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Beyond the Common Core: A Handbook for Mathematics in a PLC at Work™, Grades K–5
A Handbook for Mathematics in a PLC at Work™, Grades K–5
Focus your curriculum to heighten student achievement. Learn 10 high-leverage team actions for grades K–5 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 which actions must occur before, during, and after unit instruction with your collaborative team.
- 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: Cognitive-Demand-Level Task-Analysis Guide
Appendix C: Sources for Higher-Level-Cognitive-Demand Tasks
PRINTABLE REPRODUCIBLES
Introduction
Chapter 1
- Figure 1.2: Sample Essential Learning Standard Discussion Tool
- Figure 1.4: Discussion Tool for Making Sense of the Agreed-On Essential Learning Standards for the Unit
- Figure 1.5: Sample Unit Plan Progression of Content for Applying Properties of Operations as Strategies to Multiply for Grade 3
- Figure 1.6: Four Categories of Cognitive Demand
- Figure 1.7: Higher-Level-Cognitive-Demand Mathematical Task Discussion Tool
- Figure 1.8: Corresponding Lower-Level-Cognitive-Demand Mathematical Task-Creation Tool
- Figure 1.9: Comparing Higher- and Lower-Level-Cognitive-Demand Mathematical Tasks
- Figure 1.10: Tool for Sorting Unit Tasks by Cognitive Demand Level
- Figure 1.13: Strategies for Increasing the Cognitive Demand of Tasks
- Figure 1.14: Team Discussion Tool for Identifying Higher-Level-Cognitive-Demand Mathematical Tasks for the Unit
- Figure 1.15: Task Analysis Discussion Tool
- Figure 1.16: Assessment Instrument Quality-Evaluation Tool
- Figure 1.17: High-Quality Assessment Diagnostic and Discussion Tool
- Figure 1.20: Preparing Common Assessment Instrument Tasks Tool
- Figure 1.22: Checking for Cognitive Demand Balance on the Common Unit Assessment Instrument
- Figure 1.25: Collaborative Team Task Scoring Discussion Tool
- Figure 1.26: Assessment Instrument Alignment and Scoring Rubric Tool
- Figure 1.27: Sample End-of-Unit Test-Scoring Rubric for Figure 1.23
- Figure 1.28: Assessment Instrument Alignment and Scoring Rubric Tool
- Figure 1.29: Collaborative Homework Assignment Protocol Discussion Tool
- Figure 1.30: Homework Quality Diagnostic Tool
- Figure 1.31: Sample Unit Homework Assignment Sheet for Grade 3
- Figure 1.32: Setting Your Collaborative Team's Before-the-Unit Priorities
- Mathematical Task Questions
- Table 1.1: Before-the-Unit 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 Status Check Tool for HLTA 2—Identifying Higher-Level-Cognitive-Demand Mathematical Tasks
- Table 1.3: Before-the-Unit Status Check Tool for HLTA 3—Developing Common Assessment Instruments
- Table 1.4: Before-the-Unit Status Check Tool for HTLA 4—Developing Scoring Rubrics and Proficiency Expectations for the Common Assessment Instruments
- Table 1.5: Before-the-Unit Status Check Tool for HLTA 5—Planning and Using Common Homework Assignments
Chapter 2
- Figure 2.3: Identifying Proficiency With the Standards for Mathematical Practice
- Figure 2.4: Mathematics Instruction and Higher-Level-Cognitive-Demand Mathematical Task Scenario
- Figure 2.5: Mathematics Instruction and Higher-Level-Cognitive-Demand Mathematical Task Development Tool
- Figure 2.6: Grade 4 Problem-Solving Higher-Level-Cognitive-Demand Mathematical Task
- Figure 2.7: Selecting, Locating, and Organizing Resources Tool
- Figure 2.8: Teacher Actions That Provide Targeted and Differentiated Support
- Figure 2.9: Prompts for Targeted and Differentiated In-Class Support
- Figure 2.10: Strategies for Maintaining Higher-Level Cognitive Demand for Tasks During Instruction
