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What Every Education Leader Needs to Know About Strengthening Mathematics Instruction in the Era of the Common Core


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Title: What Every Education Leader Needs to Know About Strengthening Mathematics Instruction in the Era of the Common Core

What Every Education Leader Needs to Know About
Strengthening Mathematics Instruction in the Era
of the Common Core
  • Steve Leinwand
  • American Institutes for Research
  • SLeinwand_at_air.org
  • www.steveleinwand.com
  • March 21, 2013

What a great time to be convening to worry about
  • Common Core State Standards
  • Quality K-8 materials
  • A president who believes in science and data
  • The beginning of the end of Algebra II
  • A long overdue understanding that its
    instruction, stupid!
  • A recognition that the U.S. doesnt have all the

Todays Goal
  • To engage you in thinking about (and then being
    willing and able to act on) the issues of the
    Common Core, more effective instruction, higher
    expectations and building a culture of
    professionalism among the teaching staff. That
    is, perspectives, understandings and strategies
    for providing effective instructional leadership
    in K-12 mathematics.

Todays agenda
  • Setting a context and providing a set of critical
  • The Common Core in a nutshell
  • Our roles in shifting the culture toward greater
    transparency and collaboration
  • Questions

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)

Hong Kong Grade 3 - 2007
Hong Kong Grade 3 - 2007
Part 1
  • Contexts and Perspectives
  • (glimpses at the what, why and how of what we do)

Opening Gambit
  • Your knowledge, experience, insights, creativity,
    energy and expertise are desperately needed to
    significantly improve the knowledge and capacity
    of the nations teachers of mathematics.
  • (If you dont feed inadequate..)

The Math Leaders Field of Activity
  • The heart of ensuring instructional quality and
    producing high levels of student achievement
    includes four key elements
  • A coherent and aligned curriculum that includes a
    set of grade level content expectations,
    appropriate print and electronic instructional
    materials, with a pacing guide that links the
    content standards, the materials and the
  • High levels of instructional effectiveness,
    guided by a common vision of effective teaching
    of mathematics and supported by deliberate
    planning, reflection and attention to the details
    of effective practice
  • A set of aligned benchmark and summative
    assessments that allow for monitoring of student,
    teacher and school accomplishment at the
    unit/chapter and grade/course levels and
  • Professional growth within a professional culture
    of dignity, transparency, collaboration and
  • (What, how, how well and with what support to do
    it better)

Professional Culture

How well?
But.as we need to acknowledge, too often
  • Our curriculum is stale,
  • Our instruction is underperforming,
  • Our assessments are mediocre, and
  • Our professional development is essentially

BUTGreat News
  • Our curriculum is stale enter CCSSM
  • Our instruction is underperforming,
  • Our assessments are mediocre enter SBAC/PARCC
  • Our professional development is essentially
  • Welcome to a far more simplified world
  • Instruction and Culture

  • (in case there is any doubt)
  • Here are 5 opening perspectives on why teacher
    effectiveness is indispensable

1. Where we fit on the food chain
  • 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

2) Lets be clear
  • Were being asked to do what has never been done
  • Make math work for nearly ALL kids and get
    nearly ALL kids ready for college.
  • There is no existence proof, no road map, and
    its not widely believed to be possible.

3) Lets be even clearer
  • And because there is no other way to serve a
    much broader proportion of students
  • Were therefore being asked to teach in
    distinctly different ways.
  • Again, there is no existence proof, we dont
    agree on what different mean, nor how we bring
    it to scale.

4) Another perspective
  • 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

5) The key things we know
People wont do what they cant envision, People
cant do what they dont understand, People cant
do well what isnt practiced, But practice
without feedback results in little change,
and Work without collaboration is not
sustaining. Ergo Our job, as leader, at its
core, is to help people envision, understand,
practice, receive feedback and collaborate.
  • Comments?
  • Questions?

