There is a substantive body of research that indicates formative assessment can significantly improve student learning. Yet, this same research shows that the features of formative assessment that impact student achievement are sadly missing from many classrooms (Black, et al., 2003). This book provides teachers with guidance and suggestions for using formative assessment to improve teaching and learning in the mathematics classroom, and identifies and describes practical techniques teachers can use to build a rich repertoire of formative assessment strategies. The acronym, FACT, is used to label the techniques included in this book. FACT stands for Formative Assessment Classroom Technique. Through the varied use of FACTs, explicitly tied to a purpose for gathering information about or promoting students' thinking and learning, teachers can focus on what works best for learning and design or modify lessons to fit the needs of the students.

Table of Contents

Preface Acknowledgments About the Authors 1. An Introduction to Formative Assessment Classroom Techniques (FACTs) What Does a Formative Assessment?Centered Classroom Look Like? Why Use FACTs? How Does Research Support the Use of FACTs? Classroom Environments That Support Formative Assessment Connecting Teaching and Learning Making the Shift to a Formative Assessment-Centered Classroom 2. Integrating FACTs With Instruction and Learning Integrating Assessment and Instruction Assessment That Promotes Thinking and Learning Linking Assessment, Instruction, and Learning: The Mathematics Assessment, Instruction, and Learning Cycle (MAIL Cycle) Stages in the MAIL Cycle Engagement and Readiness Eliciting Prior Knowledge Exploration and Discovery Concept and Skill Development Concept and Procedure Transfer Self-Assessment and Reflection Selecting and Using FACTs to Strengthen the Link Between Assessment, Instruction, and Learning 3. Considerations for Selecting, Implementing and Using Data From FACTs Selecting FACTs Selecting FACTs to Match Learning Goals FACTs and the Common Core Standards for Mathematics Selecting FACTs to Match Teaching Goals The Critical Importance of Classroom Context in Selecting FACTs Planning to Use and Implement FACTs Starting Off With Small Steps Maintaining and Extending Implementation Using Data From the FACTs 4. Get the FACTs! 75 Mathematics Formative Assessment Classroom Techniques (FACTs) #1. A & D Statements #2. Agreement Circles #3. Always, Sometimes, or Never True #4. Card Sorts #5. CCC: Collaborative Clued Corrections #6. Comments-Only Marking #7. Commit and Toss #8. Concept Attainment Cards #9. Concept Card Mapping #10. Concept Cartoons #11. Create the Problem #12. Every Graph Tells a Story #13. Example, Nonexample #14. Fact-First Questioning #15. Feedback to Feed-Forward #16. Fist to Five #17. Four Corners #18. Frayer Model #19. Friendly Talk Probes #20. Give Me Five #21. Hot Seat Questioning #22. Human Scatter Graph #23. Is It Fair? #24. I Used to Think ... But Now I Know ... #25. Justified List #26. Justified True-or-False Statements #27. K-W-L Variations #28. Learning Goals Inventory (LGI) #29. Look Back #30. Matching Cards #31. Mathematician's Ideas Comparison #32. More A?More B Probes #33. Muddiest Point #34. No-Hands Questioning #35. Odd One Out #36. Opposing Views Probes #37. Overgeneralization Probes #38. Partner Speaks #39. Pass the Problem #40. P-E-O Probes (Predict, Explain, Observe) #41. Peer-to-Peer Focused Feedback #42. A Picture Tells a Thousand Words #43. POMS: Point of Most Significance #44. Popsicle Stick Questioning #45. PVF: Paired Verbal Fluency #46. Question Generating #47. Response Cards #48. Same A?Same B Probes #49. Sequencing Cards #50. Sticky Bars #51. Strategy Harvest #52. Strategy Probe #53. Student Evaluation of Learning Gains #54. Student Interviews #55. Terminology Inventory Probe (TIP) #56. Ten-Two #57. Thinking Log #58. Think-Alouds #59. Think-Pair-Share #60. Thought Experiments #61. Three-Minute Pause #62. 3-2-1 #63. Thumbs Up, Thumbs Down #64. Traffic Light Cards #65. Traffic Light Cups #66. Traffic Light Dots #67. Two-Minute Paper #68. Two or Three Before Me #69. Two Stars and a Wish #70. Two Thirds Testing #71. Volleyball, Not Ping-Pong! #72. Wait Time Variations #73. What Are You Doing and Why? #74. Whiteboarding #75. Word Sort Appendix: Annotated Resources for Mathematics Formative Assessment References Index

