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Leaders in Education Thought: Mathematics K-12 – Audio Only

Who Makes the Biggest Impact?

Vocabulary in a Mathematics Classroom

Mars Mission – Grade 6 Knowledge Building Experience

Sarah Greenwald – We All Have the Capability

Sarah Greenwald – Connecting Interests

Sarah Greenwald – Pop Culture in the Classroom

Sarah Greenwald – Bringing Humour to Math Learning

Steven Strogatz – The Math in Six Degrees of Separation

Steven Strogatz – Using Math to Explain Coincidence

Steven Strogatz – Teachers as Perpetual Learners

Steven Strogatz – Making Math Exciting for Everyone

Steven Strogatz – Math is Creativity

Steven Strogatz – Making Math Meaningful

Nathalie Sinclair – Mathematics and Infinity

Nathalie Sinclair – Geometric Problem-Solving

Nathalie Sinclair – Dynamic Geometry

Nathalie Sinclair – Visual Learning

Nathalie Sinclair – Student Engagement

Nathalie Sinclair – Resources for Teachers

Nathalie Sinclair – Improving Media Messaging

Ruth Beatty – Moving Forward

Ruth Beatty – Thinking About Math and Culture

Ruth Beatty – Uncovering Opportunities for Math Learning

Lisa Lunney Borden – Authentic Learning

Lisa Lunney Borden – Honouring and Embracing Indigenous Knowledge

Lisa Lunney Borden – Conceptual Understanding of Mathematics

Lisa Lunney Borden – Creating a Sense of Belonging

Lisa Lunney Borden – The Importance of Language

Lisa Lunney Borden – Integration of Culture in the Classroom

Lisa Lunney Borden – Building Better Relationships

Lisa Lunney Borden – Connecting Mathematical Learning in the Classroom

Marian Small – Visual Representations

Marian Small – Math Anxiety

Marian Small – Big Ideas

Alex Lawson – Constructing a Math Environment

Alex Lawson – The Continuum of Instructional Strategies

Alex Lawson – Moving to Numerical Proficiency

Alex Lawson – Building Math Strategies

Cathy Bruce – Engagement in Mathematics

Cathy Bruce – Partners in Math Teaching

Cathy Bruce – Fractions Learning Pathway

Chris Suurtamm – Math Assessment

Chris Suurtamm – Algebraic Thinking

Chris Suurtamm – Enhancements in Learning

Chris Suurtamm – Math and the Media

Chris Suurtamm – Supporting Teachers

Connie Quadrini – Concrete and Digital Learning Tools

Connie Quadrini – Students with Learning Disabilities

Connie Quadrini – Math Knowledge for Teaching

Connie Quadrini – Embrace the Messiness

Jill Gough – Advice for Educators, Parents and Senior Leaders

Jill Gough – Building Conceptual Understanding through Visualization

Jill Gough – Benefits of Technology

Jill Gough – Classroom Culture

Math Anxiety: An Important Component of Mathematical Success

Young Mathematicians: Dan Meyer – Productive vs Unproductive Struggle

Mathematical Success: A Conceptual Approach

Learning Beliefs in Mathematics

Mindsets and the Learning of Math

Mindsets and Mistakes

Young Mathematicians: Spatial Reasoning in Number Sense

Young Mathematicians: Comparing Measurements

Young Mathematicians: Jo Boaler – Mindsets and Mistakes

Young Mathematicians: Technology Examples From the Classroom

Young Mathematicians: Cathy Fosnot – Adaptive Learning & Digital Environments

Young Mathematicians: Alex Lawson – Models with “Mathematical Legs”

Young Mathematicians: Cathy Fosnot – Models and Powerful Tools

Young Mathematicians: Gestures as Mathematical Thinking – A student explains mathematical thinking using gestures.

Young Mathematicians: Survey Says – A student interprets survey results and determines next steps.

Young Mathematicians: Ways to Make 40 Cents – A student explains his problem-solving strategies.

Young Mathematicians: Playdough Play – Students engaged in play demonstrate mathematical thinking.

Young Mathematicians: What Does It Mean to be a Mathematician?

