Mathematical modeling and modeling mathematics

Foreword / Henry Pollak Preface Part I. Understanding models and modeling. Introduction / Judith S. Zawojewski and Elizabeth Difanis Phillips 1. Perspectives on modeling in school mathematics / Michelle Cirillo [and 3 others] 2. Different types of mathematical models / Kimberly Groshong Part II. Using models to represent mathematics. Introduction / Elizabeth Difanis Phillips 3. TouchCounts: visual, auditory, haptic, and symbolic models for numbers and operations / Nathalie Sinclair 4. Building conceptual understanding of probability models: visualizing chance / Stephanie Budgett, Maxine Pfannkuch, and Christine Franklin Part III. Teaching and learning about mathematical modeling. Introduction / Judith S. Zawojewski 5. Moving beyond context: challenges in modeling instruction / Sarah K. Bleiler-Baxter, Angela T. Barlow, and D. Christopher Stephens 6. Advancing the teaching of mathematical modeling: research-based concepts and examples / Werner Blum and Rita Borromeo Ferri 7. Broadening the landscape of modeling by including an emergent view / Kevin J. Reins 8. Teaching mathematics for social justice through mathematical modeling / Michelle Cirillo, Tonya Gau Bartell, and Anita A. Wager 9. Moving students from remembering to thinking: the power of mathematical modeling / Cheryl Gann [and 4 others] 10. Fostering modeling competencies for complex situations / Peter Stender and Gabriele Kaiser

Part IV. Mathematical modeling as a vehicle for STEM learning. Introduction / Judith S. Zawojewski 11. A case for mathematical modeling in the elementary school classroom / Mary Alice Carlson [and 3 others] 12. Learning secondary school mathematics through authentic mathematical modeling tasks / Laurie O. Cavey and Joe Champion 13. Modeling using data available on the Internet / Marcelo de Carvalho Borba, Mónica E. Villarreal, and Débora da Silva Soares 14. Inspiring students in integrated STEM education through modeling activities / Catherine Maiorca and Micah Stohlmann 15. A bootstrapping approach to eliciting students' informal inferential reasoning through model development sequences / Jeffrey A. McLean and Helen M. Doerr Part V. Designing modeling-oriented tasks and curricula. Introduction / Elizabeth Difanis Phillips 16. What a modeling task looks like / Heather Gould 17. Developing early foundations through modeling with data / Lyn D. English 18. Designing sequences of model development tasks / Helen M. Doerr 19. Interpreting curricula to find opportunities for modeling: case studies from Australia and Sweden / Vincent Geiger, Jonas Bergman Ärlebäck, and Peter Frejd 20. Discrete mathematical modeling in the high school curriculum / Eric Hart and W. Gary Martin

Part VI. Assessing mathematical modeling.

Introduction / Judith S. Zawojewski

21. Formative self-assessment: a critical component of mathematical modeling / Cheryl L. Eames, Corey Brady, and Richard Lesh

22. The OECD PISA: an assessment of mathematical literacy and modeling processes / Kaye Stacey

Part VII. Supporting teachers' learning about mathematical modeling.

Introduction / Elizabeth Difanis Phillips

23. The GAIMME report: mathematical modeling in the K-16 curriculum / Daniel Teague, Rachel Levy, and Kathleen Fowler

24. Supporting teachers' development as modelers and teachers of modelers / Rose Mary Zbiek

25. Theoretical and pedagogical considerations in promoting students' metacognitive modeling competencies / Katrin Vorhölter and Gabriele Kaiser.