Can You Do the Math Salute?

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How Is This Math?

The idea that math is only about numbers, calculations, and textbook exercises is one of the greatest lies we learn in school. Of course, nobody ever comes straight out and actually says that. But the whole system teaches us every day what counts for math and what doesn’t.

James Tanton’s math salute is a physical puzzle.

How in the world did he do that?

Physical puzzles don’t fit into our cultural understanding of math. But the process of figuring out the puzzle is the same problem-solving process we use to figure out other puzzles — including the puzzles we call math.

In fact, real mathematics is all about figuring out puzzles without a teacher showing you what to do. Problem-solving is a universally useful skill.

As master teacher W. W. Sawyer said:

“Everyone knows that it is easy to do a puzzle if someone has told you the answer. That is simply a test of memory. You can claim to be a mathematician only if you can solve puzzles that you have never studied before. That is the test of reasoning.”

—W. W. Sawyer, Mathematician’s Delight

So tackle the puzzle of the math salute. Show it to your kids. (And don’t be surprised if they figure it out before you do!)

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

The Professor of Legend

The traditional mathematics professor of the popular legend is absentminded.

    He usually appears in public with a lost umbrella in each hand.

      He prefers to face the blackboard and to turn his back to the class.

        He writes a, he says b, he means c; but it should be d.

          Some of his sayings are handed down from generation to generation.

            • “In order to solve this differential equation you look at it till a solution occurs to you.”
            • “This principle is so perfectly general that no particular application of it is possible.”
            • “Geometry is the science of correct reasoning on incorrect figures.”
            • “My method to overcome a difficulty is to go round it.”
            • “What is the difference between method and device? A method is a device which you used twice.”

            George Pólya
            How To Solve It

            If you’re not familiar with Polya’s work, here’s a 4-page summary of his problem-solving method.

            Or check out David Butler’s wonderful Solving Problems Poster, which encapsulates Pólya’s system in a visual, easy-to-follow way that works with younger students, too.

            4 steps to solving problems

            CREDITS: “Professor” cartoon (top) by André Santana via Pixabay.
            THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

            Have a Mathematical Thanksgiving Dinner

            With the pandemic still raging, most of us will have to adapt our normal holiday traditions to fit the new reality. We may not be able to have a big family gathering (except over Zoom), but we can still enjoy great food.

            So for those of you who are planning ahead, here is a mathematician’s menu for next week’s Thanksgiving dinner.

            Optimal Potatoes

            Green Bean Matherole

            Borromean Onion Rings

            Thanksgiving Turduckenen-duckenen

            And for Dessert

            May I suggest some of Don Cohen’s Infinite Cake?

            Click here for cake

            CREDITS: “Thankful” photo (top) by Pro Church Media via Food videos by mathemusician/doodler Vi Hart.

            Math Conversation Starter

            (Click for larger image.)

            What do you see?

            Does it make you wonder?

            How is perspective art similar to the isometric drawing in yesterday’s post? How is it different?

            You may also enjoy:

            CREDITS: William Hogarth – “The importance of knowing perspective” (Absurd perspectives), Engraving on paper. From Wikimedia Commons.

            Math Humor and Copywork

            Homeschooling Memories…

            The more years we spent homeschooling, the more I appreciated Charlotte Mason’s work and tried to incorporate her ideas into our laid-back, eclectic, not-quite-unschooling program.

            We never fit the typical Charlotte Mason mold. Mosquitos and natural laziness limited our nature walks, and our version of narration was much too informal.

            But those are just techniques, methods.

            What really interests me in Mason’s writing is the philosophy behind the methods. Two points resonated: That we must respect our children as persons in their own right. And that we must provide a generous, wide-ranging feast to their minds.

            Striving to live out those principles had a profound influence on our day-to-day homeschooling.

            Which Brings Me to Copywork

            I’ve never managed to keep a diary-style journal, though as the years roll by, I wish I had. But I’ve always enjoyed saving favorite tidbits from the books I read.

            Mason called it a commonplace book. I call it my “magpie” journal, where I collect my treasure of shiny things.

            And so I brought copywork into my homeschooling system. I taught English spelling, grammar, and mechanics through living language. My favorite exercise was to write a short quotation on the whiteboard, leaving out all punctuation and capital letters, for my children to edit.

