Saturday, May 4, 2013

Book Review: Measurement, by Paul Lockhart

In 2002, Paul Lockhart wrote A Mathematican's Lament, a 25-page exploration of much that is wrong with math education. I liked it, but I'd rather explore how to do math education right. Last year he came out with Measurement, a 398-page exploration of mathematics itself. It is delightful, and I want to recommend it to all my students in pre-calculus, calc I, and calc II. I think anyone who has some experience with geometric and algebraic reasoning can enjoy this book.

His publisher, Harvard University Press, put out a short video of Lockhart explaining the difference between math and science questions and why he thinks of math as one of the arts, with the help of a nice geometry problem. The video will give you a small taste of what's in store for you in the book.

If you watch the whole video, you'll notice that he never offers an answer for the puzzle he poses (though he suggests that there are many answers). That would be like telling the surprises from the end of a movie. He doesn't give many answers in the book either.  He does give lots of hints, and shows lots of strategies and techniques. He knows that the joy of math comes from figuring things out for yourself, so he shows us some of his favorite problems and asks us if we'd like to solve them. But he went beyond a mere compendium of puzzles, and connected the problems he shows, taking his readers on a delightful journey though size and shape (part one) and time and space (part two).

Many of the problems posed are familiar to those who study math, like this one:

And many are less familiar, like this one:

All of them are presented in the context of the larger story Lockhart tells.

You'll find the book enjoyable, even if you're not feeling up to solving these puzzles. But the more often you put down the book and pick up your pen or pencil and paper, the more fun you'll have. I only did a fraction of the problems he posed, so I'm looking forward to lots more fun the second time I read it.


  1. Thank you, Sue. You know I can't say no to math books, so I just ordered it on Amazon

    We did the parallelogram on Day 12 :)

  2. I bought that book after reading Sam Shah's recommendation on facebook. I haven't gotten very far yet, but I am loving all the puzzling I do math book reports with my 8th graders at the end of the year and will add it to my book list as my geometry students would really enjoy it.

  3. Hi Sue,
    Back near the start of the school year, a few teachers embarked on a effort to form a sort of virtual reading group, housed at Lockhart's content to tackle this book. I think we all got a bit busy, and so we didn't get much past the first 20 pages or so. Personally, one of the things that was holding me back the most was feeling that I needed to somehow find the idealized lockhartian answer or proof to every bolded question. About a month ago, I decided to simply read it through without trying to stop and solve each problem; instead I wanted to try to focus on grasping the storyline of the book as a whole, and I found it beautiful, and it left me more inspired to go back and read through it a second time to work on the problems I found most intriguing, so I'm hoping to get back to the blog about the book this summer, and would welcome your participation.

  4. I subscribed to the blog. If I can get myself signed up on something other than Google Reader before they throw it out (craziness!!), I'll be there.

  5. not everyone likes to puzzle through a problem without knowing if they are on the right track, or if they ever arrive at a correct solution, or if there is a better way. this book is not for everyone. the lack of solutions will frustrate most people.


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