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CPAM Leadership Seminar Practical Strategies for Providing School Based Leadership for More Powerful Teaching of K-12 Mathematics


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Title: CPAM Leadership Seminar Practical Strategies for Providing School Based Leadership for More Powerful Teaching of K-12 Mathematics

CPAM Leadership SeminarPractical Strategies
for Providing School Based Leadership for More
Powerful Teaching of K-12 Mathematics
  • Steve Leinwand
  • American Institutes for Research

Lets Reflect Mirrors, Changes, Engagement,
What a great time to be convening as teachers of
  • Common Core State Standards
  • Quality K-8 materials
  • 5 billion with a STEM RttT tie-breaker
  • A president who believes in science and data
  • The beginning of the end of Algebra II
  • A long overdue understanding that its
    instruction, stupid!

In other words..
  • A critical time for leadership!
  • Our leadership.
  • Your leadership.

Todays Goals
  • Engage you in thinking about (and then being
    willing and able to act on) the issues of filling
    the leadership void and shifting the culture of
    professional interaction within our departments
    and our schools.
  • Subgoals
  • validate your concerns,
  • give you some tools and ideas,
  • empower you to take risks

My Process Agenda(modeling good instruction)
  • Inform (lots of ideas and food for thought)
  • Engage (focused individual and group tasks)
  • Stimulate (excite your sense of professionalism)
  • Challenge (urge you to move from words to action)

Todays content agenda
  • Critical Perspectives
  • Problems
  • Examples
  • Themes
  • A blueprint
  • Some discussion
  • A challenge

What we know and where we fit (critical
perspective 1)
  • Economic security and social well-being
  • ? ? ?
  • Innovation and productivity
  • ? ? ?
  • Human capital and equity of opportunity
  • ? ? ?
  • High quality education
  • (literacy, MATH, science)
  • ? ? ?
  • Daily classroom math instruction

Critical perspective 2
  • Were being asked to do what has never been done
  • Make math work for nearly ALL kids.
  • But no existence proof, no road map, not
    widely believed to be possible

Critical perspective 3
  • Were therefore being asked to teach in
    distinctly different ways
  • Because there is no other way to serve a much
    broader proportion of students.
  • But again, no existence proof, what does
    different mean, how do we bring to scale?

Critical perspective 4
  • As mathematics colonizes diverse fields, it
    develops dialects that diverge from the Kings
    English of functions, equations, definitions and
    theorems. These newly important dialects employ
    the language of search strategies, data
    structures, confidence intervals and decision
  • - Steen

The pipeline perspective(critical perspective
  • 1985 3,800,000 Kindergarten students
  • 1998 2,810,000 High school graduates
  • 1998 1,843,000 College freshman
  • 2002 1,292,000 College graduates
  • 2002 150,000 STEM majors
  • 2006 1,200 PhDs in mathematics

Critical perspective 6
  • Evidence from a half-century of reform efforts
    shows that the mainstream tradition of focusing
    school mathematics on preparation for a
    calculus-based post-secondary curriculum is not
    capable of achieving urgent national goals and
    that no amount of tinkering in likely to change
    that in any substantial degree.
  • - Steen

ERGO Houston, we have a problem(or clear
indicators of a problem)
  • Look around. Our critics are not all wrong.
  • Mountains of math anxiety
  • Tons of mathematical illiteracy
  • Mediocre test scores
  • HS programs that barely work for half the kids
  • Gobs of remediation
  • A slew of criticism
  • Not a pretty picture and hard to dismiss

Your turn
  • But Steve
  • These are global problems.
  • In my neck of the woods, the three biggest
    problems I face as a professional educator are

  • Math problems
  • Structural problems
  • Hypothesis
  • Starting with math problems grounds our
    discussions and opens doors to all of the
    structural problems.
  • So lets do some math and model the process.

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Valid or Invalid?Convince us.
  • Grapple
  • Formulate
  • Givens and Goals
  • Estimate
  • Measure
  • Reason
  • Justify
  • Solve

  • The kind of learning that will be required of
    teachers has been described as transformative
    (involving sweeping changes in deeply held
    beliefs, knowledge, and habits of practice) as
    opposed to additive (involving the addition of
    new skills to an existing repertoire). Teachers
    of mathematics cannot successfully develop their
    students reasoning and communication skills in
    ways called for by the new reforms simply by
    using manipulatives in their classrooms, by
    putting four students together at a table, or by
    asking a few additional open-ended questions..

