Coaching for Math GAINS

Peel Co-Teaching Project

Anchor Session #2

April 1, 2010

Reviewing our Norms

• Start and end on time.

• Contribute to a safe learning environment that encourages risk taking; be kind.

• Listen actively; speak fearlessly.

• Invest in your own learning and the learning of others.

• All electronic communication devices off except during lunch/break.

• Suffering is optional!

Overview of the Morning1. Welcome

2. Responding to Feedback

3. How well have you been listening?

4. Sharing your journey

5. Mathematics as a social activity

6. Is your locker open?

7. Common Questions … consolidating questions for parallel tasks

We were listening …• Working on open & parallel tasks• Time to dialogue and plan with

colleagues• Logistics … how do we make it work?• Opening up my classroom to others• Purpose of Math GAINS project

Ministry perspective Peel perspective What the research says

• Making sense of the "Big Ideas"

Peel Perspective - Math GAINS Project Facilitated co-teaching activities topromote job-embedded professional

learning opportunities related to supporting the implementation of the

ongoing priorities and initiatives of the Peel District School Board

These include, but are not limited to the following –

Peel Perspective - Math GAINS

Project • Transformational Practices• School Success Planning• Differentiated Instruction• Cross-Panel Connections• Student Success / Learning to 18• Transitions (Grade, Panel, Course)• Report Card for Student Success• Alternative Programs

Research Foundation for PD

Context• Providing sufficient time;

• Engaging external expertise;

• Engaging teachers in the learning process;

• Challenging discourses;

• Providing opportunities to interact in a community of professionals.

Math GAINS• Eight release days;

• Math Coach;

• Teachers working together in school teams and working cross-panel;

• Rethinking our approach to teaching math;

• Co-planning days, anchor sessions and debriefing after demonstration lessons.

Research Foundation for PD

Content• Different aspects of

content are integrated;

• Clear links made between teaching and learning and student teacher relationships;

• Assessment is used as a focus;

• Sustainability of improved student outcomes.

Math GAINS• Big ideas, questioning, group

work skills and problem solving;

• How we teach math impacts on how well students learn and we can connect through more engaging tasks;

• Formative assessment using open and parallel tasks;

• Students can continue to improve.

Research Foundation for PD

Activities• Content and activities

aligned;

• A variety of activities needed;

• Professional instruction sequenced;

• Understandings discussed and negotiated.

Math GAINS• Developing then trying

open or parallel tasks;

• Different tasks, grades and strands covered;

• Modelling, co-planning then teaching

• Active discussion with colleagues of what works for students.

Research Foundation for PD

Learning Processes• Substantive change is

difficult;

• Some new understandings are consistent with current thinking and some are inconsistent;

• Teachers can learn to regulate their own learning.

Math GAINS• Trying questions together;

• Some tasks are similar to what we have done before, some are a new approach, with support see what works for students

• Begin to use questioning in other lessons if it supports student understanding.

How well have you been listening?

• We spend a great deal of time talking about questioning.

• How effective some of our questions will be, really depends on how well we listen to our students.

• The more we listen … the more our role will evolve from "Stand & Deliver" to …

Impress Me!As you watch this video, please consider the following questions:

1. How does the participating teacher describe her usual classroom practice?

2. What is new/different for the teacher and her students in this lesson?

3. How do the students respond to the lesson approach?

4. What observations/reflections does the teacher share in the lesson debriefing?

5. How does your co-teaching experience compare with this example?

Self Reflection

“What can I add to my practice to help

students understand the concepts I am teaching more deeply?”

A big idea of co-teaching is to reflect on your current classroom practice, whatever that may be, and ask:

“How will I know if my changes arehaving a positive impact on my students?”

Sharing Your Experience

Each person in your team will go to a different location.

With the other people at your location, form an inside/outside circle.

Each "inside" person will start. Choose one question to ask from the following list. Take turns.

Sharing Your Experience• What was the focus of the lesson that was co-

planned? How was the lesson delivered? What was the most valuable feedback from the debrief?

