Free Reproducibles
Beyond the Common Core: A Handbook for Mathematics in a PLC at Work™, Leader’s Guide
A Handbook for Mathematics in a PLC at Work™, Leader’s Guide
Focus your curriculum to heighten student achievement. Learn 10 high-leverage team actions for mathematics instruction and assessment. Discover the actions your team should take before a unit of instruction begins, as well as the actions and formative assessments that should occur during instruction. Examine how to most effectively reflect on assessment results, and prepare for the next unit of instruction.
Benefits
- Identify and cultivate the elements of mathematics instruction and assessment that yield the greatest impact on student learning.
- Increase student learning through 10 steps known as high-leverage team actions for mathematics instruction and assessment.
- Understand teacher actions that develop student understanding and skill for lower- and higher-cognitive-demand mathematical tasks every day, every lesson, every unit, every year.
- Access reproducibles and appendices to gain instructional strategies aligned with your state’s standards.
TABLE OF CONTENTS
Chapter 1: Before the Unit
Chapter 2: During the Unit
Chapter 3: After the Unit
Epilogue: Taking Your Next Steps
Appendix A: Standards for Mathematical Practice
Appendix B: Standards for Mathematical Practice Evidence Tool
Appendix C: Cognitive-Demand-Level Task-Analysis Guide
Appendix D: Sources for Higher-Level-Cognitive-Demand Tasks
Appendix E: How the Mathematics at Work High-Leverage Team Actions Support the NCTM Principles to Actions: Ensuring Mathematical Success for All
PRINTABLE REPRODUCIBLES
Introduction
Chapter 1
- End-of-Unit Test for Second Grade on Two-Digit Addition and Subtraction With Balanced Cognitive Demand
- Figure 1.2: Discussion Tool for Making Sense of the Agreed-On Essential Learning Standards for the Unit
- Figure 1.3: Sample Unit Progression for Eighth-Grade Geometry
- Figure 1.4: Four Categories of Cognitive Demand
- Figure 1.5: Sample Higher-Level-Cognitive-Demand Task Discussion Tool
- Figure 1.6: Tool for Sorting Unit Tasks by Cognitive-Demand Level
- Figure 1.7: Strategies for Increasing the Cognitive Demand of Tasks
- Figure 1.8: Team Discussion Tool for Identifying Higher-Level-Cognitive-Demand Tasks for a Unit
- Figure 1.9: Task-Analysis Discussion Tool
- Figure 1.10: Assessment Instrument Quality-Evaluation Tool
- Figure 1.11: High-Quality Assessment Diagnostic and Discussion Tool
- Figure 1.12: Tool for Planning and Preparing for Common Assessment Instrument Task Development
- Figure 1.13: Checking for Cognitive-Demand Balance on the Common Unit Assessment Instrument
- Figure 1.14: Collaborative Team Task-Scoring Discussion Prompts
- Figure 1.16: Assessment Instrument Alignment and Scoring Rubric Tool
- Figure 1.17: Collaborative Homework Assignment Protocol Discussion Tool
- Figure 1.18: Homework Quality Diagnostic Tool
- Figure 1.19: Setting Your Collaborative Team’s Before-the-Unit Priorities
- Mathematical Task Questions
- Revised Sample Assessment Questions for End-of-Unit Test on Expressions
- Table 1.1: Before-the-Unit-Begins Status Check Tool for HLTA 1–Making Sense of the Agreed-On Essential Learning Standards (Content and Practices) and Pacing
- Table 1.2: Before-the-Unit-Begins Status Check Tool for HLTA 2–Identifying Higher-Level-Cognitive-Demand Mathematical Tasks
- Table 1.3: Before-the-Unit-Begins Status Check Tool for HLTA 3–Developing Common Assessment Instruments
- Table 1.4: Before-the-Unit-Begins Status Check Tool for HLTA 4–Developing Scoring Rubrics and Proficiency Expectations for the Common Assessment Instruments
- Table 1.5: Before-the-Unit-Begins Status Check Tool for HLTA 5–Planning and Using Common Homework Assignments
Chapter 2
