Mathematics at Work™ Plan Book by Solution Tree

PL A N B O O K Timothy D. Kanold Sarah Schuhl

PL A N BOOK Timothy D. Kanold Sarah Schuhl

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Copyright © 2020 by Solution Tree Press Materials appearing here are copyrighted. With one exception, all rights are reserved. Readers may reproduce only those pages marked “Reproducible.” Otherwise, no part of this book may be reproduced or transmitted in any form or by any means (electronic, photocopying, recording, or otherwise) without prior written permission of the publisher. 555 North Morton Street Bloomington, IN 47404 800.733.6786 (toll free) / 812.336.7700 FAX: 812.336.7790 email: info@SolutionTree.com SolutionTree.com Visit go.SolutionTree.com/MathematicsatWork to download the free reproducibles in this book. Printed in the United States of America

Library of Congress Cataloging-in-Publication Data Names: Kanold, Timothy D., author. | Schuhl, Sarah, author. Title: Mathematics at Work plan book / Timothy D. Kanold and Sarah Schuhl. Description: Bloomington, IN : Solution Tree Press, [2019] | Mathematics at Work represents a series of activites for grade K-12 mathematics teachers. | Includes bibliographical references. Identifiers: LCCN 2019014112 | ISBN 9781949539530 (spiral bound) Subjects: LCSH: Mathematics teachers--In-service training. | Mathematics--Study and teaching. | Curriculum planning. Classification: LCC QA10.5 .K3575 2019 | DDC 510.71/2--dc23 LC record available at https://lccn.loc.gov/2019014112 Solution Tree Jeffrey C. Jones, CEO Edmund M. Ackerman, President Solution Tree Press President and Publisher: Douglas M. Rife Associate Publisher: Sarah Payne-Mills Art Director: Rian Anderson Managing Production Editor: Kendra Slayton Senior Production Editor: Todd Brakke Content Development Specialist: Amy Rubenstein Proofreader: Jessi Finn Cover Designer: Rian Anderson Editorial Assistant: Sarah Ludwig

Acknowledgments We wish to thank Solution Tree for their relentless dedication to providing meaningful books and programs of support for teachers and instructional coaches of mathematics! Special thanks go to Todd Brakke and Sarah Payne-Mills for suggesting this project and then believing in our vision for what it might become. Thanks too for the support of our coauthors in the writing of the Every Student Can Learn Mathematics series. For every teacher team that has used our tools and protocols to focus their work in mathematics, we give thanks to you for walking the walk of teaching mathematics and helping students to learn a discipline we love, every day. Finally, thanks to our families, who love us despite our view of the world!

—Timothy D. Kanold and Sarah Schuhl

Table of Contents Reproducible pages are in italics.

The Mathematics at Work™ Plan Book. . . . . . . . . iv About the Authors. . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Pa r t 1: Tools and Protocols. . . . . . . . . . . 1 The PLC at Work Process as the Foundation for Mathematics at Work . . . . . . . . 2 Mathematics in a PLC at Work Framework . . . . . 3

Pa r t 2: Unit Planners. . . . . . . . . . . . . . . . . 29 Year-at-a-Glance Guide . . . . . . . . . . . . . . . . . . . . . . 40

Pa r t 3: Weekly Planners . . . . . . . . . . . . . 41 What Is Collective Inquiry?. . . . . . . . . . . . . . . . . . . 43

Success Story: How the PLC at Work Process Began. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Six Elements of Quality Lesson Design. . . . . . . 83 Why Teach Each Lesson in a Unit?. . . . . . . . . . . . 85 What Is Necessary for Quality Discourse in a Lesson?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Success Story: Anoka-Hennepin School District. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 How Lessons Should Begin and End . . . . . . . . . 91

What Are Effective Norms? . . . . . . . . . . . . . . . . . . 47

How to Address Academic Vocabulary and Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

What Other Team Agreements Are Necessary?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

What Teams Can Learn From Lesson Study and Instructional Rounds . . . . . . . . . . . . . . . . . . 95

Assessment Instrument Quality Evaluation Rubric. . . . 7

What Are Mathematics SMART Goals? . . . . . . . 51

Success Story: Ramona Junior High. . . . . . . . . 97

Mathematics Intervention Program Evaluation Tool. . . . 8

Success Story: Aloha-Huber Park K–8 . . . . . . . 53

Why Have Common Independent Practice?. . . 99

Intervention Practices . . . . . . . . . . . . . . . . . . . . . . . . . . 9

What Tools Can We Use?. . . . . . . . . . . . . . . . . . . . . 55

Instructional Framework and Lesson-Design Evaluation Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

What Are Essential Learning Standards?. . . . . . 57

What to Consider for Independent Practice Assignments. . . . . . . . . . . . . . . . . . . . . 101

Your Work and Your Story. . . . . . . . . . . . . . . . . . . . . 4 Common Unit Assessment Formative Process Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Common Assessment Self-Reflection Protocol. . . . . . . 6

Protocol for Team Analysis of the Mathematics in a PLC at Work Lesson-Design Tool . . . . . . . . . . . . . . . 11 Mathematics in a PLC at Work Lesson-Design Tool. . . 12

How Teams Make Sense of Standards, Essential Learning Standards, and Lesson Targets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Evaluating the Quality of Independent Practice Assignments. . . . . . . . . . . . . . . . . . . . . . . . 14

What Are Common Mid-Unit and End-ofUnit Assessments? . . . . . . . . . . . . . . . . . . . . . . . . 61

Student Independent Practice Effectiveness Survey. . 15

How Teams Create Quality Common Assessments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Scoring Rubric and Student Confidence Scale for an Independent Practice Assignment. . . . . . . . . . . . 16

The High-Performing Mathematics Team. . . . . .17

How Teams Calibrate Scoring of Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Cultural Shifts in a PLC . . . . . . . . . . . . . . . . . . . . . . 18

How Teams Turn Data Into Information. . . . . . . . 67

Critical Issues for Team Consideration. . . . . . . . . . . . . 20

Success Story: Newhall School District. . . . . . 69

Team Feedback Sheet. . . . . . . . . . . . . . . . . . . . . . . . . 21

What Teams Learn From Student Work. . . . . . . . 71

SMART Goal Template. . . . . . . . . . . . . . . . . . . . . . . . . 22 Collaborative Lesson-Design Elements. . . . . . . . . . . . 23 Purpose and Nature of Grading Practices . . . . . . . . . . 24 Lesson-Study Time Expectations and Team Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Team Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Substitute Teacher Information. . . . . . . . . . . . . . . 27 Holidays and Birthdays. . . . . . . . . . . . . . . . . . . . . . 28

How Students Can Reflect and Set Goals From Common Assessments. . . . . . . . . . . . . . . 73 What Are Systematic Interventions?. . . . . . . . . . 75

Success Story: Don Pedro Elementary School. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Success Story: How We Established Collective Teacher Efficacy. . . . . . . . . . . . . . . 103 How to Address Common Independent Practice in Class. . . . . . . . . . . . . . . . . . . . . . . . . . 105 What a Grade Means. . . . . . . . . . . . . . . . . . . . . . . 107 How a Grade Reflects Learning . . . . . . . . . . . . . 109 Is Equity a Part of Team Grading Practices? . . 111

Success Story: Sanger Unified School District. . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Success Story: Visalia Unified School District. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 What Is a Team or Department Mathematics Vision?. . . . . . . . . . . . . . . . . . . . . . 115 How Will We Celebrate and Reflect, Refine, and Act on Our Work as a Team? . . . . . . . . . . . 117

