As you poke around, you’ll find one page for each chapter. On each page, you’ll find a variety of links, related blogposts, articles, videos, and other supplementary resources. You’ll also find the bit of the study guide relevant for just that chapter. If you’d like it in one document, here’s the complete, free study guide.

On Tracy’s personal blog, tjzager.com, you’ll find these resources duplicated, as well as forums where you can connect with other readers, ask questions, and discuss the book.

Please remember to use #becomingmath if you discuss the book on social media.

Welcome and enjoy!

]]>

I gave a brief talk about some of these ideas at ShadowCon 15:

Annie Fetter gave a short talk in tribute of her mother, called “You Call That Math?” Annie’s mother was a brilliant artist who, like my mother, didn’t see what she did as mathematics:

If you choose to create your own word cloud, here’s a page to get you going. If you’d like larger versions of the word clouds, here they are: figure 1-1 and figure 1-2.

Math Autobiographies:

- A robust resource for math autobiographies from Discovering the Art of Mathematics
- A blogpost from Kent Haines about launching the year with student math autobiographies.
- Teachers are sharing their math autobiographies on Tracy’s forums page. Here’s a powerful example from Joe Schwartz: Part 1 Part 2

I first heard “Trouble with Math in a One-Room Country School,” a powerful poem from the great Jane Kenyon, on public radio’s *The Writer’s Almanac*. I was washing dishes and had to stop. I turned off the water and stood at the sink, sponge in hand, listening. When Keillor read, “My shame was radical,” I crumpled. In the moments after, I resolved to write this book no matter what challenges may lie ahead. My mother said this poem spoke her truth best of all.

This video about one student’s humiliation in 6th grade math is a powerful example of how what we feel in math class can connect to our success or failure in math class:

Nalini Joshi, talking about why she’s a mathematician, and how she became one.

]]>*Bringing Math into the Present Day *

The Mathematics of Juggling from *Quanta Magazine *(later reprinted in *Scientific American)*. Click through to the link for video.

TED Talk: Teaching Math through Movement

TED Talk: The Beautiful Math of Coral

Beauty of Mathematics is a quick look at mathematics in the world around us.

Math Munch: interview with Nalini Joshi

*Finding Math in Our World*

Found math with Maya and Daphne

The annual Math Photo challenge is delightful, and could inspire some math hunts, math walks, and math photo challenges of your own. On twitter, look for #mathphoto15 and #mathphoto16. The 2015 website and 2016 website are great places to get started.

*Babies and Math (in case you’re interested!)*

*New York Times*article summarizing breakthrough research: Study Finds Babies at 5 Months Grasp Simple Mathematics- More recent
*Science*article about babies’ approximate number sense

*Resources related to the classroom examples:*

James Tanton‘s 5-part video series about thinking like a mathematician.

A highly readable summary of Dweck‘s research from *New York *magazine. It’s a great piece to share with families.

Shawn Towle‘s downloadable collection of postable quotes.

*Reacting to the Unexpected*

A lovely, short video about Melanie Matchett Wood, so you can put a face to the name and hear her reflect on collaboration and creativity and connection in math.

*Making It Safe*

I hope you’ll read one of the pieces in my personal canon: Herbert Kohl’s original essay, I won’t learn from you. It’s essential.

]]>*Mathematicians Make Mistakes*

Further information about Poincaré from The Story of Mathematics.

A little primer on Chaos Theory.

If you’re curious about Shiing Shen Chern, here’s a short movie about his life.

*Resources related to the classroom examples*

Michael Pershan curates Math Mistakes, a website where he compiles students’ mistakes so teachers can analyze and discuss them.

Youcubed.org has many resources about how to teach students to welcome mistakes.

*Making Mistakes and Equity*

Reshma Saujani gave a great TED talk: “Teach Girls Bravery, Not Perfection.”

If you’d like to investigate Dr. Fern Hunt and share her with your students, this website from Career Girls is a good place to start. Here’s the first video:

]]>The interview with Brian Confrey can be found in this 2009 video from the University of Bristol’s Mathematical Ethnographies Project: Are Mathematicians Creative?

Phil Daro’s “Against Answer-Getting”:

Clarity and Specificity:

Chris Luzniak video about precise language from PBS. (Click through to the video–it’s worth it!)

Videos from Justin Solonynka‘s classroom:

My Favorite No video from the Teaching Channel.

