Transcript PLMLC Day 1_TSLS_Ottawa_oct14 - GAINS

Professional Learning
for Mathematics
Leaders and Coaches—
Not just a 3-part series
Day 1
Liisa Suurtamm
Trish Steele
The Four Royal Families
Agenda
A Mathematics Coaching Cycle
Establish norms for
working together
Content Focus
Whole Group Norms
 We are all part of a learning
collective
 When speaking, address the whole
group
 Interactions are intended to move
the collective forward
 If you are in need of an answer, ask
now
 Engage fully in the moment
Big Ideas in
Patterns & Algebra
Professional Learning
for Mathematics
Leaders and Coaches
not just a 3-part series
Ministry Messages
What’s important about the
Math we Teach?
A Focus on Big Ideas
Minds-On
• A linear growing pattern starts
at -10 and grows very slowly.
What might the pattern be?
• How could you convince someone
the pattern grows slowly?
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Characteristics of
Minds-On
• How does this minds-on
engage students?
• How is it open?
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Minds-On
A linear growing pattern starts at -10
and grows very slowly. What might
the pattern be?
What do you think the
important underlying math
idea is?
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Minds-On
• What makes a pattern linear is…
OR
• It makes sense that there are a
lot of linear patterns that start
with the same term because…
OR
• Context matters in deciding how
fast a pattern grows because…
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What are Big Ideas?
“A Big Idea is a statement of
an idea that is central to the
learning of mathematics..”
Randy Charles
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“….one that connects
numerous mathematical
understandings into a
coherent whole.”
Marian Small
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Big Idea
• NOT a topic name nor an overall
expectation.
• BUT a statement that describes
a fundamental mathematical
connection.
• It provides a lens in which to
embed new learning.
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Big Ideas for Pattern & Algebra
A set of big ideas for patterns and
algebra are listed in the program
booklet you’ve received.
Take a few moments to read through
these big ideas.
Which of the Big Ideas do you think
our minds-on activity relates to?
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Big Ideas for Pattern & Algebra
Our minds-on activity relates to
both BI 1 and BI 5.
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Pattern: BI #1
• Patterns represent
identified regularities.
There is always an
element of repetition
that must be
described for the
pattern to be
extended.
• Patterns always
repeat and you have
to know how they
repeat to extend
them.
Pattern: BI #2
• Many ideas in other
strands of
mathematics are
simplified by using
patterns.
• You often use
patterns to learn
ideas about number,
geometry,
measurement, and
data.
Algebra: BI #3
• Algebraic reasoning is
a process of
describing and
analyzing generalized
mathematical
relationships and
change using words
and symbols.
• Algebraic reasoning
is a way to
understand
mathematical
relationships that
apply to a large
group of situations.
Pattern & Algebra: BI #4
• Different
representations of
relationships (e.g.
numeric, graphic,
geometric, algebraic,
verbal,
concrete/pictorial) or
patterns highlight
different
characteristics or
behaviours and serve
different purposes.
• Different
representations of
relationships or
patterns show
different things
about the
relationship and each
might be more useful
in a certain situation.
Pattern & Algebra: BI #5
• Comparing
mathematical
relationships or
patterns helps us see
that there are classes
of relationships or
patterns and provides
insight into each
member of the class.
• Comparing
mathematical
relationships or
patterns helps you
see that groups of
relationships can
behave in very
similar ways.
Pattern & Algebra: BI #6
• Limited information
about a mathematical
pattern or relationship
can sometimes, but
not always, allow us
to predict other
information about that
relationship.
• Sometimes knowing a
few things about a
pattern or
relationship allows
you to predict other
things about that
pattern or
relationship.
Getting a feel for the big ideas
• Two sets of questions will be
circulated that are designed to
bring out the big ideas.
• Choose one of those sets of
questions.
• Match each question to the big idea
it is most likely to elicit.
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Some questions about your task
• Which big idea did you find
easiest to match first?
• Which did you find hardest
to match first?
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Some questions about your task
• Which of the questions did
you like best? Why?
• What do you notice about
the question styles?
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Some questions about your task
• Why do you think it’s
important that students know
that pattern rules need to be
defined?
(Big Idea 1)
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Some questions about your task
• Can you think of other
instances where number,
geometry, measurement or
data topics are taught using
pattern concepts?
(Big Idea 2)
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Some questions about your task
• How do the questions that
matched Big Idea 3 show the
notion of generalization?