How Teams Plan for Tier 2 Interventions . . . . . . 79

Pa r t 4: References and Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

How Effective Are Tier 2 Interventions? . . . . . . . 81

References and Resources. . . . . . . . . . . . . . . . . . 121

P L A N B O O K | i i i

The Mathematics at Work™ Plan Book Mathematics at Work is built on the fundamental belief that every K–12 student can learn mathematics. To achieve this purpose, teachers and leaders of mathematics establish a reflect, refine, and act formative learning process for their students and themselves. Mathematics at Work offers a comprehensive Professional Learning Communities (PLCs) at Work ® approach to achieving mathematics success in K–12 classrooms. The Mathematics at Work framework empowers teachers, teacher teams, and mathematics education leaders to reflect on and refine current assessment, intervention, homework, and lesson designs based on high-quality, research-affirmed criteria. The PLC at Work process is one of the best and most promising models a school or district can use to build a more equitable response for student learning. The work of collaborative teacher teams—especially in mathematics—when focused on the right assessment, instruction, and intervention criteria, will erase potential inequities in student learning. These collaborative team criteria lead to the sustained and substantive schoolimprovement process that characterizes PLCs at Work. Since the mid-1990s, Richard DuFour, Robert Eaker, and Rebecca DuFour—the architects of the PLC at Work process—championed it as a model for school improvement. In a professional learning community, educators commit to working collaboratively in an ongoing process of collective inquiry and action research to achieve better results for the students they serve (DuFour, DuFour, Eaker, Many, & Mattos, 2016). The key to improving learning for students is continuous, job-embedded learning for educators as a type of collective teacher efficacy. Most plan books guide the individual classroom teacher in instructional decisions. They focus on, “What will I teach, when will I teach it, and how will I teach it?” The Mathematics at Work Plan Book is unique because it not only assists the individual teacher in unit-by-unit planning, but it also guides the collaborative team processes essential to schools that operate as PLCs. In this plan book, and throughout the Every Student Can Learn Mathematics series, we emphasize the concept of team action. Because some teachers may be the only members of a grade-level or mathematics course, we i v | M A T H E M A T I C S A T W O R K ™

recommend you work with a colleague in a grade level or course above or below your own as a vertical team. Or, work with other job-alike teachers across a geographical region as technology allows. Collaborative teams are the engines that drive the PLC at Work process. Most importantly, this plan book calls on you to develop your self-confidence and sense of collective efficacy to go far beyond the traditional questions of teaching, arriving at a relentless collaborative focus on learning—for both students and adults. Your team can refer to the books in the Every Student Can Learn Mathematics series to help with your planning efforts: Mathematics Coaching and Collaboration in a PLC at Work (Kanold, Toncheff, Larson, Barnes, Kanold-McIntyre, & Schuhl, 2018), Mathematics Assessment and Intervention in a PLC at Work (Kanold, Schuhl, Larson, Barnes, Kanold-McIntyre, & Toncheff, 2018), Mathematics Homework and Grading in a PLC at Work (Kanold, Barnes, Larson, Kanold-McIntyre, Schuhl, & Toncheff, 2018), and Mathematics Instruction and Tasks in a PLC at Work (Kanold, Kanold-McIntyre, Larson, Barnes, Schuhl, & Toncheff, 2018). The first part of the Mathematics at Work Plan Book contains an overview of the big ideas that shape Mathematics at Work, cultural shifts that you can expect in a PLC at Work, and keys to building high-performing collaborative teams. It also includes tools to help you work with your team more effectively as well as protocols for evaluating current assessment, homework, instruction, and intervention routines. You can also visit go.SolutionTree.com/MathematicsatWork to access additional online resources. The second part provides unit-planning charts to help you work as a team to determine the mathematics units for the school year. The third part includes thirty-eight weeks of unit-planning pages with text and activities to inform, inspire, and challenge you and your teammates as you take the Mathematics at Work journey. We designed these pages to help inform the nature of your collaborative work together throughout the year. You’ll also learn from other schools and districts that have embarked on the same journey. The fourth part provides references and resources for further study.

About the Authors Timothy D. Kanold, PhD, an award-winning educator, author, and consultant, is the former director of mathematics and science and superintendent of Adlai E. Stevenson High School District 125, a model professional learning community district in Lincolnshire, Illinois. Sarah Schuhl is a consultant specializing in PLCs at Work, mathematics, assessment, school improvement, and response to intervention (RTI). She has been a secondary mathematics teacher, high school instructional coach, and K–12 mathematics specialist. To book Timothy D. Kanold or Sarah Schuhl for professional development, contact pd@SolutionTree.com.

Tools and Protocols This part contains an overview of the big ideas that shape Mathematics in a PLC at Work, culture shifts that you can expect in a PLC at Work, and keys to building highperforming collaborative teams.

PART 1

The PLC at Work Process as the Foundation for Mathematics at Work

Three big ideas and four critical questions drive the work of the PLC process (DuFour et al., 2016). 1. A focus on learning: Teachers focus on all students learning at high levels as the fundamental purpose of the school. 2. A collaborative culture: Teachers work together in teams interdependently and take collective responsibility for the success of all students. 3. A results orientation: Team members are constantly seeking evidence of the results they desire—high levels of student learning. Additionally, collaborative mathematics teams in a PLC at Work focus on four critical questions (DuFour et al., 2016) as part of their instruction, task-creation, homework, and grading routines. 1. What knowledge, skills, and dispositions should every student acquire as a result of this mathematics unit, course, or grade level? 2. How will we know when each student has acquired the essential mathematics knowledge and skills? 3. How will we respond when some students of mathematics do not learn? 4. How will we extend the learning for students of mathematics who are already proficient? The four critical questions of a PLC at Work provide an equitable formative process for your professional work in mathematics assessment, intervention, instruction, homework, and grading. Imagine the access and opportunity gaps that will exist if you and your colleagues do not agree on the core learning standards for each unit as well as the level of rigor for the essential question 2 | M A T H E M A T I C S A T W O R K ™

Imagine the devastating effects on students if you do not reach team agreement on the rigor of lower- and higher-level cognitive demand for the mathematical tasks you use to engage students in mathematics lessons and assessments (question 2). Imagine the lack of student agency (voice, ownership, perseverance, and action during learning) if you do not work together to create a unified, robust formative process for helping students own their response during class, reflecting when they are and are not learning during the lesson and after each assessment (questions 3 and 4). For these reasons, we refer to our process as Mathematics in a PLC at Work. For you and your colleagues to effectively answer the four critical questions of a PLC at Work, in regard to a lesson’s instruction and tasks, requires the development, use, and understanding of lesson-design criteria that cause students to engage in the lesson, persevere through the lesson, and embrace their errors as they demonstrate learning pathways for the various mathematics tasks you present to them. Additionally, answering the critical questions well while planning for homework, grading, assessment, and intervention requires structure through the development of products for a team’s work together. It also requires a formative culture through the process of how you work with your team to use those products.

Persevere Ask: Do I seek to understand my own learning?

Receive FAST Feedback Ask: Do I embrace my errors?

Your team reflecting together and then taking action around the right mathematics lesson-design work is the key to improved student learning. The actions you and your colleagues take together can improve the likelihood of more equitable mathematics learning experiences for every K–12 student. The reflect, refine, and act cycle illustrates this perspective about the process of lifelong learning. This is a formative learning cycle. When you embrace mathematics learning as a process, you and your students: • Reflect—Work the task or tasks, and then ask, “Is this the best solution strategy?” • Refine—Receive FAST feedback and ask, “Do I embrace my errors?” • Act—Persevere and ask, “Do I seek to understand my own learning?” This cycle provides a systematic way to structure and facilitate in-depth team discussions. Additionally, the Mathematics in a PLC at Work framework on the next page focuses on six teacher team actions and two mathematics coaching actions within four primary categories. The eight actions focus on the teacher teams’ professional work and how they should respond to the four critical questions of a PLC at Work (DuFour et al., 2016). The reflect, refine, and act cycle and the Mathematics in a PLC at Work framework will guide your work in planning unit assessments, daily instruction, daily homework, grading practices, and systematic interventions.

The Learning Process

Work the Task Ask: Is this the best solution strategy?

To create a PLC at Work, focus on learning rather than teaching, work collaboratively, and hold yourself accountable for results.

(question 1): What do we want all students to know and be able to do?

Mathematics in a PLC at Work Framework Every Student Can Learn Mathematics series’ Team and Coaching Actions Serving the Four Critical Questions of a PLC at Work

2. How will we know if students learn it?

3. How will we respond when some students do not learn?

4. How will we extend the learning for students who are already proficient?

Mathematics Assessment and Intervention in a PLC at Work Team action 1: Develop high-quality common assessments for the agreed-on essential learning standards. Team action 2: Use common assessments for formative student learning and intervention. Mathematics Instruction and Tasks in a PLC at Work Team action 3: Develop high-quality mathematics lessons for daily instruction.

Team action 4: Use effective lesson designs to provide formative feedback and student perseverance. Mathematics Homework and Grading in a PLC at Work Team action 5: Develop and use high-quality common independent practice assignments for formative student learning.

Team action 6: Develop and use high-quality common grading components and formative grading routines. Mathematics Coaching and Collaboration in a PLC at Work Coaching action 1: Develop PLC structures for effective teacher team engagement, transparency, and action. Coaching action 2: Use common assessments and lesson-design elements for teacher team reflection, data analysis, and subsequent action.