Math Perceptions – Dispelling the Myth

Young Mathematicians: Persevering at Blocks

Young Mathematicians: Mistakes are Part of Mathematical Thinking – A Grade 3 student corrects her thinking as she problem-solves.

Young Mathematicians: The Mathematics Learning Environment

Case Study – San Francisco Math Camp

Gender and Change

Applying Math Outside the Classroom

Teachers are the Key

Applying the TRU Framework

Teaching for Robust Understanding of Mathematics

Developing a Mathematical Growth Mindset

We Are All Mathematicians

Shifts in Math Education

Growth Mindset in the Classroom

Growth Mindset and Well-being

Ability Grouping

What really counts in our classrooms?

Final Reflection and Next Steps

Checking for Understanding After the Consolidation

Connecting: Planning and Doing the Consolidation

Selecting and Sequencing

Monitoring for Understanding of the Task

Monitoring to Understand Strategies

Using Classroom Structures to Monitor Student Learning

Monitoring Without Leading

Anticipating the Math by Doing the Math

The Math Congress

The Minds On: Introducing the Array through Quick Images – Class 2

The Minds On: Introducing the Array through Quick Images: Class 1

Understanding the Math: Moving Students from Additive to Multiplicative Thinking

Understanding the Math: The Big Idea of Place Value

Understanding the Math: The Big Idea of Unitizing

Understanding the Math: Regrouping Numbers When Adding

Understanding the Math: Partial Products

Understanding the Math: Doubling

Understanding the Math: Moving to Skip Counting and Repeated Addition

Math Content Knowledge for Teaching

Student Discourse

The Role of the Principal

Evidence of Mathematical Learning in the Environment

The Professional Learning Environment for Mathematics

Beginning to Create a Collaborative Learning Culture

Madoc Introduction

What Algebraic Symbols Have Been and Might Become

Real World Math: The Garden Stone Problem

Critical and Creative Thinking in the Math Classroom

What makes math interesting anyway?

Making Kids Doers of Math Instead of Doing the Math

If Math is the Aspirin, Then How do you Create the Headache?

What’s Wrong with Mathematics Teaching?

Comparing Objects: Intermediate

Primary: Connecting Linear Measurement to Quantity

Primary: Anticipating Student Thinking

Comparing Objects: Overall Description

Intermediate: How Tools Can Support Students’ Transitional Understandings

Intermediate: Students Using Tools

Intermediate: Teachers Using Tools

Primary: How Tools Can Support Students’ Transitional Understandings

Primary: Students Using Tools

Primary: Anticipating Student Thinking with the Tools

Primary: Teachers Using Tools

Manipulating Objects: Overall Description

Observing Students’ Gestures and Actions with the Tools

Gestures in Math Class

Intermediate: Supporting Non-Verbal Reasoning

Intermediate: Actions with the Tools

Primary: Linking Language to Non-Verbal Reasoning

Primary: Actions with the Tools

Non-Verbal Reasoning: Overall Description

Intermediate: Composing and Decomposing to Understand Operations

Intermediate: Composing and Decomposing to Understand Quantity

Primary: Composing and Decomposing to Understand Operations

Primary: Composing and Decomposing to Understand Quantity

Composing and Decomposing: Overall Description

Scaling Up or Down: Intermediate

Scaling Up or Down: Primary

Scaling Up or Down: Overall Description

Intermediate: Proportional Reasoning and the Ribbon Task

Intermediate: Using the Array in Probability

Intermediate: Proportional Reasoning and the Array

Primary: Developing Proportional Reasoning through Unitizing

Proportional Reasoning: Overall Description

A Matching Activity to Support Visualization

Visualizing: Intermediate

Visualizing: Primary

Visualizing: Overall Description

Supporting Students with Special Needs

Intermediate: ‘Spatializing’ the Consolidation

Intermediate: ‘Spatializing’ the “Minds On”

Intermediate: ‘Spatializing’ the Curriculum Expectations

Intermediate: ‘Spatializing’ the Curriculum

Primary: Reflection and Next Steps

Primary: ‘Spatializing’ The Consolidation

Primary: ‘Spatializing’ the “Minds On”

Primary: ‘Spatializing’ the Curriculum

‘Spatializing’ Instruction and Learning – Overall Description

What are Spatial Reasoning and Spatial Visualization?

