Study Guide for Chapter 10
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:
- 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
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