#
Mathematics Formative Assessment, Volume 1
75 Practical Strategies for Linking Assessment, Instruction, and Learning

- Page Keeley - Consultant, Speaker, and Author
- Cheryl Rose Tobey - Tobey Education Group, LLC, Education Development Center, Newton, MA

Published in Association with National Council of Teachers of Mathematics

*Transform your mathematics instruction with this rich collection of formative assessment techniques*

Award-winning author Page Keeley and mathematics expert Cheryl Rose Tobey apply the successful format of Keeley's best-selling *Science Formative Assessment* to mathematics. They provide 75 formative assessment strategies and show teachers how to use them to inform instructional planning and better meet the needs of all students. Research shows that formative assessment has the power to significantly improve learning, and its many benefits include:

- Stimulation of metacognitive thinking
- Increased student engagement
- Insights into student thinking
- Development of a discourse community

The authors also provide important guidance with each technique, including usage tips and caveats, implementation examples, and suggested modifications. With practical strategies that are relevant for all grades and topic areas, *Mathematics Formative Assessment* provides the tools to transform teaching and learning in your classroom.

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 |

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 |

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 |

#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 |

*"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."*

**Montgomery County Public Schools, Rockville, MD**

*"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."*

**Denton Independent School District, TX**

*"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."*

**Kennett High School, North Conway, NH**

*"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."*

**Brooklyn Prospect Charter School, NY**

*"Coaches and other teacher leaders will find this compendium of assessment strategies invaluable."*

**National Council of Supervisors of Mathematics**

*"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."*

**NCSM Newsletter**

as a reference book

**Colg of Education, University of Texas - Brownsville**

### Sample Materials & Chapters

Chapter 1: An Introduction to Formative Assessment Classroom Techniques (FACS)