loving’the’math,’living’the’math’...loving’the’math,’living’the’math’ "...

Loving the Math, Living the Math

A Video Resource For

Ontario Math Educators


THE INTENT OF THE RESOURCE

The grade 6, 7, and 8 students in MaAhew Oldridge’s math classes are engaged, confident and proficient at acquiring conceptual understanding, a strong skill base, and a criKcal thinking stance. This resource probes into why his students love math and how their classroom experiences have contributed to their success. While this is one of many examples of an effecKve math program, there are useful ideas for ALL educators who influence students’ math journeys.

THE HISTORY OF MATTHEW’S PROGRAM

MaAhew has spent eleven years refining his math program so it aligns with the curriculum, developmental growth of concepts, and is responsive to his students. Over Kme, he has adopted a broad definiKon of mathemaKcs, an extensive repertoire of instrucKonal strategies, and increased personal knowledge of the math. His students’ posiKve aYtudes are evident in interviews and when they engage in math tasks.


THE ROLE OF TECHNOLOGY

MaAhew has also been very involved with technology and how it can enhance his mathemaKcs program, especially since Peel District School Board, has adopted a Bring Your Own Device (BYOD) policy. The resource highlights how technology has been effecKve in the math classroom, as well as a powerful tool for professional learning and assessment. The benefits and challenges of technology are analyzed.


EDUCATORS IN THE RESOURCE

Ma.hew Oldridge: Peel Math Teacher Laurie Letourneau: Peel Vice Principal Paul Alves: Peel Secondary Resource Teacher (Paul and MaAhew

regularly converse on TwiAer) Anna Presta: Peel Elementary Resource Teacher (Anna follows

MaAhew on TwiAer and uses his ideas in her work) Kim Arfo: Peel Elementary Resource Teacher Diane Stang: Provincial Math Facilitator


FURTHER RESEARCH

Throughout the video, several math experts share their research and ideas, including: Marian Small, Jo Boaler, Dan Meyer, Cathy Fosnot, Lucy West, Damian Cooper, George Hart, Sugata Mitra, Cathy Bruce, ChrisKne Suurtamm, and Ruth BeaAy. Several resources, including Ministry resources, are also highlighted, which may be useful for educators to explore in greater detail.


ORGANIZATION DVD 1 Loving the Math: CondiKons for CreaKng a Math Learning Culture Living the Math: Features of MaAhew’s Program DVD 2 Understanding the MathemaKcs The Role of Technology in Teaching and Learning MathemaKcs DVD 3 Students in AcKon: 14 student groups solving problems Some condiKons and features from DVD 1 and DVD 2 link to student clips to illustrate how they might look in the classroom. All clips can be used to extend personal math content knowledge, to pracKse using observaKons and conversaKons in assessment and for quesKoning in the moment.


IntroducCon

Loving the Math: CondiKons for CreaKng a Math Learning Culture

Living the Math: Features of MaAhew’s Program

Understanding the MathemaKcs

AYtudes about MathemaKcs

Student and Teacher Efficacy

Growth Mindsets

Engaging Students in MathemaKcs

The Three-‐ Part Lesson

A Mini Lesson: Making the MathemaKcs Explicit

The Importance of PracKce

Exploring Math through Wondering

CreaKng a CollaboraKve

Culture

Developing and Taking an Inquiry

Stance

Assessment

EsKmaKng and Making Sense of

Numbers

The Curriculum

ProporKonal Reasoning

ComputaKonal Fluency

The Role of Technology

The Value of Technology: TwiAer as a Professional Learning Tool

The Value of Technology: TwiAer for

AcKvaKng Student Thinking

Technology in the Classroom

Problem Solving with Technology

Exploring Math through InvesKgaKons

ReflecCve Thoughts

Puzzles and Games

The Strands

ManipulaKves and ConnecKng

MulKple RepresentaKons

QuesKoning in the Moment

DVD 1 DVD 2

IntroducKon Mary Jean Gallagher discusses how Ontario educators are striving to offer the best possible math programs for their students. She explains how MaAhew Oldridge is one of many math educators who conKnually makes his program more effecKve and responsive to his students. She also describes the intent of the resource and its contents.

DVD 1

MathemaKcian, George Hart, outlines the importance of posiKve aYtudes towards math. Students share their thoughts about math.

