lsa: supporting the renewed math strategy (rms) supporting the renewed math...lsa: supporting the...

LSA: Supporting the

Renewed Math Strategy (RMS)Webinars

March 7th & April 3rd, 2017

Agenda

Shelley Yearley

Voices from the Field

Reflection and Discussion

Resources and Supports

LSA: Supporting the Renewed Math Strategy

Shelley Yearley

Provincial Mathematics Lead

TLDSB/on assignment with the Ontario Ministry of Education

@shelleyyearley

First Nations Peoples

12 000 BCE

10 000 BCE

8000 BCE

6000 BCE

4000 BCE

2000 BCE

0 2000 CE

today

Pyramids of Egypt

Machu Picchu

European ContactWheel

Invented

Earliest human

occupation of Southern

Ontario

More extensive

occupation of Eastern

Ontario

PART 1Improving Student Achievement: A discussion of strategies used

Four Key Objectives of the RMS

1. Increased student achievement, well-being and engagement

2. Increased educator math knowledge and pedagogical expertise

3. A. Increased leader use of knowledge of effective mathematics pedagogy

3. B. To provide the necessary supports and conditions for school and system improvement; and

4. Increased parent engagement in their children’s mathematics learning

An Overview of Our Discussion

Why Math?

Effective Models for PL

Deeper Math Knowledge

Why Focus on Mathematics?

The Importance of Mathematics

An information- and technology-based society requires individuals who are able to think critically about complex issues, analyse and adapt to new situations, solve problems of various kinds, and communicate their thinking effectively. …

To learn mathematics in a way that will serve them well throughout their lives, students need classroom experiences that help them develop mathematical understanding; learn important facts, skills, and procedures; develop the ability to apply the processes of mathematics; and acquire a positive attitude towards mathematics.

The Ontario Curriculum: Mathematics , Grades 1-8, p. 3

Why not the way we learned?

When we add or subtract fractions, we have to find a common denominator, but not when we multiply or divide. And once we get a common denominator, we add or subtract the numerators, but not the denominators, despite the fact that when we multiply, we multiply both the numerators and denominators, and when we divide, we divide neither the numerators nor the denominators.

(Siebert & Gaskin 2006, p. 394)

Based upon research by Dr. Cathy Bruce, Trent

University and Curriculum and Assessment Policy

Branch

Adding involves combining like units

Multiplication construed as repeated addition

Multiplication construed as arrays

Addition and subtraction are inverse operations as are multiplication and division

L6 3.7% (4.3 % in 2012; 2.4 % at level 6 in 2009)

L1 96.2% (96.4% in 2012)

Level 6: Complex Problem solving; Advanced reasoning; Mastery of symbolic and formal mathematical operations

Level 5: Integrated application of procedures and concepts

Level 2: “Fully Functioning in society”

Level 1: Carry out routine procedures according to instructions

PISA 2015

L2 85.7%

But What About Basic Skills?

PISA: Canadian Student Performance in Mathematics

• The mean score is one of the highest. (516 PISA Score, rank 10/69)

• Boys' performance is one of the highest. (520 PISA Score, rank 10/69)

• The percentage of low performers (below proficiency Level 2) is one of the lowest. (14.4 %, rank 61/69)

• The percentage of low-performing boys and girls (below proficiency Level 2) is one of the lowest. (14 %, rank 62/69; 14.7 %, rank 60/69)

• The percentage of top-performing boys and girls (proficiency Level 5 or 6) is one of the highest. (17.2 %, rank 10/69: 13 %, rank 10/69)

Why (continue to) Focus on Mathematics?

Deeper Math Knowledge

Characteristics of High-Quality Professional Learning

• Classroom-embedded

• Teacher directed

• Research-supported and content rich

• Cyclical/iterative

• Sustained

• Collaborative

Dr. Cathy Bruce

From Math CAMPPP 2012; Dr. Cathy Bruce

How does your current model of professional learning align with these characteristics?

Why Content?

Research indicates focusing on specific content has significant impact.

There are challenges:

• Important mathematics vs. important in the moment mathematics

•Connecting across grades and courses

• Instructional processes and policies may appear to be taking a back seat


How do we connect across grades?

1. Think about the structure of the mathematicsFor example, adding whole numbers requires understanding addition as combining quantities with like units, as does:•Adding measurements (2 cm + 3 cm) {Measurement}• Calculating perimeter (P = 2 x 2cm + 2 x 3 cm)

{Geometry and Spatial Sense}• Building a growing pattern (total tiles = 2 x term

number + 4 [unit is tiles]) {Patterning and Algebra}• Solving missing quantity questions (5 - ? = 3)

{Patterning and Algebra}• Representing data using a graph (unit might be person

surveyed) {Data Management and Probability}• Considering the complement of an event in probability

(40% chance of winning so 60% chance of not winning) {Data Management and Probability}

How do we connect across grades?