1. What do we want all students to know and be able to do?

P L A N B O O K | 3

Your Work and Your Story

Gaining clarity on your vision for mathematics teaching improvement will result in helping your students achieve greater agency and ownership over their learning as the school year progresses. One of the best benefits of working in a community with peers is the benefit of belonging to something larger than yourself. There is a benefit to learning about mathematics from each other, as professionals. It is often in a community that we all find a deeper meaning to our work and strength in the journey as we solve the complex mathematics learning issues we face each week of the school calendar, together. Thus the mathematics assessment and intervention, instruction and tasks, and homework and grading vision of the Every Student Can Learn Mathematics series features a wide range of research-affirmed voices, tools, and discussion protocols that offer advice, tips, and knowledge for your PLC at Work–based collaborative mathematics team. As a teacher and leader of mathematics, your daily work and actions tell a story. That story reveals itself through your collaborative actions with colleagues around three important aspects of your daily work.

The Story of Your Mathematics Assessment Design and Intervention Routines Your successful assessment story uses the essential standards for each mathematics unit to drive the assessment process in your school and uses those assessments for effective mathematics intervention. The research of James Popham (2011) and others highlights highly effective mathematics assessments designed to expect student participation in a reflect, refine, and act cycle of learning; and more important, to support students to take ownership of the learning process. 4 | M A T H E M A T I C S A T W O R K ™

Although this may sound complicated, it is primarily a matter of refining your current mathematics assessment story and effort into a more efficient routine that looks something like this: design high-quality mathematics assessments, score (grade) samples of student work on those assessments together, pass quizzes and tests back to your students for an analysis and response to errors (students reflect and refine), and require your students to take action on the standards they have not yet mastered (students embrace and then act on their errors).

The Story of Your Mathematics Instruction Design and Lesson Routines Through your experiences as a mathematics teacher, and your deep dive into the research on how students learn mathematics, you examine closely the educational research in the mathematics profession and find the right criteria for K–12 mathematics lesson design. The elements of effective instruction are certain. Yet, those criteria are not prescriptive. That is, the research provides the freedom to act and teach mathematics within the well-defined boundaries of those criteria. As a mathematics teacher, leader, or school principal, you lead the way in describing how a student formatively reflects, refines, and acts when using the lesson-design criteria. In doing so, you will discover that the most effective K–12 mathematics lessons present a story of student perseverance and engagement during the lesson. That story includes great lesson openings through prior knowledge and vocabulary work development. The story then moves to great lesson development using tasks that show a balance of lower- and higher-level cognitive demand and a balance of whole-group and small-group discourse as part of a sustainable formative-feedback process. The story ends with great lesson closures that students lead. Can the students provide evidence they have learned the standard for that day? Most likely, many of these lesson-design elements are already a part of your effort. It must become your intent to bring efficiency and clarity to your use of each of these lesson-design criteria.

The Story of Your Mathematics Homework Design and Grading Routines There are two additional mathematics issues your team must address: (1) homework and (2) grading. These two very difficult topics tell a story about your professional work as a mathematics teacher or leader. When it comes to designing mathematics homework, there are many noisy voices and experts claiming advice. You can help your team cut through the noise and find the best wisdom for these important K–12 mathematics issues. In doing so, your story shows that you understand mathematics homework and grading routines through the lens of Mathematics in a PLC at Work. The criteria for a highly effective homework, grading, and design story expect students to reflect, refine, and act as part of the learning process. Whether it’s basic number sense or calculus, you answer the questions, What is the best we know about the meaningful design elements of homework assignments, the scoring of those assignments, and the effective use of those assignments in class? and How does research inform the idea of homework? When you lead the process to achieve these answers, you will realize you cannot ignore the role grading can play in inspiring students to learn mathematics—or in destroying their desire to learn mathematics. To that end, we decided to provide the best wisdom we could to help you tell a story of efficient and effective grading routines in mathematics, designed to inspire student perseverance, effort, and engagement in learning all year long. Although you may view grading as a back-burner issue to student learning, you realize that grading eventually becomes part of your required work. This reaches beyond the role of teachers. As we examined poster papers from an initial brainstorming day, we also found that we had quite a few mile markers for mathematics coaches, team leaders, and administrators. This serves as a reminder that there are many leaders pulling the mathematics teacher collaboration story forward, and so we made the decision to also provide meaningful tools and support for mathematics coaches and leaders.

Your work as a teacher of mathematics tells a story over time. That story, steeped in the decisions you make year after year, eventually becomes your career. Along the way, you must decide which parts of your journey are the most important to pursue so that your daily effort and toil can make a difference in the mathematics learning of the students you teach.

R E P R O D U C I B L E

Common Unit Assessment Formative Process Evaluation Team Common Formative Assessment Process Criteria

Description of Level 1

Essential learning standards are unclear or differ among teachers on a team.

2. Common unit

Teachers on the team give their own mid-unit assessments and end-of-unit assessments.

assessments

3. Calibration of scoring agreements and student feedback

4. Student selfassessment and action after the end-of-unit assessment

5. Student selfassessment and action from common mid-unit assessments

6. Team response to student learning using Tier 2 intervention criteria

Teachers on the team score the assessments (common or not) individually, and each gives his or her own form of feedback to students. Teachers do not ensure each student reflects on learning after the end-ofunit assessment to identify what the student has learned or not learned yet and to make a plan for future learning. Teachers do not ensure each student reflects on learning after common mid-unit assessments during a unit to identify what the student has learned or not learned yet and to make a plan for future learning while still in the unit. Teachers on the team each determine how they provide students opportunities for intervention. Teachers on the team design interventions independently of one another.

Use this tool to evaluate the current reality of the mathematics assessment process quality for your grade level or course. Unlike in other evaluation tools written into the Every Student Can Learn Mathematics series, the six criteria present in this team discussion tool are somewhat linear. Meaning, your grade-level or course-based team should identify areas to improve in your team’s formative assessment process in the order the criteria are listed. In some sense, this tool reveals why it is so important for your students to take common unit mathematics assessments that your teacher team writes. It is in the action students take on your mathematics assessment feedback (scoring), the nature in which they embrace their errors, and then your subsequent coordinated team

Limited Requirements of This Indicator Are Present

Substantially Meets the Requirements of the Indicator

Fully Achieves the Requirements of the Indicator

effort to design equitable quality interventions that this tool will significantly impact every student’s mathematics learning. Formative feedback requires intentional team planning to determine the essential learning standards to be assessed and create common unit assessments that reveal student thinking and learning. From the data revealed through student work on the assessments, your team can plan for students to reflect and set goals for continued learning. You can also plan for how your students will re-engage in learning through the shared intervention opportunities your team provides. The intent of students analyzing their performance on the end-of-unit assessment is to help each student build responsibility for his or her own learning. Although

Description of Level 4

Essential learning standards are clear and commonly worded for students and shared with students at the start and throughout the unit.

Teachers design and administer common unit assessments, analyzing and responding together to the student results by student and essential learning standard.

Teachers regularly double-score assessments to verify accurate scoring of student work (calibration) and determine the best way to provide feedback to students.

Team creates a system for students to self-assess by essential learning standard what the student has learned or not learned yet and creates an action plan to re-engage students in learning standards within team-created structures.

Team creates a formative system for students to self-assess by essential learning standard from common mid-unit assessments to identify what the student has learned or not learned yet, and creates an action plan to re-engage students in learning within team-created structures during the unit.

Team develops a collective, just-in-time response to student learning by student and by essential learning standard, creating structures and plans for students to re-engage in and demonstrate learning as a result of teacher team actions.

each student takes ownership of his or her individual progress toward each of the essential learning standards, students may still work together to meet those standards. Students can work together when your team provides equitable feedback to students, regardless of which teacher students have. Student goal setting during and at the end of each unit helps them to see what they learned well and what they still need to learn. Such collaboration with peers and this ownership of learning engage students more deeply in the learning process and provide evidence for each student that effective effort built on the reflect, refine, and act cycle of learning leads to improved mathematical understanding and success.

1. Agreed-on essential learning standards for the unit

Requirements of the Indicator Are Not Present

R E P R O D U C I B L E

Common Assessment Self-Reflection Protocol Directions: Use the following prompts to guide a team discussion of your common assessment practices for each unit. Share your results with other teams as needed. Purpose of common assessments: 1. Why do we need common mathematics assessments for each unit?

