Coaching for Math GAINS Professional Learning

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Coaching for Math GAINSProfessional Learning
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Initial Steps in Math Coaching
How going SLOWLY will help you to make
significant GAINS FAST.
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Establishing Norms

• Start and end on time
• Electronic devices off except on break

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Norms

• Start and end on time.
• Respond to the signal.
• Each person gets the chance to speak and listen.
• Participants direct their discussion to the whole
  group, not the facilitator.
• Invest in your own learning and the learning of
  others.
• Contribute to a safe environment that encourages
  risk taking be kind.
• Think and act like mathematicians.

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Overview of the Session
Practise being a math coach in a safe environment
through role play.
View some examples of the math coaching process
in action.
Clarify your personal image of what being a
mathematics coach involves.
Identify some next steps for yourself.
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Initial Meeting
Some possible questions- Who are you? Tell me
about yourself. - What are your strengths,
styles, beliefs, goals ? - What do you want me
to know about you as a math teacher?
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Coaching Strategies and Stems

• Paraphrasing
• Do I understand that you dont have access to
  computers?
• In other words you want to try some
  differentiated instruction?
• It sounds like you have explored a variety of
  resources?
• Clarifying
• What do you mean by the course is too hard?
• Is it always the case that the students in the
  class dont listen?
• How is teaching math same as/different
  fromteaching science?
• Interpreting
• What you are explaining might mean students rely
  on formulas
• Could it mean that students need more time on
  this topic?
• Is it possible that the following things could
  result from ?

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Now it's your turn

• Role play the initial meeting between coach and
  coachee.
• Ask questions to lay a foundation for your later
  work with the teacher. Use the stems to probe
  more deeply.

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What does being a math coach involve?
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What do you think now?

• In pairs, create a Frayer Model for
  Coaching

Definition Characteristics
Examples Non-examples
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The Non-negotiables

• "What coaching is not"
• Your coaching duties do not include

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It's all about trust!

• Sincerity
• Competence
• Benevolence
• Reliability

Adapted from Coaching Leaders to Attain Student
Success Gary Bloom
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Content-Focused Coaching

• Is content specific.
• Teachers' plans, strategies and methods are
  discussed in terms of student learning.
• Is based on a set of core issues of learning and
  teaching.
• Fosters professional habits of mind.
• Enriches and refines teachers' pedagogical
  content knowledge.
• Encourages teachers to communicate with each
  other in a focused, professional manner.

from Content-Focused Coaching Transforming
Mathematics Lessons, by Lucy West, p.3
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Let's hear from another expert Cathy Fosnot

• Discuss with a partner any new thoughts about
  coaching.
• Re-visit and revise your Frayer model.

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The Guide
Aligned with Grades 7-12 Literacy Guide A
prototype for other subjects A research
framework Find an indicator that addresses one
of your foci for the year
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More Precision
www.edugains.ca Library
www.tmerc.ca
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Sharpening the Instructional Focus
37 indicators in The Guide for Administrators and
Other Facilitators of Teachers Learning for
Mathematics Instruction
8 criteria in the Student Success Action
Planning Template
2006
3 strategic approaches
May 2008
1 key focus
September 2008
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Sharpening the Instructional Focus

• Three strategic approaches
• Fearless listening and speaking
• Questioning to evoke and expose thinking
• Responding to provide appropriate scaffolding and
  challenge

Driver for 2008-09
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Sharpening the DI Focus
Differentiation of content, process, and
product based on student readiness,
interest, and learning profile
2004 - 08
Differentiation based on student readiness
and differentiation at the concept
development stage
2008 - 09
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Connecting Foci

• Questioning

Fearless listening and speaking
Differentiating
Responding
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Differentiating Mathematics Instruction

• Questioning to Evoke and Expose Thinking

Materials adapted from Dr. Marian Smalls
presentation August 2008
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Questioning That Matters
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• You have introduced a counter model for
  subtracting integers. As you look at each
  question and its answer, think about its
  purpose.

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Questions That Matter
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• What is (-3) (-4)?
• Tell how you calculated (-3) (-4).
• Use a diagram or manipulatives to show how to
  calculate (-3) (-4) and tell why you do what
  you do.
• Why does it make sense that
• (-3) (-4) is more than (-3) 0?
• Choose two integers and subtract them.
• What is the difference? How do you know?