2. Think about the structure of the curriculum

For example, addition of numbers is included from grades 1 through 6 as an overall expectation for Number Sense and Numeration which states:By the end of Grade __, students will:Solve problems involving the addition and subtraction of ____ numbers, using a variety of strategiesFor Grades 7 and 8, it becomes:Apply a variety of computational strategies to solve problems

Note that addition is also reflected in the expectations for the other strands, particularly Patterning and Algebra Grade 3 states: demonstrate an understanding of equality between pairs of expressions, using addition and subtraction…

Addition and Subtraction

Key components and models include:

• composing and decomposing number

• placing numbers on the number line

• estimation and proportional reasoning

• judging reasonableness of answer

K 8 12Whole Number

Whole NumberDecimal Numbers

Decimal NumbersFractions

Fractions

Informal

Formal

Percents

Percents

Algebraic Expressions

Algebraic Expressions

Measurement

DRAFT VISUAL

Let’s Compose Numbers

• Let's count apples

• Let's count buttons

• Let's count litres

• Let's count half litres

• Let's count y's

• We could also call this unit counting. We can count by any unit. We can compose and decompose any quantity of units.

y y y

Unit Thinking is PowerfulIt allows students to connect their understanding of operations across number systems.

Foods2 cups + 3 cups 2

cup units+ 3 cup units5 cup units= 5 cups

Technology2 inches + 3 inches 2

inch units+ 3 inch units5 inch units= 5 inches

Don’t be Afraid to Select One Topic

Focus on one topic allows educators to:

•Deeply understand the mathematics

• See connections across mathematics topics

• Practice pedagogy

• Collect data of impact of shifts in practice

• Build their own efficacy

• See impact of strategies on student achievement

Effective Professional Learning

Characteristics of High-Quality Professional Learning

•Classroom-embedded

•Teacher directed

•Research-supported and content rich

•Cyclical/iterative

•Sustained

•Collaborative

Dr. Cathy Bruce


Big Challenge: Facilitating math when you don’t know it all

Complexities of facilitating math - no simple or quick solutions

It is easier with:

(i) in-between session learning

(ii) sustained team inquiry

(iii) content focus that moves beyond surface learning

(iv) Networking with your context/site and across sites

Remember to honour people who are not particularly strong in math; for that person inquiry involves risk-taking and learning stance. None of us know it all…


One Model for Sustained Professional Learning

•Board Level PL

•Single Content Focus

•Deepen Content Knowledge

•Examining Student Thinking

•Pre-Assessment

School Based PL

Moderated Marking

Planning in Response to Student Need

•Board Level PL•Deepen Content Knowledge•Examining Student Thinking

School Based PL

Reflecting on Tasks


•Board Level PL



•Post-Assessment

School Based PL

Reflecting on Tasks

Moderated Marking


coaching

coaching

• At <<my school>> this year I have seen some interesting things occurring as a result of our

move away from reliance on one particular resource that had in my opinion a very narrow

scope, limited largely to memorizing procedural “tricks” to gain fluency with algorithms. A

previous focus on this resource limited our teachers’ opportunity to see where students may

have been struggling with conceptual understanding – the work that they were doing just

didn’t offer the opportunity for them to demonstrate it.…

• I’m seeing my staff diversify their instructional approaches and provide a more balanced

approach to learning opportunities for students, which include not only work with algorithms,

but also opportunities to explore concepts through open-ended problem solving, through the

use of manipulatives, through discussion of the students’ own work, and so on.

• Every one of my classroom teachers is involved in system level professional learning in

numeracy this year…. Now when I hear teachers talk about the work students are doing in

math (or perhaps suffice it to say “I now hear teachers talking about what their students are

doing in math”) they are talking about the assets and challenges for students that have been

uncovered as a result of them being able to see and hear some of the students’ thinking. The

closed tasks … just weren’t providing the opportunity to teachers to see or hear students

thinking.

• While we have a long way to go to gain a deeper understanding of those areas, it has been

exciting to find the space in which to consider them.

School Principal

A Model of Mathematics Leadership

•Family of Schools Collaborative Action Research

•Single Content Focus



•Pre-Assessment

Staff Meetings

Content-based activity



•Examining Student Thinking in classrooms

•Plan next steps

Staff Meetings




•Examining Student Thinking in classrooms

•Plan next steps

Staff Meetings


monitoring

monitoring

And on for a total of 6 CAR meetings

I was so glad you called and invited me and two of my teachers to participate in the (research) work you are doing this year. I loved my involvement in the past. What a great capacity building opportunity for me. I will share with you that I took the activities we did with students (in the previous research project) and did at least one of them every staff meeting. It was amazing to see the staff engage in math learning and having fun at it. My staff was very appreciative of the opportunity to build their capacity around (content). So excited to be involved again.