What is this Resource About?

What about EQAO?

Games Support Understanding and Fluency

Conceptual Understandings and Procedural Fluency – We Need Both

Skills People Really Use

Inquiry: Learning from What Works and What Doesn’t

Using the Array to Model Multiplication Situations: The Apartment Problem

Using the Array to Model Multiplication and Division Situations: The Cookie Problem

Understanding the Multiplication Landscape

Inquiry: A Need and a Want to Know

Introduction: Revisiting Thinking about Representations and Models

Further Reflection on the Collaborative Inquiry

The Power of Manipulatives and Learning Tools

Digging Deeper into Student Profiles and Mathematical Thinking

Math Content Knowledge: The Caterpillar and Leaves Task

Some Observations from the Collaborative Inquiry

Math Content Knowledge: The Matchstick Task

Framework of the Collaborative Inquiry

Introduction: Questions Guiding the Collaborative Inquiry

More Math

Culturally Responsive Mathematics

Paying Attention to Spatial Reasoning

Conditions for Effective Teaching of Mathematics

Math Beyond Number

Math Knowledge for Teaching

A Strong Learning Environment


In the Heart of the Practice

Math For Young Children

Math Questions about Building Design

Calculating the Height of a Building

Architecture and Mathematics

White Spaces in the Curriculum

What’s Wrong with Mathematics Teaching?

Teach and Assess for Transfer

Reliability and Validity

Individual Accountability

Feedback and Mindset


Essential Questions About Assessment

Curriculum, Assessment and Instruction

Culminating Task

Backward Design

Authentic Assessment

Assessment Strategies

A Dynamic Model for Assessment

Design with the End in Mind

What is the Point?

The Administrator’s Role

Technology and Mathematics

Substance not Structures

Parents: Be Intentional and Casual

It’s About Learning

Focus on Reasoning

Math Anxiety

Mental Math


Improving Spatial Reasoning


Spatial Language


Spatial Thinking

What is Spatial Reasoning?