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Differences in Intent
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• Do you want students to
• be able to get an answer?
• What is (-3) (-4)?
• be able to explain an answer?
• Explain how you calculated (-3) (-4).
• see how a particular aspect of mathematics
  connects to what they already know?
• Use a diagram or manipulatives to show how to
  calculate (-3) (-4) and tell why you do what
  you do.

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Differences in Intent
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• Do you want students to
• be able to describe why a particular answer makes
  sense?
• Why does it make sense that (-3) (-4) is
  more than (-3) 0?
• be able to provide an answer?
• Choose two integers and subtract them. What is
  the difference? How do you know?
• Which of these types of questions are important
  to you? All of them? Some of them? Why?

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It is important that
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• even struggling students meet questions with
  these various intents, including making sense of
  answers and relating to other math ideas, and
  meet with success.
• questions focus on the math that matters.

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Your answer is.?

• A graph goes through the point (1,0). What could
  it be?
• What makes this an accessible, or inclusive, sort
  of question?

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Possible responses
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• x 1
• y 0
• y x- 1
• y x2 - 1
• y x3 - 1
• y 3x2 -2x -1

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What good questions can do

• Good questions
• Evoke student thinking.
• Expose student thinking.
• Help students see and drill into big Ideas

• For good questions to work
• Students must be able to listen and speak
  fearlessly.
• Students must be provided appropriate scaffolding
  and challenge.

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The coach can help teachers

• identify the Big Math ideas in the lessons they
  plan to teach.
• develop questions that focus students on making
  sense of the math.
• craft questions that help students make
  connections.
• create questions that probe for student
  understanding.

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Opening up Questions

• Conventional question
• You saved 6 on a pair of jeans during a 15 off
  sale. How much did you pay?
• vs.

You saved 6 on a pair of jeans during a sale.
What might the percent off have been? How much
might you have paid?
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Or

• You saved some money on a jeans sale.
• Choose an amount you saved 5, 7.50 or 8.20.
• Choose a discount percent.
• What would you pay?

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Or

• Conventional question
• What is 52 62 33?
• vs.

Represent 88 as the sum of powers.
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Possibilities
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• 12 12 . 12 (88 of them)
• 22 22 22 (22 of them)
• 52 52 52 22 22 22 12
• 52 62 33

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Similarities and Differences
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• How are quadratic equations like linear ones? How
  are they different?
• How is calculating 20 of 60 like calculating the
  number that 60 is 20 of? How is it different?
• How is dividing rational numbers like dividing
  integers? How is it different?

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Some opening up strategies
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• Start with the answer instead of the question.
• Ask for similarities and differences.
• Leave the values in the problem somewhat open.

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How could you open these questions up?

• Add 3/8 2/5.

• A line goes through (2,6) and has a slope of -3.
• What is the equation?

• Graph y 2(3x - 4)2 8.

• Add the first 40 terms of
• 3, 7, 11, 15, 19,

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Using Parallel Tasks

• Offer 2-3 similar tasks that meet different
  students needs, but make sense to discuss
  together.

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Parallel Questions

• Task A 1/3 of a number is 24. What is the
  number?
• Task B 2/5 of a number is 24. What is the
  number?
• Task C 40 of a number is 24. What is the
  number?

How do you know the number is more than 24? Is
the number more than double 24? How did you
figure out your number?
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Parallel Questions

• Task 1
• Find two numbers where
• - the sum of both numbers divided by 4 is 3.
• - twice the difference of the two numbers is -36.
• Task 2
• Solve (x y) / 4 3 and 2(x y) -36

How did you use the first piece of information?
The second piece? How did you know the numbers
could not both be negative?
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The Processes
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• Problem solving
• Reasoning and proving
• Reflecting
• Selecting tools and strategies
• Connecting
• Representing
• Communicating

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Coachs Role
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• Helping teachers realize they must identify the
  math that matters
• Helping teachers practice developing questions
  that focus on students making sense of the math
• Helping teachers practice developing questions
  that focus on building connections- how new math
  ideas are
• related to and built on older ones