Part 2
  • The Common Core for Math in a Nutshell

Take-away perspectives
  • For as long as most of us can remember, the K-12
    mathematics program in the U.S. has been aptly
    characterized in many rather uncomplimentary
    ways underperforming, incoherent, fragmented,
    poorly aligned, unteachable, unfair, narrow in
    focus, skill-based, and, of course, a mile wide
    and an inch deep.

Lets continue to be honest
  • Most teachers are well aware that there have
    been far too many objectives for each grade or
    course, few of them rigorous or conceptually
    oriented, and too many of them misplaced as we
    ram far too much computation down too many
    throats with far too little success.

  • Hope and change have arrived! Like the long
    awaited cavalry, the new Common Core State
    Standards (CCSS) for Mathematics presents us with
    a once in a lifetime opportunity to rescue
    ourselves and our students from the myriad
    curriculum problems weve faced for years.

  • Coherent
  • Fair
  • Teachable
  • more specifically

Some design elements of the CCSSM
  • Fewer, clearer, higher
  • Fairer rational grade placement of
  • procedures
  • NCTM processes transformed into
  • mathematical practices
  • Learning trajectories or progressions
  • Spirals of expanding radius less
  • repetitiveness and redundancy
  • A sequence of content that results in all
  • reaching reasonable algebra in 8th grade
  • Balance of skills and concepts what to know
  • what to understand

CCSSM Grade 6 (pp. 41-45)
  • Ratios and Proportional Relationships
  • Understand ratio concepts and use ratio
  • reasoning to solve problems.
  • The Number System
  • Apply and extend previous
  • understandings of multiplication and
  • division to divide fractions by
  • fractions.
  • Compute fluently with multi-digit
  • numbers and find common factors
  • and multiples.
  • Apply and extend previous
  • understandings of numbers to the
  • system of rational numbers.
  • Expressions and Equations
  • Apply and extend previous
  • understandings of arithmetic to
  • algebraic expressions.
  • Reason about and solve one-variable
  • equations and inequalities.
  • Represent and analyze quantitative
  • relationships between dependent and
  • independent variables.
  • Geometry
  • Solve real-world and mathematical
  • problems involving area, surface area,
  • and volume.
  • Statistics and Probability
  • Develop understanding of statistical
  • variability.
  • Summarize and describe distributions.

  • Grade 6 Understand ratio concepts and use ratio
    reasoning to solve problems.
  • 1. Understand the concept of a ratio and use
    ratio language to describe a ratio relationship
    between two quantities. For example, The ratio
    of wings to beaks in the bird house at the zoo
    was 21, because for every 2 wings there was 1
    beak. For every vote candidate A received,
    candidate C received nearly three votes.
  • 2. Understand the concept of a unit rate a/b
    associated with a ratio ab with b ? 0, and use
    rate language in the context of a ratio
    relationship. For example, This recipe has a
    ratio of 3 cups of flour to 4 cups of sugar, so
    there is 3/4 cup of flour for each cup of sugar.
    We paid 75 for 15 hamburgers, which is a rate
    of 5 per hamburger.1
  • 3. Use ratio and rate reasoning to solve
    real-world and mathematical problems, e.g., by
    reasoning about tables of equivalent ratios, tape
    diagrams, double number line diagrams, or
  • a. Make tables of equivalent ratios relating
    quantities with whole number measurements, find
    missing values in the tables, and plot the pairs
    of values on the coordinate plane. Use tables to
    compare ratios.
  • b. Solve unit rate problems including those
    involving unit pricing and constant speed. For
    example, if it took 7 hours to mow 4 lawns, then
    at that rate, how many lawns could be mowed in 35
    hours? At what rate were lawns being mowed?
  • c. Find a percent of a quantity as a rate per
    100 (e.g., 30 of a quantity means 30/100 times
    the quantity) solve problems involving finding
    the whole, given a part and the percent.
  • d. Use ratio reasoning to convert measurement
    units manipulate and transform units
    appropriately when multiplying or dividing

  • These Standards are not intended to be new
  • names for old ways of doing business. They are
  • a call to take the next step. It is time for
  • to work together to build on lessons learned
  • from two decades of standards based reforms.
  • It is time to recognize that standards are not
  • just promises to our children, but promises we
  • intend to keep.
  • CCSS (2010, p.5)

8 CCSSM Mathematical Practices
  • Make sense of problems and persevere in solving
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the
    reasoning of others.
  • Model with mathematics.