• How did your students react to the lesson? How did they feel about all of the observers present?

• The biggest surprise of co-teaching is …

• A change in your practice that has resulted from your involvement in the GAINS project is …

Math as a Social Activity

As you watch this video clip, record the steps the teacher takes to create the learning environment he wants for his students.

Break Time!

There are 1000 lockers in the long hall of the Peel District High School. In preparation for the beginning of school, the janitor cleans the lockers and paints fresh numbers on the locker doors. The lockers are numbered from 1 to 1000.

The Locker Problem

The Locker Problem … continued In your family of schools team, identify

3 people who will act as observers. The remaining team members will work

on the problem in "the fishbowl". They may divide themselves up into smaller groups if they wish to.

Send one of the observers to the materials table to collect the forms they will use to record their observations.

The Locker Problem … continued Explore the problem in your groups.

Various manipulatives are available for use from the materials table.

Record your findings on chart paper. Be sure to explain the mathematics

that will justify why your answer is correct.

The Locker Problem … continuedWhen the school's 1000 students return from summer vacation, they decide to celebrate the beginning of the school year by working off some energy.

Student #1: opens every locker.

Student #2: starts at locker #2 and closes every 2nd locker.

Student #3: starts at locker #3 and opens or closes every 3rd locker.

This process continues ... until all 1000 students have entered the school.

Which locker doors are open once every student has arrived?

Consolidation of the Locker Problem

Life in the Fishbowl observers share their observations with their team members

Presentation of Solutions a math congress

Parallel Tasks Revisited

Focusing Our Lens on

Common Questions

Possible Lesson Goals

• Find the distance from a point to a line segment

AND / OR

• Apply the geometric properties of circles, midpoints, line segments, and perpendicular lines to the real world

Consider this example:

The diagram shows the locations of Katie’s, Krista’s and A.J.’s homes.

The Parallel Tasks

Option 1 A. J. and Krista want to meet somewhere that is equally distant from each of their homes. Where could they meet?

Option 2

Katie, Krista, and A. J. want to meetsomewhere that is equally distant from all three of their homes. Where could they meet?

OR

Possible Tools

• GSP • Grid paper• Rulers• Soft measuring tapes and/or string

The Solutions

Option 1There are actually many solutions to Option 1.

All the points on the perpendicular that meets the middle of the line segment between A.J.’s and Krista’s house are equally distant from each house.

The Solutions

Option 14

3

2

1

-1

2 4 6 8

Krista

AJ

Katie

The Solutions

Option 2There is only one solution to Option 2.

Students need to find the single point at the centre of the circle that passes through all three of the points representing the locations of the homes.

The Solutions

Option 2

Meeting Student Needs

• The first option allows students the opportunity to apply their knowledge of lines to solve a real life problem.

• The second option allows those students needing a challenge the opportunity to apply their knowledge of lines and circles to solve a real life problem.

Other Variations

• Choose points with positive coordinates for students who struggle with integer calculations, and points with negative coordinates for those who do not.

• Choose points with whole number coordinates for students who struggle with fractions or decimals, and fractional coordinates for students who do not.

Common Questions

Whichever task the students complete, the teacher could ask:

How did you find the meeting spot? Is there another way to solve the problem? What tools did you use to help you?Is there more than one possible meeting spot? How do you know?How could you verify your meeting spot is equally distant from all three homes?

Principles to Keep in Mind

• Parallel tasks need to be created with variations that allow struggling students to be successful and proficient students to be challenged (consider common student stumbling blocks when creating your tasks).

• The tasks and common questions should be constructed in such a way that will allow all students to participate together in follow-up discussions.

Consolidating Questions

Consolidating questions can be used to tie big ideas together at the end of a lesson or activity.

Common questions can serve as consolidating questions when the main activity of a lesson has been a parallel task.

Your Turn!

There are six different parallel tasks at your table.

