Day 1

Professional Learning for Mathematics Leaders and

Coaches—Not just a 3-part series

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?

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• How could you convince someone the pattern grows slowly?

Characteristics of Minds-On

• How does this minds-on engage students?

• How is it open?

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Minds-OnA linear growing pattern starts at -10 and grows very slowly. What might the pattern be?

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What do you think the important underlying math idea is?

Minds-On

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•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…

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•Context matters in deciding how fast a pattern grows because…

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.

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• It provides a lens in which to embed new learning.

Big Ideas for Pattern & AlgebraA 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.

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Which of the Big Ideas do you think our minds-on activity relates to?

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)28

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.

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Building lesson goals

You can use a big idea to hone in on an appropriate lesson goal.

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Topic

Expectations

Goals

Big Ideas

Consolidating Question

Example:

Students will recognize when a graphical model is more useful and when an algebraic one is.

Topic: Linear RelationsExpectation: 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.

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

Consolidating Question

Relationships Among Big Ideas, Curriculum Expectations and

Lesson GoalsCurriculum 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 # 4Different

representations…

• Students will recognize that solving an equation means determining an equivalent equation where the solution is more obvious

These equations are equivalent:

X = 42x – 7 = 13x + 7 = x + 15

it’s sure easier to see the unknown value in one of them.

Solve first degree equations• BI # 4Different 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.

ORWhy 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 # 3Algebraic 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 # 3Algebraic 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 QuestionA 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•

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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

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.

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• That includes knowing why you have that goal. --- What’s the point of it?

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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,….

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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.

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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..

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Goal(s) for a Specific Lesson

Students will recognize when it’s useful to use generalization when describing a pattern.

Big Idea(s) Addressed by the Expectations

Algebraic reasoning is a way to understand mathematical relationships that apply to a large group of situations.

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

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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?

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Does the ‘Consolidation’ need to be adjusted? If so, how?

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. 65

Identify properties of linear relationsGoal(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

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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

http://www.edugains.ca/newsite/math/coachformath.htm#Professional_Learning_for_Mathematics_Leaders_and_Coaches_–_not_just_a_3_part_series_–_

Coaching for Math GAINS

Let’s consolidate

Walk over to someone you’ve not talked to before.

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• 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.

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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