A Mathematician at Play Puzzle #1

I’ve been collaborating with the English-language newspaper in India called The Hindu for the past few months, producing puzzles for a column called A Mathematician at Play.

It’s a great collaboration. I produce the puzzles, and they make them look beautiful.

I’m going to start sharing these puzzles on the Math for Love blog. Some of these puzzles are classics, others are original. All of them involve some kind of thinking or insight that strikes me as pretty, or surprising, or delightful.

Puzzles will go out Mondays for the next few months.
Answers will go out Fridays.

The first puzzle, below, is a series of grid puzzles. I hope you have fun trying these out! Share them with your kids or students, or work on them with your friends, and let me know what you think in the comments!

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Teachers Making Teachers Better

I’ve just witnessed one of the best back-and-forths ever on Twitter, and I had to share it. It’s a phenomenal example of the pileup that allows great teachers to push each other and discover more was possible in their lesson ideas and plans than they had thought.

This is why you should join the Math Twitter Blog o Sphere (#MTBoS, #iteachmath)

Overcoming Confirmation Bias with the 2, 4, 6 Puzzle

The promise of mathematics is that it will teach students to think.

Sadly, there’s been no solid evidence that math class actually succeeds, statistically speaking, in achieving this end. A pessimist would conclude it’s a hopeless project. But far more likely is that math classes, statistically speaking, haven’t been spending much time doing tasks that lead students to think, or learn to think.

The researcher Peter Cathcart Wason came up with a series of games and tests in the sixties to explore common failures in human reasoning. The first of these was the 2, 4, 6 Puzzle.

Happily, the 2, 4, 6 Puzzle is a delightful and devious way to play with kids (and adults!) in your life, be they students or children. Our writeup of the lesson is here.

The brilliance of the game is that it demonstrates to the player how staying in their comfort zone, avoiding “errors,” and sticking with safe guesses prevents them from solving the puzzle. It teaches inductive reasoning, and why avoiding confirmation bias is important.

In other words, it teachers students how to think.

Equally delightful is that the math students can get into as they explore the puzzle. The more math people know, the more they tend to do as they play.

Update: my 9-year old just schooled me. Gave me 16 2/3, 31 1/3, 50 as his pattern and then started laughing deviously. His pattern is below. pic.twitter.com/9pCRWQAAaB

— Robert Kaplinsky (@robertkaplinsky) October 15, 2017

Math can teach students to think. Now we just need to make sure our math classes to the same.