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June 21, 2025

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The personal blog of Gary S. Stager, Ph.D.

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  • About
    • Publications
    • Videos
    • Publicity Photos
  • Working with Gary
    • Services
1:1 computing / creativity / general / project-based learning / teaching / technology

Virtual Learning Lunch – Construction of Mathematical Knowledge

Gary Stagerby Gary StagerJanuary 10, 2016July 25, 2020

Here are some objects to think with to get you started.

Pack a lunch, fire up a colortini and watch the pictures as they fly through the air!

Seymour Papert’s Mathland

Read Gary Stager’s Personal Road to Reinventing Mathematics Education.

Conrad Wolfram’s TED Talk


Teaching kids real math with computers

Kamii Videos

Double-Column Addition

Multiplication of Two-digit Numbers

Multidigit Division

Making Change – The difficulty of constructing “tens” solidly

Constance Kamii Direct vs Indirect Ways of Teaching Number Concepts at Ages 4-6
A comprehensive lecture explaining Piagetian ideas showing that although number concepts cannot be taught directly, they can be taught indirectly by encouraging children to think.

Kamii Games

  • Arithmetic Games with Playing Cards
  • Modifying a Board Game (Sorry) to Foster Kindergartners’ Logico-Mathematical Thinking

  • Lining-Up the 5s – A Card Game
  • Kamii Game Cards to download and print
  • Kamii on Games over Worksheets (article)

Videos Suggesting a Potential MicroWorlds (coding) Activity for Constructing Understanding of Fractions

“Debbie” from the research of Idit Harel

Minds-in-Play from the research of Yasmin Kafai.

Math in the World (A beautiful view)

The Beauty of Math in Coral and Crochet by Margaret Wertheim at TED.

Stephen Wolfran’s Introduction to Wolfram Language


Stephen Wolfram’s Introduction to the Wolfram Language

The Invent to Learn Guide to Getting Started with Wolfram Language

Important Articles by Stephen Wolfram

  • What is a Computational Essay?
  • How to Teach Computational Thinking
  • High-School Summer Camp: A Two-Week Path to Computational Thinking
  • Machine Learning for Middle Schoolers
  • Two Hours of Experimental Mathematics

Askwith Forum: Stephen Wolfram and Howard Gardner – Best Education in Computational Thinking 

Making Programming Accessible to Everyone with Wolfram Language

Stephen Wolfram Computational Universe in the MIT Artificial General Intelligence class lecture (March 2018)

All of these links are live at cmkfutures.com/wolfram

Gary Stager

Veteran educator Gary Stager, Ph.D. is the author of Twenty Things to Do with a Computer – Forward 50, co-author of Invent To Learn — Making, Tinkering, and Engineering in the Classroom, publisher at Constructing Modern Knowledge Press, and the founder of the Constructing Modern Knowledge summer institute. He led professional development in the world’s first 1:1 laptop schools thirty years ago and designed one of the oldest online graduate school programs. Gary is also the curator of The Seymour Papert archives at DailyPapert.com. Learn more about Gary here.

TaggedcodingConrad WolframConstance Kamiiconstructionismgary stagerhoward gardnerLogomathmathematics educationSeymour PapertStephen Wolfram

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