Purposes of Assessment

Learning the Content Knowledge

Planning Moves for Teachers

Success Criteria and Learning Goals in Math Learning

Parents as Partners – Math Messages

Getting Kids Motivated – Overcoming Math Anxiety

Assessment and Feedback

Inclusion Through Knowledge Forum

Promising Practices in Mathematics Learning and Teaching – Play all

Module 3: Leadership for Learning

Module 2: Engaging and Relevant Instruction

Module 1: Welcoming and Inclusive Environments


Assessing Impact

Parents Agree, Inquiry Matters

Queen Alexandra graduates sharing their insights

Sharing the Learning

Inquiry Projects at the Junior Level

Presenting a Disaster

Preparing for a Disaster

An Authentic Inquiry

Discussing the Hot Topics

Knowledge Building Lets Them Discover

Promoting Voice through Engagement

Intermediate Students Share Their Thinking on Inquiry Projects

Academic Press Day

We are All Instructional Leaders

Role of the Principal

Navigating the Tension between Educator and System Directed Learning

Learning Alongside Students and Colleagues

Using Manipulatives to Represent Thinking – The Number Line

Understanding Formulas

The Value of Mistakes

The Role of Administrators

Proportional Reasoning Across the Grades

Connections between Concepts and Units

Making and Proving Conjectures

Attitudes about Mathematics

Overall Introduction

The Benefits of Math Talk

Sharing the Professional Learning with Students

Reflecting on the Collaborative Culture

Questioning in Conversations

Student Clip Glimpses of Grade 12 Students Problem Solving 2

Student Clip Glimpses of Grade 12 Students Problem Solving 1

Creating and Sustaining a Collaborative Classroom Culture

Conversations and Evaluation

Student Clip – Developing and Proving Conjectures

Grade 7 Conversations – Using Diagrams to Visualize

Grade 7 Conversations – Using Area

Grade 7 Conversations – Understanding Similarity and Properties of Shapes

Grade 7 Conversations – The Challenge of Using Calculations

Grade 7 Conversations – Reflection and Next Steps

Grade 6 Conversations – Using Manipulatives to Represent Thinking

Grade 6 Conversations – Reflection

Grade 6 Conversations – Observing Students in Action

Descriptive Feedback to Prompt Conversations in Math

Grade 5 Conversations – Using Benchmarks

Grade 5 Conversations – Using a Scale

Grade 5 Conversations – Using a Diagram

Grade 5 Conversations – Next Steps

Grade 5 Conversations – Formulas and Conversions

Grade 5 Conversations – Distinguishing between Perimeter and Area

Unitizing and Counting Money

The Importance of Spatial Reasoning

Teacher Efficacy

Student Clip – Developing Teacher and Student Efficacy

Reflection on the Journey

Numbers to 1000

Moving from One to One Counting to Skip Counting

Introduction to Conversations in Secondary

Introduction to Junior/Intermediate Conversations

Introduction to Junior Conversations

Introduction to Conversations in Primary

Classifying Numbers

From Planning the Math to Doing the Math – Content Knowledge and Algebraic Reasoning

“Chapter One Problem”: Getting Started in the Classroom

First Language and Social Identity

Learning Math Vocabulary in Context

Flexible Groupings: Small Picture Perspective

No Flying Elbows: Building a Talk Community

Communicate with Parents About Mathematics: Extending Understandings

What Language Do You Dream In? Don’t Make Assumptions

We Are All Teachers of English Language Learners

Frame a Challenge of Practice

Who Owns the Learning?

Connect the Dots Across the School: Supporting Families and Educators

Consolidation: Math Circle

“A Different Kind of Success”: More than a Mark

That Community Feeling: Safe, Authentic, Transparent

Flexible Groupings: Big Picture Perspective

Creating the Conditions for Learning Mathematics: Overview

SIM Conference in Barrie

Cohort Tracking

All Students Can Learn

EQAO: Designing Questions

Secondary Mathematics – Issues of Access and Success

Putting EQAO in Context

Discourse about “The Basics”

Aboriginal Education for all Students


Grade 8: Glimpses of Incorporating Technology when Solving the Movie Theatre Problem

Self-Organized Learning

Self-Organized Learning Environment

The Power of Math Inquiry

Grade 6: Problem Solving with Technology

Math Curriculum: What teachers need to know

The Need for Powerful Tools: Formal and Informal Understanding in Math

The Power of Collaborative Learning

Pushing Our Own Thinking: Teaching and Learning Math

Doing Computations with Understanding

The Multiplication Landscape

Big Ideas, Strategies and Modelling

Basic facts or conceptual understandings? A False Dichotomy

What is numeracy?

Integrated Learning In Mathematics

Deepening Our Understanding: Literacy and Mathematics Behaviours in Block Play

Re-imagining Literacy and Mathematics Behaviours

Re-imagining the Learning

Re-thinking Literacy Structures

Literacy and Mathematics Behaviours Throughout the Day

Skills in a Technological Society

A Tool, Not a Rule

The Art of Mathematics

Creativity and Mathematically Interesting Problems

Representing: Purpose guides the way

Leadership Matters

Changing Classrooms

Effective Professional Learning

Computational Fluency

Problem Solving: An Inquiry Approach

Productive vs Unproductive Struggle: Understanding Student Thinking

Curiosity, Content and the Correct Answer

The Impact of Assessment

Multimodal Learning

Hands on Mathematics

The Art of Math

Think about Why

Building Fluency with +/- Facts

Assessment “Good for All Students”

Another Look at Triangulation

Rethinking Reporting in a Technical Age

Culture of Engagement and Curiosity

Rethinking Quantitative and Qualitative Assessment

Beyond “Do You Know It?”: The Achievement Chart

Mental Math: Thinking Flexibly with Numbers

Mathematical Success: A Conceptual Approach

Learning Beliefs in Mathematics

STEM Implications

Math Perceptions: Dispelling the Myth

Mindsets and the Learning of Math

Mindsets and Mistakes

Shifts in Math Education

Timed Learning and Math Anxiety

Why is numeracy important?