Rather, they must thoroughly overhaul their
thinking about what it means to know and
understand mathematics, the kinds of tasks in
which their students should be engaged, and
finally, their own role in the classroom.
NCTM Practice-Based Professional Development
for Teachers of Mathematics
  • People wont do what they cant envision.
  • People cant do what they dont understand.
  • ERGO Our job as leaders is to help people
  • So lets use some EXAMPLES to do this.

Example 1
  • Ready
  • Set
  • Find the difference _ 10.00
  • 4.59

Example 2
  • 1.59 ) 10
  • vs.
  • You have 10.00
  • Big Macs cost 1.59 each
  • So?

Example 3
  • F 4 (S 65) 10
  • Find F when S 81
  • Vs.
  • First I saw the blinking lights then the officer
    informed me that
  • The speeding fine here in Vermont is 4 for every
    mile per hour over the 65 mph limit plus a 10
    handling fee.

Example 4
  • Solve for x 16 x .75x lt 1
  • Vs.
  • You ingest 16 mg of a controlled substance at 8
    a.m. Your body metabolizes 25 of the substance
    every hour. Will you pass a 4 p.m. drug test
    that requires a level of less than 1 mg? At what
    time could you first pass the test?

Dear sirs
  • I am in Mrs. Eaves Pre-algebra class at the
    Burn Middle School. We have been studying the
    area of shapes such as squares and circles. A
    girl in my class suggested that we compare the
    square and round pizzas sold by your store. So
    on April 16 Mrs. Eaves ordered one round and one
    square pizza from your store for us to measure,
    compare and

The search for sense-making/future leaders
  • What is the reason for the difference in the
    price per square inch of these two pizzas? Is it
    harder to cook a round pizza? Does it take
    longer to cook? Because if 3.35 cents per square
    inch is acceptable for the square pizza, then the
    same price per square inch should be used for the
    round pizza, making the price 10.31 instead of
  • Thanks for the tasty lesson in pizza values.
  • Sincerely,
  • Chris Collier

Ice Cream Cone!!
  • You may or may not remember that the formula for
    the volume of a sphere is 4/3pr3 and that the
    volume of a cone is 1/3 pr2h.
  • Consider the Ben and Jerrys ice cream sugar
    cone, 8 cm in diameter and 12 cm high, capped
    with an 8 cm in diameter sphere of deep,
    luscious, decadent, rich triple chocolate ice
  • If the ice cream melts completely, will the cone
    overflow or not? How do you know?

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The Basics (Acquire) an incomplete list
  • Knowing and Using
  • , -, x, facts
  • x/ by 10, 100, 1000
  • 10, 100, 1000,., .1, .01more/less
  • ordering numbers
  • estimating sums, differences, products,
    quotients, percents, answers, solutions
  • operations when and why to , -, x,
  • appropriate measure, approximate measurement,
    everyday conversions
  • fraction/decimal equivalents, pictures, relative

The Basics (continued)
  • percents estimates, relative size
  • 2- and 3-dimensional shapes attributes,
  • read, construct, draw conclusions from tables and
  • the number line and coordinate plane
  • evaluating formulas
  • So that people can
  • Solve everyday problems
  • Communicate their understanding
  • Represent and use mathematical entities

Some Big Ideas (Meaning)
  • Number uses and representations
  • Equivalent representations
  • Operation meanings and interrelationships
  • Estimation and reasonableness
  • Proportionality
  • Sample
  • Likelihood
  • Recursion and iteration
  • Pattern
  • Variable
  • Function
  • Change as a rate
  • Shape
  • Transformation
  • The coordinate plane
  • Measure attribute, unit, dimension
  • Scale
  • Central tendency

Questions that big ideas answer(Transfer)
  • How much? How many?
  • What size? What shape?
  • How much more or less?
  • How has it changed?
  • Is it close? Is it reasonable?
  • Whats the pattern? What can I predict?
  • How likely? How reliable?
  • Whats the relationship?
  • How do you know? Why is that?

