Math Know-How

Thomasenia Lott Adams, PhD, is a mathematics teacher educator/researcher in the School of Teaching & Learning and the Associate Dean of Research (ADR) in the College of Education at the University of Florida (UF), Gainesville, FL. Dr. Adams' scholarship includes funded grants at the national and state levels, including her role as Co-Principal Investigator on the Florida STEM Teacher Induction and Professional Support Center funded by the Florida Department of Education and the UF Noyce Scholars Program: Raising STEM EduGators funded by the National Science Foundation. She has a commendable lists of publications and conference presentations is a senior author of the Go Math! elementary mathematics textbook series published by Houghton Mifflin Harcourt. She is also author on several publications of the National Council of Teachers of Mathematics (NCTM) and Solutions Tree. Service posts to her credit include editor of the Mathematical Roots Department in Mathematics Teaching in the Middle School and co-editor of Investigations Department of Teaching Children Mathematics both published by NCTM. Dr. Adams has also served as board member of the Association of Mathematics Teacher Educators board member of the School Science and Mathematics Association and past president of the Florida Association of Mathematics Teacher Educators. Dr. Adams is a previous recipient of the Mary L. Collins Teacher Educator of the Year Award for the Florida Association of Teacher Educators. She has participated in major efforts to improve teaching and learning of mathematics, including serving as a mathematics coach across grades K-12, being co-author of K-12 mathematics professional development programs and leader for the mathematics and science job-embedded professional development and graduate degree program for middle and high school teachers. She is also an accomplished mentor of mathematics education doctoral students. She received a Bachelor of Science in mathematics from South Carolina State College, a Master of Education and Doctorate of Philosophy in Instruction & Curriculum from UF in 1990 and 1993, respectively. Joanne LaFramenta is a retired middle school mathematics teacher with a master's degree in teaching from the University of Chicago. She taught in public schools for more than thirty years in elementary, middle, and high school, as well as in community college and university levels. Her career as a teacher of middle school mathematics began in 1985, in California as the state began an ambitious program of reform, an effort to improve both mathematics teaching and learning. She is a National Board Certified Teacher of Early Adolescence/Mathematics. She graduated from the University of Florida in the summer of 2011, with a degree of Doctor of Philosophy in Curriculum and Instruction, emphasis in mathematics education. She now serves as a research associate and adjunct instructor at the University of Florida.

Preface Acknowledgments About the Authors 1. Common Core State Standards for Mathematics: Mathematics Content and Mathematical Practices Creating the Common Core State Standards for Mathematics Theoretical Basis of the Common Core State Standards for Mathematics Structure of the Common Core State Standards for Mathematics Two Brief Notes Summary Questions and Tasks for Reflection 2. Making Mathematics Teaching Decisions Learning: The Primary Purpose of School and the Primary Goal of Teaching The Nature of Learning Formative Assessment: Discovering the Prior Knowledge Types of Formative Assessment Practices Making the Decisions of Teaching Summary Questions and Tasks for Reflection 3. Using the Pacing Guide Effectively Pacing Guides for Mathematics Instruction Role of the Mathematics Pacing Guide How Do Mathematics Standards Influence the Pacing Guide? Pacing and Mastery Summary Questions and Tasks for Reflection 4. Approach to Planning Mathematics Instruction Perspective: Mathematics Content Perspective: Models of Instruction 4-A Way to Mathematical Success Overarching Instructional Strategies Summary Questions and Tasks for Reflection 5. Facilitating Differentiated Instruction Introduction to Differentiated Instruction Specific Points About Differentiated Instruction Summary Questions and Tasks for Reflection 6. Teaching and Learning Mathematics With Manipulatives Young Students Learn Best When Mathematics Is Linked to a Real-World Context Selection of Manipulatives Use of Manipulatives Tools in the Practice Standards Summary Questions and Tasks for Reflection 7. Appropriate Use of Technology Technology in the Classrooms Technology for the Learner Effective Implementation in the Classroom Evaluating the Use of the Technology Technology for the Teacher Summary Questions and Tasks for Reflection 8. Reflecting on the Teaching Practice of Mathematics What Is Reflection on Teaching? Connecting Anticipations and Results Measuring the Outcomes The Formal Reflection Process Summary Questions and Tasks for Reflection 9. Understanding the Learner The Expectations From the Common Core State Standards Initiative (CCSSI) The Special Case of Gloria Jean Merriex Culturally Responsive Teaching Summary Questions and Tasks for Reflection 10. Mathematics Assessment 101 Introduction Summative Assessment Authentic Assessment Summary Questions and Tasks for Reflection 11. Conclusion All Eyes on Mathematics Education Appendix: Resources for Teachers References Index

"Math Know-How is a useful resource that underlines best practices for effective mathematics instruction. In a responsive way, the authors made a necessary contribution to help teachers understand how to help develop students' mathematics thinking. The book will be helpful to new and experienced elementary teachers of mathematics." -- Dr. Diana Elysee, Assistant Principal "As we shift from our individual state standards to Common Core State Standards for mathematics, this book will be a valuable resource in establishing strategies and instructional techniques to better equip teachers for the overwhelming transition for teaching mathematics with a new way of thinking. As a master teacher, it will be a resource that I will turn to for mentoring teachers." -- Nena Matthews, 5th Grade Math and Science Teacher "This resource is a compendium of research-based ideas, tools, and insights that provide teachers, as ever-emerging professionals, the ammunition needed to formulate and implement strategies for success in the mathematics classroom. The material is presented in such a way as to offer pragmatic overviews in digestible chapters that paint a mosaic of the multitude of issues that teachers must face for effective and efficient learning environments. The author engages the reader in reflective questioning - avoiding the notion that effective teaching "just happens" - and instead, providing a view that this is a profession that demands study and dedicated and informed effort to assist students in understanding the richness and beauty that can be found in mathematics." -- William R. Speer, Director