The Numberline: Model And Equivalence

Models: Powerful Tools for Thinking

Does a Circle Have Sides?

Taking Up Work


Set Up for Measurement Activity

Opening Routines

Planning Teacher Debrief

Questioning and Math Talk

Strategies and Tools

Flexible Grouping


Teacher Debrief: Play All

Highlights Summary and Independent Practice

Sharing: Group 3

Sharing: Group 2

Sharing: Group 1


Using Feedback

Working On It: Play All

Using Friendly Numbers

Constructing Equivalent Rates

Using Unit Rate


Introducing the Lesson Problem

Activating Prior Knowledge

Plan for the math by Doing the Math

Assessment for Learning


Gallery Walk

Solving the Problem

Minds On

Setting Learning Goals and Success Criteria

Planning for Engagement

Having a Partner Helps!

Do You Understand What I Did?

How Does This Relate to Me?

It’s OK to Disagree!

Understanding Geometric Figures: Introduction

Consolidating and Implementing

Students in Action: What do you notice? (with annotations)

Students in Action: What do you notice? (without annotations)

Constructing Triangles Using a Compass

Measuring Angles

Making 2-D Shapes with Set Squares

Exploring the Relationship Between a Rectangle (Square) and a Right Triangle

Analysing the Relationship Between Rectangles and Squares

Constructing a Square Through Paper Folding

Constructing a Rectangle Through Paper Folding

Constructing a Right Angle Through Paper Folding

Examining Triangles and Quadrilaterals Using Sides and Vertices

In Depth: Drawing Line Segments to Construct 2-D Shapes

Research About Students’ Development of Geometric Thinking

Educators in Mathematical Studies – In Brief

Marian Small: Making Assessment Work

A Growth Mindset in Math Class

Models with Mathematical Legs

Open Questions and Contexts

What is Developmental Dyscalculia?

Transforming Classroom Culture

Math Talk: Implications

Professional Learning: Key Features

Explicit Teaching

Instructional Ideas

Evaluation and Collaboration

Professional Learning: Research Supported

Bringing Math to Life

Learning and Technology: Benefits and Challenges

The Mathematician’s Way

How do we know?