1. Work in groups of 2 or 3.2. Choose a task.3. Solve the problem. 4. List student stumbling blocks that

might be addressed by offering each choice.

5. List common questions that could be asked of all students at the end of the task.

6. Record your work on chart paper, and post according to tasks.

Welcome Back!

Effective teaching involves risk taking … by both the teacher and the student.

Overview of the Afternoon1. Connecting Big Ideas with

Expectations and Lesson Goals

2. Consolidating Questions

3. Time to Practice & Share

4. A Few Words About Logistics

5. Group Communication: SharePoint

Relationship among Expectations, Big Ideas, &

Lesson Goals

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Topic

Expectations

Goals

Big Ideas

Relationship among Expectations, Big Ideas, &

Lesson Goals

48

Sometimes you can reframe the big ideas for your topic. For example, a trig big idea might be:

Relationship among Expectations, Big Ideas, &

Lesson Goals

49

Limited information about a periodic relationship can

sometimes, but not always, reveal other information about

that relationship.

Or…

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When a relationship appears to be periodic in nature, then it is

appropriate to consider a trigonometric function to model

the relationship.

Relationship among Expectations, Big Ideas, and

Lesson Goals

We will use the Posing Powerful Questions Template (PPQT) as a tool.

51

An Example …

Curriculum ExpectationsDetermine other representations of a linear relation, given one representation.

Big Idea(s) Addressed by the Expectations

Goal(s) for a Specific Lesson

Lesson Title: Grade/Program: 7

What Big Idea is being Addressed?

Most likely BI 4

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List the Big Idea(s) …

Curriculum ExpectationsDetermine other representations of a linear relation, given one representation.

Big Idea(s) Addressed by the ExpectationsDifferent representations of relationships or patterns show different things about them and which is more useful depends on the situation.

Goal(s) for a Specific Lesson

Lesson Title: Grade/Program: 7

Create Your Lesson Goal

Curriculum ExpectationsDetermine other representations of a linear relation, given one representation.

Big Idea(s) Addressed by the ExpectationsDifferent representations of relationships or patterns show different things about them and which is more useful depends on the situation.

Goal(s) for a Specific LessonStudents will recognize when a graphical model is more useful and when an algebraic one is more useful.

Lesson Title: Grade/Program: 7

What does this mean for consolidating the lesson?

You need to ask a question or two that gets RIGHT to your goal.

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A Consolidation Question Might be:

Goal(s) for a Specific LessonStudents will recognize when a graphical model is more useful and when an algebraic one is.

Big Idea(s) Addressed by the ExpectationsDifferent representations of relationships or patterns show different things about them and which is more useful depends on the situation.

Curriculum ExpectationsDetermine other representations of a linear relation, given one representation.

Lesson Title: Grade/Program: 7

Consolidate/Debrief Sample Question(s)You have a graph 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? For which values of x would you use the algebraic form?

Another Example

Consider the expectation: “Solve first degree equations with non-fractional coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1)…”

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Another Example…

Which big idea do you think it most closely relates to?

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Another Example…

You might have picked

BI 4

thinking that solving an equation means representing it

in a different, easier to recognize form.

60

Another Example…

You might have picked

BI 6

thinking that you had some information that could give you

other information.

61

Another Example…

You might have picked

BI 3

thinking that an equation is a way to describe a change and

solving it is just about “undoing” the change.

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What might the lesson goal be?

Your lesson goal should be informed by which of those big

ideas you want to focus on.

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Option #1

Curriculum ExpectationsSolve first degree equations with non-fraction coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1).

Big Idea(s) Addressed by the ExpectationsDifferent representations of relationships or patterns show different things about them and which is more useful depends on the situation.

Goal(s) for a Specific LessonStudents will recognize that solving an equation means determining an equivalent equation where the solution is more obvious.

Lesson Title: Grade/Program: 7

To clarify what this means …

These equations are equivalent:

x = 4

2x – 7 = 1

3x + 7 = x + 15

But, it's sure easier to see the unknown in one of them!