Loving the Math: CondiCons for CreaCng a Math Learning Culture

AYtudes About MathemaKcs

Student and Teacher Efficacy

Growth Mindsets

Engaging Students in MathemaKcs

CreaKng a CollaboraKve Culture

Taking an Inquiry Stance

Jo Boaler shares her research about growth versus fixed mindsets in mathemaKcs. Students talk about growth mindsets. This links to a clip of students problem solving, who have expressed that they have improved at math over the years.

Cathy Bruce discusses her research in this area. Students discuss their beliefs about their math abiliKes. This links to a clip of students problem solving with strong efficacy and persistence.

Damian Cooper outlines some features of an engaging classroom. Student interviews reveal strong engagement in math. This links to a group of enthusiasKc students passionately problem solving.

MaAhew discusses how he created such a culture, and how fermi quesKons can be a good starKng point. Students discuss how collaboraKon helps them to learn mathemaKcs.

Dan Meyer highlights the benefits and challenges of transforming the classroom culture to an inquiry stance. MaAhew discusses this too. Its effecKveness in the classroom becomes evident, through student interviews and their acKons while solving problems.

DVD 1

Living the Math: Features of MaAhew’s Math Program

The Three-‐Part Lesson




Assessment


Puzzles and Games

ReflecKve Thoughts

DVD 1

Building a Comprehensive Math Program


The Three-‐Part Lesson : An Overview

AcKvaKng Student Thinking

SelecKng Engaging Problems

ConsolidaKng the MathemaKcal Thinking

Flexibility: The Three Parts Blur

Lucy West and Marian Small discuss the need for flexibility and an understanding of the intent of a three-‐part lesson. MaAhew explains how he does this on rotary.

Dan Meyer discusses features that acKvate thinking. MaAhew shares his problem and why it was so engaging. We see and hear students truly immersed in the problem.

The purpose of consolidaKon and its components are highlighted.

This segment highlights the importance of providing Kme for students to finish their thinking and plan for an effecKve consolidaKon.

A lesson starts with summarizing ideas from the previous day’s consolidaKon, and ends with the minds on for the next day’s lesson.

Marian Small discusses three types of open problems and MaAhew shares how he selects quesKons for his students. Different DirecKons features problems which may spark students to go off in a different direcKon. It links to a group that does exactly this.

A Variety of SoluKons reveals problems that can have many answers. It links to students that jusKfy why several answers are possible.

Contextual and Noncontextual Problems and their values are discussed

DVD 1

Living the Math: Features of Ma.hew’s Math Program

A Mini Lesson: Making the Math

Explicit



Exploring Math through

InvesKgaKons

Dan Meyer stresses the importance of pracKce. Marian Small highlights what to pracKce in math. MaAhew explains how he incorporates pracKce and shows some TIPS4RM examples.

Lucy West discusses other models for learning math, including inquiries. MaAhew explains how he uses brainstorming to get students to wonder about the math around them.

Lucy West and Sugata Mitra discuss the value of math invesKgaKons. MaAhew and his students talk about their independent math invesKgaKons that they did in class.

Dan Meyer talks about how more explicit lessons fit into a math program. In response to what happens in the consolidaKon, MaAhew does a mini lesson on the cross product rule to ensure that it is understood conceptually and not as a trick.

Puzzles and Games George Hart and Jo Boaler discuss the role of puzzles and games in math, while some of MaAhew’s students engage in them.

DVD 1

Living the Math: Features of Ma.hew’s Math Program

The Three-‐ Part Lesson




Assessment


Assessment for Learning is discussed in terms of Growing Success – observaKons, conversaKons, and products. MaAhew discusses the value of conversaKons in his program. Students express their opinions about conversaKons and assessment.

Assessing MathemaKcal Thinking Through ObservaKons and ConversaKons: Two student conversaKons are presented, which educators can analyze for understandings, parKal understandings, possible quesKoning, and next steps.

Puzzles and Games

Assessment and Technology: Damian Cooper discusses the potenKal for technology making assessment more reliable, but a mindshii is needed. MaAhew and Paul explain how technology can capture the process of mathemaKcal thinking.

DVD 1

Features of MaAhew’s Math Program


Mini Lessons



Assessment


Puzzles and Games

ReflecKve Thoughts

Jo Boaler shares her research on students who display greater achievement and engagement when learning from a mulKdimensional approach versus being told how to do methods. MaAhew offers suggesKons for making the math ‘come alive.”

