Copyright©2010byCorwin All rights reserved. When forms and sample documents are included, their use is authorized only by educators, local school sites, and/or noncommercial or nonprofit entitiesthathavepurchasedthebook.Exceptforthatusage,nopartofthisbookmaybe reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permissioninwritingfromthepublisher. Forinformation: Corwin SAGEPvt.Ltd. ASAGECompany B1/I1MohanCooperative 2455TellerRoad IndustrialArea ThousandOaks,California91320 MathuraRoad,NewDelhi110044 (800)233-9936 India Fax:(800)417-2466 www.corwinpress.com SAGELtd. SAGEAsia-Pacific 1Oliver’sYard Pte.Ltd. 55CityRoad 33PekinStreet#02-01 LondonEC1Y1SP FarEastSquare UnitedKingdom Singapore048763 PrintedintheUnitedStatesofAmerica LibraryofCongressCataloging-in-PublicationData Balka,Don. Aguidetomathematicsleadership:sequencinginstructionalchange/DonS.Balka,TedH. Hull,RuthHarbinMiles. p.cm. Includesbibliographicalreferencesandindex. ISBN978-1-4129-7543-8(pbk.) 1. Mathematics—Study and teaching. 2. Educational leadership. I. Hull, Ted H. II. Miles,RuthHarbin. III. Title. QA11.2.B342010 510.71—dc22 2009031802 Thisbookisprintedonacid-freepaper. 09 10 11 12 13 10 9 8 7 6 5 4 3 2 1 AcquisitionsEditor: CathyHernandez EditorialAssistant: SarahBartlett ProductionEditor: VeronicaStapleton CopyEditor: NancyConger Typesetter: C&MDigitals(P)Ltd. Proofreader: JenniferGritt Indexer: SheilaBodell CoverDesigner: RoseStorey GraphicDesigner: ScottVanAtta Contents List of Figures vii Preface viii Acknowledgments xvi About the Authors xviii PART I: PREPARING THE FOUNDATION 1 1. Understanding and Clarifying Leadership in Mathematics 2 What Is Leadership and Who Is a Leader? 4 Building a Culture of Success 5 NCTM Principles and NCSM Leadership Principles 6 2. Engaging and Empowering Staff 12 Staff Inclusion and Effective Communication 13 Leadership Decision Making 15 Instructional Leadership 16 Dynamics of Engagement and Empowerment 19 Expectations and Challenges 24 PART II: ALEADERSHIP MODEL 25 3. Articulating the Curriculum 26 CurriculumAlignment 27 Opportunity to Learn 30 Scope, Sequence, and TimelineAlignment 34 Rigorous Curriculum 38 4. Implementing the Curriculum 45 Curriculum Implementation 46 Monitored Implementation 47 Monitored Progress 56 5. Incorporating Effective Instructional Strategies 64 Incorporating Effective Instructional Strategies forAll 65 Student Collaboration in the Form of Teamwork 66 Using Group-Worthy Problems 72 Incorporating Instructional Strategies for ELLStudents 76 Matching Materials to Desired Instructional Strategies 84 Using Data to Inform Practice 1:Analyzing Student Work 86 Using Data to Inform Practice 2:Analyzing StudentAssessments 89 6. Providing Timely and Targeted Feedback 93 Using Pertinent Data 94 Targeted Information 98 Building Trust 104 7. Establishing Professional Learning Communities 108 Establishing Collaboration 109 Building Community 111 Facilitating Reflection 115 8. Fostering Professional Development 118 Structuring Effective Professional Development 119 Mentoring and Coaching 122 OtherApproaches to Professional Development 124 PART III: CONTINUING THE WORK 127 9. Reflecting on How Students Learn Mathematics 128 What Mathematics Must or Should Students Learn? 129 What Methods and Tools Will Be Most Effective in Helping Students Learn? 129 What Does Research Say? 131 How Do Students Learn to Become Problem Solvers? 133 How Do Students Learn to Communicate Mathematics? 