Welcome to the Lockhart Reading group

This is a blog dedicated to exploring the beauty of mathematics. We will be doing this in a somewhat unconventional way—this blog will house a conversation about the book, Measurement, by Paul Lockhart. The conversation is open to anyone. Initially, 30 people ranging in age from 14 to 55, from all around the world and a variety of mathematical backgrounds will try to learn together by reading this fascinating book.

Perhaps it is best to begin with some short introductions. If you’re planning on engaging this conversation, please add a short comment telling us a little bit about yourself. Who you are (at least your first name), where you’re from, and in a couple of sentences, why you’re interested in learning more about the beauty of math.

I’ll also let the book’s author, Paul Lockhart, give you a sense of where we’re going.


~ by John Burk on September 18, 2012.

36 Responses to “Welcome to the Lockhart Reading group”

  1. […] Welcome to the Lockhart Reading Group. […]

  2. I’m John Burk, and I teach Math and Physics at St. Andrew’s School in Delaware. I had the idea of starting this group when I read the first few pages of this book and found them so compelling that I wanted to share them with someone else. I’m interested in learning more about the beauty of math because it’s a subject I teach, and I want to find more ways to help my students see math as beautiful and poetic instead of stultifying and dull.

    • I am from West Michigan and teach chemistry and physics at Oakridge High School. My love of math really came upon me as an adult because of teaching. Actually, the struggles my students had learning the math I use and teach in the sciences caused me to begin to explore why they meet with such difficulty learning mathematic principles and how I can help them. I can’t wait until the book arrives and we can begin our journey!

  3. John, great idea getting this started – it’s exciting to be part of a book club that doesn’t involve reading fiction!

    I joined this reading group having never heard of the book before but if the beauty of mathematics is the core theme then I’m sure that I’ll enjoy reading it and discussing it on this forum.

    Dan Pearcy
    (Maths Teacher)

  4. Hi-

    I’m Paul Salomon, a 29-year old Brooklyn math nerd.teacher.artist. I actually work at Saint Ann’s School in the math department with Paul Lockhart. I’ve looked through a very old (1999) draft of this book, but I hear there are lots of updates. I’m very excited to dig in and work through some lovely problems with you all. From what I gather, there are lots of problems offered in the book, but in many cases, without included solutions. It’s our job to do the math. 🙂

    Looking forward to it,

  5. Hi, I’m Preston Firestone, and I’m a freshman student at St. Andrew’s School (where Mr. Burk teaches). I’ve been in various accelerated math tracks over the years, and I’m really excited to learn even more.

  6. I’m Michael Pershan. I’m a math and computer science teacher in NYC. I’m still working through some of the math anxieties that I carried around during my school years. I was never, never the sharpest student in any math classroom that I sat in, and I was always jealous when I heard others talk about “the beauty of math.” I never could see that, and I figured that it was because of some deficiency of my own. These days I think I’m more equipped to see the beauty of math (teaching helps) and I’d like to give it another shot.

  7. I am Michael Porrazzo. I am the Chair of the Math Department at Kimball Union Academy in Meriden, NH. John’s invitation to join this group came to me via a recent email from the St. Andrew’s School communications team. I read “Lockhart’s Lament” a number of years ago and subsequently engaged colleagues in discussions about the implications of Paul’s message for mathematics education. Seeing the Lockhart name arise again, I was drawn to the idea of conversing with other mathematically interested folks outside my four walls here in New Hampshire, using Lockhart’s Measurement book as a backbone. Oh, and I also welcome the pressure to keep up with reading a book that for me would otherwise be relegated to a vacation “to do” list. 🙂

  8. Hi, I’m Malke Rosenfeld. I am a percussive dancer, teaching artist and creator of an integrated math-dance program for elementary students called Math in Your Feet. I realized a couple years ago that, in addition to learning math ‘concepts’, children were engaging in some real mathematical activity and thinking in my program; the problem was I didn’t know enough math to describe it to my satisfaction. That inspired me to embark on a quest to learn as much as I can about what math *really* is. Along the way I’ve discovered a deep and abiding love for this art form, even if my technical skills and experience are still at the beginner level. I got Lockhart’s book last weekend and quickly realized that, despite its conversational tone, it was not going to be a quick read, lol! When I saw this group forming I jumped right in — I’m excited to have a learning community for this book!