Design of common mathematics assessments: 2. Do we write the essential learning standards on our tests? Who currently identifies and decides the essential learning standards for each unit?

3. Which assessments are common for our team (for example, quizzes, exit slips, mid-unit assessments, projects, and end-of-unit assessments)?

4. Who creates the assessments and the mathematics tasks (questions) for each assessment?

5. How do we organize the assessments (for example, by assessment type, or by essential learning standard)?

6. Do we expect students to show their work on the assessment? What work do we expect?

7. Are there common scoring agreements for each mathematics task (problem) on the assessment?

Use of common mathematics assessments: 8. Are students currently required to respond to errors made after taking common assessments?

9. What percentage of a student’s final grade is based on the result of a common assessment?

10. How does our team currently analyze data from common assessments to inform instructional decisions in the next unit?

Use the self-reflection team assessment protocol as a survey for each member of your team. Then, use your responses for a subsequent discussion with each member of your grade-level or course-based mathematics team. Share your personal unit-by-unit assessment practices and routines with one another. You can use each team member’s responses to find initial common ground for your collective mathematics assessment work. Discuss your responses and, as a collaborative team, reach consensus and determine how you will build your common assessments and how you will use those assessments to support formative student learning routines.

R E P R O D U C I B L E

Assessment Instrument Quality Evaluation Rubric High-Quality Assessment Criteria

1. Identification of and

2. Balance of higher- and lower-level-cognitivedemand mathematical tasks

3. Variety of assessment-task formats and use of technology

4. Appropriate and clear scoring rubric (points assigned or proficiency scale)

Essential learning standards are unclear, absent from the assessment instrument, or both. Some of the mathematical tasks (questions) may not align to the essential learning standards of the unit. The organization of assessment tasks is not clear. Emphasis is on procedural knowledge with minimal higher-level-cognitive-demand mathematical tasks for demonstration of understanding. Assessment contains only one type of questioning strategy—selected response or constructed response. There is little to no modeling of mathematics or use of tools. Use of technology (such as calculators) is not clear. Scoring rubric is not evident or is inappropriate for the assessment tasks.

Description of Level 4

Essential learning standards are clear, included on the assessment, and connected to the assessment tasks (questions).

Test is rigor balanced with higher-level- and lower-level-cognitive-demand mathematical tasks present and aligned to the essential learning standards.

Assessment includes a blend of assessment types and modeling tasks or use of tools. Use of technology (such as calculators) is clear.

Scoring rubric is clearly stated and appropriate for each mathematical task.

5. Clarity of directions

Directions are missing or unclear. Directions are confusing for students.

6. Academic language

Wording is vague or misleading. Academic language (vocabulary and notation) is not precise, causing a struggle for student understanding and access.

Academic language (vocabulary and notation) in tasks is direct, fair, accessible, and clearly understood by students. Teachers expect students to attend to precision in response.

Assessment instrument is sloppy, disorganized, and difficult to read, and it offers no room for student work.

Assessment is neat, organized, easy to read, and well-spaced, with room for student work. There is also room for teacher feedback.

Few students can complete the assessment in the time allowed.

Students can successfully complete the assessment in the time allowed.

7. Visual presentation

8. Time allotment

A great place to begin your initial work as a professional learning community team in mathematics is the collaborative design and writing of your common unit assessments. DuFour et al. (2016) describe the importance of using common assessment instruments this way: “One of the most powerful, high-leverage strategies for improving student learning available to schools is the creation of frequent, high-quality common assessments by teachers who are working collaboratively to help a group of students acquire agreed-on knowledge and skills” (p. 141). Creating common assessments to use during and at the end of each unit ensures equity in the rigor of the mathematics problems used for the assessments. It will

also help your team to backward-map your instruction during the unit as you prepare the students for the expected and required rigor. Ideally, your team should create these common unit assessments before the unit begins. You can use the eight criteria in this evaluation rubric to determine the quality of your current common unit assessments. A rating of 1 has a description attached and would be considered poor performance with these test criteria. A rating of 4 indicates your current common assessments act as an exemplar in these criteria we could all learn from. Regardless of your self-rating, make it a team goal to keep improving the quality of your unitby-unit mathematics assessments.

Directions are appropriate and clear.

You should also note that, if you do not collaborate to become a 4 in each category, the first four mathematics assessment design criteria listed here often create places of great inequity in your mathematics assessment process and professional work. Perhaps the most important are the identification of and emphasis on essential learning standards, the balance of higher- and lower-levelcognitive-demand tasks, the variety of assessment-task formats and use of technology, and the appropriate scoring rubric. Yet, these are also the most limiting aspects of many mathematics unit assessments—both during and at the end of a unit.

emphasis on essential learning standards (student-friendly language)

Description of Level 1

Requirements Limited Substantially Fully of the Requirements Meets the Achieves the Indicator Are of the Indicator Requirements Requirements Not Present Are Present of the Indicator of the Indicator

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Mathematics Intervention Program Evaluation Tool Mathematics Program Tier 2 Criteria

Teachers provide optional opportunities, often before or after school, for students to get individual or small-group help.

2. Targeted by essential learning standard

Teachers provide individual assistance as needed or gather a group of struggling students that a sole screener or diagnostic assessment identifies rather than a skill identified from common unit assessments.

3. Fluid and flexible

Teachers place students in an intervention where they remain due to results from a diagnostic assessment as a response to mandated services.

4. Just in time

Students get help before the end of a grading period or when they request help.

5. Proven to show evidence of student learning

Teachers provide intervention to students and hope students learn. Students may be receiving intervention support from a person not highly qualified in mathematics. There is little evidence that the intervention is helping students learn the essential standards for the grade level or course.

The third critical question of a PLC at Work expects your team and school to develop a robust response to the question: What will be our response when students do not learn the expected standards for each grade level or course? You can use this evaluation tool to rate and evaluate the quality of your response to intervention and learning using evidence based on a recent common unit assessment.

Limited Requirements of This Indicator Are Present

Substantially Meets the Requirements of the Indicator

Fully Achieves the Requirements of the Indicator

How do your current mathematics intervention programs score? You should expect to develop an intervention program that scores 4s in all five of the intervention criteria. Which of the five criteria for a high-quality mathematics intervention program are currently part of your collaborative team practice? What do you need to do to strengthen your mathematics intervention program?

Description of Level 4

Team requires students to learn if they are not yet proficient with essential learning standards and provides systematic structures during the school day to ensure student learning. Team commonly plans for continued learning in the next mathematics unit, as needed.

Team designs and administers common unit mathematics assessments to analyze and collectively respond to the data to identify specific students needing targeted intervention by each essential learning standard.

Team regularly analyzes student data from common unit mathematics assessments and allows students to move in and out of the required additional time and support in learning.

Students get real-time feedback, and the team plans its interventions for the essential learning standards within a mathematics unit or at the start of the next unit using current common assessment results.

Team monitors student progress within the intervention or within class to see if the intervention is effective and results in student demonstrations of proficiency learning for each essential standard. Team members continue monitoring instructional strategies that impact learning and re-engagement. Each adult implementing the team-designed mathematics intervention is the bestqualified person for the role.

Each of the five criteria is necessary for continued student learning when a student has not yet learned an essential learning standard, as evidenced by the end-ofunit common mathematics assessment. The challenge is to create an effective system that allows students to engage in the intervention, while simultaneously practicing the essential learning standards for the next unit.

1. Systematic and required

Description of Level 1

Requirements of the Indicator Are Not Present

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Intervention Practices

The intent of your mathematics interventions should be to provide students with the additional time and support necessary to learn your grade-level or course-based essential learning standards.

Directions: Use the following prompts to guide team discussion of your current team intervention practices. Purpose of a team intervention: 1. Why do you need a team response when designing interventions for essential learning standards?

Plan for team intervention: 2. How do you identify students in need of intervention?

3. How do you determine the targeted content and skills to address through Tier 2 interventions?

4. Who provides the Tier 2 interventions for students in your class or across your team? When? How do you and your colleagues share the responsibility of interventions for students across your grade level or course?

5. How are your interventions a just-in-time required opportunity for growth in learning?

6. How do students move in and out of interventions? How often?

Effectiveness of interventions: 7. How do you know if your interventions are effective?

8. How do students know their time spent learning in an intervention is effective?

The questions on this page aim to help you and your team understand one another’s perspectives related to your systematic Tier 2 interventions as a team. In other words, how does your team respond when common assessment data, during or at the end of a unit, reveal some students have learned the essential learning standards and others have not? Your professional response as individual teachers and as a teacher team reveals your current beliefs about the need for interventions and the plan for making those interventions effective.

