Coaching for Math GAINSProfessional Learning

Initial Steps in Math Coaching

How going SLOWLY will help you to make significant GAINS FAST.

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

Overview of the Session

Clarify your personal image of what being a mathematics

coach involves.

View some examples of the math coaching process in

action.

Practise being a math coach in a safe environment

through role play.

Identify some next steps for yourself.

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?

Initial Meeting

Coaching Strategies and Stems• Paraphrasing• 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 • 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• 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

Examples

Non-examples

Coaching

The Non-negotiables

"What coaching is not"• • •

Your coaching duties do not include …•

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

(Fosnot, 2002)

• Discuss with a partner any new thoughts about coaching.

• Re-visit and revise your Frayer model.

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 Precisionwww.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

May 2008

September 2008

2006

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

DifferentiatingResponding

Fearless listening and speaking

Differentiating Mathematics Instruction

Questioning to Evoke and Expose Thinking

Materials adapted from Dr. Marian Small’s presentation August 2008

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.

22

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?

23

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.]

24

Differences in IntentDo 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?

25

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.

26

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?

Possible responses

• x = 1

• y = 0

• y = x- 1

• y = x2 - 1

• y = x3 - 1

• y = 3x2 -2x -1

28

(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.

Possibilities

• 12 + 12 + …. + 12 (88 of them)

• 22 + 22 + … + 22 (22 of them)

• 52 + 52+ 52+ 22 + 22 + 22 + 12

• 52 + 62+ 33

34

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?

35

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.

36

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?

The Processes

• Problem solving

• Reasoning and proving

• Reflecting

• Selecting tools and strategies

• Connecting

• Representing

• Communicating

41

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

42