2.1; Social and Sociomathematical Norms;251
6.7.2.2; Teacher Expertise in Establishing Social and Sociomathematical Norms;252
6.7.3; Method;254
6.7.4; Results;257
6.7.4.1; Initial Difference in the Structure of Lessons Between Teachers;257
6.7.4.2; Similarity Between Teachers: Similar Social Norms;257
6.7.4.3; Critical Difference Between Teachers: Sociomathematical Norm of Difference;258
6.7.4.4; Subtle Difference Between Teachers: Sociomathematical Norm of Notation;262
6.7.5; Discussion;263
6.7.5.1; Teacher's Role in Sustaining Sociomathematical Norms;263
6.7.5.2; Elements and Development of Teacher Expertise;264
6.8;References;267
6.9;Expertise of Mathematics Teaching Valued in Taiwanese Classrooms;269
6.9.1; Introduction;269
6.9.2; Identifying and Examining Expert Teachers Classroom Instruction in Taiwan: Research Background and Theoretical Perspectives;271
6.9.2.1; Identifying Expert Teachers from Taiwanese's Perspectives;271
6.9.2.2; Theoretical Perspectives;272
6.9.2.2.1; A Prototype View of Expertise in Mathematics Teaching;273
6.9.2.2.2; Examining Experts' Teaching in Light of Features of Good Mathematics Instruction Valued in Various Countries;274
6.9.3; Method;276
6.9.3.1; Identification and Selection of Expert Teachers;276
6.9.3.2; Participants;276
6.9.3.3; Data Collection and Analysis;277
6.9.4; Prototypical Features of Expertise Displayed in Experts Mathematics Teaching;279
6.9.4.1; Developing and Sequencing Problems or Tasks for and in Classroom Instruction;280
6.9.4.1.1; Skilled in Creating and Using Tasks with High-Level Demands and Realistic Context for Evoking Multiple Solutions and Eliciting the Anticipated Solutions;280
6.9.4.1.2; Skilled in Sequencing the Problems to be Posed on the Basis of Students' Learning;282
6.9.4.2; Selecting and Sequencing Students' Solutions for the Whole-Class Discussion;283
6.9.4.2.1; Skilled in Predicting the Anticipated Multiple Solution Methods;283
6.9.4.2.2; Skilled in Sequencing Students' Various Solutions for Class Discussion on the Basis of Multiple Representations and Conceptual Development;286
6.9.4.3; Creating More Opportunities for Students to Engage in Discussions and Interact with More Students;287
6.9.4.3.1; Skilled in Asking Various Questions for Different Purposes;287
6.9.4.3.2; Skilled in Asking Key Questions in Time and Asking Follow-Up Questions;289
6.9.4.4; Responding to Students During the Class Discussion;290
6.9.4.4.1; Skilled in Interpreting Students' Productions;290
6.9.4.4.2; Skilled in Highlighting and Summarizing the Main Point at the End of the Discussion;292
6.9.4.5; Transiting from One Activity to Another;292
6.9.4.5.1; Skilled in Transition from One Activity to Another Corresponding to Students' Learning;292
6.9.4.5.2; Skilled in Creating Specific Problems/Tasks for Assessing Students' Understanding and as a Part of Preparation for the Next Lesson;294
6.9.5; Concluding Remarks;294
6.10;References;295
7;Part IV Cross-National Comparison and Reflections ;298
7.1;Cross-Nationally Comparative Results on Teachers Qualification, Beliefs, and Practices;299
7.1.1; Introduction;299
7.1.2; Theoretical Background;300
7.1.2.1; Teacher Expertise and Teacher Quality in Mathematics;300
7.1.2.2; Teachers' Beliefs About the Nature of Teaching and Learning;302
7.1.2.3; Classroom Teaching Practices;303
7.1.2.4; Cross-Cultural Comparison of Teacher Beliefs About the Nature of Teaching and Learning and Classroom Teaching Practices;304
7.1.2.5; Aims and Hypotheses;305
7.1.3; Method;306
7.1.3.1; Sample and Description of Population Characteristics;306
7.1.3.2; Measures;307
7.1.3.3; Statistical Modelling;309
7.1.4; Results;310
7.1.4.1; Teacher Qualification;310
7.1.4.2; Teachers' Beliefs About the Nature of Teaching and Learning;311
7.1.4.3; Classroom Teaching Practices and Their Relationship with Teachers' Beliefs About the Nature of Teaching and Learning;314
7.1.4.4; Relationships Between Teachers' Professional Background and Their Beliefs About the Nature of Teaching and Learning and Classroom Teaching Practices;317
7.1.5; Discussion;319
7.1.5.1; Cross-National Differences and Similarities in Levels and Patterns of Teacher Quality;319
7.1.5.1.1; Similarities Between Countries;319
7.1.5.1.2; Differences Between Countries in Terms of Teacher Qualification;320
7.1.5.1.3; Differences Between Countries in Terms of Teacher Beliefs About the Nature of Teaching and Learning;321
7.1.5.1.4; Differences Between Countries in Terms of Classroom Teaching Practices;321
7.1.5.2; Associations Between Different Indicators of Teacher Quality;322
7.1.5.3; Conclusions and Implications for Research and Practice;323
7.2;References;324
7.3;Reflections on Teacher Expertise;330
7.3.1; Conceptualizing Research on Teaching Expertise;330
7.3.2; A Theory of Teaching; Deconstructing One Example of Expertise;336
7.3.3; Discussion;342
7.4;References;343
7.5;Reflections and Future Prospects;345
7.5.1; Conceptualizing and Specifying Teacher Expertise;346
7.5.2; Cultural Differences;349
7.5.3; Areas of Future Research Directions;352
7.6;References;354
7.7;Index;356