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Instructional Framework and Lesson-Design Evaluation Tool Substantially Fully Limited Requirements Requirements Meets the Achieves the of the of This Requirements Requirements Indicator Are Indicator Are of the of the Not Present Present Indicator Indicator

Description of Level 1

1. Essential Learning Standards: The Why of the Lesson

The lesson references an essential learning standard but doesn’t have a clear learning target, and there is no evidence of consistent standard or target language across the collaborative team.

2. Prior-Knowledge Warm-Up Activities

Either there is no warm-up activity to the lesson content or the warm-up activity exists, but does not clearly support students’ accessing prior knowledge needed for the lesson.

3. Academic The lesson does not address academic language Language explicitly with a formal plan for ensuring Vocabulary as student clarity. Part of Instruction 4. Lower- and Higher-LevelCognitiveDemand Mathematical Task Balance

There is no evidence of a balance of lower- and higher-level-cognitive-demand tasks. There are no specific strategies for engaging students in the sense-making or application of the content.

5. W hole-Group and Small-Group Discourse Balance

There are no specific strategies for how students will discuss and share their thinking with their peers. The lesson plan relies solely on whole-group discourse from the front of the classroom with only the teacher evaluating the responses to each student question.

6. Lesson Closure for Evidence of Learning

The lesson plan includes either no summary or a teacher-led summary of the lesson (as opposed to a student-led summary). There is no opportunity for students to evaluate if they meet and understand the learning target for the day.

The true purpose of any mathematics lesson is to maximize student engagement, communication, and perseverance during the lesson based on the tasks you have chosen. The tasks you choose must help students learn the essential learning standards for the current mathematics unit of study. Your daily lessons should provide an opportunity for your students to reflect, refine, and act during the lesson. You should expect your students to use the mathematical tasks you have chosen and the formative feedback you provide during the lesson to refine their errors in the process of learning the mathematics learning target or standard each day.

Description of Level 4

The lesson design declares a daily learning target aligned to an essential learning standard for the unit. Teachers share a context for that learning target with students during the lesson.

There is a prior-knowledge warm-up task that includes an opportunity for students to work together and engage in thinking about the mathematics necessary to persevere during the lesson.

You and your team can use this lesson-design evaluation tool to evaluate the quality of your current mathematics lessons. It will help you identify areas of strength and areas for lesson-design growth as you assess the strengths and weaknesses of your current instructional planning for mathematics. These six research-affirmed lessondesign elements also provide an instructional framework for highly effective mathematics lessons every day. Some of these elements may already be present in your daily planning; you just need to work with your other team members to brainstorm and share creative ideas about how to most effectively implement the criteria.

There is evidence of focused vocabulary instruction to support the learning of the mathematics content across grade-level or course-based teams. There is a balance of higher-level- and lower-levelcognitive-demand mathematical tasks within the lesson plan with specific focus on formative routines, and feedback from peers and the teacher during the lesson.

There are intentional plans for the type of discourse (whole group or small group) that students will experience for each mathematical task and portion of the lesson. There is a commitment to balancing student time to process and communicate with one another (what you see and hear the students doing) against the time given to teacher-directed instruction. The lesson includes a student-led closure activity to determine if the lesson helped students understand the learning target or essential learning standard for the day.

Other criteria may not yet be present in your lessons and only score a 1 or 2 using the evaluation tool. You can decide how to adjust your daily lesson design to better impact student perseverance and learning in your mathematics classroom by improving on these nonnegotiable aspects of the mathematics lesson. Your daily lesson-design preparation throughout the school year has a certain rhythm to it, and these six lesson-design criteria can serve that.

High-Quality Lesson-Design Indicators

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Protocol for Team Analysis of the Mathematics in a PLC at Work Lesson-Design Tool Directions: Closely examine the components in the Mathematics in a PLC at Work lesson-design tool (page 12). With your colleagues, discuss how you could use parts or all of the tool to help your current efforts to plan mathematics lessons for your grade level or course. Strengths Identify what you currently do that is a strength for each component.

Challenges Identify any components that you currently do not address or do not address well in your lesson-planning process, and list how you might improve these components.

1. Essential learning standards: the why of the lesson

2. Prior-knowledge warm-up activities

3. Academic language vocabulary as part of instruction

4. Lower- and higherlevel-cognitivedemand mathematical task balance

5. Whole-group and small-group discourse balance

6. Lesson closure for evidence of learning

Lesson-Design Element

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Mathematics in a PLC at Work Lesson-Design Tool Preparing for the Lesson Unit: Date: Lesson description:

Learning target: State the specific learning outcome(s) for this lesson. Use, “Students will be able to . . .”

Academic language vocabulary: State the academic vocabulary expectations for the lesson. Describe how you will explicitly address any new vocabulary.

Beginning-of-Class Routines Prior knowledge: Describe the warm-up activity you will use. How does the warm-up activity connect to students’ prior knowledge, connect to an analysis of homework progress, or connect to future learning?

During-Class Routines Task 1: Cognitive Demand (Circle one): High or Low What are the learning activities to engage students in learning the target? Be sure to list materials as necessary.

What will the teacher be doing? • How will you present and then monitor student response to the task? • How will you expect students to demonstrate proficiency of the learning target during in-class checks for understanding? • How will you scaffold instruction for students who are stuck during the lesson or the lesson tasks (assessing questions)? • How will you further learning for students who are ready to advance beyond the standard during class (advancing questions)?

What will the students be doing? • How will you actively engage students in each part of the lesson? • What type of student discourse does this task require—whole group or small group? • What mathematical thinking (reasoning, problem solving, or justification) are students developing during this task?

Task 2: Cognitive Demand (Circle one): High or Low What are the learning activities to engage students in learning the target? Be sure to list materials as necessary.

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Essential learning standard: State the essential content and process standard for the unit you address during this lesson. • Content—Write as an I can statement. • Process—Write as an I can statement.

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End-of-Class Routines Common homework: Describe the independent practice teachers will assign when the lesson is complete.

Lesson closure for evidence of learning: How will lesson closure include a student-led summary? By the end of the lesson, how will you measure student proficiency and that students develop a deepened (and conceptual) understanding of the learning target or targets for the lesson?

Teacher end-of-lesson reflection: (To be completed by the teacher after the lesson is over) Which aspects of the lesson (tasks or teacher or student actions) led to student understanding of the learning target? What were common misconceptions or challenges with understanding, if any? How should you address these in the next lessons?

There is a difference between mathematics lesson planning and mathematics lesson design. Lesson planning tends to be more formal and focus on a rote script that the teacher follows for the lesson. Lesson design tends to allow for quite a bit of teacher freedom within welldefined, research-affirmed parameters. Much like the PLC at Work culture, lesson design tends to be simultaneously loose and tight; that is, the design elements must be present, but the method for implementing those elements has a broad and deep application. This lesson-design tool helps ensure your teacher team reaches mathematics lesson clarity on all six of the

lesson-design elements known to significantly impact student learning. Thus, your collaborative grade-level or course-based team is uniquely structured to provide the time and support it needs to interpret the mathematics standards for the unit, embed balanced student-engaged discourse practices into daily lessons, and reflect together on the effectiveness of your implementation, sharing evidence of student learning each day.

learning standard every day. Take special notice of the expectation that, for every mathematical task or problem you use to teach the lesson, you should design what you expect the students to be doing as well as your own movements and actions. Framing the mathematics lesson from the students’ point of view is a powerful perspective for understanding how the students make meaning during the lesson.

You can use this tool during your planning for the instruction of the mathematics lesson as a way to support the focus and design of the balanced-cognitivedemand mathematics tasks you choose to teach each page 2 of 2

Task 3: Cognitive Demand (Circle one): High or Low What are the learning activities to engage students in learning the target? Be sure to list materials as necessary.

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Evaluating the Quality of Independent Practice Assignments High-Quality Independent Practice Indicators

Requirements Limited Substantially Fully of the Requirements Achieves the Meets the Indicator Are of the Indicator Requirements Requirements Not Present Are Present of the Indicator of the Indicator

Description of Level 1

Homework is primarily assigned to give a student a grade.

2. Assignments are the same

Each teacher on the team creates his or her own assignments and does not share with others.

for every teacher on the grade-level or course team.

