Employing Mathematical Modeling to Engage Students at All Levels Mathematical modeling plays an increasingly important role both in real-life applications-in engineering, business, the social sciences, climate study, advanced design, and more-and within mathematics education itself. This 2016 volume of Annual Perspectives in Mathematics Education (APME) focuses on this key topic from a wide variety of perspectives and distinguishes it from modeling mathematics. The book's 25 chapters are grouped into seven sections:* Understanding Models and Modeling* Using Models to Represent Mathematics* Teaching and Learning about Mathematical Modeling* Mathematical Modeling as a Vehicle for STEM Learning* Designing Modeling-Oriented Tasks and Curricula* Assessing Mathematical Modeling* Supporting Teachers' Learning about Mathematical Modeling Written by leading mathematics educators, mathematicians, and researchers, the chapters in this volume include reflections on the meaning and practice of modeling, case studies, research observations, and proven strategies for implementation in the classroom and in teacher education. With its thorough consideration of this essential subject, this year's volume of APME supports educators at all levels as they incorporate modeling in their instructional practice to improve the learning of mathematics and its applications for all students.

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 VorhÃœlter 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 Ã?rlebÃnck, 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 VorhÃœlter and Gabriele Kaiser