As we enter the 21st century, there is an urgent need for new approaches to mathematics education emphasizing its relevance in young learners' futures. Modeling Students' Mathematical Modeling Competencies explores the vital trend toward using real-world problems as a basis for teaching mathematics skills, competencies, and applications. Blending theoretical constructs and practical considerations, the book presents papers from the latest conference of the ICTMA, beginning with the basics (Why are models necessary? Where can we find them?) and moving through intricate concepts of how students perceive math, how instructors teach-and how both can become better learners. Dispatches as varied as classroom case studies, analyses of math in engineering work, and an in-depth review of modeling-based curricula in the Netherlands illustrate modeling activities on the job, methods of overcoming math resistance, and the movement toward replicable models and lifelong engagement. A sampling of topics covered: - How students recognize the usefulness of mathematics Creating the modelingoriented classroom Assessing and evaluating students' modeling capabilities The relationship between modeling and problemsolving Instructor methods for developing their own models of modeling New technologies for modeling in the classroom Modeling Students' Mathematical Modeling Competencies offers welcome clarity and focus to the international research and professional community in mathematics, science, and engineering education, as well as those involved in the sciences of teaching and learning these subjects.

InhaltsangabeChapter 1. Introduction: ICTMA and the Teaching of Modeling and Applications, Gabriele KaiserPart I: The Nature of Models & Modeling Modeling: What Is It? Why Do It? Richard Lesh and Thomas FennewaldSection 1: What Are Models? Chapter 2. Modeling Theory for Math and Science Education, David Hestenes Chapter 3. Modeling a Crucial Aspect of Students' Mathematical Modeling, Mogens Niss Chapter 4. Modeling Perspectives in Math Education Research, Christine Larson, Guershon Harel, Michael Oehrtman, Michelle Zandieh, Chris Rasmussen San, Robert Speiser and Chuck Walter  Section 2: Where Are Models & Modelers Found? Chapter 5. Modeling to Address Techno-Mathematical Literacies in Work, Richard Noss and Celia Hoyles Chapter 6. Mathematical Modeling in Engineering Design Projects, Monica E. Cardella Chapter 7. The Mathematical Expertise of Mechanical Engineers - The Case Of Mechanism Design, Burkhard AlpersSection 3: What Do Modeling Processes Look Like? Chapter 8. Modeling & Quantitative Reasoning: The Summer Jobs Problem, Christine Larson Chapter 9. Tracing Students' Modeling Processes in School, N. Mousoulides, M. Pittalis, C. Christou and B. SriramanSection 4: What Creates The Need For Modeling? Chapter 10. Turning Ideas into Modeling Problems, Peter Galbraith, Gloria Stillman and Jill Brown Chapter 11. Remarks on a Modeling Cycle and Interpretating Behaviours, Christopher Haines and Rosalind Crouch Chapter 12. Model Eliciting Environments as 'Nurseries' for Modeling Probabilistic Situations, Miriam Amit and Irma Jan Chapter 13. Models as Tools, Especially for Making Sense of Problems, Bob Speiser And Chuck Walter Chapter 14. In-Depth Use of Modeling in Engineering Coursework to Enhance Problem Solving, Renee M. Clark, Larry J. Shuman and Mary Besterfield-Sacre Chapter 15. Generative Activities: Making Sense of 1098 Functions, Sarah M. DavisSection 5: How Do Models Develop? Chapter 16. Modeling the Sensorial Perception in the Classroom, Adolf J. I. Riede Chapter 17. Assessing A Modeling Process Of A Linear Pattern Task, Miriam Amit and Dorit Neria Chapter 18. Single Solution, Multiple Perspectives, Angeles DominguezSection 6: How Is Modeling Different Than Solving? Chapter 19. Problem Solving Versus Modeling, Judith Zawojewski Chapter 20. Investigating The Relationship Between The Problem And The Solver: Who Decides What Math Gets Used? Guadalupe Carmona and Steven Greenstein Chapter 21. Communication: The Essential Difference Between Mathematical Modeling & Problem Solving, Tomas Højgaard Jensen Chapter 22. Analysis Of Modeling Problem Solutions With Methods Of Problem Solving, Gilbert GreefrathPart II: Modeling In School Classrooms Modeling In K-16 Mathematics Classrooms - And Beyond, Richard Lesh, Randy Young and Thomas FennewaldSection 7: How Can Students Recognize the Need for Modeling? Chapter 23. Modeling With Complex Data In The Primary School, Lyn D. English Chapter 24. Two Cases Studies Of Fifth Grade Students Reasoning About Levers, Paula Guerra, Linda Hernández, Ahyoung Kim, Muhsin Menekse and James Middleton Chapter 25. Don't Disrespect Me: Affect In An Urban Math Class, Roberta Y. Schorr, Yakov M. Epstein, Lisa B. Warner and Celia C. AriasSection 8: How Do Classroom Modling Communities Develop? Chapter 26. Interdisciplinary Modeling Instruction: Helping Fifth Graders Learn About Levers, Brandon Helding, Colleen Megowan-Romanowicz, Tirupalavanam Ganesh and Shirley Fang Chapter 27. Modeling Discourse In Secondary Science And Mathematics Classrooms, M. Colleen Megowan-Romanowicz Chapter 28. A Middle Grade Teacher's Guide To