3. Daily assignments for independent practice are aligned with the essential learning standards of the unit.

4. Independent practice assignments for the unit are appropriately balanced for cognitive demand.

5. Independent practice assignment sets for each unit exhibit spaced and massed practice.

6. All assignments engage students in practice for an appropriate amount of time.

7. Each team member scores assignments consistently using agreed-on scoring instruments.

Students are not able to make connections between the daily independent practice problems and the learning standards of the unit. Independent practice problems are not balanced for rigor. Emphasis is on lowerlevel-cognitive-demand tasks. The assignments represent superficial thought as to the problems chosen and consist mostly of massed practice.

The duration of a given assignment is random with no regard to students’ grade level or working speed. Each teacher scores assignments using his or her own scoring instrument.

Highly effective teams of mathematics teachers also choose to develop and design common homework assignments. Improving the quality of your independent practice assignments for students is a priority of your work together. To accomplish this, use this tool to evaluate both the product of your current mathematics independent practice assignments (homework) and the process of how to use them wisely. This tool provides seven criteria you can use to reflect on your current homework routines and evaluate those routines on the 1–4 scale. When reflecting on the scores you assigned for each of the seven independent practice assignment criteria, consider which of the seven indicators were surprising to

The team understands homework is primarily for independent practice and serves as a formativeassessment learning loop for students.

The team develops the same assignments collaboratively for all students in the grade level or course.

you. As you advance your team’s approach to the design of independent practice assignments and routines, consider the following. • Rebrand homework as independent practice, so students and families understand the value of at-home assignments as an integral part of the formative learning process.

Students know independent practice is essential to helping them demonstrate knowledge of the essential learning standards of the unit. Independent practice is appropriately balanced with higher- and lower-level-cognitive-demand tasks (a ratio of 3:1).

The assignments represent carefully team-chosen problems or tasks, and there are no more than eight to ten problems per assignment. Spaced practice from several lessons of the unit or previous units is included in addition to massed practice.

The team strategically determines the appropriate duration of a given assignment with specific attention given to students’ needs, grade level, and working speed.

The team designs a common scoring instrument and develops agreements about its application. Students use the scoring instrument as a self-evaluation tool.

• Use your common independent practice assignments to provide teacher-team shared intervention and support for every student in the grade level or course. • If you are a singleton teacher, reach out through social media or video chat to engage peers in the homework discussion.

• Understand that the variance created when your grade-level or course-based teams fail to develop common homework assignments contributes to gaps in achievement and opportunity. • Reach a team agreement to design high-quality common independent practice for each unit during the year.

1. The primary purpose of homework is independent practice.

Description of Level 4

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Student Independent Practice Effectiveness Survey

Consider providing students with two to three questions and gathering their responses (orally or in writing) as evidence of effective independent-practice routines. Students can provide keen insight into the independent-practice world. You can use this survey as a sample tool for students or adapt it to fit your needs and grade level. Your students can provide powerful insights into your current use of independent practice. Before asking students to respond, take time to explain this is a risk-free space, so they can share their thoughts honestly. As you work collaboratively with your colleagues to ensure daily mathematics assignments are limited to no more than eight to ten tasks, you should interview your students, individually or in small groups, to learn how much time assignments are taking them to complete. Gauge their opinions about being given all answers (so they can formatively check their work and try again) and their response to self-assigning competence and confidence scores to their independent practice.

Directions: Think about your independent practice assignments. The purpose of this survey is to help our teacher team design mathematics assignments that help improve your learning. 1. What type of mathematics independent practice helps you understand the unit lessons?

2. Do you like to receive the answers to the assigned problems? Why or why not?

3. Do you retry a problem right away if you make an error or mistake? Why or why not?

4. Who do you talk to if you need help with your mathematics independent practice?

5. What type of mathematics independent practice assignments do you not like? Which do not seem to help you improve your learning?

6. If you could provide one recommendation to your mathematics teacher to design better independent practice, what would that be?

An alternative data source you might consider to fuel a rich discussion about effective independent practice is the voice of your students. To gather feedback on the effectiveness of the assigned independent practice for students, you can simply ask them! What are students saying about the effectiveness of independent practice on their learning?

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Scoring Rubric and Student Confidence Scale for an Independent Practice Assignment Scoring Rubric Level 1 I do not understand the assignment.

I am able to start the problems using my class notes, but I can’t explain why I am finding correct solutions or incorrect solutions.

Level 3 I understand the assignment. I am getting mostly correct solutions. I recognize how to do each and every problem, but I am making errors resulting in a few incorrect solutions.

Level 4 I completely understand the assignment. I am getting all correct solutions. I immediately understand how to do every problem. I answer problems with complete accuracy and see connections among problems.

Confidence Scale Level 1 No Confidence I do not feel confident in my responses to the assignment. I need to be retaught the concepts in a different way. I don’t even know where to begin.

Level 2 Low Level of Confidence I am beginning to understand the concepts but can’t seem to figure out key steps in the problem. Sometimes I get the right answer but cannot explain why.

The best method of grading a mathematics homework assignment is to ask your students to self-assign a grade. After your students have completed an independent practice assignment, teach them how to reflect on their own understanding. Engaging in honest selfreflection is an important life skill for developing student self-efficacy. Also, guide students to assign two self-ref lection scores to assess the learning experience of doing their homework—assign one score for proficiency and one score for confidence. To self-assign a proficiency score,

Level 3 Confident

Level 4 High Level of Confidence

I believe that I completed the assignment accurately, but I do not understand how this concept relates to other mathematical concepts we have been taught. I can only complete the assignment using one strategy.

use the scoring rubric as a starting point, and modify the language to match your grade-level or course-based expectations. Similarly, adapt the confidence scale for your grade level or course to allow students to self-assign a confidence score using a different four-point scale. Developing student self-efficacy and agency in learning begins with self-awareness. Asking students to rate their own performance and confidence is a tangible strategy leading to self-efficacy. But your students should not stop at the self-awareness stage. The next step is for them to seek feedback from peers or family members.

I know that I completed the assignment accurately. I understand how this concept relates to other mathematical concepts. I would feel confident teaching my peers this content.

Students should also reach out to a peer or study group outside of class to engage in a five- to ten-minute discussion for each independent practice assignment. During the discussion, students can review each other’s work as well as share feedback and strategies that might lead to deeper understanding. Elementary students can do this with their families or an older sibling. Students can conduct peer- or family-feedback sessions through traditional face-to-face study groups. They can also use gateway technology, such as Skype, FaceTime, Google Hangouts, or three-way calling, to name a few.

I am not sure where to begin. I am trying but not getting any correct solutions.

Level 2 I understand part of the assignment. I am getting a few correct solutions.

The High-Performing Mathematics Team

As a teacher of mathematics in your school or district, you support the team process by creating a safe space for your team members to take risks, engage in productive perseverance, make mistakes, and learn from your mistakes. You do this through five specific highperforming team practices. 1. Create a trusting environment: Each mathematics team member feels valued and that his or her opinions are important. Team members are accountable to each other and address conflict as needed.

2. Develop your relational intelligence: Mutual respect is evident during collaborative team time. The strong passion for meaningful mathematics is observable in action steps as the team responds to the four critical questions of a PLC at Work.

other and the work you will do together that is necessary to ensure success for all learners. You and your team members identify the core values for your team’s mathematics work and take action on the expected work.

3. Communicate effectively with your colleagues: Team members listen to each other and ask clarifying questions to understand their colleagues’ thinking. Team members understand decisions as agreements that each individual on the team agrees to honor.

These five high-performing practices of your team will facilitate your successful completion of the most important work products your team creates. We illustrate these products on this page and provide guidelines for how your team works together on understanding the loose and tight nature of its work as a team.

4. Demonstrate passion and persistence: Team members are diligent in their work and exhibit a positive attitude toward meeting team SMART goals and the vision for achieving those goals. Team members learn from mistakes, and they embrace any failures as a way to improve the work of the team.

As part of this process, your high-performing gradelevel or course-based mathematics teams will choose to respond to the four critical PLC at Work questions (see page 2; DuFour et al., 2016).

5. Commit to the PLC at Work process: As team members, you are committed to each

To create equity and access to meaningful mathematics for every student, high-performing team members collectively share the responsibilities of the team and improve the student learning of mathematics in their school.

What Is Tight?

What Is Loose?

Common unit assessments

• Give students agreed-on common mid-unit and unit assessments. • Administer each common assessment in an agreed-on way in each class. • Discuss student results on common assessments and look at actual student work as examples.

