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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.
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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)