Early Years: Challenges

Experiencing Applied Mathematics

Many Models for Learning

Models for Thinking

Early Years: Interventions

Thoughts About Inquiry

Professional Learning: The Role of the Principal

The Power of the Number Line

Success Criteria

Nurturing Creativity

A Primary Task

Math Talk: Negotiating Meaning and More



Professional Learning: Scaling Up

Another Primary Task

Instructional Big Ideas

Activation and Accessibility

Early Years: Learning Through Task Based Interviews

Explore Ideas Creatively


Introducing Models

Anxiety, Neuroscience, and Mind Sets

Math Talk: Math Talk Guidelines

Skills, Estimation, and Practice

Professional Learning: Efficacy

Learning and Technology: Information to Experience, Consumption to Production

A Junior Task



Representing Fractions: Linear Models

Equivalent Fractions: Grade 4

Comparing and Ordering Fractions: Visualization

Professional Learning in Mathematics

Improper and Mixed Fractions: Grade 4

How Concepts Develop

Student Reflections

Building a Collaborative Team

Fractions as Division

The Textbook

Representing Fractions: Visualization

Comparing and Ordering Fractions: Estimation and Benchmarks

The Language of Fractions

Equivalent Fractions: Grade 5

Representing Fractions: Area Models

Improper and Mixed Fractions: Grade 5

Improper and Mixed Fractions: Grade 6

The Written Diagnostic

Representing Fractions: How Concepts Develop

Content Knowledge for Teaching

Equivalent Fractions: Grade 6

The Curriculum

Representing Fractions: Set Models

Comparing and Ordering Fractions: Student Strategies

The Big Ideas

The Oral Diagnostic

Unit Planning as a Division

Analyzing and Interpreting Students’ Thinking

Setting the Context for Inquiry

Studying Mathematics for Teaching

Reflections on the Study Group’s Organizational Framework

The Public Research Lesson

Goals of Inquiry, Study, Action

Organizing for the Public Research Lesson

Next Actions in Classroom and Schools

Examining the Public Research Lesson

Developing Student Thinking

Engaging Parents in Math

Math Collaboration

Primary Math Class

Alignment Through a Math Project

A Principal Shares Student Feedback about Math

Another Perspective, Another Look

Connecting Math Problems to the Real World

Discovering Student Voice

FoS SO Talks about the Impact of PLTs

John Hattie: Homework and Its Value

John Hattie Talks about Learning Intentions

Doug Clements: Early Math Learning

Doug Clements: Integrated Concrete Concepts

Doug Clements: Intentional Play-Based Learning

Doug Clements: Learning Trajectories

Lucy West: Making Meaning

Lucy West: Culture of Classroom Discourse

Lucy West: Student Voice

Lucy West: Talk, Task, Feedback

Lucy West: Questioning

Math Talk, Conferencing and Professional Learning

Analysis of Consolidating Student Thinking

Analysis of Activating and Developing Student Learning

Thinking About Today’s Lesson

Analysing Yesterday’s Lesson

Lucy West – Culture of Classroom Discourse

Steven Katz

Marian Small: Responding to a Range of Student Thinking During Instruction

Marian Small: Preparing for Differentiated Instruction

Deborah Ball

Lucy West – Student Voice

Co-teaching as a Whole School Strategy

A Group or Network Approach to Co-teaching

Powerful Professional Learning

Co-teaching is Co-learning

Part 3 – After

Reflecting on Student Solutions

Part 2 – During

Part 1 – Before

Students Thinking about Mathematics

Building Self-Efficacy

Students View Themselves as Mathematicians

Early Math Learning

Intentional Play-based Learning

Intentional Instruction

Integrated Concrete Concepts

Learning Trajectories

Classroom Visit #2

Debrief of Classroom Visit #1

Classroom Visit #1

Setting the Context

Principal Team Debrief

Learning Team Debrief

Debrief of Classroom Visit #2

Grade 8: Group F

Grade 7: Group I

Grade 7: Group K

Grade 7: Group J

Grade 7: Group L

Grade 7: Group M

Grade 8: Group B

Grade 8: Group A

Grade 8: Group C

Grade 8: Group G

Grade 8: Group D

Grade 8: Group E

Manipulatives and Multiple Representations

Attitudes about Mathematics

The Curriculum – Understanding Developmental Growth in Curriculum Expectations

The Curriculum – Understanding the Mathematics Curriculum

Student and Teacher Efficacy

A Mini Lesson: Making the Mathematics Explicit

Introduction with Mary Jean Gallagher

The Three-Part Lesson: Consolidating the Important Ideas

The Benefits of Technology: Infused Learning

Exploring Mathematics through Investigations

Assessing Mathematical Thinking through Observations and Conversations

The Value of Technology: Twitter as a Vehicle for Professional Learning

The Value of Technology: Twitter for Activating Student Thinking

Technology for Discovering New Frontiers

Technology and Collaboration

Developing and Taking an Inquiry Stance

Proportional Reasoning in Grade 8: Overall Assessment and Next Steps for the Unit and for High School

Proportional Reasoning in Grade 7

The Three-Part Lesson: Activating Student Thinking

Flexibility: The Three Parts of a Lesson Blur

Proportional Reasoning in Grade 6

Exploring Mathematics through Wondering

Questioning the Moment: Glimpses of Grade 8 Students Solving the Movie Theatre Problem

Estimating and Making Sense of Numbers

Proportional Reasoning in Grade 8: Analyzing the Thinking

The Three-Part Lesson: Selecting Engaging Problems – Different Directions

The Three-Part Lesson: An Overview

The Three-Part Lesson: Selecting Engaging Problems – A Variety of Solutions

Engaging Students in the Mathematics

Proportional Reasoning in the Primary and Junior Grades

Reflective Thoughts

The Importance of Practice

Assessment and Technology

Growth Mindsets in Mathematics

Puzzles and Games

Computational Fluency

The Strands

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