- Figure 2.11: Checking for Understanding Versus Using the Formative Assessment Process Tool
- Figure 2.12: Mathematics Instruction Scenario Revisited
- Figure 2.13: Grade-Level Tasks Revisited for Formative Assessment Feedback and Action Considerations
- Figure 2.14: First-Grade Higher-Level-Cognitive-Demand Mathematical Task for Reasoning
- Figure 2.15: During-Instruction Formative Assessment Process Tool
- Figure 2.16: Planning for the Formative Assessment Process—Grade K
- Figure 2.17: Planning for the Formative Assessment Process—Grade 2
- Figure 2.18: Planning for the Formative Assessment Process—Grade 4
- Figure 2.19: End-of-Unit Test for Second Grade on Two-Digit Addition and Subtraction With Balanced Cognitive Demand
- Figure 2.20: Preparing for the End-of-Unit Assessment Tool
- Figure 2.21: Mathematical Practices Lesson-Planning Tool
- Figure 2.22: Learning About the Mathematical Practices Lesson-Planning Tool
- Figure 2.23: Sample Mathematical Practices Lesson-Planning Tool for Third-Grade Plane Geometry
- Figure 2.24: Lesson Study Student Data Observation Tool
- Figure 2.25: Reflection Debriefing Prompts to Follow Implementation of the CCSS Mathematical Practices Lesson-Planning Tool
- Figure 2.26: Setting Your Collaborative Team's During-the-Unit Priorities
- Table 2.1: Common Understandings of Key Terms
- Table 2.2: In-Depth Study of the Standards for Mathematical Practice Tool
- Table 2.3: During-the-Unit Status Check Tool for HLTA 6—Using Higher-Level-Cognitive-Demand Mathematical Tasks Effectively
- Table 2.4: During-the-Unit Status Check Tool for HLTA 7—Using In-Class Formative Assessment Processes Effectively
- Table 2.5: 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: Formative Feedback With Action Tool
- Figure 3.4: Student Feedback Discussion Questions for 6 √ó 7
- Figure 3.5: Student Feedback Team Discussion Tool
- Figure 3.6: Student Action Plan Template for Response to an End-of-Unit Assessment
- Figure 3.7: Tool for Student Self-Assessment and Feedback
- Figure 3.8: Student Progress-Tracking Chart
- Figure 3.9: Collaborative Team Data-Analysis Protocol
- Figure 3.11: Reflection Questions on Student Work on an End-of-Unit Assessment
- Figure 3.13: Collaborative Team Scoring and Calibration Activity
- Figure 3.14: Collaborative Team Proficiency Target Reflections
- Figure 3.15: Setting Your Collaborative Team's After-the-Unit Priorities
- Table 3.1: After-the-Unit 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 Status Check Tool for HLTA 10—Ensuring Evidence-Based Adult Goal Setting and Action for the Next Unit of Study
Epilogue
Appendices
SUGGESTED RESOURCES
Chapter 1
- ACT Aspire, "Exemplar Mathematics Test Questions”
- College Board, "College Board Tests”
- Common Core State Standards Initiative
- Marzano Research
- National Council of Teachers of Mathematics
- Partnership for Assessment of Readiness for College and Careers
- Partnership for Assessment of Readiness for College and Careers, "PARCC Task Prototypes and New Sample Items for Mathematics”
- Smarter Balanced Assessment Consortium
- Smarter Balanced Assessment Consortium, "Sample Items and Performance Tasks”
Chapter 2
Appendix C
- 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
- National Council of Supervisors of Mathematics, "Illustrating the Standards for Mathematical Practice”
- National Council of Supervisors of Mathematics Illuminations
- The National Science Digital Library, Common Core State Standards for Mathematics (list of aligned resources)
- 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”