8 CCSSM Mathematical Practices
  • 5. Use appropriate tools strategically.
  • 6. Attend to precision.
  • 7. Look for and make use of structure.
  • 8. Look for and express regularity in repeated

from Everybody Counts
  • Virtually all young children like mathematics.
    They do mathematics naturally, discovering
    patterns and making conjectures based on
    observation. Natural curiosity is a powerful
    teacher, especially for mathematics.

  • Unfortunately, as children become socialized by
    school and society, they begin to view
    mathematics as a rigid system of externally
    dictated rules governed by standards of accuracy,
    speed, and memory. Their view of mathematics
    shifts gradually from enthusiasm to apprehension,
    from confidence to fear. Eventually, most
    students leave mathematics under duress,
    convinced that only geniuses can learn it.

Accuracy, Speed and Memory
  • Tell the person sitting next to you what is the
    formula for the volume of a sphere.
  • V 4/3 p r3
  • 4/3 ? r? 3? p?

Sucking intelligence out
  • Late one night a shepherd was guarding his flock
    of 20 sheep when all of a sudden 4 wolves came
    over the hill.
  • Boys and girls, how old was the shepherd?

Sothe problem is
  • If we continue to do what weve always done.
  • Well continue to get what weve always gotten.

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  • 7. Add and subtract within 1000, using concrete
    models or drawings and strategies based on place
    value, properties of operations, and/or the
    relationship between addition and subtraction
    relate the strategy to a written method.
    Understand that in adding or subtracting
    three-digit numbers, one adds or subtracts
    hundreds and hundreds, tens and tens, ones and
    ones and sometimes it is necessary to compose or
    decompose tens or hundreds.

Ready, set..
  • 10.00
  • - 4.59

Find the difference
  • Who did it the right way??
  • 910.91010
  • - 4. 5 9
  • How did you get 5.41 if you didnt do it this way?

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  • Algebra
  • The intense study of the last three letters of
    the alphabet

So what have we gotten?
  • Mountains of math anxiety
  • Tons of mathematical illiteracy
  • Mediocre test scores
  • HS programs that barely work for more than half
    of the kids
  • Gobs of remediation and intervention
  • A slew of criticism
  • Not a pretty picture!

If however..
  • What weve always done is no longer acceptable,
  • We have no choice but to change some of what we
    do and some of how we do it.

  • 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
Development for Teachers of Mathematics
So 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.

Some data

40 4
10 2
30 4

Predict some additional data

40 4
10 2
30 4

All the numbers so?

45 4
25 3
15 2
40 4
10 2
30 4
20 3
A lot more information (where are you?)

Roller Coaster 45 4
Ferris Wheel 25 3
Bumper Cars 15 2
Rocket Ride 40 4
Merry-go-Round 10 2
Water Slide 30 4
Fun House 20 3
Fill in the blanks
Ride ??? ???
Roller Coaster 45 4
Ferris Wheel 25 3
Bumper Cars 15 2
Rocket Ride 40 4
Merry-go-Round 10 2
Water Slide 30 4
Fun House 20 3
  • At this point,
  • its almost anticlimactic!

The amusement park page 35
Ride Time Tickets
Roller Coaster 45 4
Ferris Wheel 25 3
Bumper Cars 15 2
Rocket Ride 40 4
Merry-go-Round 10 2
Water Slide 30 4
Fun House 20 3
The Amusement Park
  • The 4th and 2nd graders in your school are going
    on a trip to the Amusement Park. Each 4th grader
    is going to be a buddy to a 2nd grader.
  • Your buddy for the trip has never been to an
    amusement park before. Your buddy want to go on
    as many different rides as possible. However,
    there may not be enough time to go on every ride
    and you may not have enough tickets to go on
    every ride.

