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

November 2011 | 256 pages | Corwin
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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 studentsÆ thinking and learning, teachers can focus on what works best for learning and design or modify lessons to fit the needs of the students.
 
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

"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
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."

Lyneille Meza, Coordinator of Data & Assessment
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."

Zsuzsanna Laughland, Mathematics Teacher
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."

Daniel Kikuji Rubenstein, Executive Director
Brooklyn Prospect Charter School, NY

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

NCSM Newsletter, Spring 2012
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."

Kay Gilliland, Editor
NCSM Newsletter

as a reference book

Dr Zhidong Zhang
Colg of Education, University of Texas - Brownsville
September 3, 2012
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