  • Powerful teaching
  • Productivity
  • Collaboration
  • Real solutions
  • A vision of effective teaching and learning

Powerful Teaching
  • Provides students with better access to the
  • Context
  • Technology
  • Materials
  • Collaboration
  • Enhances understanding of the mathematics
  • Alternative approaches
  • Multiple representations
  • Effective questioning

We are more productive when we
  • Change some of WHAT we teach (shifting
    expectations to more rational and responsive
  • Change some of HOW we teach (shifting pedagogy to
    more research-affirmed approaches)
  • Change how we interact and grow

  • Most teachers practice their craft behind closed
    doors, minimally aware of what their colleagues
    are doing, usually unobserved and under
    supported. Far too often, teachers frames of
    reference are how they were taught, not how their
    colleagues are teaching. Common problems are too
    often solved individually rather than by seeking
    cooperative and collaborative solutions to shared
  • - Leinwand Sensible Mathematics

Real solutions
  • Changes in our professional culture
  • Ongoing opportunities for substantive, focused,
    professional interaction
  • Ongoing activities that reduce professional
  • A focus on the tasks, the teaching and the
    student work

Its instruction, silly!
  • Research, classroom observations and common
    sense provide a great deal of guidance about
    instructional practices that make significant
    differences in student achievement. These
    practices can be found in high-performing
    classrooms and schools at all levels and all
    across the country. Effective teachers make the
    question Why? a classroom mantra to support a
    culture of reasoning and justification. Teachers
    incorporate daily, cumulative review of skills
    and concepts into instruction. Lessons are
    deliberately planned and skillfully employ
    alternative approaches and multiple
    representationsincluding pictures and concrete
    materialsas part of explanations and answers.
    Teachers rely on relevant contexts to engage
    their students interest and use questions to
    stimulate thinking and to create language-rich
    mathematics classrooms.

  • A Vision of Teaching and Learning
  • An effective and coherent mathematics program
    should be guided by a clear set of content
    standards, but it must be grounded in an equally
    clear and shared vision of teaching and learning
    the two critical reciprocal actions that link
    teachers and students largely determine
    educational impact.
  • Where is your vision of effective teaching and
    learning of mathematics?

Elements of a Vision
  • Effective mathematics instruction in thoughtfully
  • The heart of effective mathematics instruction is
    an emphasis on problem solving, reasoning and
  • Effective mathematics instruction balances and
    blends conceptual understanding and procedural
  • Effective mathematics instruction relies on
    alternative approaches and multiple

Elements of a Vision (cont.)
  • Effective mathematics instruction uses contexts
    and connections to engage students and increase
    the relevance of what is being learned.
  • Effective mathematics instruction provides
    frequent opportunities for students communicate
    their reasoning and engage in productive
  • Effective mathematics instruction incorporates
    on-going cumulative review.
  • Effective mathematics instruction maximizes time
    on task.
  • Effective mathematics instruction employs
    technology to enhance learning.

Elements of a Vision (cont.)
  • Effective mathematics instruction uses multiple
    forms of assessment and uses the results of this
    assessment to adjust instruction.
  • Effective mathematics instruction integrates the
    characteristics of this vision to ensure student
    mastery of grade-level standards.
  • Effective teachers of mathematics reflect on
    their teaching, individually and collaboratively,
    and make revisions to enhance student learning.

  • Questions
  • (Whats not clear?)
  • and
  • Discussion
  • (Whats disturbing you most?)

Resulting in
  • A Blueprint
  • for Cultural Change
  • A curriculum, accessible resources, and
    minimal-cost strategies based on the work of

The Curriculum
  • The mathematics we teach
  • The teaching we conduct
  • The technology and materials we use
  • The learning we inculcate
  • The equity we foster

The Resources
  • Curriculum guides, frameworks and standards
  • Textbooks, instructional materials
  • Articles, readings
  • Observations
  • Demonstration classes
  • Video tapes
  • Web sites
  • Student work, lesson artifacts
  • Common finals and grade level CRTs
  • Disaggregated test scores
  • Buddies, colleagues
  • Notice the cost!

