**ERIC Number:**ED566541

**Record Type:**Non-Journal

**Publication Date:**2016-Apr-5

**Pages:**280

**Abstractor:**ERIC

**Reference Count:**N/A

**ISBN:**978-0-87353-974-6

**ISSN:**N/A

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

National Council of Teachers of Mathematics

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. 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. After a foreword (Henry Pollak) and preface, this book is divided into seven parts. Part I, Understanding Models and Modeling, contains an introduction (Judith S. Zawojewski and Elizabeth Difanis Phillips) and the following chapters: (1) Perspectives on Modeling in School Mathematics (Michelle Cirillo, John A. Pelesko, Mathew D. Felton-Koestler, and Laurie Rubel); and (2) Different Types of Mathematical Models (Kimberly Groshong). Part II, Using Models to Represent Mathematics, contains an introduction (Elizabeth Difanis Phillips) and the following chapters: (3) TouchCounts: Visual, Auditory, Haptic, and Symbolic Models for Numbers and Operations (Nathalie Sinclair); and (4) Building Conceptual Understanding of Probability Models: Visualizing Chance (Stephanie Budgett, Maxine Pfannkuch, and Christine Franklin). Part III, Teaching and Learning about Mathematical Modeling, contains an introduction (Judith S. Zawojewski) and the following chapters: (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, Tamar Avineri, Julie Graves, Maria Hernandez, and Daniel Teague); and (10) Fostering Modeling Competencies for Complex Situations (Peter Stender and Gabriele Kaiser). Part IV, Mathematical Modeling as a Vehicle for STEM Learning, contains an introduction (Judith S. Zawojewski) and the following chapters: (11) A Case for Mathematical Modeling in the Elementary School Classroom (Mary Alice Carlson, Megan H. Wickstrom, Elizabeth A. Burroughs, and Elizabeth W. Fulton); (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 (Cathrine Maiorca and Micah Stohlmann); and (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, contains an introduction (Elizabeth Difanis Phillips) and the following chapters: (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); and (20) Discrete Mathematical Modeling in the High School Curriculum (Eric Hart and W. Gary Martin). Part VI, Assessing Mathematical Modeling, contains an introduction (Judith S. Zawojewski) and the following chapters: (21) Formative Self-Assessment: A Critical Component of Mathematical Modeling (Cheryl L. Eames, Corey Brady, and Richard Lesh; and (22) The OECD PISA: An Assessment of Mathematical Literacy and Modeling Processes (Kaye Stacey). Part VII, Supporting Teachers' Learning about Mathematical Modeling, contains an introduction (Elizabeth Difanis Phillips) and the following chapters: (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); and (25) Theoretical and Pedagogical Considerations in Promoting Students' Metacognitive Modeling Competencies (Katrin Vorhölter and Gabriele Kaiser).

Descriptors: Mathematics Education, Mathematical Models, Mathematics Instruction, STEM Education, Mathematics Curriculum, Curriculum Design, Theory Practice Relationship, Case Studies, Curriculum Implementation, Teacher Education, Foreign Countries, Achievement Tests, International Assessment, Secondary School Students

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/

**Publication Type:**Books; Collected Works - General; Reports - Descriptive

**Education Level:**Secondary Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**National Council of Teachers of Mathematics

**Identifiers - Location:**Australia; Sweden

**Identifiers - Assessments and Surveys:**Program for International Student Assessment