About the Author

Cheryl Rose Tobey is a Senior Mathematics Associate at EDC. She is the implementation director for the Pathways to Mathematics Achievement Study and a mathematics specialist for the NSF-funded Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) and Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students (DPD) projects. She also serves as a project director for an Institute for Educational Science (IES) project, Eliciting Mathematics Misconceptions (EM2). Her work is primarily in the areas of formative assessment and professional development. Prior to joining EDC, Tobey was the senior program director for mathematics at the Maine Mathematics and Science Alliance (MMSA), where she served as the co-principal investigator of the mathematics section of the NSF-funded Curriculum Topic Study, and principal investigator and project director of two Title IIa State Mathematics and Science Partnership projects. Prior to working on these projects, Tobey was the co-principal investigator and project director for MMSA's NSF-funded Local Systemic Change Initiative, Broadening Educational Access to Mathematics in Maine (BEAMM), and she was a fellow in Cohort 4 of the National Academy for Science and Mathematics Education Leadership. She is the coauthor of four published Corwin books, including three books in the Uncovering Student Thinking Series and Mathematics Curriculum Topic Study: Bridging the Gap Between Standards and Practice. Before joining MMSA in 2001 to begin working with teachers, Tobey was a high school and middle school mathematics educator for 10 years. She received her BS in secondary mathematics education from the University of Maine at Farmington and her MEd from City University in Seattle. Page Keeley is the senior science program director at the Maine Mathematics and Science Alliance (MMSA). She directs projects in the areas of leadership, professional development, standards and research on learning, formative assessment, and mentoring and coaching, and consults with school districts and organizations nationally. She has been the principal investigator on three NSF-funded projects: the Northern New England Co-Mentoring Network, a school-based mentoring program that supported science and mathematics professional learning communities for middle and high school mentors and new teachers; Curriculum Topic Study- A Systematic Approach to Utilizing National Standards and Cognitive Research; and PRISMS- Phenomena and Representations for Instruction of Science in Middle School, a National Digital Library collection of Web resources aligned to standards and reviewed for instructional quality. In addition she is a co-PI on two statewide projects: Science Content, Conceptual Change, and Collaboration (SC4), a state MSP focused on conceptual change teaching in the physical sciences for K--8 teachers and a National SemiConductor Foundation grant on Linking Science, Inquiry, and Language Literacy (L-SILL). Keeley is the author of ten nationally published books, including four books in the Curriculum Topic Study series (Corwin Press), four volumes in the Uncovering Student Ideas in Science: 25 Formative Assessment Probes series (NSTA Press), Science Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning (Corwin and NSTA Press), and Mathematics Formative Assessment: 50 Practical Strategies for Linking Assessment, Instruction, and Learning (in press). Keeley taught middle and high school science for 15 years. At that time she was an active teacher leader at the state and national level. She received the Presidential Award for excellence in Secondary Science Teaching in 1992 and the Milken National Educator Award in 1993. She has served as an adjunct instructor at the University of Maine, is a Cohort 1 Fellow in the National Academy for Science and Mathematics Education Leadership, served as a science literacy leader for the AAAS/Project 2061 Professional Development Program, and has served on several national advisory boards. She is a frequent speaker at national conferences and served as the 63rd President of the National Science Teachers Association (NSTA) for the 2008-09 term.

Reviews

"This book is a wonderful resource for integrating formative assessment into student-centered instruction. The authors describe numerous ways teachers can access the many levels of student understanding. It belongs on every mathematics teacher's shelf." -- Edward C. Nolan, PreK-12 Mathematics Specialist 20110406 "This book contains an incredible set of Math FACTs -- Formative Assessment Classroom Techniques. If you have been curious about Formative Assessment or how to implement it in your math classroom, this book provides the tools to get you started." -- Lyneille Meza, Coordinator of Data & Assessment 20110406 "This book features formative assessment strategies specifically written for math and can be used in any math class. A book that we have been waiting for." -- Zsuzsanna Laughland, Mathematics Teacher 20110406 "This book is a game-changer! By putting theory into practical digestible units, Mathematics Formative Assessment gives teachers of all levels a bank of techniques to design standards-aligned classes. I wish I had something like this 20 years ago when I was first teaching." -- Daniel Kikuji Rubenstein, Executive Director 20110406 "Coaches and other teacher leaders will find this compendium of assessment strategies invaluable." -- NCSM Newsletter, Spring 2012 20120315 "Most important, Keeley and Tobey discuss extensively the use of teh data generated to inform teaching. Coaches and other teacher leaders will find this compendium of assessment strategies invaluable." -- Kay Gilliland, Editor 20120503