10

I greatly admire Paul Lockhart's Measurement (Harvard Press). Many of you know him through A Mathematician's Lament. One review of Measurement said,

“Here Lockhart offers the positive side of the math education story by showing us how math should be done. Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.”

But I do not see a way to integrate this into a conventional mathematics course (say, for undergraduates).

Q. Can anyone see a way to use Lockhart's Measurement in mathematics education, either in a conventional course, or as a supplement, or for guided independent study?

          Measurement: Table of Contents:
          MeasContents

Added. One could imagine Part One supplementing a first course in Geometry, and Part Two supplementing Calculus I. But the style is so unique that I can't decide if it would be better for these sections to proceed or to follow geometry/calculus. But really the true thrust of the book is to understand what it means to pursue mathematics.

I like this quote (where "we" = "we mathematicians"):

We're always working at the edge of the unknown, and we're always stuck.

A few SE citations of Measurement:
Joseph O'Rourke
  • 29,827
  • 6
  • 61
  • 140
  • 2
    This sounds interesting. Enough so that perhaps you can give a few examples after your citations of some specific topics 'covered' (I assume, from the Lament, that there isn't coverage in the usual sense)? For those of us who haven't read Measurement, this question could easily become an insider knowledge game if the answers also assume one has read it. Not that you intended that, of course! Just trying to be proactive - hope people have ideas! – kcrisman May 03 '19 at 03:36
  • 1
    @kcrisman: Good point. I've pasted in the table of contents, but you are right: there is not coverage in the usual sense. – Joseph O'Rourke May 03 '19 at 11:32
  • 3
    This is a wildly insufficient response, but since relatively little has been posted thus far: I lent a copy of this book to a student who was looking for extra math reading. She returned it after reading a bit and finding it not to be engaging. (FWIW: I have taught a lesson using the Lament before; see part two here (pdf).) Anyway: If Measurement is to be used in a course, then my $n=1$ experience is that more structure than offering it as an independent reading will be necessary. Sorry I don't have more! – Benjamin Dickman May 04 '19 at 16:47
  • (1) Frankly, the very first sentence of the Lament says enough for me to completely discard it: "A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory." One can see where he leads from a mile away. No, I do not agree with the analogy. The importance of being able to compare amounts, to do basic arithmetic, to calculate percents, to figure out whether one can make it on the remaining gas without filling up, all these small things happen every day. – Rusty Core May 08 '19 at 18:36
  • (2) Music is optional, on another hand it can be done without much theory (yes, I am fully aware of musical theory, but it is not needed for basic singing or even decent playing and arranging). He is lamenting that future bright minds are indoctrinated and spoiled. The problem is, most school students are not the bright minds he is imagining, they just want to get out this de-facto juvenile prison, where they are stuck for six hours a day for thirteen years of their life. When I learned about "Measurement" I put it my Amazon list. Six years since, it still sits in the list. – Rusty Core May 08 '19 at 18:37
  • I just ran across an MAA review of Measurement. She says, "It could easily be classified as a textbook for use in a 12th-grade mathematics elective, a mathematics service course, college geometry, or in a capstone course for mathematics majors." – Joseph O'Rourke May 08 '19 at 23:15
  • PS. Lockhart has a new book out, Arithmetic. – Joseph O'Rourke May 08 '19 at 23:17
  • (1) I wonder why you quoted the opinion part, but omitted the more factual part, "the foci of the book are classic and analytic geometry". (2) "The author then discusses the nature of problem-solving: “What is a problem?”, “How do we teach problem-solving?” " — Polya's name is conspicuously absent from the review. (3) Reading the table of contents http://www.hup.harvard.edu/catalog.php?isbn=9780674284388&content=toc I got a feeling that the book is better suited for enrichment of a middle schooler, than as a high school textbook. – Rusty Core May 09 '19 at 17:48
  • 1
    @RustyCore: I myself do not entirely agree with the MAA review. I certainly don't think it could serve as a textbook. I just thought I would include a reviewer's opinion on the question I posed. I've read both Polya and Lockhart. Both are valuable, but quite different. – Joseph O'Rourke May 09 '19 at 17:52

0 Answers0