School Principal

(Content) doesn’t make me feel nauseous anymore!

Punctuated Learning…

Based upon research by Dr. Cathy Bruce, Trent University and Curriculum and Assessment Policy Branch

Punctuated Instruction Map for Grade 5/6Created by Ontario Classroom Teachers

Based on research with Dr. Cathy Bruce and the Curriculum and Assessment Policy Branch

DRAFT

33

Reflect and Discuss

Take a few minutes to reflect on what you have heard.

Discuss in your teams your thoughts and what impact

this might have on your work in Math.

Share your ideas and questions in the chat window.

Voices from the Field

Reciprocal Teaching for Math

How Can Reciprocal Teaching Improve

Success for Math?

Presented by:

Chad Warren, Principal, CWDHS

Lynne Vink, Co-Head of Math & C.S., CWDHS

RMS Secondary Teacher Lead, UGDSB

Luke Kordupel, Intermediate Math Teacher, John Black P.S.

Reciprocal Teaching

Reciprocal teaching is a cooperative

instructional strategy originally used for

reading comprehension

Why? Students struggled with retention

and connecting previous learning

Hattie’s analysis ranks reciprocal teaching

within the top influences on student

achievement

Students support each other and increase

willingness to take risks in math situations

Everybody Solves

→ Each student solves the problem

independently using their choice(s) of strategy

Everybody Shares

→ Group members take turns sharing their

solutions and providing their individualized

solutions

These role

cards were

created for

grade 7/8

students

but can be

simplified

for

younger

students

Activity: Getting to Know the

Roles

Each person selects a role

Take a few minutes to carefully read about

the role

In ten words or less, identify the main

responsibility/responsibilities of the role

Share your summary in the appropriate chat

window

Implementing Reciprocal Teaching

▶ Process of introducing it to a class

▶ Importance of establishing group norms

▶ Meeting the needs of students with

modified programs

▶ Data collection

Learnings

Findings from data

Challenges of implementation

Slowing down the process

Teacher buy-in

St. Andrew Catholic School

St. Andrew Catholic School is located in the North

Rexdale section of Toronto. Approximately 75% of our

students come from the Middle East and speak Assyrian

and/or Arabic. For many of these students, St. Andrew

provides their first formal schooling experience.

Approximately 20% of our students hail from Nigeria and

Ghana and many of these students are also refugees

with limited schooling. The final 5% of our students

represent a smattering of various ethnicities and

cultures.

We are a vibrant and colourful community!

Debby Culotta, Principal

Monica Rohel, Vice-Principal

Math Study Groups

Pre-primary focus: Geometry and Spatial Sense

Primary/Junior focus: Proportional Reasoning

Intermediate Focus: Number Sense/Proportional

Reasoning

5 sessions per division beginning in October and

ending in April

Focus on building teacher content knowledge; study

relevant research; teachers do the math; analysis

of student work; co-planning and co-teaching

Moderated marking of released EQAO questions

Student Led learning Walk

Visual learning trajectory of a specific

curriculum expectation in mathematics with

student work, learning goals and success criteria

Family Math Sessions

Three Sessions of Family Math (preprimary, primary and

junior)

Student leaders to help facilitate the activities

P and VP circulate to monitor parent

engagement/learning

Math Facilitator

Co-planning, co-teaching with grade 4

teachers(teacher questioning, building math

content knowledge of teachers, co-creation

of success criteria)

Assessment design and moderated marking

with teachers

Gap closing with small group of grade 3

students

Co-planning of math study groups for

preprimary, primary and junior groups

Monitoring grade 4 student achievement with

a focus on problem-solving and application

School Wide Monitoring

Thrice yearly, for the past three years, Grade

1-8 students answer an equality question to

assess whether our focus on understanding

equivalency has transferred to our students

Year 2014-

2015

November

19%

February

49%

May 60%

Year 2015-2016 November 59% February 60% May 67%

Year 2016-2017 October 70% February 72%

Classifying

Quadrilaterals

Pre (Released EQAO

Questions)

Post (Released

EQAO Questions)

Grade 4 Class 1 59% 95%

Grade 4 Class 2 52% 71%

Data Management

Class 1 40 80

Class 2 40 66

Reflect & Discuss

Take a few minutes to reflect on what you have heard.

Discuss in your teams your thoughts and what impact

this might have on your work in Math.

Share your ideas and questions in the chat window.

Supports for Leading Professional Learning

Mathematics Knowledge for Teaching

An Overview of Our Discussion

Leadership for Learning

Supports for PL

Monitoring

Math for Leading Collaborative Inquiry

• What do teachers need to know and be able to do to effectively carry out the work of teaching mathematics? (Ball, Hill, & Bass, 2005)

• What do leaders need to know and be able to do to effectively carry out the work of leading mathematics?

