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

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


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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

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What a great time to be convening to worry about
math!

• 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
  answers.

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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.

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Todays agenda

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

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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)

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Hong Kong Grade 3 - 2007
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Hong Kong Grade 3 - 2007
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Part 1

• Contexts and Perspectives
• (glimpses at the what, why and how of what we do)

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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..)

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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
  calendar
• 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
  support.
• (What, how, how well and with what support to do
  it better)

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Professional Culture

What?
How?
How well?
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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
  useless!

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BUTGreat News

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

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

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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

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2) Lets be clear

• Were being asked to do what has never been done
  before
• 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.

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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.

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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
  concerns.

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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.
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• Comments?
• Questions?

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Part 2

• The Common Core for Math in a Nutshell

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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.

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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.

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But.

• 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.

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Why?

• Coherent
• Fair
• Teachable
• more specifically

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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
  students
• reaching reasonable algebra in 8th grade
  
• Balance of skills and concepts what to know
  and
• what to understand

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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.

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• 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
  equations.
• 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
  quantities.

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Promises

• 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
  states
• 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)

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8 CCSSM Mathematical Practices

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

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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
  reasoning.

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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.

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• 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.

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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?

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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?

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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.

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Ready, set..

• 10.00
• - 4.59

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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

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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!

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If however..

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

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• 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..

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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
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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.

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Some data




40 4
10 2
30 4

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Predict some additional data




40 4
10 2
30 4

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All the numbers so?

45 4
25 3
15 2
40 4
10 2
30 4
20 3
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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
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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
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• At this point,
• its almost anticlimactic!

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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
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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.

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• 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.

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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
  care
• Difficult, unlikely, to do alone!!!

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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
  learn

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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

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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

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So.

• 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.

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• Thank you!
• SLeinwand_at_air.org

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Part 3

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

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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.
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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

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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
  on
• 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

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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
  assessments
• 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.

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 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
  us)

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The only antidotes Ive ever seen work

• Sharing
• Supporting
• Risk-taking

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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
  investigation.
• Professional development/interaction that focuses
  on the work of teaching and is drawn from
• - mathematical tasks
• - episodes of teaching
• - illuminations of students thinking
•  

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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
  understand.
• Cant know it all need differentiation and
  team-work
• Professional sharing is part of my job.
• Professional growth (admitting we need to grow)
  is a core aspect of being a professional

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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

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