Create and administer any common mid-unit assessments in addition to the common unit assessments.

Instructional strategies

Create lessons and instructional resources that support the team’s instructional focus for student perseverance.

Choose instructional strategies to support individual student needs.

Mathematical tasks chosen

Collectively choose performance tasks to use in each unit and reach agreement on the balance of the cognitive demand of those daily tasks.

Choose additional tasks as needed to meet individual students’ needs.

Lesson-design criteria

Address the six common lesson components for instruction in the Mathematics in a PLC at Work lesson-design tool (available at go.SolutionTree.com/MathematicsatWork).

Design how each lesson is taught using those components.

Common homework

Collectively choose the best independent practice that is massed and spaced.

Make adjustments to assignments to meet individual student needs and special circumstances.

Common grading

• Grade common mid-unit and unit assessments in an agreed-on way. • Discuss student results by standard on the common unit assessments and look at actual student work as examples.

Nothing about the scoring of the common assessments should be loose.

Interventions during core instruction

Using student work from common assessments and daily tasks, together analyze current Tier 1 strategies to improve upon in your lesson designs.

• Implement classroom interventions. • Implement classroom extensions.

Interventions to support core instruction

Using student work from common assessments and tasks, establish a Tier 2 collective and targeted response to student learning by essential mathematics standards for each unit.

Although the teacher team works together to ensure every student receives the same required intervention and support, it is possible that individual students receive additional support as needed.

The primary purpose of your collaborative team in mathematics is to work together to overcome the complex issues you face each and every day. High-performing grade-level or course-based mathematics teams engage in constant inquiry and action research. Your team understands that the PLC at Work is “an ongoing process in which educators work collaboratively in recurring cycles of collective inquiry and action research to achieve better results for the students they serve” (DuFour et al., 2016, p. 10).

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Cultural Shifts in a PLC A Shift in Fundamental Purpose to a focus on learning

From emphasis on what was taught . . .

to a fixation on what students learned

From coverage of content . . .

to demonstration of proficiency

From providing individual teachers with curriculum documents such as state standards and curriculum guides . . .

to engaging collaborative teams in building shared knowledge regarding essential curriculum

A Shift in Use of Assessments From infrequent summative assessments . . .

to frequent common formative assessments

From assessments to determine which students failed to learn by the deadline . . .

to assessments to identify students who need additional time and support

From assessments used to reward and punish students . . .

to assessments used to inform and motivate students

From assessing many things infrequently . . .

to assessing a few things frequently

From individual teacher assessments . . .

to collaborative team–developed assessments

From each teacher determining the criteria to use in assessing student work . . .

to collaborative teams clarifying the criteria and ensuring consistency among team members when assessing student work

From an over-reliance on one kind of assessment . . .

to balanced assessments

From focusing on average scores . . .

to monitoring each student’s proficiency in every essential skill A Shift in the Response When Students Don’t Learn

From individual teachers determining the appropriate response . . .

to a systematic response that ensures support for every student

From fixed time and support for learning . . .

to time and support for learning as variables

From remediation . . .

to intervention

From invitational support outside of the school day . . .

to directed (that is, required) support occurring during the school day

From one opportunity to demonstrate learning . . .

to multiple opportunities to demonstrate learning A Shift in the Work of Teachers

From isolation . . .

to collaboration

From each teacher clarifying what students must learn . . .

to collaborative teams building shared knowledge and understanding about essential learning

From each teacher assigning priority to different learning standards . . .

to collaborative teams establishing the priority of respective learning standards

From each teacher determining the pacing of the curriculum . . .

to collaborative teams of teachers agreeing on common pacing

From individual teachers attempting to discover ways to improve results . . .

to collaborative teams of teachers helping each other improve

From privatization of practice . . .

to open sharing of practice

From decisions made on the basis of individual preferences . . .

to decisions made collectively by building shared knowledge of best practice

From “collaboration lite” on matters unrelated to student achievement . . .

to collaboration explicitly focused on issues and questions that most impact student achievement

From an assumption that these are “my students, those are your students” . . .

to an assumption that these are “our students”

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From a focus on teaching . . .

A Shift in Focus to an internal focus on steps the staff can take to improve the school

From a focus on inputs . . .

to a focus on results

From goals related to completion of projects and activities . . .

to SMART goals demanding evidence of student learning

From teachers gathering data from their individually constructed tests in order to assign grades . . .

to collaborative teams acquiring information from common assessments in order to inform their individual and collective practice and respond to students who need additional time and support

A Shift in School Culture From independence . . .

to interdependence

From a language of complaint . . .

to a language of commitment

From long-term strategic planning . . .

to planning for short-term wins

From infrequent generic recognition . . .

to frequent specific recognition and a culture of celebration that creates many winners A Shift in Professional Development

From external training (workshops and courses) . . .

to job-embedded learning

From the expectation that learning occurs infrequently (on the few days devoted to professional development) . . .

to an expectation that learning is ongoing and occurs as part of routine work practice

From presentations to entire faculties . . .

to team-based action research

From learning by listening . . .

to learning by doing

From learning individually through courses and workshops . . .

to learning collectively by working together

From assessing impact on the basis of teacher satisfaction (“Did you like it?”) . . .

to assessing impact on the basis of evidence of improved student learning

From short-term exposure to multiple concepts and practices . . .

to sustained commitment to limited focused initiatives

From an external focus on issues outside of the school . . .

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Critical Issues for Team Consideration Team Name: Team Members: Use the following rating scale to indicate the extent to which each statement is true of your team. 1

Not True of Our Team Our Team Is Addressing This True of Our Team 1. We have identified team norms and protocols to guide us in working together. 2.

We have analyzed student achievement data and established SMART goals to improve on this level of achievement we are working interdependently to attain. (SMART goals are specific and strategic, measurable, attainable, results oriented, and time bound.)

Each team member is clear on the knowledge, skills, and dispositions (that is, the essential learning) that students will acquire as a result of our course or grade level and each unit within the course or grade level.

We have aligned the essential learning with state and district standards and the high-stakes assessments required of our students.

We have identified course content and topics we can eliminate to devote more time to the essential curriculum.

We have identified strategies and created instruments to assess whether students have the prerequisite knowledge and skills. We have developed strategies and systems to assist students in acquiring prerequisite knowledge and skills when they are lacking in those areas.

We have developed frequent common formative assessments that help us determine each student’s mastery of essential learning.

11. We have established the proficiency standard we want each student to achieve on each skill and concept examined with our common assessments. 12.

We use the results of our common assessments to assist each other in building on strengths and addressing weaknesses as part of an ongoing process of continuous improvement designed to help students achieve at higher levels.

13.

We use the results of our common assessments to identify students who need additional time and support to master essential learning, and we work within the systems and processes of the school to ensure they receive that support.

14.

We have agreed on the criteria we will use in judging the quality of student work related to the essential learning of our course, and we continually practice applying those criteria to ensure we are consistent.

15.

We have taught students the criteria we will use in judging the quality of their work and provided them with examples.

16.

We have developed or utilized common summative assessments that help us assess the strengths and weaknesses of our program.

We have agreed on how to best sequence the content of the course and have established pacing guides to help students achieve the intended essential learning.

7. We have identified the prerequisite knowledge and skills students need in order to master the essential learning of each unit of instruction. 8.

10.

17. We have established the proficiency standard we want each student to achieve on each skill and concept examined with our summative assessments. 18.

We formally evaluate our adherence to team norms and the effectiveness of our team at least twice each year.

The powerful collaboration that characterizes PLCs at Work is a systematic process in which teachers work together to analyze and improve their classroom practice. Teachers work in teams, engaging in an ongoing cycle of questions that promotes deep team learning. This process, in turn, leads to higher levels of student achievement. The “Critical Issues for Team Consideration” guide the collective inquiry and action research of each collaborative team in a PLC at Work. You and your teammates will be challenged to build shared knowledge—to learn together—about each issue and ultimately generate a product as a result of your collective inquiry and action research.

R E P R O D U C I B L E

Team Feedback Sheet Team Name: Meeting Date: Team Goals: Team Members Present:

Team Members Absent (List Reason):

Topics or Meeting Outcomes:

Questions or Concerns:

Administrator: Date:

Frequent, timely communication between the teams and administration is essential to the success of PLCs at Work. How will your team communicate on a regular basis with your supervisors and administrators? The “Team Feedback Sheet” is one way to facilitate two-way communication. During every team meeting, a team member takes responsibility for completing the form, either electronically or on hard copy. The feedback sheet and any products your team completes at each meeting are submitted to the department chair or building administrator overseeing the team’s work. The administrators monitor teams’ work, respond immediately to any questions or concerns, provide feedback on the products, and engage in ongoing two-way communication. Administrators can also attend team meetings, either at the team’s invitation or in response to evidence that a team is experiencing difficulty.