- Figure 2.2: Identifying Proficiency With the Standards for Mathematical Practice
- Figure 2.3: Mathematics Instruction and Higher-Level-Cognitive-Demand Mathematical Task Development Tool
- Figure 2.4: Teacher Actions That Provide Targeted and Differentiated Support
- Figure 2.5: Prompts for Differentiated In-Class Support and Student Perseverance
- Figure 2.6: Sample Transformations Using the Coordinate Grid
- Figure 2.7: Strategies for Maintaining Higher-Level-Cognitive-Demand Tasks During Instruction
- Figure 2.8: Checking for Understanding Versus Using the Formative Assessment Process Tool
- Figure 2.9: Grade 8 Higher-Level-Cognitive-Demand Reasoning Task
- Figure 2.10: Walkthrough Formative Assessment Observation Tool
- Figure 2.12: Small-Group Discourse Peer-to-Peer Engagement Tool
- Figure 2.13: Mathematical Practices Lesson-Planning Tool
- Figure 2.14: Learning About the Mathematical Practices Lesson-Planning Tool
- Figure 2.15: Mathematical Practices Lesson-Study Planning and Analysis Tool
- Figure 2.16: Lesson-Study Student Data Observation Tool
- Figure 2.17: Reflection and Debriefing Prompts to Follow Implementation of the Mathematical Practices Lesson-Planning Tool
- Figure 2.18: Setting Your Collaborative Team’s During-the-Unit Priorities
- Table 2.1: During-the-Unit Status Check Tool for HLTA 6–Using Higher-Level-Cognitive-Demand Mathematical Tasks Effectively
- Table 2.2: During-the-Unit Status Check Tool for HLTA 7–Using In-Class Formative Assessment Processes Effectively
- Table 2.3: During-the-Unit Status Check Tool for HLTA 8–Using a Lesson-Design Process for Lesson Planning and Collective Team Inquiry
Chapter 3
- Figure 3.2: Collaborative Team Student Feedback Discussion Tool
- Figure 3.4: Student Action Plan Template for Response to an End-of-Unit Assessment
- Figure 3.5: Tool for Student Self-Assessment and Feedback
- Figure 3.6: Collaborative Team Data-Analysis Protocol
- Figure 3.7: Collaborative Team Scoring and Analysis Activity
- Figure 3.8: Sample Unit 1 Learning Standard Tracking Tool
- Figure 3.9: Collaborative Team SMART Goal-Setting Reflections
- Figure 3.10: Setting Your Collaborative Team’s After-the-Unit Priorities
- Sample Student Self-Assessment–End-of-Unit Test Cover Page
- Student Action Plan Template for Response to an End-of-Unit Assessment
- Sample Student Self-Assessment, Goal Setting, and Action Plan
- Table 3.1: After-the-Unit-Ends Status Check Tool for HLTA 9–Ensuring Evidence-Based Student Goal Setting and Action for the Next Unit of Study
- Table 3.2: After-the-Unit-Ends Status Check Tool for HLTA 10–Ensuring Evidence-Based Adult Goal Setting and Action for the Next Unit of Study
- Tool for Student Self-Assessment and Feedback
Epilogue
Appendices
- Appendix D: Sources for Higher-Level-Cognitive-Demand Tasks
- Appendix E: How the Mathematics at Work High-Leverage Team Actions Support the NCTM Principles to Actions: Ensuring Mathematical Success for All
SUGGESTED RESOURCES
- All Things PLC
- Common Core Conversation, “Math Resources”
- EngageNY, “New York State Math Curriculum”
- Howard County Public Schools Secondary Mathematics Common Core Wiki
- Illustrative Mathematics
- Inside Mathematics, “Common Core State Standards for Mathematical Practice”
- Mathematics Assessment Project
- Mathematics Vision Project
- National Council of Supervisors of Mathematics, “Illustrating the Standards for Mathematical Practice”
- National Council of Teachers of Mathematics
- National Council of Teachers of Mathematics Illuminations
- Partnership for Assessment of Readiness for College and Careers, “PARCC Task Prototypes and New Sample Items for Mathematics”
- Smarter Balanced Assessment Consortium, “Sample Items and Performance Tasks”
- Virgina Department of Education, “Mathematics”