The Creative Enterprise of Mathematics Teaching Research : Elements of Methodology and Practice – From Teachers to Teachers

The Creative Enterprise of Mathematics Teaching Research presents the results and methodology of work of the teaching-research community of practice of the Bronx (TR Team of the Bronx). It has a twofold aim of impacting both teachers of Mathematics and researchers in Mathematics Education. This volume can be used by teachers of mathematics who want to use research to reflect upon and to improve their teaching craft, as well as by researchers who are interested in uncovering riches of classroom learning/teaching for research investigations. This book represents the results of a collaboration of instructors discussing their own instruction research, analyzed through a conceptual framework obtained via the synthesis of creativity research and educational learning theories, based upon the work of Piaget and Vygotsky. The editors see an urgent need for creative synthesis of research and teaching, an example of which is presented in the book. Two central themes of the book are the methodology of TR/NYCity model and creativity, more precisely, creativity of the Aha moment formulated by Arthur Koestler (1964) in a very profound but little known theory of bisociation exposed in his work “The Act of Creation”. Incorporation of the theory of bisociation into classroom teaching of mathematics provides the key to enable students who may struggle with mathematics to engage their own creativity, become involved in their learning process and thus reach their full potential of excellence. Creativity in teaching remedial mathematics is teaching gifted students how to access their own giftedness. Front Matter....Pages i-xix The Main Themes of the Book....Pages 1-2 Teaching-Research New York City Model (TR/NY City)....Pages 3-21 Creativity Research and Koestler....Pages 23-41 Underserved Students and Creativity....Pages 43-55 Underserved Students and Creativity....Pages 57-62 The Didactic Contract, A Handshake and a Compromise....Pages 63-73 Focus on Creativity – Literacy – Numeracy....Pages 75-93 The Poznan Theatre Problem....Pages 95-106 The Creative Learning Environment....Pages 107-126 The Reflections of the Teacher-Researcher Upon the Creativity Principle....Pages 127-131 Reflection and Case Study of Creative Learning Environment....Pages 133-144 Tools of Teaching-Research....Pages 145-147 How to Arrive at a Teaching-Research Question?....Pages 149-161 How to Approach a Teaching Experiment?....Pages 163-170 Qualitative and Quantitative Analysis....Pages 171-178 Teaching Research Interviews....Pages 179-197 Use of Concept Maps in Classroom Research....Pages 199-202 Pictorial Scaffolding in the Schema Construction of Concepts....Pages 203-212 Concept Maps....Pages 213-228 The Method Learning Routes....Pages 229-243 Discovery Method and Teaching-Research....Pages 245-252 Teacher as the Designer of Instruction....Pages 253-265 Koestler’s Theory as a Foundation for Problem-Solving....Pages 267-286 Comparative Study of Three Approaches to Teaching Rates....Pages 287-297 Rate and Proportion Teaching Sequence....Pages 299-315 Proportional Reasoning and Percent....Pages 317-328 Rate Teaching Sequence....Pages 329-342 Two Learning Trajectories....Pages 343-349 Learning Trajectory....Pages 351-371 Learning Trajectory....Pages 373-393 Calculus....Pages 395-424 From Arithmetic to Algebra....Pages 425-443 Teaching Research Communities....Pages 445-453 Algebra/English as a Second Language (ESL) Teaching Experiment....Pages 455-473 “Just Tell Us the Formula!” Co-Constructing the Relevance of Education in Freshman Learning Communities....Pages 475-486 Professional Development of Teacherresearchers (Pdtr) in Tamil Nadu, India....Pages 487-498 PDTR: The Development of a Teacher Researcher....Pages 499-518 Epilogue....Pages 519-520 Back Matter....Pages 521-536 The Creative Enterprise of Mathematics Teaching Research presents the results and methodology of work of the teaching-research community of practice of the Bronx (TR Team of the Bronx). It has a twofold aim of impacting both teachers of Mathematics and researchers in Mathematics Education. This volume can be used by teachers of mathematics who want to use research to reflect upon and to improve their teaching craft, as well as by researchers who are interested in uncovering riches of classroom learning/teaching for research investigations. This book represents the results of a collaboration of instructors discussing their own instruction research, analyzed through a conceptual framework obtained via the synthesis of creativity research and educational learning theories, based upon the work of Piaget and Vygotsky. The editors see an urgent need for creative synthesis of research and teaching, an example of which is presented in the book. Two central themes of the book are the methodology of TR/NYCity model and creativity, more precisely, creativity of the Aha moment formulated by Arthur Koestler (1964) in a very profound but little known theory of bisociation exposed in his work zThe Act of Creationy. Incorporation of the theory of bisociation into classroom teaching of mathematics provides the key to enable students who may struggle with mathematics to engage their own creativity, become involved in their learning process and thus reach their full potential of excellence. Creativity in teaching remedial mathematics is teaching gifted students how to access their own giftedness