DVD 1

Understanding the MathemaCcs

EsKmaKng and Making Sense of

Numbers

The Curriculum

ComputaKonal Fluency

ChrisKne Suurtamm discusses how the curriculum is both problem and skill based. MaAhew and other educators discuss how concepts grow in the curriculum from grade to grade, and then analyze the curriculum expectaKons about rates, the focus of the featured lessons

The Strands MaAhew and other educators discuss how the strands interconnect and how we need to make those connecKons explicit to students.

Marian Small discusses the value of esKmaKon and knowing whether calculated numbers make sense. There are examples of students trying to make sense of numbers while problem solving.

Dan Meyer, Cathy Fosnot, and Jo Boaler discuss computaKonal fluency and how conceptual understanding must underpin any procedures. They define computaKonal fluency within the context of the 21st century

ManipulaKves and MulKple

RepresentaKons

Ruth BeaAy discusses the importance of manipulaKves and mulKple representaKons, and how making connecKons between representaKons leads to beAer understanding.

Marian Small discusses how teachers need to pracKce how to quesKon in the moment. This links to an example of MaAhew quesKoning a group of students while they are problem solving.

QuesKoning in the Moment

DVD 2

Understanding the MathemaCcs

ProporKonal Reasoning

ProporKonal Thinking in the Primary and Junior Grades

ProporKonal Thinking in Grade 7



Since rates are the focus in MaAhew’s class, the bigger ideas of proporKonal reasoning are highlighted. The development of proporKonal thinking over Kme and how concepts build throughout the grades are discussed.

MaAhew and other educators discuss how it develops in the early grades, using the Paying AAenKon to ProporKonal Reasoning Document.

MaAhew and other educators discuss the proporKonal thinking evident in the grade 6 soluKons. We also see students in acKon.

By analyzing student work, MaAhew and other educators discuss the proporKonal thinking that is evident. This links to a group of grade 7 students who solve a problem.

By analyzing student soluKons, MaAhew and other educators discuss the proporKonal thinking that is evident. Educators also discuss how this understanding prepares students for high school. This links to a grade 8 group solving a problem.

DVD 2

The Role of Technology

TwiAer as a Vehicle for Professional

Learning

TwiAer for AcKvaKng Student

Thinking


Problem Solving with Technology

Dan Meyer discusses the effecKveness of TwiAer for professional learning. MaAhew discusses, with other educators, how he uses TwiAer to further his own professional learning on a regular basis.

MaAhew shows how TwiAer can be an engaging way to present problems to students.

The grade 6 class uses various forms of technology and applicaKons to solve a problem. This gives a glimpse at what a BYOD classroom can look like.

DVD 2


Cathy Bruce talks about the value of technology for discovering innovaKve soluKons. A grade 6 student uncovers a unique way to solve the problem, which would have been unlikely without technology.

Cathy Bruce discusses how the role of technology has changed over Kme. Several students naturally use technology to enhance their problem solving and criKcal thinking.

Cathy Bruce discusses how collaboraKon can look when students work together with technology. We witness this new form of collaboraKon in MaAhew’s math classrooms.

Cathy Bruce discusses some benefits of technology. MaAhew’s students share how technology is valuable to them in math class.

Technology to Enhance Problem

Solving

Technology for Discovering New

FronKers in MathemaKcs

Technology and CollaboraKon

The Benefits of Technology:

Infused Learning

The Challenges of Technology

Cathy Bruce discusses some of the challenges of incorporaKng technology in educaKon, including equity. MaAhew reflects on his journey with using technology in his classrooms.

DVD 2

DVD 3 -‐ Student Groups Linking to Other Clips Student Group Link

Grade 8: Group A AYtudes About MathemaKcs

Grade 8 : Group B Growth Mindsets

Grade 8: Group C Student and Teacher Efficacy

Grade 8: Group D Engaging Students in MathemaKcs

Grade 8: Group E Assessing MathemaKcal Thinking Through ObservaKons and ConversaKons

Grade 8: Group F Developing and Taking an Inquiry Stance

Grade 8: Group G AcKvaKng Student Thinking

Grade 8: Group H ProporKonal Reasoning in Grade 8

Grade 7: Group I SelecKng Problems: A Variety of SoluKons

Grade 7: Group J CreaKng a CollaboraKve Culture

Grade 7: Group K EsKmaKng and Making Sense of Numbers

Grade 7: Group L ProporKonal Reasoning in Grade 7

Grade 7: Group M SelecKng Problems: Different DirecKons

Grade 7: Group N Assessment for Learning

DVD 3 DVD 1

DVD 2

loving’the’math,’living’the’math’...loving’the’math,’living’the’math’ "...

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