Math Expressions

Math Expressions
 
 

Companion Content

Introduction: A Culture of Mathematical Expression

Chapter 1: A Culture of Collaboration and Inquiry

Chapter 2: Mathematical Discourse

Chapter 3: Reading in Mathematics

Chapter 4: Writing in Mathematics

Introduction: A Culture of Mathematical Expression

Professional Resources

Becoming a Facilitator of Mathematical Expression

What Is the Role of the Teacher?
Environmental Inquiry: A Pedagogical Framework, Natural Curiosity: A Resource for Teachers, The Laboratory School at the Dr. Eric Jackman Institute of Child Study. Ontario Institute for Studies in Education, 2011
http://www.naturalcuriosity.ca/environmental.php?pgcat=branch1&sfield=eight

Graduating from Teacher to Facilitator in the Technology-Rich Classroom
Carol M. Webb, 2001
http://www.4teachers.org/testimony/webb/

 

Supporting Learners with Math Anxiety

Equity for All Students in the New Millennium: Disabling Math Anxiety
Joseph M. Furner and Mary Lou Duffy, Intervention in School and Clinic, November 2002
http://isc.sagepub.com/content/38/2/67.extract

A Teacher’s Quick Guide to Understanding Mathematics Anxiety
DesLey Viator Plaisance, LATM Journal, Louisiana Association of Teachers of Mathematics, 2011
http://www.lamath.org/journal/vol6no1/anxiety_guide.pdf

Study Suggests There May Be a Neurological Basis for Math Anxiety
From the Stanford University press release, 2012
http://therapytoronto.ca/news/?p=1972

Math Anxiety
Counseling Center, Texas State University
http://www.counseling.txstate.edu/resources/shoverview/bro/math.html

 

Supporting English Language Learners

Equity of Literacy-Based Math Performance Assessments for English Language Learners
Clara Lee Brown, Bilingual Research Journal: The Journal of the National Association for Bilingual Education, 2005
http://www.tandfonline.com/doi/abs/10.1080/15235882.2005.10162839#preview

Multilingualism in the English-Language Classroom: Pedagogical Considerations
Jim Cummins, TESOL Quarterly, June 2009
http://onlinelibrary.wiley.com/doi/10.1002/j.1545-7249.2009.tb00171.x/abstract

TIPS for English Language Learners in Mathematics, Grades 7, 8, 9 Applied, 10 Applied
Ontario Ministry of Education, 2005
http://www.edugains.ca/resourcesELL/Resources/TIPSforELLMath4All.pdf

Understanding and Supporting Children’s Mathematical Vocabulary Development
Rheta Rubenstein and Denisse Thompson, Teaching Children Mathematics, October 2002
http://www.nctm.org/publications/article.aspx?id=21326

What Can a Mathematics Teacher Do for the English Language Learner?
Texas Comprehensive Center, 2006
http://txcc.sedl.org/resources/ell_materials/mell/

 

Assessing Math Learning

Growth for Every Student
Limestone District School Board, Ontario, 2008
http://www.limestone.on.ca/programs/elementary/Math%20Resources/Growth%20for%20Every%20Studentfinal.pdf

Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools, First Edition, Covering Grades 1 to 12

Ontario Ministry of Education, 2010
http://www.edu.gov.on.ca/eng/policyfunding/growSuccess.pdf

Chapter 1: A Culture of Collaboration and Inquiry

Chapter 1 - Professional Resources

Cooperative Learning

Exploring Mathematics Talk in Elementary Classrooms
Cathy Mark Krpan, Partnerships for Professional Learning: Literacy & Numeracy Initiatives, Ontario Institute for Studies in Education, 2009
http://www.oise.utoronto.ca/oise/UserFiles/File/LNS%20PUBLICATION_FINAL.pdf

Supporting Struggling Learners: Collaborative Problem Solving in Mathematics
Cathy Marks Krpan, Inquiry into Practice: Reaching Every Student Through Inclusive Curriculum, Ontario Institute for Studies in Education, 2009
http://www.oise.utoronto.ca/cms/oisefiles/ITE%20PUB%202011_COMPLETE/HTML/index.html#/103/zoomed

Cooperative Learning Instruction Strategies
Teachnology: The Online Teacher Resource
http://www.teach-nology.com/currenttrends/cooperative_learning/

Chapter 1 - Tools

All Tools (.PDF 43kb 3 pgs)