Resources for automaticity:

- Number Talks essay from Kathy Richardson
- Talking Math with Your Kids – a great website to give to parents
- Fluency without Fear from YouCubed.org

BBC documentary about Andrew Wiles’ solution of Fermat’s Last Theorem:

Dan Meyer‘s TED talk:

Phil Daro‘s “Against Answer Getting”:

Joining the Math-Twitter-Blog-o-Sphere (#MTBoS):

Makeover blogs:

- Fawn Nguyen: When I Let Them Own the Problem (middle school)
- Joe Schwartz: Meatball Surgery (elementary school)
- Joe Schwartz: What He Said (elementary school)
- Dan Meyer‘s collection of makeover blogs (high school)

Low Floors, High Ceilings, and Open Middles:

- NRICH article Using Low Threshold High Ceiling Tasks in Ordinary Classrooms
- Dan Meyer’s Video Games & Making Math More Like Things Students Like talk, in which he discusses open middle problems:

- Open Middle: Challenging Math Problems Worth Solving is an excellent, free collection of open middle problems curated by teachers Robert Kaplinsky, Nannette Johnson, and Bryan Anderson

Productive Struggle and Destructive Struggle

- Robert Kaplinsky‘s Ignite talk:

- Francis Su, current president of the Mathematical Association of America, wrote an MAA Focus piece about teaching and productive struggle, reprinted here: The Value of Struggle

*101questions*

*Notice and Wonder*

Annie Fetter‘s ignite talk about Notice and Wonder is a great starting point:

Notice and Wonder Blogs from the Math Forum at NCTM team, especially Max Ray-Riek, Annie Fetter, and Suzanne Alejandre:

- Noticing and Wondering in Elementary School
- Noticing and Wondering in Middle School
- Noticing and Wondering in High School
- Using Problems of the Week–Getting Started
- Problem Solving: It Has to Begin with Noticing and Wondering
- Free Scenarios for Notice and Wonder
- Sense-Making? Aren’t We Already Doing That in Literacy?

*Problem Posing*

- Christopher Danielson‘s What did you learn?
- Making Sense a blogpost of mine about students’ thinking about word problems
- Springboarding a blogpost of mine about students posing problems after counting

*When Students’ Questions Drive Teaching and Learning: “Are Shapes Math?”*

- Van Hieles’ Theory of Geometric Thought
- An article from
*Teaching Children Mathematics*about teaching geometry with Van Hieles’ model. *Which One Doesn’t Belong?*is an outstanding pair of books (student book and teacher’s guide) from Christopher Danielson that will help you teach geometry in a meaningful, question-driven way. Highly recommended.

A beautiful blogpost from @TAnnalet about 3rd-grade students’ questions about infinity: “Like Someone Walking Through Time Without Noticing He Is.”

]]>Margaret Wertheim‘s TED talk: The Beautiful Math of Coral

The Institute for Figuring‘s Crochet Coral Reef page.

*Connecting Math and the World*

- Get the Math from PBS thirteen, featuring well structured, CCSS-aligned math challenges issued from professionals in fashion, sports, music, video game design, etc.
- We Use Math from BYU and Maths Careers from the Institute of Mathematics and its Applications profile math in different careers.
- Rethinking Schools, Radical Math, and Mathalicious ($) are outstanding resources for integrating social justice issues with mathematics.

*Connecting Math to Math*

Multiple Representations:

- Principles to Actions, from NCTM, has a strong section on representations.
- Tripathi’s excellent article is here, for
*MTMS*subscribers.

Relational Thinking:

- Richard Skemp’s powerhouse article from 1976, Instrumental Understanding and Relational Understanding, downloaded from http://www.skemp.org.uk/
- A webinar I gave at the Global Math Department, in which I discussed some of these ideas.

*Connecting Math to Self*

Counting Collections:

- Kindergarten lesson from the Teaching Channel
- 3rd grade lesson from the Teaching Channel
- Counting Collection videos, planning templates, etc. from tedd.org

*New Connections*

Terry Tao’s post: There’s more to mathematics than rigour and proofs

Leone Burton’s article: Why is Intuition so Important to Mathematics but Missing from Mathematics Education? ($)

Evelyn Lamb‘s article introducing readers to Bill Thurston: The Mathematical Legacy of William Thurston

A lovely video of Thurston, showing how he used his imagination, manipulatives, and diagrams to visualize mathematics. “From Knots to Narnia.”

