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Practical Strategies for Ensuring that No Teacher of Mathematics is Left Behind. NC Summer Mathematics Leadership Institute Steve Leinwand . Today’s Goals.

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practical strategies for ensuring that no teacher of mathematics is left behind

Practical Strategies for Ensuring that No Teacher of Mathematics is Left Behind

NC Summer Mathematics Leadership Institute

Steve Leinwand

today s goals
Today’s 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.


  • model leadership behavior,
  • identify some tools and ideas, and
  • empower you to take risks.
today s content agenda
Today’s content agenda
  • Problems
  • Examples
  • Themes
  • A blueprint
  • Some discussion
  • A challenge
today s process agenda modeling good instruction
Today’s process agenda(modeling good instruction)
  • Inform (lots of ideas and food for thought)
  • Stimulate (engage your sense of professionalism)
  • Challenge (urge you to move from words to action)
  • Math problems
  • Structural problems


Starting with math problems grounds our discussions and opens doors to all of the structural problems.

So let’s do some math and model the process.

  • What math?
    • Measurement
    • Customary vs metric
    • Dimension
    • Estimation
  • The power of claims – often false or invalid – convince me as reasoning and communication
  • Collaboration
houston we have a problem or clear indicators of a problem
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

houston we have a bigger problem or clear causes of problems
Houston, we have a bigger problem(or clear causes of problems)
  • Societal needs and expectations are different from even 10 years ago and changing rapidly;
  • The kids are different and changing rapidly;
  • The traditional status quo isn’t working well enough;
  • We’re being asked to teach in distinctly different ways from how we were taught; and
  • We’re being asked to make math work for ALL kids
“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


But it’s all been words.

example 1
Example 1:



Find the difference: _ 10.00


People won’t do what they can’t envision.

People can’t do what they don’t understand.

ERGO: Our job as leaders is to help people ENVISION and UNDERSTAND!

example 2
Example 2:

1.59 ) 10.00


You have $10.00

Big Macs cost $1.59 each


you choose
You choose….
  • The one right way to get the one right answer that no one cares about and isn’t even asked on EOGs or EOCs


  • Where am I? (the McDonalds context)
  • Ten? Convince me.
  • About how many? How do you know?
  • Exactly how many? How do you know?
  • Oops – On sale for $1.29 and I have $20.
example 3
Example 3:

F = 4 (S – 65) + 10

Find F when S = 81


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
Example 4:

Solve for x: 16 x .75x < 1


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?

  • Powerful Teaching
  • Productivity
  • False solutions
  • Real solutions
powerful teaching
Powerful Teaching
  • Provides students with better access to the mathematics:
    • Context
    • Technology
    • Materials
    • Collaboration
  • Enhances understanding of the mathematics:
    • Alternative approaches
    • Multiple representations
    • Effective questioning
the productivity theme more math by more people
The PRODUCTIVITY theme(more math by more people)
  • Training
  • Reallocation
  • Data
  • Technology
  • Accountability
  • Incentives
we are more productive when we
We are more productive when we:
  • Change some of WHAT we teach (shifting expectations to more rational and responsive expectations)
  • Change some of HOW we teach (shifting pedagogy to more research-affirmed approaches)
  • Change how we interact and grow
america have we got some solutions for you top down non solution solutions
America, have we got some “solutions” for you(top-down non-solution solutions)
  • NCLB/High-stakes tests
  • A set of impossible to attain expectations and mindless exhortations to improve
  • Hollow, unsupported calls to be more productive
  • More of the same, but tamp it down slower, push it in harder and sprinkle it on finer
  • More accountability (often penalties without incentives, often on the wrong outcomes)
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.

- Leinwand – “Sensible Mathematics”

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


(What’s not clear?)



(What’s disturbing you most?)

resulting in
Resulting in:

A Blueprint

for Cultural Change

A curriculum, accessible resources, and minimal-cost strategies based on the “work of teaching”

the curriculum
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
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!

strategies for the mathematics 1
Strategies for the mathematics 1:
  • Conduct annual collegial discussions for each grade and each course:
  • What works, what doesn’t work?
  • What math, what order, what’s skipped, what’s supplemented?
  • What’s expected, not expected?
  • What’s 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 doesn’t work
  • Appropriate/inappropriate course/grade placement and overlaps

3. Baby/bath water discussions and decisions about specific topics

  • What’s still important, what’s no longer important?
  • Do I care if my own kids can do this?
strategies for the mathematics 2
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.

some big ideas
Number uses and representations

Equivalent representations

Operation meanings and interrelationships

Estimation and reasonableness




Recursion and iteration




Change as a rate



The coordinate plane

Measure – attribute, unit, dimension


Central tendency

Some Big Ideas
questions that big ideas answer
Questions that “big ideas” answer:
  • How much? How many?
  • What size? What shape?
  • How much more or less?
  • How has it changed?
  • Is it close? Is it reasonable?
  • What’s the pattern? What can I predict?
  • How likely? How reliable?
  • What’s the relationship?
  • How do you know? Why is that?
strategies for strengthening the teaching
Strategies for strengthening the teaching:

1. Use classroom visits to broaden perspectives and stimulate discussions

  • Typical and demonstration classes
  • Building a sense of we’re 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. Here’s the data, what’s the math and what questions best elicit the


putting it all together one way
Putting it all together one way

Good morning class.

Today’s objective: Find the surface area of right circular cylinders.

Open to page 384-5.

Example 1: 3 S.A.= 2πrh + 2 πr2

4 Find the surface area.

Page 385 1-19 odd

putting it all together another way
Putting it all together another way

Overheard in the ER as the sirens blare:

“Oh my, look at this next one. He’s completely burned from head to toe.”

“Not a problem, just order up 1000 square inches of skin from the graft bank.”

You have two possible responses:

  • Oh good – that will be enough.


  • Oh god – we’re in trouble.
Which response, “oh good” or “oh god” is more appropriate?
  • Explain your thinking.
  • Assuming you are the patient, how much skin would you hope they ordered up?
  • Show how you arrived at your answer and be prepared to defend it to the class.
strategies for increasing the learning
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. What’s 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 well?
strategies for reaching more students
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 classes/courses

3. Policy implication discussions

  • Algebra 1 placement
  • Grouping by reading levels
  • Heterogeneous grouping mandates
  • Pull-out programs
strategies to tie it all together
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 well

5. Conduct annual math nights

okay your turn again
Okay: Your turn again

So, which ones can’t you do?

(A discussion to debunk the

inevitable “yeah, buts”)

the obstacles to change
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, won’t work, already tried it, kids don’t care, they won’t let us)
the only antidotes i ve ever seen work
The only antidotes I’ve ever seen work
  • Sharing
  • Supporting
  • Risk-taking

Your challenge:

Administer the antidotes!

to recapitulate share practice based professional interaction
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 investigation.
  • 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
To recapitulate: Support The mindsets upon which to start
  • We’re all in this together
  • People can’t do what they can’t envision. People won’t do what they don’t understand. Therefore, colleagues help each other envision and understand.
  • Can’t 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
to recapitulate take risks it all comes down to taking risks
To recapitulate: Take RisksIt 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.