LITMIR.BIZ

Скачать книгу

Thank you for your contribution to these thoughts and ideas. We credit you and appreciate you deeply.

      We would also like to thank Erin Null, who started with one vision of this book, received a draft of another interpretation, and worked with us to land on the third—and we think best—vision. Your patience, support, and diligence pushed us continually forward. We also extend a profound debt of gratitude to Paula Stacey, who asked us the questions we needed to answer in a way that made the manuscript better. As we finish the series of books, we recognize Amy Marks, Tori Mirsadjadi, Jessica Vidal, and the entire Corwin team for helping to keep our work consistent and presenting it so carefully.

      Thank you also to Debbie Thomas, Barbara Dougherty, Kimberly Rimbey, Julie McNamara, Linda Levi, Terrie Galanti, Johnny Lott, and Jeff Shih, whose thoughtful comments challenged us to know better and do better. We are indebted to you for your positive feedback, but even more so for your constructive criticism. Any flaws that remain are ours alone.

      I would first like to thank Linda and Sara for trusting me enough to invite me to join this project. I appreciate your confidence, but more than anything, I appreciate your friendship. I also want to thank Dr. Megan Murray of the University of Hull, who introduced me to the idea that addition and subtraction problems weren’t all the same. To the staff of GBW, Julie, Pat, Kim and her students, and Michelle and her friend the second-grade teacher: Thank you for sharing your time and brilliant students who have helped us collect and interpret their thinking from many different angles. I want to thank my daughter Cassandra and her friends for fielding random questions about math, chemistry, and physics at all hours of the day and night. The book is better because of your guidance. Finally, thank you to my husband, Greg, who watched me take the big leap of writing three books and never questioned my sanity.

      —Kim

      Thanks to Linda for starting us down this road with rich conversations. Thanks to Kim for coming on this journey with us. I appreciate your knowledge, your experience, your care, and your friendship. Thanks to Margie Mason, who first brought me into the world of mathematics education, and to all my friends and colleagues in this community, including those at ETA hand2mind and ORIGO Education, who have encouraged and supported me along the way. Thank you to the teachers who came before me, particularly my mother and grandmother, for showing me that learning is important and good teaching is invaluable. And thanks to Bill, for loving and supporting me always.

      —Sara

      Writing a book is always a challenge! While it seems that writing on a topic you feel passionate about should be easier, it is actually a bigger challenge because you want to get it right. I thank Kim and Sara for their vision and our many long conversations. I learned so much from both of you. I want to thank the elementary teachers and coaches with whom I work who challenge my thinking and force me to make ideas clearer. I thank my colleagues Ruth Harbin Miles, Annemarie Newhouse, and Jerry Moreno, whose friendship I value and who make this career a joy.

      —Linda

      Publisher’s Acknowledgments

      Corwin gratefully acknowledges the contributions of the following reviewers:

      Kevin Dykema

      Middle School Math Teacher

      Mattawan Middle School

      Mattawan, MI

      Julie McNamara

      Assistant Professor of Mathematics Education

      California State University, East Bay

      Hayward, CA

      Kimberly Rimbey

      Executive Director of Curriculum, Instruction, and Assessment

      Buckeye Elementary School District

      Buckeye, AZ

      About the Authors

      Kimberly Morrow-Leongis an adjunct instructor at George Mason University in Fairfax, Virginia, and a consultant for Math Solutions. She is a former grade 5–9 classroom teacher, researcher at American Institutes for Research, K–8 mathematics coach, and coordinator of elementary professional development for the National Council of Teachers of Mathematics (NCTM). She recently completed an elected term as vice president and 2018 program chair for NCSM, Leadership in Mathematics Education. She holds a BA in French language and a master’s degree in linguistics (TESOL). She also holds an MEd and PhD in mathematics education leadership from George Mason University. Kim is the 2009 recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) from Virginia. She is happiest when working with teachers and students, putting pencils down and getting messy with manipulatives!

      Sara Delano Moorecurrently serves as director of professional learning and chair of the Mathematics Advisory Board at ORIGO Education. A fourth-generation educator, Sara’s work emphasizes the power of deep understanding and multiple representations for learning mathematics. Her interests include building conceptual understanding to support procedural fluency and applications, incorporating engaging and high-quality literature into mathematics and science instruction, and connecting mathematics with engineering design in meaningful ways. Prior to joining ORIGO Education, Sara served as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator at the University of Kentucky, director of the Kentucky Center for Middle School Academic Achievement, and director of mathematics and science at ETA hand2mind. She has authored numerous articles in professional journals and is a contributing author to Visible Learning for Mathematics. She has also coauthored the grades 3–5 and grades 6–8 volumes of the Teaching Mathematics in the Visible Learning Classroom series for Corwin Mathematics. Sara earned her BA in natural sciences from Johns Hopkins University, her MSt in general linguistics and comparative philology from the University of Oxford, and her PhD in educational psychology from the University of Virginia. She lives in Kent, Ohio.

      Linda M. Gojakworked as an elementary mathematics specialist and classroom teacher for 28 years. She directed the Center for Mathematics and Science Education, Teaching, and Technology at John Carroll University for 16 years, providing support for districts and more than 10,000 teachers. Linda continues to work with K–8 mathematics teachers and coaches nationally and internationally. She is a recipient of the PAEMST from Ohio. She served as the president of NCTM, NCSM, and the Ohio Council of Teachers of Mathematics. Linda is the coauthor of three other books for Corwin Mathematics—The Common Core Math Companion, K–2; The Common Core Math Companion, 6–8; and Visible Learning for Mathematics, Grades K–12. Linda also wrote Path to Problem Solving for Grades 3–6 (ETA hand2mind, 2008) and What’s Your Math Problem? (Teacher Created Materials, 2011).

      CHAPTER ONE Introduction Why You Need to Teach Students to Mathematize

      Imagine you are a new teacher. You are teaching eighth grade at a new school and are eager to get to know your students—their interests, skills, and how prepared they are to meet the challenges of eighth grade. You have just emerged from your teacher education program knowing various approaches you have seen modeled in classrooms and described in the literature, some of which you have tried with varying degrees of success. You aren’t sure what approaches you want to use but are excited about challenging your students, introducing the rigor you have read so much about. But first, you need to know what your students can and can’t do.

      You decide to start with a couple of word problems, ones that involve relatively simple mathematical operations:

      Mrs. King wanted her American history students to do a project about the Emancipation Proclamation. Скачать книгу