Indicators of Success for a Collaborative Mathematics Classroom
.PDF 22kb 1pg

Observation Checklist for a Collaborative Mathematics Classroom
.PDF 23mb 1pg

Indicators of Success for Descriptive Feedback
.PDF 32kb 1pg

Chapter 1 - Line Masters

All Line Masters (.PDF 63kb 4pgs)

LM 1.1 Cooperative Math Chart
.PDF 32kb 1pg

LM 1.2 Cooperative Group Roles for Mathematics [Primary]
.PDF 38kb 1pg

LM 1.3 Cooperative Group Roles for Mathematics [Junior/Intermediate]
.PDF 22kb 1pg

LM 1.4 Observation Checklist for Cooperative Work
.PDF 24kb 1pg

Chapter 2: Mathematical Discourse

Chapter 2 - Professional Resources

Mathematical Discourse

Equity for English Language Learners in the Mathematics Classroom
Gina Borgioli, Teaching Children Mathematics, October 2008
http://www.nctm.org/publications/article.aspx?id=22261

Describing Levels and Components of a Math-Talk Learning Community
Kimberly Hufferd-Ackles, Karen C. Fuson, Miriam Gamoran, Journal for Research in Mathematics Education, March 2004
http://www.nctm.org/publications/article.aspx?id=17479

Unpacking the Nature of Discourse in Mathematics Classrooms
Eric Knuth and Dominic Peressini, Mathematics Teaching in the Middle School, January 2001
http://www.nctm.org/publications/article.aspx?id=19872

Exploring Mathematics Talk in Elementary Classrooms
Cathy Mark Krpan, Partnerships for Professional Learning: Literacy & Numeracy Initiatives, Ontario Institute for Studies in Education, 2009
http://www.oise.utoronto.ca/oise/UserFiles/File/LNS%20PUBLICATION_FINAL.pdf

Supporting Struggling Learners: Collaborative Problem Solving in Mathematics
Cathy Marks Krpan, Inquiry into Practice: Reaching Every Student Through Inclusive Curriculum, Ontario Institute for Studies in Education, 2009
http://www.oise.utoronto.ca/cms/oisefiles/ITE%20PUB%202011_COMPLETE/HTML/index.html#/103/zoomed

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics, 2000
http://www.nctm.org/standards/content.aspx?id=16909

Fostering Mathematical Thinking and Problem Solving: The Teacher’s Role
Nicole Rigelman, Teaching Children Mathematics, February 2007
http://www.nctm.org/publications/article.aspx?id=22041

Using “Think-Time” and “Wait-Time” Skillfully in the Classroom
Robert J. Stahl, ERIC Resource Center, 1994
http://www.eric.ed.gov/PDFS/ED370885.pdf

Let’s Talk: Promoting Mathematical Discourse in the Classroom
Catherine A. Stein, Mathematics Teacher, November 2007
http://www.nctm.org/publications/article.aspx?id=19362

A Classroom Perspective on the Principle of Moderate Challenge in Mathematics
Julianne C. Turner and Debra K. Meyer, The Journal of Educational Research, August 2010
http://www.tandfonline.com/doi/abs/10.3200/JOER.97.6.311-318

A Teacher’s Meditation of a Thinking-Aloud Discussion in a 6th Grade Mathematics Classroom
Betina Zolkower and Sam Shreyar, Educational Studies in Mathematics, 2007
http://www.springerlink.com/content/8526484n24032244/


A Resource of Multilingual Math Words

English as an Additional Language
Emaths
http://www.emaths.co.uk/index.php/4-teachers/other-resources/eal

 

Bansho

Three-part Problem-Solving, Clip 3 Bansho
Webcast, Curriculum Services Canada, 2008
http://resources.curriculum.org/secretariat/may2_bansho.shtml

Chapter 2 - Tools

All Tools (.PDF 456kb 32pgs)

Indicators of Success for Mathematical Discourse
.PDF 22kb 1pg

Observation Checklist for Mathematical Discourse
.PDF 24kb 1pg

My Math Talk [Primary]
.PDF 31kb 1pg

Indicators of Success for Effective Mathematical Discourse [Junior/Intermediate]
.PDF 32kb 1pg

Talk Prompts
.PDF 129kb 1pg

Pattern Block Designs
.PDF 256kb 9pgs

Cards for Clothesline Activity
.PDF 62kb 10pgs

Word Problems for Math Congress
.PDF 28kb 8pgs

Chapter 2 - Line Masters

All Line Masters (.PDF 194kb 8pgs)