Deborah Ball’s must-read article about manipulatives: Magical Hopes: Manipulatives and the Reform of Math Education, courtesy of American Educator: The Professional Journal of the American Federation of Teachers, v16 n2 p14-18,46-47 Sum 1992.

Figure 9.6: The Estimation Cycle

Figure 9.7: Lesson components that encourage students to build mathematical intuition

John Stevens‘s *Would You Rather?* resource (home of the quarters problem and lots of other rich tasks)

Andrew Stadel‘s fantastic resource: Estimation 180

Andrew Stadel‘s blog: http://mr-stadel.blogspot.com/

Kristin Gray‘s blog: https://mathmindsblog.wordpress.com/

Joe Schwartz‘s blogposts about Estimation 180:

- Our First Real 3-Act about mileage
- That’s Gold, Jerry! Gold!!
- Building Number Sense
- Boogers and Bloody Noses

Andrew Gael‘s blog: https://thelearningkaleidoscope.wordpress.com/

]]>*About Proof*

- Ben Orlin‘s hilarious Two-Column Proof that Two-Column Proofs are Terrible
- Avery Pickford‘s thoughtful series starts with Proof Doesn’t Begin with Geometry: Redefining Proof
- Ben Blum-Smith’s strong series starts with Nuggets II: Proof
- Dan Meyer‘s If Proof is Aspirin, Then How Do You Create the Headache?
- NRICH has many useful articles about proof.
- Lockhart’s Lament is essential reading.

*Choral Counting*

- TEDD.ORG: Choral Counting videos, planning protocols, etc.
- Laretha Todd’s Count (3rd grade): Discover Number Patterns with Skip Counting
- Drew Crandall‘s Count & Lesson (3rd grade): Reasoning about Multiplication and Division
- Drew Crandall‘s Assessment of Count with Exit Tickets (3rd grade): Assess and Plan with Exit Tickets
- Theresa Tse’s Skip Counting and Counting Collection (1st grade): Counting Collections to 100
- Kristin Gray‘s blogs about Choral Counting with Decimals: 1, 2, 3

*Visual Patterns*

- Peter Liljedahl‘s article: Repeating Pattern or Number Pattern: the Distinction is Blurred
- Visual Patterns from Fawn Nguyen
- Fawn‘s blog about Visual Patterns
- Example Pattern Talks from Fawn
- Lots of excellent blogs about Visual Patterns
- Beatty article summarizing research on growing patterns and kids’ thinking
- Paying Attention to Algebraic Reasoning from the Ontario Ministry of Education

*True/False*

- TEDD.ORG True/False
- Video: Reasoning about Division from the Teaching Channel, or unedited at True/False Equation, 4th grade with Lynn Simpson.

*Number Talks*

- Kathy Richardson and Ruth Parker’s Number Talks Toolkit.
- Cathy Humphreys and Ruth Parker’s
*Making Number Talks Matter.*

*Games*

- Mike Lawler‘s blogs about Nim, Drips, and Train, in response to my questions on Twitter:
- Games that Lead to Generalizations and Proof-Like Reasoning (Brainstormed by the #MTBoS). (Shareable link: http://tinyurl.com/proofgames)
- A stellar compilation from Daniel Finkel
- NRICH is a great website with many games. For example:
- Marilyn Burns‘s article 4 Win-Win Math Games hints at some of the games she’s created and taught during her career. Four Strikes and You’re Out is particularly fantastic.
- Avery Pickford‘s Using Mastermind to Model the Life Cycle of a Problem
- Numberphile has many videos featuring practicing mathematicians exploring the math of games. Get started with How to Always Win at Dots and Boxes with Elwyn Berlekamp.

*Crafting Claims*

- Kristin Gray: Articulating Claims in Math
- Chris Luzniak video of students conjecturing: Give Students Ownership
- When thinking about “leaving the door open,” read this terrific article from Karen Karp, Sarah Bush, and Barb Dougherty: 13 Rules That Expire. (Free for NCTM members that subscribe to
*Teaching Children Mathematics*, $ for others)

*Always, Sometimes, Never*

- Malcolm Swan and Jim Ridgway on Always, Sometimes, Never
- Elementary Always, Sometimes, Never google doc (shareable link is tinyurl.com/K6ASN)
- Andrew Stadel‘s whiteboarding blog about placemat
- Always, Sometimes, Never blogs:
- Fawn Nguyen
- Kristin Gray 1 and 2
- Grace Chen
- Chris Hunter
- Lisa Bejerano
- Kate Nowak

]]>We should not teach "keyword" or "clue word" strategies in math.