            Do you use copywork or keep a commonplace book? I’d love to hear your experiences or read one of your favorite quotations.

            Please comment below!

            Math Humor Quotes

            As you probably guessed, my personal magpie journal overflows with mathematics. Inspirational, insightful, or simply instructive — if it catches my eye, I grab it. But my kids always prefer the funny bits.

            Here are a few of my favorites:

            Arithmetic is neither fish nor beast; therefore it must be foul.


            Mathematics: a wonderful science, but it hasn’t yet come up with a way to divide one tricycle among three little boys.

            —Earl Wilson

            Logic is a systematic method of coming to the wrong conclusion with confidence.

            —Anonymous (similar to a comment by Morris Kline)

            You propound a complicated mathematical problem: give me a slate and a half an hour’s time, and I can produce a wrong answer.

            —George Bernard Shaw

            I pulled these quotations from the (out of print) Dictionary of Mathematical Quotations by Donald Spencer. Quotes range from thought-provoking to inane, including an assortment of “anonymous” bumper-sticker or T-shirt-style quotes not usually included in a quotation book. I do wish Spencer had included documentation with the quotes. Even though I’d probably never look them up, I’m still curious about where the quotes came from.

            If you’d like to add mathematical copywork to your school repertoire, you’ll find the following online sources useful:

            CREDITS: Feature photo (top) by Bruce Guenter via Flickr (CC BY 2.0).

            What Is Mathematics?

            Here’s a bit of fun to brighten up your Monday:

            Mathematics: Measuring x Laziness² by Zogg from Betelgeuse (Martin Kuppe).

            For Further Exploration

            James Grime explains the “Aldebaranian” curve calculator in this video:

            And here is the “Map of Mathematistan”. Click to zoom in.


            Credit: I contacted @ZoggTheAlien for permission to use the sketch. He said, “Feel free to use it. It’s a Galactic Commons license; you can use it if you don’t claim it’s made by one of your species.”

            Please Add Your Comments Below


            • Do you have a favorite place in the Land of Mathematics? Why do you like it?
            • Most children find themselves stuck in the inner city of Arithmetics. How can we help them get out and explore the landscape?

            howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

            Unending Digits… Why Not Keep It Simple?


            Unending digits …
            Why not keep it simple, like
            Twenty-two sevenths?

            —Luke Anderson

            Math Poetry Activity

            Encourage your students to make their own Pi Day haiku with these tips from Mr. L’s Math:

            And remember, Pi Day is also Albert Einstein’s birthday! Check out this series of short videos about his life and work: Happy Birthday, Einstein.

            CREDITS: Today’s quote is from Luke Anderson, via Background photo courtesy of Robert Couse-Baker (CC BY 2.0) via Flickr.

            howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

            Quotable: I Do Hate Sums


            I’ve been looking for quotes to put at the beginning of each chapter in my math games books. I found a delightful one by Mrs. LaTouche on the Mathematical Quotations Server, but when I looked up the original source, it was even better:

            I am nearly driven wild with the Dorcas accounts, and by Mrs. Wakefield’s orders they are to be done now.

            I do hate sums. There is no greater mistake than to call arithmetic an exact science. There are Permutations and Aberrations discernible to minds entirely noble like mine; subtle variations which ordinary accountants fail to discover; hidden laws of Number which it requires a mind like mine to perceive.

            For instance, if you add a sum from the bottom up, and then again from the top down, the result is always different.

            Again if you multiply a number by another number before you have had your tea, and then again after, the product will be different. It is also remarkable that the Post-tea product is more likely to agree with other people’s calculations than the Pre-tea result.

            Try the experiment, and if you do not find it as I say, you are a mere sciolist*, a poor mechanical thinker, and not gifted as I am, with subtle perceptions.

            Of course I find myself not appreciated as an accountant. Mrs. Wakefield made me give up the book to [my daughter] Rose and her governess (who are here), and was quite satisfied with the work of those inferior intellects.

            — Maria Price La Touche
            The Letters of A Noble Woman
            London: George Allen & Sons, 1908

            *sciolist: (archaic) A person who pretends to be knowledgeable and well informed. From late Latin sciolus (diminutive of Latin scius ‘knowing’, from scire ‘know’) + -ist.

            howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.