2.1 Student Discourse Observation Sheet
.PDF 24kb 1pg

2.2 Interview Sheet
.PDF 20kb 1pg

2.3 Concept Attainment: Shapes with Line Symmetry [Yes Cards]
.PDF 63kb 1pg

2.4 Concept Attainment: Shapes with Line Symmetry [No Cards]
.PDF 67kb 1pg

2.5 Concept Attainment: Shapes with Area Less Than or Equal to 6 Square Units [Yes Cards]
.PDF 41kb 1pg

2.6 Concept Attainment: Shapes with Area Less Than or Equal to 6 Square Units [No Cards]
.PDF 49kb 1pg

2.7 Concept Attainment: Prime Numbers [Yes and No Cards]
.PDF 34b 1pg

2.8 Wanted!
.PDF 40kb 1pg

 

Chapter 3: Reading in Mathematics

Chapter 3 - Professional Resources

Reading in Mathematics

The Answer Is 20 Cookies. What Is the Question?
Angela T. Barlow and Janie M. Cates, Teaching Children Mathematics, December 2006/January 2007
http://www.nctm.org/publications/article.aspx?id=22030

A Problem-Solving Alternative to Using Key Words
Lisa Clement and Jamal Bernhard, Mathematics Teaching in the Middle School, March 2005
http://www.nctm.org/publications/article.aspx?id=20390

The Thought-Filled Curriculum
Arthur L. Costa, Educational Leadership, February 2008
http://www.ascd.org/publications/educational_leadership/feb08/vol65/num05/The_Thought-Filled_Curriculum.aspx

Mathematics and Cognition
Arthur Hyde, Educational Leadership, November 2007
http://www.ascd.org/publications/educational-leadership/nov07/vol65/num03/Mathematics-and-Cognition.aspx

Knowledge Change as a Function of Mathematics Experience: All Contexts are Not Created Equal
Nicole M. McNeil and Martha W. Alibali, Journal of Cognition and Development, 2005
http://www.tandfonline.com/doi/abs/10.1207/s15327647jcd0602_6

Reciprocal Teaching as a Comprehension Strategy for Understanding Mathematical Word Problems
Delinda van Garderen, Reading & Writing Quarterly, 2004
http://www.tandfonline.com/doi/abs/10.1080/10573560490272702

Online Mathematics Dictionary

A Maths Dictionary for Kids
Jenny Eather
http://www.amathsdictionaryforkids.com/

Chapter 3 - Tools

All Tools (.PDF 874kb 26pgs)

Indicators of Success for Reading in Mathematics
.PDF 22kb 1pg

Observation Checklist for Reading in Mathematics
.PDF 23kb 1pg

My Math Reading: Word Problems [Primary]
.PDF 31kb 1pg

Indicators of Success for Understanding Word Problems [Junior/Intermediate]
.PDF 31kb 1pg

Mathematical Picture Book List
.PDF 65kb 5pgs

Word Problems
.PDF 27kb 8pgs

Math in the Environment
.PDF 511kb 7pgs

Mathematical Recipes
.PDF 61kb 2pgs

Chapter 3 - Line Masters

All Line Masters (.PDF 209kb 7pgs)

3.1A Biography Glyphs
.PDF 69kb 1pg

3.1B Biography Glyphs
.PDF 52kb 1pg

3.2 Train Recipe Card
.PDF 45kb 1pg

3.3 My Train
.PDF 48kb 1pg

3.4 Mathematical Recipes [Whole Numbers]
.PDF 39kb 1pg

3.5 Mathematical Recipes [Fractions and Percents]
.PDF 47kb 1pg

3.6 Mathematical Recipes [Algebra]
.PDF 42b 1pg

 

Chapter 4: Writing in Mathematics

Chapter 4 - Professional Resources

Writing in Mathematics

Investigating Mathematical Thinking Using Open Writing Prompts
Leslie Aspinwall and Julie Aspinwall, Mathematics Teaching in the Middle School, March 2003
http://www.nctm.org/publications/article.aspx?id=20106

Blueprint for Writing in Middle School Mathematics
Juliet A. Baxter, John Woodward, Deborah Olson, and Janet Robyns, Mathematics Teaching in the Middle School, September 2002
http://www.nctm.org/publications/article.aspx?id=20047

