Readings

= Recommended Readings =

CH 1

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Hoffman, L., & Brahier, D. (2008). Improving the planning and teaching of mathematics by reflecting on research. Mathematics Teaching in the Middle School, 13 (7), 412–417.This article addresses how a teacher’s philosophy and beliefs influence his or her mathematics instruction. Using TIMSS and NAEP studies as a foundation, the authors talk about posing higher-level problems, asking thought-provoking questions, facing students’ frustration, and using mistakes to enhance under-standing of concepts. They pose a set of reflective questions that are good for self-assessment or discussions with peers. ======

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__**Books **__Lambdin, D., & Lester, F. K., Jr. (2010). Teaching and learning mathematics: Translating research for elementary school teachers.Reston, VA: NCTM.  Using the most current research on the teaching and learning of mathematics, this book translates research into meaningful chapters for classroom teachers. Built around major questions on avariety of topics, the authors highlight the importance of research in helping teachers be reflective and to assist in the day-to-day judgments teachers make as they support all learners.National Research Council. (2001). Adding it up: Helping chil-dren learn mathematics. J. Kilpatrick, J. Swafford, &B. Findell (Eds.). Mathematics Learning Study Committee,Center for Education, Division of Behavioral and SocialSciences and Education. Washington, DC: National Acad-emy Press.The hallmark of this book is the formulation of five strands of“mathematical proficiency”: conceptual understanding, proce-dural fluency, strategic competence, adaptive reasoning, and pro-ductive disposition. Educators and policy makers will cite this book for many years to come. ======

CH 2
Articles Berkman, R. M. (2006). One, some, or none: Finding beauty in ambiguity. Mathematics Teaching in the Middle School, 11(7), 324–327. This article offers a great teaching strategy for nurturing rela- tional thinking. Examples of the engaging “one, some, or none” activity are given for geometry, number, and algebra activities. Carter, S. (2008). Disequilibrium & questioning in the primary classroom: Establishing routines that help students learn. Teaching Children Mathematics, 15(3), 134–137. This is a wonderful teacher’s story of how she infused the con- structivist notion of disequilibrium and the related idea of pro- ductive struggle to support learning in her first-grade class. Hedges, M., Huinker, D., & Steinmeyer, M. (2005). Unpacking division to build teachers’ mathematical knowledge. Teaching Children Mathematics, 11(9), 478–483. This article describes the many concepts related to division. Suh, J. (2007). Tying it all together: Classroom practices that promote mathematical proficiency for all students. Teaching Children Mathematics, 14(3), 163–169. As the title implies, this is a great resource for connecting the NRC’s Mathematics Proficiencies (National Research Council, 2001) to teaching. Books Lampert, M. (2001). Teaching problems and the problems of teach- ing. New Haven, CT: Yale University Press. Lampert reflects on her personal experiences in teaching fifth grade and shares with us her perspectives on the many issues and complexities of teaching. It is wonderfully written and easily accessed at any point in the book.

CH 3

Articles Hartweg, K., & Heisler, M. (2007). No tears here! Third-grade problem solvers. Teaching Children Mathematics, 1 3(7), 362–368. These authors elaborate on how they have implemented the before, during, and after lesson phases. They offer suggestions for supporting student understanding of the problem, ideas for ques- tioning, and templates for student writing. The data they gath- ered on the response of teachers and students are impressive! Reinhart, S. C. (2000). Never say anything a kid can say! Math- ematics Teaching in the Middle School, 5(8), 478–483. The author is an experienced middle school teacher who ques- tioned his own “masterpiece” lessons after realizing that his stu- dents were often confused. This classic article shares a teacher’s journey to a teaching through problem solving approach. Rein- hart’s suggestions for questioning techniques and involving stu- dents are superb. Rigelman, N. R. (2007). Fostering mathematical thinking and problem solving: The teacher’s role. Teaching Children Mathematics, 13(6), 308–314. This is a wonderful article for illustrating the subtle (and not so subtle) differences between true problem solving and “procedural- izing” problem solving. Because two contrasting vignettes are offered, it gives an excellent opportunity for discussing how the two teachers differ philosophically and in their practices. Books Boaler, J., & Humphreys, C. (2005). Connecting mathematical ideas: Middle school video cases to support teaching and learning. Portsmouth, NH: Heinemann. This book offers cases from Cathy Humphreys’s classroom based on different content areas and issues in teaching. Each case is followed by a commentary. Accompanying the book are two CDs that provide videos of the cases. Buschman, L. (2003). Share and compare: A teacher’s story about helping children become problem solvers in mathematics. Res- ton, VA: NCTM. Larry Buschman describes how he makes problem solving work in his classroom. Much of the book is written as if a teacher were interviewing Larry as he answers the kinds of questions you may also have. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann. The authors of this significant and classic book make one of the best cases for developing mathematics through problem solving.

CH 4

Articles Holden, B. (2008). Preparing for problem solving. Teaching Children Mathematics, 14(5), 290–295. This excellent “how to” article shares how a first-grade teacher working in an urban high-poverty setting incorporated differen- tiated instruction. Holden describes how she prepared her class- room and her students to be successful through six specific steps. Reeves, C. A., & Reeves, R. (2003). Encouraging students to think about how they think! Mathematics Teaching in the Middle School, 8(7), 374–377. When students (and adults) get into a habit of mind—or, in this case, a pattern for solving a problem—they often continue to use this pattern even when easier methods are available. The authors explore this idea with simple tasks you can try. Williams, L. (2008). Tiering and scaffolding: Two strategies for providing access to important mathematics. Teaching Chil- dren Mathematics, 14(6), 324–330. Using a second-grade fraction lesson and a third-grade geometry lesson as examples, Williams shares how they were tiered and then how scaffolds, or supports, were built into the lesson. A very worthwhile article. Books Litton, N. (1998). Getting your math message out to parents: A K–6 resource. Sausalito, CA: Math Solutions Publications. Litton is a classroom teacher who has practical suggestions for communicating with family members. The book includes chapters on parent conferences, newsletters, homework, and family math night. ONLINE RESO