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Lesh, Richard

Modeling Students' Mathematical Modeling Competencies

Lesh, Richard - Modeling Students' Mathematical Modeling Competencies, ebook

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ISBN: 9789400762718
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Table of contents

1. Introduction: ICTMA and the Teaching of Modeling and Applications
Gabriele Kaiser

Part I. The Nature of Models & Modeling

2. Introduction to Part I Modeling: What Is It? Why Do It?
Richard Lesh, Thomas Fennewald

Section 1. What Are Models?

3. Modeling Theory for Math and Science Education
David Hestenes

4. Modeling a Crucial Aspect of Students’ Mathematical Modeling
Mogens Niss

5. Modeling Perspectives in Math Education Research
Christine Larson, Guershon Harel, Michael Oehrtman, Michelle Zandieh, Chris Rasmussen, Robert Speiser, Chuck Walter

Section 2. Where Are Models & Modelers Found?

6. Modeling to Address Techno-Mathematical Literacies in Work
Richard Noss, Celia Hoyles

7. Mathematical Modeling in Engineering Design Projects
Monica E. Cardella

8. The Mathematical Expertise of Mechanical Engineers – The Case of Mechanism Design
Burkhard Alpers

Section 3. What Do Modeling Processes Look Like?

9. Modeling and Quantitative Reasoning: The Summer Jobs Problem
Christine Larson

10. Tracing Students’ Modeling Processes in School
Nicholas Mousoulides, M. Pittalis, C. Christou, Bharath Sriraman

Section 4. What Creates “The Need For Modeling”

11. Turning Ideas into Modeling Problems
Peter L. Galbraith, Gloria Stillman, Jill Brown

12. Remarks on a Modeling Cycle and Interpreting Behaviours
Christopher R. Haines, Rosalind Crouch

13. Model Eliciting Environments as “Nurseries” for Modeling Probabilistic Situations
Miriam Amit, Irma Jan

14. Models as Tools, Especially for Making Sense of Problems
Bob Speiser, Chuck Walter

15. In-Depth Use of Modeling in Engineering Coursework to Enhance Problem Solving
Renee M. Clark, Larry J. Shuman, Mary Besterfield-Sacre

16. Generative Activities: Making Sense of 1098 Functions
Sarah M. Davis

Section 5. How Do Models Develop?

17. Modeling the Sensorial Perception in the Classroom
Adolf J. I. Riede

18. Assessing a Modeling Process of a Linear Pattern Task
Miriam Amit, Dorit Neria

19. Single Solution, Multiple Perspectives
Angeles Dominguez

Section 6. How is Modeling Different than Solving?

20. Problem Solving Versus Modeling
Judith Zawojewski

21. Investigating the Relationship Between the Problem and the Solver: Who Decides What Math Gets Used?
Guadalupe Carmona, Steven Greenstein

22. Communication: The Essential Difference Between Mathematical Modeling and Problem Solving
Tomas Højgaard

23. Analysis of Modeling Problem Solutions with Methods of Problem Solving
Gilbert Greefrath

Part II. Modeling in School Classrooms

24. Modeling in K-16 Mathematics Classrooms – and Beyond
Richard Lesh, Randall Young, Thomas Fennewald

Section 7. How Can Students Recognize the Need for Modeling?

25. Modeling with Complex Data in the Primary School
Lyn D. English

26. Two Cases Studies of Fifth Grade Students Reasoning About Levers
Paula Guerra, Linda Hernández, Ahyoung Kim, Muhsin Menekse, James Middleton

27. Don’t Disrespect Me: Affect in an Urban Math Class
Roberta Y. Schorr, Yakov M. Epstein, Lisa B. Warner, Cecilia C. Arias

Section 8. How Do Classroom Modeling Communities Develop?

28. Interdisciplinary Modeling Instruction: Helping Fifth Graders Learn About Levers
Brandon Helding, Colleen Megowan-Romanowicz, Tirupalavanam Ganesh, Shirley Fang

29. Modeling Discourse in Secondary Science and Mathematics Classrooms
M. Colleen Megowan-Romanowicz

30. A Middle Grade Teacher’s Guide to Model Eliciting Activities
Della R. Leavitt, Cynthia M. Ahn

31. The Students’ Discussions in the Modeling Environment
Joneia Cerqueira Barbosa

32. The Social Organization of a Middle School Mathematics Group Discussion
William Zahner, Judit Moschkovich

33. Identifying Challenges within Transition Phases of Mathematical Modeling Activities at Year 9
Gloria Stillman, Jill Brown, Peter Galbraith

34. Realistic Mathematical Modeling and Problem Posing
Cinzia Bonotto

35. Modeling in Class and the Development of Beliefs about the Usefulness of Mathematics
Katja Maass

Section 9. How Do Teachers Develop Models of Modeling?

36. Insights into Teachers’ Unconscious Behaviour in Modeling Contexts
Rita Borromeo Ferri, Werner Blum

37. Future Teachers’ Professional Knowledge on Modeling
Gabriele Kaiser, Björn Schwarz, Silke Tiedemann

38. Theory Meets Practice: Working Pragmatically Within Different Cultures and Traditions
Fco. Javier García, Katja Maass, Geoff Wake

39. Secondary Teachers Learn and Refine Their Knowledge During Modeling Activities in a Learning Community Environment
César Cristóbal Escalante

40. An Investigation of Teachers’ Shared Interpretations of Their Roles in Supporting and Enhancing Group Functioning
Betsy Berry

41. Mathematical Modeling: Implications for Teaching
Maria Salett Biembengut, Nelson Hein

42. A Professional Development Course with an Introduction of Models and Modeling in Science
Genaro Zavala, Hugo Alarcon, Julio Benegas

43. Modeling as Isomorphism: The Case of Teacher Education
Sergei Abramovich

44. Mathematical Modeling and the Teachers’ Tensions
Andréia Maria Pereira Oliveira, Jonei Cerqueira Barbosa

45. A Case Study of Two Teachers: Teacher Questions and Student Explanations
Lisa B. Warner, Roberta Y. Schorr, Cecilia C. Arias, Lina Sanchez

46. Pre-service Teachers’ Perceptions of Model Eliciting Activities
Kelli Thomas, Juliet Hart

Section 10. How Do New Technologies Influence Modeling in School?

47. Modeling Practices with The Geometer’s Sketchpad

Nathalie Sinclair, Nicholas Jackiw

48. A Principal Components Model of Simcalc Mathworlds
Theodore Chao, Susan B. Empson, Nicole Shechtman

49. Modeling Random Binomial Rabbit Hops
Sibel Kazak

50. Investigating Mathematical Search Behavior Using Network Analysis
Thomas Hills

51. Mathematical Modeling and Virtual Environments
Stephen R. Campbell

Section 11. What is The History of Modeling in Schools?

52. On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics
Jonas Bergman Ärlebäck, Christer Bergsten

53. The Dutch Maths Curriculum: 25 Years of Modelling
Pauline Vos

Keywords: Education, Mathematics Education, Mathematical Modeling and Industrial Mathematics

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