  • The bus will drop you off at 1000 a.m. and pick
    you up at 100 p.m. Each student will get 20
    tickets for rides.
  • Use the information in the chart to write a
    letter to your buddy and create a plan for a fun
    day at the amusement park for you and your buddy.

Why do you think I used this task?
  • Standards dont teach, teachers teach
  • Its the translation of the words into tasks and
    instruction and assessments that really matter
  • Processes are as important as content
  • We need to give kids (and ourselves) a reason to
  • Difficult, unlikely, to do alone!!!

Next steps
  • Build familiarity
  • Grade by grade and course by course discussions
  • Professional collaboration
  • Crosswalks
  • The mathematical practices
  • Think 10 per year
  • Focus on instructional quality/opportunity to

Whats to be afraid of?
  • Ok weve got the standards, go do em
  • Another fad with political intrusion
  • Doomed by the same lack of capacity that got us
    into this mess in the first place
  • Assessment compromises
  • Not enough time gel
  • We forget that its instruction stupid
  • We ignore the essential roles of school and
    department culture

But whats to be so hopeful about?
  • Systemic alignment of standards, materials,
    assessments and professional development
  • Less attention to WHAT math and more attention to
    HOW to best teach it
  • Greater collaboration around clearer and common
    goals and better data
  • Market incentives for technology and video
  • A chance to finally focus primarily in
    instruction and learning

  • While we acknowledge the range and depth of the
    problems we face,
  • It should be comforting to see the availability
    and potential of solutions to these problems.
  • Now go forth and start shifting YOUR schools
    mathematics program to better serve our students,
    our society and our future.

  • Thank you!
  • SLeinwand_at_air.org

Part 3
  • Building More Effective K-12 Mathematics Classes
  • We All Have a Role to Play and the Culture Needs
    to Shift

Once again
People wont do what they cant envision, People
cant do what they dont understand, People cant
do well what isnt practiced, But practice
without feedback results in little change,
and Work without collaboration is not
sustaining. Ergo Our job, as leader, at its
core, is to help people envision, understand,
practice, receive feedback and collaborate.
To collaborate, we need time and structures
  • Structured and focused department meetings
  • Before school breakfast sessions
  • Common planning time by grade and by department
  • Pizza and beer/wine after school sessions
  • Released time 1 p.m. to 4 p.m. sessions
  • Hiring substitutes to release teachers for
    classroom visits
  • Coach or principal teaching one or more classes
    to free up teacher to visit colleagues
  • After school sessions with teacher who visited,
    teacher who was visited and the principal and/or
    coach to debrief
  • Summer workshops
  • Department seminars

To collaborate, we need strategies 1
  • Potential Strategies for developing professional
    learning communities
  • Classroom visits one teacher visits a colleague
    and the they debrief
  • Demonstration classes by teachers or coaches with
    follow-up debriefing
  • Co-teaching opportunities with one class or by
    joining two classes for a period
  • Common readings assigned, with a discussion focus
  • 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?
  • Technology demonstrations (graphing calculators,
    SMART boards, document readers, etc.)
  • Collaborative lesson development

To collaborate, we need strategies 2
  • Potential Strategies for developing professional
    learning communities
  • Video analysis of lessons
  • Analysis of student work
  • Development and review of common finals and unit
  • Whats the data tell us sessions based on state
    and local assessments
  • Whats not working sessions
  • Principal expectations for collaboration are
    clear and tangibly supported
  • Policy analysis discussions, e.g. grading,
    placement, requirements, promotion, grouping
    practices, course options, etc.

  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

To recapitulate Share Practice-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 school
    culture toward greater collegial interaction and
    collective growth.
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