135 10. Putting It All Together 137 Looping, or Recycling, Through the Developmental Stages 138 Mathematics Leaders’ Influence 139 Guiding Questions for Critiquing the Developmental Stages 140 References 143 Index 149 List of Figures Figure 0.1 Outline of Developmental Stages ix Figure 1.1 Developmental Stages: Mathematics Leadership Model Graphic 10 Figure 1.2 Aligning the Stages With the Principles 11 Figure 2.1 Quadrant Graphic and Positive-Negative Graphic 20 Figure 2.2 Empowerment-Engagement Continuum 23 Figure 3.1 Graphic Organizer forAdding and Subtracting Rational Numbers 37 Figure 3.2 Unit Flowchart Example 39 Figure 4.1 Classroom-Visit Tally: Students 52 Figure 4.2 Classroom-Visit Tally: Teachers 53 Figure 4.3 Example of ItemAnalysis 57 Figure 5.1 Group-Worthy Problem 75 Figure 5.2 Random Digits 79 Figure 5.3 KWLH Chart 82 Figure 5.4 Series of Events Chain 83 • vii Preface T his book is for leaders responsible for improving the mathematics achievement of students. The process presented in the following pages will be useful to leaders who want their teachers, grade levels, departments, schools, and districts to successfully build a high-quality mathematics program based upon the five principles identified by the National Council of Teachers of Mathematics (NCTM; 2000): equity, cur- riculum,teaching,learning,andassessment,aswellasthefourleadership principles identified by the National Council of Supervisors of Mathematics in the PRIME Leadership Framework (NCSM; 2008): equity leadership, teaching and learning leadership, curriculum leadership, and assessment leadership. To facilitate leaders’ actions toward positive change, we present in this book a developmental, sequential process, which is shown in Figure 0.1, Outline of Developmental Stages. While the process unfolds over many monthsandislongtermbynature,wealsoshowmathematicsleadershow toeffectivelyfocustheirtimeandenergysoastoachieveshorter-termgoals and objectives. Leaders will find guidance for change initiatives that are smallenoughtomanage,yetlargeenoughtomatter.Wehaveincorporated NCTMPrinciplesandNCSMLeadershipPrinciplesthroughouteachstage of the process and offer recommendations that are logical, supported by research, and easy to follow. Suggestions for targeting equity are also providedindiscussionofeachstageofthemodel. The improvement process we describe begins with refining, honing, aligning, and implementing the mathematics curriculum. Curriculum improvement is critical to long-term success and student achievement. In addition, the curriculum is a recognized part of the leader’s sphere of influence. Initiating improvement within the mathematics curriculum does notrequirepermissiontopurchasenewprograms,toadjustschedules,orto seekoutsideresources.Mathematicsleadersneedonlytomakethedecision tobegin. • viii • Preface ix Figure0.1 OutlineofDevelopmentalStages Goal:EngagingandEmpoweringStaff Leadership Goal:The mathematics leader ensures that processes are in place to empowerandengagestaff. Amathematicsleaderguaranteesthat: • Staffisincludedindecisionmaking. • Communicationstructuresareinplace. • Dynamicsofengagementandempowermentareunderstood. StagesforEngaging DevelopmentalStage:ArticulatingtheCurriculum Themathematicsleaderensuresthattheschooldistrict,campus,orschoolhasaclearly articulatedmathematicscurriculum. Amathematicsleaderguaranteesthat: • Thecurriculumisalignedtonational,state,andlocalstandards. • Allstudentsaregiventheopportunitytolearnappropriatecontent. • Thescope,sequence,andtimelinealigntotheinstructionalyear. • Thecurriculumisrigorous. DevelopmentalStage:ImplementingtheCurriculum Themathematicsleaderensuresthatthemathematicscurriculumisimplementedas designed. Amathematicsleaderguaranteesthat: • Thedevelopedcurriculumplanisfollowed. • Studentprogressismonitoredviaongoingbenchmarkassessments. DevelopmentalStage:IncorporatingEffectiveInstructionalPractices Themathematicsleaderensuresthateffectiveinstructionalpracticesareimplemented. Amathematicsleaderguaranteesthat: • Avarietyofinstructionalstrategiesareused. • Instructionalmaterialsmatchdesiredclassroominstructionalpractices. • Dataareusedtoinformpractice. StagesforEmpowering DevelopmentalStage:ProvidingTimelyandTargetedFeedback Themathematicsleaderensuresthattimelyfeedbackconcerningcurriculumimple- mentationandclassroomstrategiesareprovidedtoappropriatepersonnel. Amathematicsleadermustguaranteethat: • Pertinentdataaregatheredandusedtoinformlearning. • Informationistargetedtogrouporspecificteacherneeds. • Trustisbuiltthroughoutthestaff. (Continued)