  9. Hi! I’m a high school mathematics teacher in western New York. Really was intrigued with your convex quadrilateral proposal. I took the night to create a “baby” proof why the midpoints create a parallelogram. I figured you can divide the convex quadrilateral in half to create two triangles, then in a short version use the Triangle Midsegment Theorem. I had forgotten how fun it is to sit back and prove the smallest of mathematical idea. Thanks for bringing up that topic. It was fun to discover!

  10. I’m Mark Hammond and I teach physics and chemistry at St. Andrew’s School. I’m looking forward to reading this book with all of you!

  11. My name is Bradford Hansen-Smith. I fold circles to understand pattern and the transformational nature of the circle as it relates to all forms of patterned and transformational movement. It is an easy, comprehensive and direct way of learning geometry that underlies 2-D, 3-D construction and higher math concepts. I have for as long as I have been folding circles been working with young students, teachers and parents as part of my exploration.
    I have not read this book, but agree with your “lament.” I was intrigued by your introduction video and how little we understand about what we are doing. My observations to your question about any quadrilateral and parallelogram can be seen at; http://dl.dropbox.com/u/58628385/Parallelogram.pdf

  12. Hello everyone!

    I’m Elizabeth and am a Junior in High School. I am aiming to become a math teacher because I love math and enjoy helping others understand their math. Right now I’m taking AP Calculus BC, and I think finding derivatives is fun! I just hope I’m not getting myself into trouble joining this because I am sooo busy with school this year. 😀

    • Elizabeth,
      Don’t worry—I don’t think we’re going to read more than 5-6 pages per week, and you can be as involved or uninvolved with the conversation as you like. Since everything is taking place on the blog, if you have a week that’s too busy, you can always read about what was discussed later.

      • Ok. Oh, and I forgot to say where I am from. I’m from New Jersey…the Garden State. 🙂

    • So glad to have you in the group, Elizabeth! The second half of this book is really about calculus. I’m sure you’ll love it. 🙂

      • Thank you! 🙂 Hopefully by the time we get to the second half, I’ll have learned enough calculus to understand it. I’ve been reading the comments on this first assignment and everything (well, almost everything) seems to be over the top of my head! But I just got the book so hopefully reading it will clear everything up. 😀

      • I’m sure there’s going to be all levels of discussion going on here, but just know you can ALWAYS comment and ask for more explanation. Please do, especially if I go over your head. I hate that, because I’m hear to interact. 🙂 Enjoy the reading. Ttyl.

      • Ok! 🙂

  13. I am the chair of a pk-9 mathematics department at an independent day and boarding school in Massachusetts. I teach math in grades 6-9; however I oversee the curriculum and adults teaching math pk-9. Throughout my 20+ years of teaching I have taught students in primary, elementary, middle, and upper schools. My main focus in teaching math is for my students to think creatively and to be creative when working with and learning about mathematical concepts. I stay away form traditional math books as much as I can. I much prefer to use art, history, architecture, and texts, such as The Number Devil, to approach math teaching. In my work with the adults in my school, I have the same goal as with the students – modeling and teaching them to think about math in creative ways so that they can better engage the students and focus on instilling in them an excitement about the “mathematical reality.” I am looking forward to reading Measurement and engaging in conversation about how to spread the connection between creativity and math education.

    • Julie, from what you have explained I suggest folding circles might be worth your looking into since it reveals the integration of art and math that is unlike any other activity.

    • Julie,
      You might also be interested in tomorrow night’s (Tuesday, Sept 25) meeting of the Global Math Department, which will feature a number of teachers at St. Ann’s School in Brooklyn discussing how they teach an integrated course in mathematics and art. The meeting takes place online, and is free. Clicking on the above link will take you to registration for the event, which starts at 9pm EST.

    • Hey, Julie. Your school sounds great. What is it called? I hope you were able to check out the Global Math Department presentation today about Math Art. There’s a recording if not. Looking forward to hearing more from you.

  14. Hello all. I’m Meg, a private instructor in western Mass. I mostly teach ancient Greek, Latin, and German. I also teach Euclid’s _Elements_ directly from the text––and with a look at the Greek for those of my students who have proficiency in Greek language. I’m a graduate of St. John’s College (the “Great Books school”), where I studied the history of mathematics. Thanks for hosting this group!