R E P R O D U C I B L E

SMART Goal Template School year:

SMART goal: Department:

Team:

Team leader: Identify a student achievement SMART goal (strategic and specific, measurable, attainable, results oriented, and time bound):

Action Steps and Products What steps or activities will you initiate to achieve your goals? What products will you create?

Team Members Who is responsible for initiating or sustaining the action step or product?

Time Frame What is a realistic time frame for each step or product?

Results and Evaluation How will you assess your progress? What evidence will you use to show you are making progress?

Team members:

R E P R O D U C I B L E

Collaborative Lesson-Design Elements Directions: Use the following prompts to guide discussion about your current lesson design. Purpose of the lesson: 1. What is the fundamental purpose of a mathematics lesson?

2. How do you inform your students of the relevance—the why—for the day? Do you inform them in writing or verbally?

Essential elements of a mathematics lesson: Respond to each question with a yes or no, and then briefly explain how you make the lesson-design choice or why you do not make the lesson-design choice. 3. Do you choose a warm-up or prior-knowledge mathematics question or task to begin each lesson?

4. Do you choose to discuss and connect key vocabulary words for the lesson?

5. Do you choose lower-level- and higher-level-cognitive-demand mathematical tasks that align to the essential standard for each lesson? If so, is it a collaborative teacher team activity?

6. Do you intentionally choose whole-group and small-group discourse activities as part of the lesson experience?

7. Do you close each lesson with a student-led summary?

The team should design mathematics lessons to ensure both relevant and meaningful student learning experiences. Think about the essential standards you are currently trying to help students learn. You can use the seven questions in this tool to focus your team’s lesson-design discussions about the real purpose of any mathematics lesson—facilitating your students’ learning and ownership of the essential standard or learning target for that day. The choices you make regarding the mathematics problems and tasks, and the nature of the mathematical discourse during the lesson, are the means for how you help your students to “do mathematics” and learn the essential standards for the unit.

R E P R O D U C I B L E

Purpose and Nature of Grading Practices

Yet, your grading routines should be an ever-evolving process, and you should judge them against whether your assigned grades reflect the only plausible purpose in a PLC culture: grades provide students with feedback on their progress toward mastering the essential learning standards of the grade level or course. There is no other purpose—not to teach responsibility, not to compare students against one another, and not to reveal performance on assignments designed for mathematics practice. Thus, as part of your PLC culture-building work, you define the purpose of grading as an essential component of the formative assessment and learning process for students. It is a process that provides students with feedback on their progress toward proficiency with or mastery of the intended essential learning standards.

Directions: Use the following prompts to guide discussion of your grading practices. Purpose of grading: 1. How would you describe the purpose of assigning grades to your students?

2. To what degree does a student’s grade reflect his or her understanding of essential learning standards?

3. Why is it important that your team develop common expectations for grading?

4. What does a student have to do or demonstrate to earn a C in your grade or course?

Design of grading systems: 5. What are the major components of your grading system?

6. How do mathematics assignments versus tests factor into a student’s overall grade?

7. How do you compile evidence of student learning to calculate a final grade at the end of the marking period or semester?

Working with your team members, you can use this tool to guide a discussion about developing a deeper understanding of your grading practices. During the discussion, dig deep into routines that have been hard to change. Your grading routines will often remain unchanged and unchallenged for the better part of your career (Guskey, 2015). Ask team members to explain their practice using the lens of this overarching question: How do our team’s grading practices contribute to improved student learning? Your response to “What is the purpose of grading?” is an essential first step in the process of understanding grading reform.

R E P R O D U C I B L E

Lesson-Study Time Expectations and Team Reflection

Each team member can complete the lesson-study reflection activity at the end of the debrief session, after the lesson-study observation activity. Once completed, share your learning about the lesson and brainstorm ideas about next steps for teaching the lesson again. As you work with your team members toward making instruction more transparent, instructional rounds and lesson studies become two formal (yet valuable) protocols for fine-tuning various aspects of your instruction.

Time Expectations Lesson-Study Element

Amount of Time Needed

Expectation

Defining the problem

One hour

Determine what we want to learn by engaging in the collaborative process.

Planning the lesson

Two to four weeks

Plan the lesson prior to the scheduled lesson-study day; include the resources we will need for the lesson.

Previewing the lesson

One hour

Preview the lesson so every observer understands what to expect in the lesson; review norms.

Teaching the lesson

One class period

Decide which teacher will teach the lesson the first time for evaluation of effectiveness. That person then teaches the lesson.

Analyzing the evidence: 1. Evaluating the lesson 2. Revising the lesson

Two to three hours

Debrief the first lesson and make revisions to the lesson plan. Evaluate the evidence we observe and collect during the lesson. Understand what we might change in the lesson to improve student understanding.

Teaching the revised lesson

One class period

Determine who will teach the lesson the second time. That person then teaches the revised lesson.

Evaluating and reflecting again

One hour

Debrief the lesson study and plan action steps.

Team Reflection Each team member should respond to the following questions individually at the end of the debrief session. Once completed, each team member can share his or her responses about next steps for the team. 1. What: What did you learn from the mathematics lesson study?

2. So what: How did the mathematics lesson study challenge your assumptions or expectations?

3. Now what: Where do we go from here? What’s the next step of our daily mathematics lesson designs?

Lesson study is the ultimate reflect, refine, and act teacherlearning process. However, you must still consider the time demands of lesson study. The first time a team comes together to co-plan a lesson, it will likely take more time to get every team member’s perspective into one lesson. Encourage the team to work on the lesson for two to four weeks prior to the scheduled day of observing the lesson in action. Subsequent lesson studies generally do not require as much planning time. The timeexpectations tool provides an example of the approximate time commitment your team will need for each element of a lesson study.

Team Information Team Contacts Phone

Day

Time

Location

Team Meeting Times

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Name

Substitute Teacher Information Classroom Procedures

Teacher: Room:

When students finish early:

Administrator:

Room:

Student assistants:

When students are disruptive:

Supplies and Information

School map or floor plan:

When students are well-behaved:

School crisis response plan:

First-aid kit:

Instructional Assistants and Student Teachers

Lesson plans and materials:

Art supplies:

Students With Special Needs Name

Support Teacher

Special Needs or Service

Time or Location

Helpful Contacts

P L A N B O O K | 2 7

February

March

April

May

June

October November December January

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September

Holidays and Birthdays

“This comprehensive and practical resource further enhances practitioners’ understanding of what it takes to ensure that all students learn mathematics. Tim Kanold and Sarah Schuhl provide the tools for teams to build their collaborative culture, focus on students’ learning and achieve results. The Mathematics at Work Plan Book is a must-have resource that serves teacher teams to understand what it takes to do the right work.”

PL A N B O O K

—Kit Norris, Educational Consultant and Coauthor, Engage in the Mathematical Practices: Strategies to Build Numeracy and Literacy With K–5 Learners

"Wow! This is the plan book mathematics teachers and leaders have been seeking! While many schools subscribe philosophically to professional learning communities, Kanold and Schuhl provide teachers, teams, and leaders with the tools and protocols necessary to ensure that collaborative work is intentional, leads to equitable mathematics teaching, and achieves success for every student." —Matt Larson, Past President of National Council of Teachers of Mathematics; Associate Superintendent for Instruction, Lincoln Public Schools, Nebraska

Access a wealth of well-researched ideas, activities, and unit and weekly planning pages for implementing team-based mathematics practices in a professional learning community (PLC). Mathematics teams will:

•

Review the foundational ideas and core concepts of Mathematics at Work—a comprehensive PLC at Work® approach to achieving student success in mathematics

•

Acquire a variety of reproducible tools designed to support the work of PLCs and collaborative teams in teaching mathematics

•

Recognize the positive cultural shifts that occur in schools and districts that follow the PLC at Work process

•

Access unit and weekly planners to assist in organizing and implementing the Mathematics at Work process

•

Read stories from teachers, principals, and district leaders who have seen dramatic, inspiring change in their schools through Mathematics at Work

Visit go.SolutionTree.com/MathematicsatWork to download the free reproducibles in this book.

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