Part 2: Spatial Reasoning as an Essential Building Block of Pre-K and Kindergarten Education

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

Vocabulary in a Mathematics Classroom

Powerful Ideas on Knowledge Building in Mathematics

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 – 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

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

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: 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: The Mathematics Learning Environment

Case Study – San Francisco Math Camp

Applying Math Outside the Classroom

Teaching for Robust Understanding of Mathematics

Developing a Mathematical Growth Mindset

Growth Mindset in the Classroom

What really counts in our classrooms?

Final Reflection and Next Steps

Checking for Understanding After the Consolidation

Connecting: Planning and Doing the Consolidation

Monitoring for Understanding of the Task

Monitoring to Understand Strategies

Using Classroom Structures to Monitor Student Learning

Anticipating the Math by Doing the Math

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

Evidence of Mathematical Learning in the Environment

The Professional Learning Environment for Mathematics

Beginning to Create a Collaborative Learning Culture

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: Anticipating Student Thinking with the Tools

Manipulating Objects: Overall Description

Observing Students’ Gestures and Actions with the Tools

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: 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: 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?

Games Support Understanding and Fluency

Conceptual Understandings and Procedural Fluency – We Need Both

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

Culturally Responsive Mathematics

Paying Attention to Spatial Reasoning

Conditions for Effective Teaching of Mathematics

Math Questions about Building Design

Calculating the Height of a Building

White Spaces in the Curriculum

What’s Wrong with Mathematics Teaching?

Essential Questions About Assessment

Curriculum, Assessment and Instruction

A Dynamic Model for Assessment

Parents: Be Intentional and Casual

Learning the Content Knowledge

Success Criteria and Learning Goals in Math Learning

Parents as Partners – Math Messages

Getting Kids Motivated – Overcoming Math Anxiety

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

Parents Agree, Inquiry Matters

Queen Alexandra graduates sharing their insights

Inquiry Projects at the Junior Level

Knowledge Building Lets Them Discover

Promoting Voice through Engagement

Intermediate Students Share Their Thinking on Inquiry Projects

We are All Instructional Leaders

Navigating the Tension between Educator and System Directed Learning

Learning Alongside Students and Colleagues

Using Manipulatives to Represent Thinking – The Number Line

Proportional Reasoning Across the Grades

Connections between Concepts and Units

Making and Proving Conjectures

Sharing the Professional Learning with Students

Reflecting on the Collaborative Culture

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

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

The Importance of Spatial Reasoning

Student Clip – Developing Teacher and Student Efficacy

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

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

Connect the Dots Across the School: Supporting Families and Educators

“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

Secondary Mathematics – Issues of Access and Success

Aboriginal Education for all Students

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

Self-Organized Learning Environment

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

Enhancing Problem Solving with Technology

Adaptive Learning and Digital Environments

Doing Computations with Understanding

Big Ideas, Strategies and Modelling

Basic facts or conceptual understandings? A False Dichotomy

Integrated Learning In Mathematics

Deepening Our Understanding: Literacy and Mathematics Behaviours in Block Play

Re-imagining Literacy and Mathematics Behaviours

Re-thinking Literacy Structures

Literacy and Mathematics Behaviours Throughout the Day

Skills in a Technological Society

Creativity and Mathematically Interesting Problems

Representing: Purpose guides the way

Effective Professional Learning

Problem Solving: An Inquiry Approach

Productive vs Unproductive Struggle: Understanding Student Thinking

Curiosity, Content and the Correct Answer

Building Fluency with +/- Facts

Assessment “Good for All Students”

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

Math Perceptions: Dispelling the Myth

Mindsets and the Learning of Math

Timed Learning and Math Anxiety

The Numberline: Model And Equivalence

Models: Powerful Tools for Thinking

Set Up for Measurement Activity

Social Justice Math: Doing the Math

Social Justice Math: Being in the Learner’s Role

Social Justice Math: Consolidation

Social Justice Math: Teacher Reflections

Social Justice Math: Shared Leadership

Social Justice Math: Collaborative Inquiry

Social Justice Math: Building a Culture of Learning

Social Justice Math: Activating Prior Knowledge

Social Justice Math: Student Reflections

Social Justice Math: Teacher Reflections

Social Justice Math: Gallery Walk

Highlights Summary and Independent Practice

Introducing the Lesson Problem

Social Justice Math: Accountable Talk

Plan for the math by Doing the Math

Setting Learning Goals and Success Criteria

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

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

What is Developmental Dyscalculia?

Transforming Classroom Culture

Professional Learning: Key Features

Professional Learning: Research Supported

Learning and Technology: Benefits and Challenges

Experiencing Applied Mathematics

Professional Learning: The Role of the Principal

Math Talk: Negotiating Meaning and More

Professional Learning: Scaling Up

Early Years: Learning Through Task Based Interviews

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

Representing Fractions: Linear Models

Comparing and Ordering Fractions: Visualization

Professional Learning in Mathematics

Improper and Mixed Fractions: Grade 4

Representing Fractions: Visualization

Comparing and Ordering Fractions: Estimation and Benchmarks

Representing Fractions: Area Models

Improper and Mixed Fractions: Grade 5

Improper and Mixed Fractions: Grade 6

Representing Fractions: How Concepts Develop

Content Knowledge for Teaching

Representing Fractions: Set Models

Comparing and Ordering Fractions: Student Strategies

Analyzing and Interpreting Students’ Thinking

Setting the Context for Inquiry

Studying Mathematics for Teaching

Reflections on the Study Group’s Organizational Framework

Goals of Inquiry, Study, Action

Organizing for the Public Research Lesson

Next Actions in Classroom and Schools

Examining the Public Research Lesson

Alignment Through a Math Project

A Principal Shares Student Feedback about Math

Another Perspective, Another Look

Connecting Math Problems to the Real World

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: Culture of Classroom Discourse

Lucy West: Talk, Task, Feedback

Math Talk, Conferencing and Professional Learning

Analysis of Consolidating Student Thinking

Analysis of Activating and Developing Student Learning

Lucy West – Culture of Classroom Discourse

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

Marian Small: Preparing for Differentiated Instruction

Co-teaching as a Whole School Strategy

A Group or Network Approach to Co-teaching

Powerful Professional Learning

Reflecting on Student Solutions

Students Thinking about Mathematics

Students View Themselves as Mathematicians

Intentional Play-based Learning

Manipulatives and Multiple Representations

The Curriculum – Understanding Developmental Growth in Curriculum Expectations

The Curriculum – Understanding the Mathematics Curriculum

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

Developing and Taking an Inquiry Stance

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 – Contextual and Non-contextual Problems

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

Engaging Students in the Mathematics

Creating a Collaborative Culture

Proportional Reasoning in the Primary and Junior Grades

The Three-Part Lesson: Finishing the Thinking and Planning for Consolidation

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