    • Meg,
      I just received a copy of Lockhart’s book Measurement. I was hoping to contact him, but by your self-description, you might be a terrific person to ask my question. i am a professor of philosophy writing a new book on ‘proof’ in early Greek philosophy. I think it begins with deiknumi — making visible. The part I’m struggling with is the enlargement of the Pythagorean theorem at VI.31. Do you have any clear “showing” of the intuition of “Duplicate ratio”?

  15. Hello everybody, I’m Grant, a 30 year old Montessori teaching assistant working with children ages 3-6. I’m also a musician/artist/Go player… many artful hobbies. I’ve been very intrigued with how math concepts are taught, and just recieved this book for Christmas. My partner and I have decided to start working through this book, and in the spirit of collaboration I decided to see what the internet had to offer. She and I are a little confused about how to approach even the initial problems, I keep bringing in math I already know, and it seems like it should not be necessary. I hope this group is still active, its fascinating to have this wonderful resource for learning and exploring the art of mathematics!

    • Hi Grant!
      Thanks for the comment—this site still is alive, but I’ve been swamped with teaching related stuff, so I haven’t had the time to updated it as regularly as I would like. But I am planning on posting something next week, and hopefully we can keep this going in the new year.

  16. My name is Patrick, and I’m excited to be a part of this dialogue. Studied math in college, now make a living using those skills, and have lots of crazy ideas about how it could be better taught.

    Realize I’m a bit late to this party so please don’t think I’m a troll!

  17. Hello. My name is Bill. I am a special education teacher who co-teaches math and science in a public middle school in New York State. I am reading Measurement for pleasure and to hopefully discover nonstandard approaches to understanding and enjoying math at any level.

    • Bill, there is nothing more nonstandard, more inclusive, or more fun that you can give your students to learn math than have them fold circles, observe, discuss, and discover for themselves, which is what learning is all about. The circle we draw is a static 2-D image, we do not realize folding circles is dynamic, comprehensive, and generates all the same traditional fundamental math concepts, theorems, relationships, plus much more. If your students can fold a paper circle in half they will be able to do this. We do not know this because we do not fold circles or expect anything to be there. If you want effective nonstandard check out folding circles.

  18. Hi Everyone ! I am interested in doing math collaboratively, and my guess is that people who like Paul Lockharts writing are probably the kind of people that I would like to do math with. A blog seems to me to be a pretty good place to do math, because it is time and location independent. I understand that this blog was founded for exploring the book “Measurement” by Paul Lockhart, so my desire to explore math more generally might not be a perfect fit. But, from what I have read frome “Measurement”, there seems to be more than enough concepts and problems to work on in “Measurement” to last us a while. Maybe we can work together in the style of the “Polymath” blog ? I also noticed that this blog has reading assignments, and the last post is from some time back. Is anyone here still keen on working through “Measurement” ? Do you think that we could collaborate ? Also, I wrote this introduction having just read this post and the comments and some of the other posts, I have not exhaustively read every post and every comment yet. I look forward to hearing from you !

    • Hi Gabriel-
      This group is quite dead, I’m afraid. BUT, It’s great to hear that you want to explore some math. Let me make some recommendations. First, I hope you know of mathmunch.org. There is surely a lot there that you would enjoy. Second, you should take a look at http://www.collaborativemathematics.org. Finally, if you want to read Measurement, which I really really love, and you want someone to discuss with, shoot me an email. Happy to dig in with you. I’d also be happy to be math buddies and share whatever cool math problems you decide to work on.

      Paul Salomon
      paulsalomon27 [at] g mail

  19. I couldn’t find a way of contacting the author (searching for a homepage or an email didn’t yield any results), but would like to submit an error in the book “Measurement” for future revisions, if anyone knows how to contact the author or can forward this to him.

    In Section 29 of Part One (p. 179) the construction being discussed and the following question are wrong (“Why is the focal constant of a hyperbola equal to the side of the diamond?”). The “focal constant” (difference between distances to foci) can be arbitrarily small for the same distance between foci, so it can’t be the same as the side of a rhombus built on the foci. A correct construction is a rhombus with sides perpendicular to the tangent lines, whose height is then equal to the focal constant.

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