Chapter 10: Mathematicians Reason

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
• A Choral Counting Planning Tool that Kassia Omohundro Wedekind and I developed

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:
  • First exploration of Drips
  • Does the choice of objects matter?
• 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:
  • Odds and Evens
  • Strike it Out
• 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