Mathematics Formative Assessment, Volume 1

Page is a prolific author of over twenty national best-selling and award-winning books, including twelve books in the Uncovering Student Ideas in Science series, four books in the first edition Curriculum Topic Study series, and four books in the Science and Mathematics Formative Assessment- Practical Strategies for Linking Assessment, Instruction, and Learning series. Several of her books have received prestigious awards in educational publishing.  She has authored numerous journal articles and contributed to several book chapters. She is a frequent invited speaker at regional, national, and international conferences on the topic of formative assessment in science, understanding students’ (and teachers’) thinking, and teaching for conceptual understanding.Prior to leaving the classroom to work at the Maine Mathematics and Science Alliance in 1996, Page taught middle and high school science for 15 years. At that time she was an active teacher leader at the state and national level, serving two terms as President of the Maine Science Teachers Association and NSTA District II Director 1995-1998 and NSTA Executive Board member (prior to the Board and Council restructuring in 1997). She received the Presidential Award for Excellence in Secondary Science Teaching in 1992 and the Milken National Distinguished Educator Award in 1993.Since leaving the classroom in 1996, her work in leadership and professional development has been nationally recognized.  In 2008 she was elected the 63rd President of the National Science Teachers Association (NSTA), the world′s largest organization of K-12, university, and informal science educators. In 2009 she received the National Staff Development Council’s (now Learning Forward) . In 2013 she received the Outstanding Leadership in Science Education award from the National Science Education Leadership Association (NSELA) and in 2018, The Distinguished Service to Science Education Award from NSTA.  She has served as an adjunct instructor at the University of Maine, was a Cohort 1 Fellow in the National Academy for Science and Mathematics Education Leadership, was a science literacy leader for the AAAS/Project 2061 Professional Development Program, and served on several national advisory boards. She has a strong interest in global science education and has led science/STEM education delegations to South Africa (2009), China (2010), India (2012), Cuba (2014), Iceland (2017), Panama (2018), and Costa Rica (2019).Prior to entering the teaching profession, Page was a research assistant for immunogeneticist, Dr. Leonard Shultz, at the Jackson Laboratory of Mammalian Genetics in Bar Harbor, Maine. She received her B.S. in Life Sciences/pre-veterinary studies from the University of New Hampshire and her Masters degree in Science Education from the University of Maine. In her spare time she enjoys travel, reading, photography, fiber art, and dabbles in modernist cooking and culinary art. A Maine resident for almost 40 years, Page and her husband currently reside in Fort Myers, FL and Wickford, RI. Page can be contacted at pagekeeley@gmail.com or through her web site at www.uncoveringstudentideas.orgCheryl Rose Tobey is a senior mathematics associate at Education Development Center (EDC) in Massachusetts. She is the project director for Formative Assessment in the Mathematics Classroom: Engaging Teachers and Students (FACETS) and a mathematics specialist for Differentiated Professional Development: Building Mathematics Knowledge for Teaching Struggling Students (DPD); both projects are funded by the National Science Foundation (NSF). She also serves as a director of development 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 six published Corwin books, including seven books in the Uncovering Student Thinking series (2007, 2009, 2011, 2013, 2014), two Mathematics Curriculum Topic Study resources (2006, 2012), and Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction and Learning (2011). Before joining MMSA in 2001 to begin working with teachers, Tobey was a high school and middle school mathematics educator for ten years. She received her BS in secondary mathematics education from the University of Maine at Farmington and her MEd from City University in Seattle. She currently lives in Maine with her husband and blended family of five children.

• PrefaceAcknowledgmentsAbout the Authors1. 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 AssessmentConnecting Teaching and LearningMaking the Shift to a Formative Assessment-Centered Classroom2. Integrating FACTs With Instruction and LearningIntegrating Assessment and InstructionAssessment That Promotes Thinking and LearningLinking Assessment, Instruction, and Learning: The Mathematics Assessment, Instruction, and Learning Cycle (MAIL Cycle)Stages in the MAIL CycleEngagement and ReadinessEliciting Prior KnowledgeExploration and DiscoveryConcept and Skill DevelopmentConcept and Procedure TransferSelf-Assessment and ReflectionSelecting and Using FACTs to Strengthen the Link Between Assessment, Instruction, and Learning3. Considerations for Selecting, Implementing and Using Data From FACTsSelecting FACTsSelecting FACTs to Match Learning GoalsFACTs and the Common Core Standards for MathematicsSelecting FACTs to Match Teaching GoalsThe Critical Importance of Classroom Context in Selecting FACTsPlanning to Use and Implement FACTsStarting Off With Small StepsMaintaining and Extending ImplementationUsing Data From the FACTs4. 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 SortAppendix: Annotated Resources for Mathematics Formative AssessmentReferencesIndex

"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."