Danielle BlairSandra FraserConnie Quadrini

From Danielle Blair, Provincial Mathematics Lead

Leadership

Leadership Content Knowledge

The knowledge of a subject that enables you to help others get better at the teaching of the

subject.

Leadership for Learning• Recognizes and values that leadership

is shared• Prioritizes the importance of reflection

– individual and the collective• Enhances the collective growth mind-

set in the service of student achievement and well-being

• Influences, motivates and inspires


Effect Size of Action of School Leaders

Establishing goals and expectations

Strategic resourcing

Planning, coordinating and evaluating curriculum

Promoting and taking part in teacher learning

Ensuring an orderly and supportive environment

ES = 0.42

ES = 0.31

ES = 0.42

ES = 0.84

ES = 0.27

Robinson et al. (2008, p. 657)


Principals report that they have increased clarity with:• how the use of the tiles “revealed the math thinking”

and how, as leaders, we need to experience the math dissonance ourselves to really “get it” in a deeper way. As a leader I am more equipped to have learning conversations with teachers regarding the use of manipulatives as tools to represent thinking. The continuum of learning is varied and a leader and a teacher must have that specific, specialized content knowledge in order to move students to the next step in their thinking.

• [that] it is OK to do questions more than once with the same group of students.

• [the way that increased math knowledge allows me to recognize] evidence of effective teaching and learning in classrooms.

Monitoring Impact

Based upon research by Dr. Cathy Bruce, Trent University and Curriculum and Assessment Policy

Branch

Year 1 Research Findings: Punctuated Instruction

SampleData Set

Year 3: Grade 4 PD Outcomes

Based upon research by Dr. Cathy Bruce, Trent University and one district school board.

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Pre Mean

Post Mean

All classesPre: 5.26Post: 11.14

What Students Said About Punctuated Fractions Instruction

• One teacher asked her 19 grade 4 students:

• Did you like learning math this way?• 2 students said no• 1 student’s response was unclear• 16 students said yes

Student A:I do not like learning math when one week we do this

and the other week we that. I like doing math when we do

1 part at a time.

Student B:I like learning math this was because we’re not just learning one specific thing at one time, we’re learning a bunch of things together. This is a easier and more fun way of learning. I have definitely learned a lot more that way.

Student C:I do not like learning this way, I love it because it makes me focus on more than one thing. It also helps me by if I do one unit at a time I might forget it or what we are learning.

Supports for Professional Learning

Available Professional Learning Resources

Mathematics Content•Algebraic Reasoning•Proportional Reasoning• Fractions• Spatial Reasoning

Classroom Dynamics•Set-up•Management•Relationships

Professional Learning

Facilitation

Supporting Students with LD

in Math

Mathematical Knowledge for Teaching Adobe Connect Single Sessions

• Algebraic Reasoning: Functional Thinking

• Fractions: Ways We Use Fractions

• Fractions: Unit Fractions

• Proportional Reasoning: Absolute and Relative Thinking

• Engaging Students with the mathies Learning Tools

• TIPS4Math Blended Learning: Using the Virtual Learning Environment

• TIPS4Math Blended Learning: Grades 4 to 6

• TIPS4Math Blended Learning: Grades 7 and 8

• TIPS4Math Blended Learning: Grade 9 Applied

66

Session Resources

•A prepared, scripted PowerPoint presentation

•A detailed presentation guide including:•overview• learning activities•Questions to Stimulate Conversation•Aha moments•materials list•Adaptations to different time lengths

•Prepared Blackline Masters, videos and student work samples

Scripted PPT

Presentation Guide -Overview

Presentation Guide –Details

Presentation Guide –Adaptations

Mathematical Knowledge for Teaching: Adobe Connect 4-Part Series

•Operation Sense: From Arithmetic to Algebra

•Building Number Sense in the Early Years

•Measurement

•Spatial Reasoning

72

Facilitation Adobe Connect Sessions

Implementing the Professional Learning Modules

• Algebraic Reasoning: Functional Thinking

• Fractions: Ways We Use Fractions

• Fractions: Unit Fractions

• Proportional Reasoning: Absolute and Relative Thinking

• Classroom Dynamics (includes Classroom Management, Classroom Set-Up and Relationships for Learning)

Access the modules at edugains.ca (soon)

Thank You!

[email protected]

@shelleyyearley

mailto:[email protected]

LSA Resources and Supports

LSA District Facilitators

Symposium

Tuesday, April 25, 2017: 8:30am-3:30pm (Toronto Airport

Marriott)

System Leader Session - Monday, April 24, 2017: 3:00pm-5:00pm

(Toronto Airport Marriott)

The Learning Exchange – thelearningexchange.ca

LSA Website – http://lsaontario.org

http://www.thelearningexchange.ca/

http://lsaontario.org/

Thank You!

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