Never forget
  • Its not a PLC, its the content of, and
    follow-up and change that emerges from, the
    professional sharing and interaction that
    enhances the day-in-and-day-out opportunities for
    kids to learn mathematics!

Strategies for the mathematics 1
  • Conduct annual collegial discussions for each
    grade and each course
  • What works, what doesnt work?
  • What math, what order, whats skipped, whats
  • Whats expected, not expected?
  • Whats on the common final/grade level CRT?
  • What gets recorded in a written action plan
  • 2. Conduct periodic mathematics strand or topic
    discussions (algebra, fractions, statistics)
  • What works, what doesnt work
  • Appropriate/inappropriate course/grade placement
    and overlaps
  • 3. Baby/bath water discussions and decisions
    about specific topics
  • Whats still important, whats no longer
  • Do I care if my own kids can do this?

Strategies for the mathematics 2
  • 4. Common readings and focused discussions to
    truly build communities of learners
  • To what degree are we already addressing the
    issue or issues raised in this article?
  • In what ways are we not addressing all or part of
    this issue?
  • What are the reasons that we are not addressing
    this issue?
  • What steps can we take to make improvements and
    narrow the gap between what we are currently
    doing and what we should be doing?
  • 5. Collectively and collaboratively give
    yourselves permission to adjust the curriculum on
    the assumption that you own the curriculum to a
    greater degree than most assume.

Strategies for strengthening the teaching
  • 1. Use classroom visits to broaden perspectives
    and stimulate discussions
  • Typical and demonstration classes
  • Building a sense of were all in this together
    and face common problems
  • 2. The roll the videotape strategy.
  • Our own lessons
  • Annenberg tapes (
  • NCTM Reflections lessons (
  • 3. Collaboratively craft powerful lessons
    ( and
  • 4. Heres the data, whats the math and what
    questions best elicit the
  • math?

Strategies for increasing the learning
  • 1. Analyze student work
  • Look at what my kids did!
  • What does work like this tell us we ought to do?
  • 2. Review of common finals/grade level CRTs data
  • 3. Whats on the test? or examining the truism
    that what we assess and
  • how we assess communicates what we value
  • Types of items/tasks/questions
  • Content and processes measured
  • Contexts, complexity, appropriateness,
    memorization required
  • 4. Annual action planning sessions
  • What are we doing well?
  • What can we do to expand what is working?
  • What are we not doing as well?
  • What can we do to improve what is not working as

Strategies for reaching more students
  • 1. What do the data tell us? sessions
  • 2. What do the videotapes tell us sessions
  • Compare and contrast two higher level
    classes/courses with two lower level
  • 3. Policy implication discussions
  • Algebra 1 placement
  • Grouping by reading levels
  • Heterogeneous grouping mandates
  • Pull-out programs

Strategies to tie it all together
  • 1. Use faculty, grade-level and department
    meetings as opportunities to inform, stimulate,
    challenge and grow by adapting the faculty
    seminar model
  • 2. Implement intensive induction procedures,
    processes and traditions
  • 3. Cultivate and assign topic resource people
  • 4. Appoint course committees what, how, how
  • 5. Conduct annual math nights

Okay Your turn again
  • So, which ones cant you do?
  • (A discussion to debunk the
  • inevitable yeah, buts)

 The obstacles to change
  • Fear of change
  • Unwillingness to change
  • Fear of failure
  • Lack of confidence
  • Insufficient time
  • Lack of leadership
  • Lack of support
  • Yeah, but. (no money, too hard, wont work,
    already tried it, kids dont care, they wont let

The only antidotes Ive ever seen work
  • Sharing
  • Supporting
  • Risk-taking
  • Your challenge
  • Administer the antidotes!