Analyzing relationships or
change?
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Some questions about your task
• How could the questions that
matched Big Idea 4 broaden a
student’s understanding of
the value of multiple
representations?
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Some questions about your task
• How could the questions that
matched Big Idea 5 help
broaden students’ ideas of
what kinds of relationships
there are?
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Some questions about your task
• Why do you think Big Idea 6
is a valuable one for student
focus?
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You just experienced…
a parallel task.
We will talk more about these,
but these two very related tasks
were adjusted to meet your
needs but treated together in
our consolidation.
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Sharing big ideas with
students..
• makes it easier for them to
make connections to prior
knowledge and to move
forward in new directions.
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Why use big ideas?
By thinking about the big ideas, it
becomes easier to develop
appropriate lesson goals and
appropriate consolidating
questions to bring them out.
35
Building lesson goals
You can use a big idea to hone in on
an appropriate lesson goal.
Topic
Expectations
Consolidating
Question
Big
Ideas
Goals
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Example:
Topic: Linear Relations
Expectation: Determine
other representations of a
linear relation, given one
representation.
BI 4: Different
representations of
relationships or patterns show
different things about them
and which is more useful
depends on the situation.
Consolidating Question
You have a graph of a linear relation
with x-values from -10 to +10
plotted. You want to know the
values of y for specific values of x.
For which values of x would you use
the graphical form? the algebraic
form?
Lesson Goal
Students will recognize
when a graphical model
is more useful and when
an algebraic one is.
Relationships Among Big Ideas,
Curriculum Expectations and
Lesson Goals
Curriculum Expectation:
Solve first degree equations with non-fraction coefficients using
a variety of tools (eg. 2x + 7 = 6x -1)
Task 1: You are given 3 lesson goals, 3 Big Ideas,
and 3 consolidating questions.
Determine which lesson goal connects to which Big
Idea for this expectation and identify the appropriate
consolidation question.
Solve first degree equations
• BI # 4
Different
representations…
• Students will
recognize that solving
an equation means
determining an
equivalent equation
where the solution is
more obvious
These equations are
equivalent:
X=4
2x – 7 = 1
3x + 7 = x + 15
it’s sure easier to see
the unknown value in
one of them.
Solve first degree equations
• BI # 4
Different representations…
• Students will recognize
that solving an equation
means determining an
equivalent equation
where the solution is
more obvious
Consolidation Question:
Agree or disagree.
The equation
5x – 4 = 17 + 3x
is really the equation
x = 10.5 in disguise,
just easier to solve.
OR
Why might someone say
that solving an equation
is about finding what
easier question is being
disguised?
Solve first degree equations
• BI # 6
…knowing a few things…
• Students will recognize
that solving an equation
means that you know
some information (an
output and a rule), so you
should be able to figure
out the other information
(the input)
Solve first degree equations
• BI # 6
…knowing a few things…
• Students will recognize
that solving an equation
means that you know
some information (an
output and a rule), so you
should be able to figure
out the other information
(the input)
• Consolidation Question
You know ONE of these two
things: x = 2y = 20 OR 3x
+ 2 = 20.
Which one lets you figure
out what x is? Why?
Solve first degree equations
• BI # 3
Algebraic reasoning is a
way to understand…
• Students will recognize
that solving an equation
means using the change
rule embedded in the
equation symbolically to
describe one specific
example of the effect of
the change
Solve first degree equations
• BI # 3
Algebraic reasoning is a
way to understand…
• Students will recognize
that solving an equation
means using the change
rule embedded in the
equation symbolically to
describe one specific
example of the effect of
the change
• Consolidation Question
A rule suggests that you
triple a number and
subtract if from 2. What
equation would you solve
to figure out the input if
you know the output is 5?
How would you solve it?
Relationship among
Expectations, Big Ideas,
Goals
Looking at the Posing Powerful
Questions Template (PPQT) as a
tool.
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Posing Powerful Questions
Goal(s)
• for a Specific Lesson
Curriculum Expectations:
Solve first degree equations with non-fraction coefficients
using a variety of tools (eg. 2x + 7 = 6x -1)
Big Idea(s) Addressed by the Expectations
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It’s so important…
Getting a goal clear in your
own mind can make a big
difference in increasing the
likelihood that students will
learn what you hope they will
learn.
47
• That includes knowing
why you have that goal. --What’s the point of it?
48
Why you want to do this…
If you decide on the goal, you
are more likely to know what
questions to ask, what activity
to use,….