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Option #1

Goal(s) for a Specific LessonStudents will recognize that solving an equation means determining an equivalent equation where the solution is more obvious.

Big Idea(s) Addressed by the ExpectationsDifferent representations of relationships or patterns show different things about them and which is more useful depends on the situation.

Curriculum ExpectationsSolve first degree equations with non-fraction coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1).

Lesson Title: Grade/Program: 7

Consolidate/Debrief Sample Question(s)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 equation is being disguised?

Option #2

Curriculum ExpectationsSolve first degree equations with non-fraction coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1).

Big Idea(s) Addressed by the ExpectationsSometimes knowing a few things about a pattern or relationship allows you to predict other things about that pattern or relationship.

Goal(s) for a Specific LessonStudents 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).

Lesson Title: Grade/Program: 7

Option #2

Goal(s) for a Specific LessonStudents 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).

Big Idea(s) Addressed by the ExpectationsSometimes knowing a few things about a pattern or relationship allows you to predict other things about that pattern or relationship.

Curriculum ExpectationsSolve first degree equations with non-fraction coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1).

Lesson Title: Grade/Program: 7

Consolidate/Debrief Sample Question(s)You know one of these two things: x + 2y = 20 OR 3x + 2 = 20

Which one lets you figure out what the value of x is? Why?

Option #3

Curriculum ExpectationsSolve first degree equations with non-fraction coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1).

Big Idea(s) Addressed by the ExpectationsAlgebraic reasoning is a process of describing and analyzinggeneralized mathematical relationships and change using wordsand symbols.

Goal(s) for a Specific LessonStudents 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.

Lesson Title: Grade/Program: 7

Option #3

Goal(s) for a Specific LessonStudents 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.

Big Idea(s) Addressed by the ExpectationsAlgebraic reasoning is a process of describing and analyzinggeneralized mathematical relationships and change using wordsand symbols.

Curriculum ExpectationsSolve first degree equations with non-fraction coefficients using a variety of tools (e.g. 2x + 7 = 6x – 1).

Lesson Title: Grade/Program: 7

Consolidate/Debrief Sample Question(s)A change rule suggests that you triple a number and add then 2 to it. What equation would you solve to find the input, if you know the output is 23? How would you solve it?

What's Really Important is …

getting a goal clear in your own mind. This 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.

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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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Now…

Choose a lesson in a resource that you brought.

OR

Choose one of the PPQT lesson outlines on your table.

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Let’s consolidate• Find a partner that you have not worked with before.

• Work with your partner to restate the goal to focus more clearly on a big idea.

• Write a consolidating question to match your goal.

• Share what you've done with the other members of your team. 75

Here's Your Challenge

With a partner, choose 1 or 2 of these goals.

Focus them to relate more explicitly to one or more of the big ideas.

Write consolidating questions to match your goal.

Use the PPQT to record all of your thinking. 76

Consider These Lesson Goals1. Represent a relation using a table of values,

a graph or an equation.

2. Identify direct and partial variations.

3. Identify properties of linear relations.

4. Represent a linear relation in a different form.

5. Recognize whether a relation is linear or nonlinear.

77The preceding stated goals were taken from a series of lessons on linear relations in a grade 9 text.

Logistics - Math GAINS Project • PAM Code 59 is to be used to book supply

coverage for any release time related to this project

• when using PAM Code 59, please provide Krystal Wilson and Alan Jones with relevant details and information (who, when, where, what)

<names of teachers> from <name of school> will be attending a co-planning session at <name of host school> on <date of co-planning session>

Logistics - Math GAINS Project

• up to 10% of our overall funding allocation may be used to purchase resources to support the co-teaching activities

• approximately $1000 is available for each school involved in the project to purchase instructional and professional resources

• possible resources include thinking tools such as manipulatives and technology, and/or professional resources to support questioning, big ideas, differentiated instruction, etc.

• completed purchase orders are to be submitted to Krystal Wilson and Alan Jones

SharePoint

Thank you.

Don’t forget your homework!