Full stop.#keywords pic.twitter.com/8JmtUyE8lF

— Tracy Johnston Zager (@TracyZager) March 1, 2016

Marcus du Sautoy’s full essay: How Mathematicians Are Storytellers and Numbers Are the Characters

*Cultivating Skepticism: Convince Yourself, Convince a Friend, Convince a Skeptic*

*New York Times’s*puzzle/article about confirmation bias- Veritasium‘s short film about confirmation bias:

- Wendy Petti’s Convince Me

*What Counts as Proof?*

- You can find many of Harel and Sowder’s papers at Harel’s publications link
- The Math Forum‘s Ask Dr. Math on inductive vs. deductive reasoning
- Plus Magazine has a nice introduction to optical illusions that might help you push students past “it looks like…” as a justification
- Stylianides’s excellent article Breaking the Equation ‘Empirical Argument = Proof’ at NRICH
- Dan Meyer‘s discussion of the relationship between doubt and proof

*Knocking on Proof’s Door: Justifications with Younger Students*

- Even and Odd Numbers: A Journey into the Algebraic Thinking Practice of Justification A two-part series on justification at the
*Teaching Children Mathematics blog*(no membership needed). Part 1, Part 2 - Kristin Gray’s students work with claims about area and perimeter

*Math as a Verb*

* *

*Proof and Equity*

- To get your feet wet with Danny Bernard Martin‘s work, you can start browsing these publications.

*Yuri Matijasevich and Julia Robinson*

- Yuri Matijasevich’s description of working with Julia Robinson
- Film Trailer–Julia Robinson and Hilbert’s Tenth Problem

- Full movie details–Julia Robinson and Hilbert’s Tenth Problem

*Thinking Partnerships*

- Think Time and Collaborative Learning Excellent, brief video from the Teaching Channel. (2:19)
- How to Teach Math as a Social Activity video of 5th and 6th graders

- Fullilove and Treisman: Mathematics Achievement Among African American Undergraduates at the University of California, Berkeley: An Evaluation of the Mathematics Workshop Program
- Treisman: Studying Students Studying Calculus: A Look at the Lives of Minority Mathematics Students in College
- Video of groups reflecting on their work from NRICH.
- Peter Liljedahl’s website
- More on Vertical, Non-Permanent Surfaces:

*Cross-Pollination*

- My blogpost series about building number lines in kindergarten.
- Lovely blogpost from Simon Gregg about credit for productive mistakes.
- Teaching Channel video of Laretha Todd’s class giving credit: Can You Share Who Said That? (1:32)

*Math Disputes*

Chris Luzniak and Making Math Debatable:

- PBS video: Encouraging Debate
- PBS video: Get a Second Sentence
- Complete PBS series: Making the Case
- Chris’s website and blog

Resources for Mathematical Disputes:

- Christopher Danielson‘s book,
*Which One Doesn’t Belong?*and the website it inspired, Which One Doesn’t Belong?, Crowdsourced by the #MTBoS; curated by Mary Bourassa. - Would You Rather Math? A website from John Stevens
- KenKen from NCTM

*Peer Feedback*

- Video: Austin’s Butterfly: Building Excellence in Student Work–Models, Critique, and Descriptive Feedback from Ron Berger (6:18)

- More video and resources from Ron Berger and Expeditionary Learning about Critique

Clarence Stephens and the “Potsdam Miracle”:

- Potsdam Professor Armond Spencer: On Attracting and Retaining Mathematics Majors—Don’t Cancel the Human Factor
- Rafe Kinsey’s blogpost: The Potsdam Miracle: Lessons in Revolutionizing Undergraduate Mathematics
- MAA article about Clarence Stephens

If you’d prefer to chat on facebook, here’s the discussion group.

On twitter, check out and use #BecomingMath.

*Summer 2017 teacher-organized online book club sign-up and schedule.*

Reviews of and blogposts about *Becoming the Math Teacher You Wish You’d Had:*

Amie Albrecht

Jennifer Fairbanks

David Butler

Middleweb

Additional forums, discussion boards, and book chats will be posted here as they come online. To let me know about a new one, please email tracyzager@gmail.com. Thanks!

]]>