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Beyond the Common Core A Handbook for Mathematics in a PLC at Work, High School
A Handbook for Mathematics in a PLC at Work™, High School
Focus your curriculum to heighten student achievement. Learn 10 high-leverage team actions for grades 9–12 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: 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
PRINTABLE REPRODUCIBLES
Introduction
- Figure I.1: High-Leverage Team Actions Aligned to the Four Critical Questions of a PLC
- Figure 1.3: Sample Essential Learning Standard Discussion Tool for Linear and Exponential Functions
- Figure 1.4: Predicting World Population: Creating and Comparing a Linear, Quadratic, and Exponential Function
- Figure 1.5: Discussion Tool for Making Sense of the Agreed-On Essential Learning Standards for the Unit
- Figure 1.6: Sample Unit Plan Progression of Content for a Quadratic Functions Unit of Study
- Figure 1.7: Sample Unit Progression for Exponential Functions—Across Standards
- Figure 1.8: Four Categories of Cognitive Demand
- Figure 1.9: Tool for Sorting Unit Tasks by Cognitive-Demand Level
- Figure 1.10: Sample Higher-Level-Cognitive-Demand Task Discussion Tool
- Figure 1.11: Strategies for Increasing the Cognitive Demand of Tasks
- Figure 1.12: Team Discussion Tool for Identifying Higher-Level-Cognitive-Demand Tasks for a Unit
- Figure 1.13: Task-Analysis Discussion Tool
- Figure 1.14: Assessment Instrument Quality-Evaluation Tool
- Figure 1.15: High-Quality Assessment Diagnostic and Discussion Tool
- Figure 1.16: Tool for Planning and Preparing for Common Assessment Instrument Task Development
- Figure 1.17: Sample Assessment Questions for Essential Learning Standard F-IF.1
- Figure 1.18: Checking for Cognitive-Demand Balance on the Common Unit Assessment Instrument
- Figure 1.19: Revised Sample Assessment Items With Improved Cognitive-Demand Balance
- Figure 1.21: Sample Student Responses for Photography Task
- Figure 1.22: Collaborative Team Task Scoring Discussion Prompts
- Figure 1.23: Sample Algebra 1 or Integrated Mathematics I Exponential Functions Exam
- Figure 1.24: Assessment Instrument Alignment and Scoring Rubric Tool
- Figure 1.25: Collaborative Homework Assignment Protocol Discussion Tool
- Figure 1.26: Homework Quality Diagnostic Tool
- Figure 1.27: Sample Homework Assignment Sheet for Advanced Algebra
- Figure 1.28: Setting Your Collaborative Team's Before-the-Unit Priorities
- Mathematical Task Questions
- Sample Unit Progression
- Table 1.1: Before-the-Unit-Begins Status Check Tool—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 HTLA 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
- Figure 2.3: Identifying Proficiency With the Standards for Mathematical Practice
- Figure 2.4: Geometry Quadrilateral Activity
- Figure 2.5: Mathematics Instruction and Higher-Level-Cognitive-Demand Task Scenario
- Figure 2.6: Fuel for Thought Task
- Figure 2.7: Teacher Actions That Provide Differentiated Feedback and Support
- Figure 2.8: Prompts for Differentiated In-Class Support and Student Perseverance
- 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: Geometry Circles Higher-Level-Cognitive-Demand Reasoning Task
- Figure 2.14: Demonstrating Reasoning Rubric
- Figure 2.15: Walk-Around Formative Assessment Process Tool
- Figure 2.16: Planning for the Formative Assessment Process Example—Algebra
- Figure 2.17: Planning for the Formative Assessment Process—Functions Task
- Figure 2.18: Planning for the Formative Assessment Process—Algebra 2
- Figure 2.20: Small-Group Discourse Peer-to-Peer Engagement Tool
- Figure 2.21: Connecting In-Class Formative Assessment Process Work to the End-of-Unit Assessment Tool
- Figure 2.22: Mathematical Practices Lesson-Planning Tool
- Figure 2.23: Learning About the CCSS Mathematical Practices Lesson-Planning Tool
- Figure 2.24: Mathematical Practices Lesson-Study Planning and Analysis Tool
- Figure 2.25: Lesson-Study Student Data Observation Tool
- Figure 2.26: Sample Mathematical Practices Lesson-Planning Tool for High School Exponential Functions Unit
- Figure 2.27: Reflection Debriefing Prompts to Follow Implementation of the CCSS Mathematical Practices Lesson-Planning Tool
- Figure 2.28: Setting Your Collaborative Team's During-the-Unit Priorities
- Planning for the Formative Assessment Process Sample—Algebra
- Sample Introduction to Geometry Assignment Tracker and Self-Assessment Form
- Sample Lesson-Design Study Model
- Sample Standards for Mathematical Practices Tool
- Template for Planning for the Formative Assessment Process
- Template for Small-Group Discourse Peer-to-Peer Engagement Tool
- Table 2.1: Common Understandings of Key Terms
- Table 2.2: During-the-Unit Status Check Tool for HLTA 6—Using Higher-Level-Cognitive-Demand Mathematical Tasks Effectively
- Table 2.3: During-the-Unit Status Check Tool for HLTA 7—Using In-Class Formative Assessment Processes Effectively
- Table 2.4: During-the-Unit Status Check Tool for HLTA 8—Using a Lesson-Design Process for Lesson Planning and Collective Team Inquiry
- Figure 3.2: Sample Student Responses for Photography Task
- Figure 3.3: Collaborative Team Student Feedback Discussion Question Tool
- Figure 3.4: Team Reflection Activity for Group Scoring an Assessment
- Figure 3.9: Collaborative Team Data-Analysis Protocol
- Figure 3.10: Collaborative Team Scoring and Calibration Activity
- Figure 3.11: Analysis of Student Work Tool
- Figure 3.13: Collaborative Team SMART Goal-Setting Reflections
- Figure 3.15: Setting Your Collaborative Team's After-the-Unit Priorities
- SMART Goal Worksheet
- SMART Goal Worksheet: American Government
- 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
- Appendix D: Sources for Higher-Level-Cognitive-Demand Tasks
- Figure E.1: Tool for Assessing Your Actions and Setting Your Team Priorities
- ACT Aspire
- All Things PLC
- The College Board, "College Board Tests”
- 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
- National Science Digital Library, "Common Core Math Top Picks”
- 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”
- Prentice Hall
- SHS Advanced Algebra Honors
- Smarter Balanced Assessment Consortium
- Smarter Balanced Assessment Consortium, "Sample Items and Performance Tasks”
Chapter 1
Chapter 2
Chapter 3
Epilogue
