This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age.
Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work:
This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.
Contents: Preface. Part I: Introduction to a Models and Modeling Perspective. R. Lesh, H.M. Doerr, Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving. R. Lesh, K. Cramer, H.M. Doerr, T. Post, J.S. Zawojewski, Model Development Sequences. R. Lehrer, L. Schauble, Origins and Evolution of Model-Based Reasoning in Mathematics and Science. R. Lesh, G. Carmona, Piagetian Conceptual Systems and Models for Mathematizing Everyday Experiences. P.E. Kehle, F.K. Lester, Jr., A Semiotic Look at Modeling Behavior. Part II: A Models and Modeling Perspective on Teacher Development. H.M. Doerr, R. Lesh, A Modeling Perspective on Teacher Development. R.Y. Schorr, R. Lesh, A Modeling Approach for Providing Teacher Development. K.K. Clark, R. Lesh, A Modeling Approach to Describe Teacher Knowledge. K. McClain, Task-Analysis Cycles as Tools for Supporting Students' Mathematical Development. M. van Reeuwijk, M. Wijers, Explanations Why? The Role of Explanations in Answers to (Assessment) Problems. Part III: Models and Modeling as Viewed by Heavy Users of Mathematics. R. Lesh, J.S. Zawojewski, G. Carmona, What Mathematical Abilities Are Needed for Success Beyond School in a Technology-Based Age of Information? W. Oakes, A.G. Rud, Jr., The EPICS Model in Engineering Education: Perspective on Problem-Solving Abilities Needed for Success Beyond Schools. G. Kardos, The Case for Cases. C.D. Aliprantis, G. Carmona, Introduction to an Economic Problem: A Models and Modeling Perspective. T. Johnson, R. Lesh, A Models and Modeling Perspective on Technology-Based Representational Media. M.J. Dark, A Models and Modeling Perspective on Skills for the High Performance Workplace. Part IV: Models and Modeling in Problem Solving and Learning. L. English, R. Lesh, End-in-View Problems. J.S. Zawojewski, R. Lesh, A Models and Modeling Perspective on Problem Solving. J.S. Zawojewski, R. Lesh, L. English, A Models and Modeling Perspective on the Role of Small Group Learning Activities. G. Harel, R. Lesh, Local Conceptual Development of Proof Schemes in a Cooperative Learning Setting. R. Lesh, F.K. Lester, Jr., M. Hjalmarson, A Models and Modeling Perspective on Metacognitive Functioning in Everyday Situations Where Problem Solvers Develop Mathematical Constructs. J.A. Middleton, R. Lesh, M. Heger, Interest, Identity, and Social Functioning: Central Features of Modeling Activity. Part V: Models and Modeling Before and After Middle School. S.J. Lamon, Beyond Constructivism: An Improved Fitness Metaphor for the Acquisition of Mathematical Knowledge. K. Cramer, Using a Translation Model for Curriculum Development and Classroom Instruction. M. Carlson, S. Larsen, R. Lesh, Integrating a Models and Modeling Perspective With Existing Research and Practice. B. Shternberg, M. Yerushalmy, Models of Functions and Models of Situations: On the Design of Modeling-Based Learning Environments. Part VI: Next Steps. F.K. Lester, Jr., P.E. Kehle, From Problem Solving to Modeling: The Evolution of Thinking About Research on Complex Mathematical Activity. R. Lesh, H.M. Doerr, In What Ways Does a Models and Modeling Perspective Move Beyond Constructivism?