49
Make it yours
Even if you get a lesson from
a valued resource, you have to
make your OWN decision
about what to pull out of that
lesson.
50
For example…
• Let’s look at this lesson
from Grade 7 TIPS.
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For example…
•Stated goals:
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If this is the goal..
Goal(s) for a Specific Lesson
Students will recognize when it’s useful to use generalization when describing a
pattern.
Curriculum Expectations
-Represent linear growing patterns, using a variety of tools and strategies
-Make predictions about linear growing patterns, through investigation, with
concrete materials
-Compare pattern rules that generate a pattern by adding or subtracting a
constant or multiply or dividing by a constant to get the next term with pattern
rules that use the term number to describe the general term
Big Idea(s) Addressed by the Expectations
Algebraic reasoning is a way to understand mathematical relationships that
apply to a large group of situations.
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Does the ‘Minds On’ need to be
adjusted? If so, how?
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Does the ‘Action’ need to be adjusted?
If so, how?
60
Does the ‘Consolidation’ need to be
adjusted? If so, how?
61
Maybe…
Consolidate/Debrief Sample Question(s)
Complete this statement:
The way someone figures out terms 3, 4, 5 and 6 might
be very different from the way that person figures out
term 100 because….
Here are several goals
The following stated goals were
taken from a series of lessons on
linear relations in a grade 9 text.
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• Represent a relation using a table of
values, a graph or an equation
• Identify direct and partial variations
• Identify properties of linear relations
• Represent a linear relation in a
different form
• Recognize whether a relation is linear
or nonlinear
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Task: Using the Posing
Questions Template
• With a partner, choose 1 of these
goals.
• Focus them to relate more explicitly
to one or more of the big ideas.
• Write a possible consolidating
question.
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Identify properties of linear relations
Goal(s) for a Specific Lesson
Students will recognize why any two points on a line can be
used to determine the slope and how that can be done.
Curriculum Expectations
Determine, through investigation, various formulas for the
slope of a line segment or a line and use the formulas to
determine the slope of a line segment or a line.
Big Idea(s) Addressed by the Expectations
Limited information about a mathematical relationship can
sometimes allow us to predict other information about that
relationship.
Possible Consolidation Question
Consolidate/Debrief Sample Question(s)
Use pictures, numbers, words, or graphs and explain why
it doesn’t matter if x-values are 1 apart or 2 apart or even
20 apart to calculate a slope.
Possible Consolidation Question
Consolidate/Debrief Sample Question(s)
Describe a situation that a linear relation would model.
Tell how to change one thing about it so that a linear
relation doesn’t work any more as a model.
Move to Breakout Rooms
Group A & B
(Liisa & Linda)
Room:
Group C & D
(Trish & Chris)
Room:
Small Group Norms
 We are all part of a learning
collective
 When speaking, address the whole
group
 Everyone has a voice
 Draw on your colleagues’ expertise
and offer your own
 Engage fully in the moment
Breakout: Group A & B
• Choose a patterning/algebra lesson
in the resource you brought.
• Work with a partner to rewrite a
lesson goal to focus on a ‘big idea’,
and write one or more consolidating
questions
• Use the PPQT to record all of your
thinking
71
Breakout: Group C & D
• Partner up (experienced vs new to
coaching)
• Select one of the lessons in the
PPQ template
• Practice providing feedback on
sample lesson goals and
consolidation questions
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Plenary: In Board Teams
• Provide and receive feedback on sample
lesson goals and consolidation questions
Suggested ‘To Do’ Between Session
A Mathematics Coaching Cycle
Establish norms for
working together
Professional Learning Protocols - Draft
•Starting Points for Building Supportive Coaching
Relationships
•Lesson Planning
•Teaching/Co-Teaching
•Post Lesson Debrief
Developing Classroom Protocols
View and Discuss Opportunities
Between Sessions
Coaching for Math GAINS
http://www.edugains.ca/newsite/math/coachformath.htm#Professional_Learning_
for_Mathematics_Leaders_and_Coaches_–_not_just_a_3_part_series_–_
Let’s consolidate
Walk over to someone you’ve not
talked to before.
• Share one idea that came up that
reinforces what you already do
when creating lesson goals.
Offer one idea that came up that might change how you create lesson goals.
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Exit Ticket
• 3 things I’ve learned during today’s
session…
• 2 questions I still have about today’s
session…
• 1 way I see this professional learning
experience impacting my work…
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