Transcript OAME Leadership

Coaching for Math GAINS
Professional Learning
Initial Steps in Math Coaching
How going SLOWLY will help you to
make significant GAINS FAST.
Establishing Norms
• Start and end on time
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• Electronic devices off except on break
Overview of the Session
View some examples of the
math coaching process in
action.
Practise being a math coach
in a safe environment
through role play.
Clarify your personal image
of what being a mathematics
coach involves.
Identify some next steps for
yourself.
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?
Coaching Strategies and Stems
• Paraphrasing
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Do I understand that… you don’t 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
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What do you mean by … the course is too hard?
Is it always the case that …the students in the class don’t listen?
How is… teaching math same as/different from…teaching science?
• Interpreting
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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… ?
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.
What does being a math coach
involve?
What do you think now?
In pairs, create a Frayer Model for “Coaching”
Definition
Characteristics
Coaching
Examples
Non-examples
The Non-negotiables
"What coaching is not"
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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
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
Let's hear from another expert:
Cathy Fosnot
• Discuss with a partner any
new thoughts about
coaching.
• Re-visit and revise your
Frayer model.
(Fosnot, 2002)
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
More Precision
www.edugains.ca
Library
www.tmerc.ca
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
3 strategic approaches
1 key focus
2006
May 2008
September 2008
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
Sharpening the DI Focus
Differentiation of content, process, and
product based on student readiness,
interest, and learning profile
Differentiation based on
student readiness
and
differentiation at the
concept development
stage
2004 - 08
2008 - 09
Connecting Foci
Questioning
Fearless listening
and speaking
Responding
Differentiating
Differentiating
Mathematics Instruction
Questioning to Evoke
and Expose Thinking
Materials adapted from Dr. Marian Small’s presentation August 2008
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Questioning That Matters
You have introduced a counter model for
subtracting integers. As you look at each
question and it’s answer, think about its
purpose.
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Questions That Matter
• 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
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
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:
• 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.
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
(1,0)
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.
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.
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?
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?
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
• 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”
• Start with the answer instead of the
question.
• Ask for similarities and differences.
• Leave the values in the problem
somewhat open.
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,…
Using Parallel Tasks
• Offer 2-3 similar tasks that meet
different students’ needs, but make
sense to discuss together.
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?
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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Coach’s Role
• 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