134 pages. ISBN 978-0-9776939-6-2
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Download sample activities from the book (PDF), and try them out with your children!
Camp Logic is a book for teachers, parents, math circle leaders, and anyone who nurtures the intellectual development of children. It is not necessary to have any mathematical background at all to use these activities – only to have a willingness to dig in and work toward solving problems where there is no clear path to a solution.
The games and activities in this book give students an informal and playful introduction to the very nature of mathematics and its underlying structure. Students may be surprised to see that many of the games and puzzles involve very little if any arithmetic, and when they do, the arithmetic is not what makes the puzzle challenging. Rather, the challenge is the reasoning itself. The theme that runs throughout the activities, and in fact throughout the subject of mathematics, is the idea of an “implication,” that new information can be derived from old through a chain of reasoning. While the idea of implication is subtle, and students may be years away from a formal understanding, they can practice and sharpen their intuitions with interesting puzzles, stories, and games. In doing so they will develop some of the same skills that they will be harnessing in learning more traditional mathematical material.
Mark Saul is the director of the Center for Mathematical Talent at the Courant Institute of Mathematical Sciences, New York University. He grew up in the Bronx, got his BA from Columbia University and PhD from New York University. He then spent 35 years in and around New York, teaching mathematics in classrooms from grades 3 through 12. He is a 1984 recipient of the Presidential Award for Mathematics and Science Teaching. Saul has served as President of the American Regions Mathematics League, mathematics field editor of Quantum (the English-language version of the Russian journal Kvant), a board member of the National Council of Teachers of Mathematics, and a member of the Mathematical Sciences Education Board for the National Research Council. His publications include numerous articles and books.
Sian Zelbo holds a degree in law from the University of Texas and an MA in math education from Teachers College Columbia University. Sian was a practicing lawyer when she decided to return to school to explore her latent interest in mathematics. Sian is the associate director of the Center for Mathematical Talent at the Courant Institute of Mathematical Sciences, New York University. She also teaches math at the Speyer Legacy School in New York City and works with various other schools as a math education consultant. Sian’s interest is in helping young people discover and develop their own interest and ability in mathematics through extracurricular activities that focus on mathematical reasoning and problem solving.
Dr. Saul and Ms. Zelbo started this project out of a shared desire to reach students who may not be aware of their own mathematical potential. Many people wrongly believe that mathematics is nothing more than the content of the tests students take in school. Because of this limited view, the natural ability that all students have for mathematical reasoning and problem solving is not nurtured. When young people have access to meaningful problems that help them see beyond this view of math, their own relationship with the subject changes. They begin to see math as interesting, creative, and accessible, and they see themselves as mathematically adept.
The games and activities in this book give students an informal and playful introduction to the very nature of mathematics and its underlying structure. Students may be surprised to see that many of the games involve very little if any arithmetic, and when they do, the arithmetic is not what makes the puzzle challenging. Rather, the challenge is the reasoning itself. The theme that runs throughout the activities, and in fact throughout the subject of mathematics, is the idea of an “implication,” that new information can be derived from old through a chain of reasoning. While the idea of implication is subtle, and students may be years away from a formal understanding, they can practice and sharpen their intuitions with interesting puzzles, stories and games, and in doing so they will develop some of the same skills that they will be harnessing in learning more traditional mathematical material.
This book includes material that Dr. Saul and Ms. Zelbo have developed together over the years as part of their work with the Center for Mathematical Talent, an outreach program that operates through NYU’s Courant Institute and is funded by the Alfred P. Sloan Foundation. The activities have been field tested in classrooms and math circles with students ages 8 and up from diverse backgrounds. The book can be used as the curriculum for a ‘course’, and because the activities are modular, they can also be used as enrichment in the regular classroom. Students will gain a feel for the nature of mathematical reasoning and will get practice with some of the concepts and skills that lie at the very heart of mathematics.
Questions and answers
Animal Puzzles (Introduction to Logical Reasoning)
The Game of Giotto (Practice with Logical Reasoning)
A Says B Lies (Introducing Proof by Contradiction.)
Linguistics Puzzle (More Proof by Contradiction)
Giotto Puzzles (Analyzing the Logical Structure of Giotto)
Watermelon Language (Logic Applied to Number Systems)
Jittery Soldiers (An Introduction to Invariants)
The Black and Red Problem (An Introduction to Parity)
Parity Problem Set
Discuss solution to Black and Red Problem (A Surprising Connection to Parity)
Ginger’s Pigeons (Proofs with the Pigeonhole Principle)
The Mouse-and-Cheese Problem: Another example of Parity
Nim (An Introduction to Mathematical Induction)
Two-Row Nim and One-Piece Chess (Induction and the Idea of Isomorphisms)
Leap Frog (Another Example of the Use of Invariants)
Hidden Cards Puzzle (Practice with Logical Deductions)
Magic Squares and 15 Game (More Practice with invariants and isomorphisms)
Congratulations, Sian and Mark! You have inspired so many children in our community. Now kids (and adults) all over the world will have access to your brilliant and exciting approach to math.
Thank you for all you do Sian and Mark, to support those of us who are passionate about our kids not having an ‘I hate math’ mentality by third grade. And thank you for helping me see the creative side of math through our PAL Workshop Series that I was never taught growing up.
Congratulations on your contribution to mathematical education for kids. It is such a worthwhile endeavor
and you are certainly an inspiration.
Sian gave my daughter the gift of Math! A girl who was not sure about it was transformed into a confident, excited, inventive student.
May her book inspire hundreds of children in the same way. Congratulations Sian!
I’m proud to be one of your first customers. I’ll test your book on our 7-yr old Paul! He loves math.
Love to you and your family,
I pre-ordered Camp Logic and to date have not received my pdf or kindle copy to date. Can you please let me know when I will receive my copy.
I just got the print proof yesterday! I am about to send the update to crowd funders and those who preordered. We should be delivering print and ebooks in the next few weeks. The book came out so good!
Very neat. Thanks for sharing; Jesus Christ Bless! :)
What are the ages of children that would benefit from these activities.
I just ran a math circle today using page 24 — the first Lewis Carroll Puzzle (last week we played the game of Giotto). We spent the entire hour “discussing” the problem. It was so much fun and the discussion so valuable. The age group was 8 to 12.
How is your math circle doing now, Kristin? Glad the puzzles work well!