To recapitulate SharePractice-based
professional interaction
  • Professional development/interaction that is
    situated in practice and built around samples of
    authentic practice.
  • Professional development/interaction that employs
    materials taken from real classrooms and provide
    opportunities for critique, inquiry, and
  • Professional development/interaction that focuses
    on the work of teaching and is drawn from
  • - mathematical tasks
  • - episodes of teaching
  • - illuminations of students thinking

To recapitulate Support The mindsets upon which
to start
  • Were all in this together
  • People cant do what they cant envision. People
    wont do what they dont understand. Therefore,
    colleagues help each other envision and
  • Cant know it all need differentiation and
  • Professional sharing is part of my job.
  • Professional growth (admitting we need to grow)
    is a core aspect of being a professional

To recapitulate Take Risks It all comes down to
taking risks
  • While nothing ventured, nothing gained is an
    apt aphorism for so much of life, nothing
    risked, nothing failed is a much more apt
    descriptor of what we do in school.
  • Follow in the footsteps of the heroes about whom
    we so proudly teach, and TAKE SOME RISKS

  • Thank you.
  • Now go forth and start shifting YOUR department,
    school and district culture toward greater
    collegial interaction and collective growth.

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Bonus Slides
  • Dignity
  • Transparency
  • Collaboration
  • Quality
  • Accountability
  • AKA the Gospel According to Steve

Whats missing in so many of our schools and
  • Dignity rarely treated as professionals
  • Transparency we hide, were isolated
  • Collaboration we rarely share
  • Quality much can be done better
  • Accountability weak, often minimal, and for the
    wrong outcomes

Dignity - yin
  • Too often
  • Its top-down
  • They assume were ignorant
  • They really think they know best
  • And the kids are treated even worse!
  • Envision the magnetometer at a high school.
  • Hear the tone of disdain and sarcasm in the
    middle school corridor

Dignity - yang
  • Instead
  • When professionals are treated like
    professionals, its simply amazing how they
    tend to act like professionals!
  • When students are treated with respect.
  • Dignity and respect are essential precursors to
    trust and a healthy work environment!

Transparency -yin
  • Too often
  • We hide behind closed doors
  • We hoard lest other steal our ideas
  • We rarely observe what our colleagues are doing
  • We rarely videotape ourselves practicing our

Transparency - yang
  • Instead, consider
  • Never knowing when a colleague will wander in
  • Feeling completely welcome in everyone elses
  • Collegial reviews of lesson videos
  • School-wide access to our test results and
  • Would you really want your surgeon to operate
    in secret?

Collaboration - yin
  • In 1971
  • I could do it all
  • 3 textbooks
  • 2 walls of blackboard
  • 1 overhead projector and pull-down screen
  • Lots of chalk and boxes on ditto masters!
  • Who needed to collaborate?

Collaboration - yang
  • In 2010
  • Textbooks Videos Websites Applets
    Blogs Document cameras LCD projectors
    Powerful calculators Even more powerful
    computers Interactive white boards HeyMath
    Successmaker PowerPoint Geometer Sketchpad
    Fathom Etc.
  • No one can do it all or know it all
  • We must collaborate!

Quality - yin
  • Too often
  • We punt
  • We settle
  • We cut corners
  • We dont polish stones
  • We fail to reflect and revise.

Quality - yang
  • Instead
  • Models of excellence
  • Strong visions of teaching and learning math
  • Well developed plans
  • Videos of instructional quality
  • Exemplars of student work

Accountability - yin
  • Too often, a litany of yeah, buts
  • Its the kids
  • Its their parents
  • Its the middle school and those teachers
  • Its the elementary program and teachers who
    dont know math
  • They dont do their homework
  • They dont know their facts
  • They just dont care

Accountability - yang
  • Instead
  • I can meet them ¾ of the way
  • I can strive to engage them with interesting
  • I can take affirmative actions to reteach rather
    than blame
  • I can hold myself accountable for their learning
    if they just try a little

Logic Model (part 1)
  • Until and unless we are treated, and we treat
    each other, with dignity and respect, there will
    not be enough trust for transparency.

Logic Model (part 2)
  • Until and unless we have much greater
    transparency and openness (a mindset that we can
    learn from each other), there are few incentives
    to collaborate.

Logic Model (part 3)
  • Until and unless we collaborate, and remember
    that learning (our students as well as our own)
    is a socially mediated process, it is unlikely we
    will significantly improve the overall quality of
    our work.

Logic Model (part 4)
  • And until and unless this foundation is built,
    there is insufficient support and an inadequate
    culture for meaningful accountability that
    ensures that every student who tries has the
    opportunity to learn.
  • Amen.