Beyond Essentialism: The Complexity of Language in Teaching Mathematics to Latina/o Students, American Educational Research Journal, December 2002
Rochelle Gutiérrez,
http://aer.sagepub.com/content/39/4/1047.abstract

Academic Emotions in Students’ Self-Regulated Learning and Achievement: A Program of Qualitative and Quantitative Research
Reinhard Pekrun, Thomas Goetz, Wolfram Titz, and Raymond P. Perry, Educational Psychologist, 2002
http://www.tandfonline.com/doi/abs/10.1207/S15326985EP3702_4#preview

 

Graphic Organizers

Q & A: What’s the Big Deal with Graphic Organizers?
Edwin Ellis
http://www.graphicorganizers.com/About-MSS/q-a-a-whats-the-big-deal-with-graphic-organizers.html

What Are Graphic Organizers?
Instructional Strategies Online, Saskatoon Public Schools
http://olc.spsd.sk.ca/de/pd/instr/strats/graphicorganizers/index.html

Mind Mapping Resources
The University of British Columbia
http://wiki.ubc.ca/Mind_Mapping_Resources

Institute for Human and Machine Cognition Concept Map Tools
http://cmap.ihmc.us/

The Theory Underlying Concept Maps and How to Construct and Use Them
Joseph D. Novak and Alberto J. Cañas, Institute for Human and Machine Cognition, 2008
http://cmap.ihmc.us/publications/researchpapers/theorycmaps/theoryunderlyingconceptmaps.htm

What Is a Concept? …From a Concept Mapping Perspective
Alberto J. Cañas and Joseph D. Novak, Institute for Human and Machine Cognition, 2009
http://cmap.ihmc.us/docs/Concept.html

What Are Propositions? …From a Concept Mapping Perspective
Alberto J. Cañas, Institute for Human and Machine Cognition, 2009
http://cmap.ihmc.us/docs/Proposition.html

What Are Linking Words? …From a Concept Mapping Perspective
Alberto J. Cañas, Institute for Human and Machine Cognition, 2009
http://cmap.ihmc.us/Docs/linkingwords.html

Chapter 4 - Tools

All Tools (.PDF 695kb 15pgs)

Indicators of Success for Writing in Mathematics
.PDF 22kb 1pg

Observation Checklist for Writing in Mathematics
.PDF 24kb 1pg

My Math Writing [Primary]
.PDF 31kb 1pg

Indicators of Success for Writing [Junior/Intermediate]
.PDF 31kb 1pg

Five-Frames and Ten-Frames
.PDF 31kb 2pgs

My Math Pictures [Primary]
.PDF 31kb 1pg

Indicators of Success for Effective Pictures in Mathematical Writing [Junior/Intermediate]
.PDF 310kb 1pg

Mind Map Visual Overview
.PDF 330kb 1pg

Concept Map Visual Overview
.PDF 223kb 1pg

Mathematics is like…because…
.PDF 118kb 1pg

My Math Mind Map [Primary]
.PDF 31kb 1pg

Indicators of Success for an Effective Math Mind Map
.PDF 32kb 1pg

My Math Concept Map
.PDF 31kb 1pg

Indicators of Success for an Effective Math Concept Map
.PDF 39kb 1pg

Chapter 4 - Line Masters

All Line Masters (.PDF 185kb 14pgs)

4.1A VVWA [Primary]
.PDF 18kb 1pg

4.1B VVWA [Junior/Intermediate]
.PDF 18kb 1pg

4.2 Frayer Model
.PDF 18kb 1pg

4.3 Frayer Model
.PDF 18kb 1pg

4.4 Three-Part Concept Circle
.PDF 45kb 1pg

4.5 Four-Part Concept Circle
.PDF 42kb 1pg

4.6 Four-Part Concept Circle
.PDF 47kb 1pg

4.7 Five-Part Concept Circle
.PDF 50kb 1pg

4.8 Six-Part Concept Circle
.PDF 52kb 1pg

4.9 Eight-PartConcept Circle
.PDF 50kb 1pg

4.10 Sample Linking Words for Concept Maps
.PDF 19kb 1pg

4.11 Mind Map Elements
.PDF 18kb 1pg

4.12 Concept Map Elements
.PDF 18kb 1pg

4.13 Discovery Sheet
.PDF 18kb 1pg