Friday, April 18, 2014

A Review of Mathematician’s Lament by Paul Lockhart

    Paul Lockhart makes many interesting points in his book Mathematician’s Lament.  He argues that mathematics education in schools today is far from where it should be.  The author thinks that mathematics is an art, cheapened and stripped down to formulas and definitions.  Although I think reform is needed in mathematics classrooms today, Lockhart’s idea of reform is not practical.
    Lockhart’s main theme of the book is that mathematics is an art form and should be treated as such.  Just as art is taught with a blank canvas, students should be given a blank canvas to explore mathematics as they please.  Although I agree that mathematics is so much more than procedure and “plug and chug” formulas, can anyone really expect a middle schooler to work on mathematics for an hour every day given no guidance or instruction?  There has to be some structure in a mathematics classroom especially for younger students. 
    The author makes it clear that we stress notation too much in our classrooms.  What I don’t understand is how he expects students to create and explore mathematics with no base to start from.  You have to crawl before you can walk and you have to be able to add numbers before you can create mathematics.
    In “Mathematician’s Lament” the author states that there should be no mathematics curriculum, no standardized test, and no regulation of mathematics teachers cross country because teachers are being too bogged down by scores to actually teach mathematics.  There are several alarming implications to this.  First, if there were no regulations then teacher performance would probably decline because there is no way to keep them accountable.  Second, there is a sad truth that many teachers do not have enough mathematical understanding to guide students through any and every mathematics the students will explore.  Teachers teach procedures mostly because they were taught procedures.  There are ways to encourage teachers to branch out, but taking away all standards and expectations is not one of them. Finally, students who can achieve high level mathematics will never be taught the mathematical background needed to succeed.
    Lockhart writes that mathematics is a fun art form that has only a few real life applications.  This point breaks my heart, because I believe mathematics is fun, but I also believe that mathematics is important.  He makes it seem like the only purpose of mathematics fun, making it essentially unimportant to teach in schools.  In his argument to reform, he goes so far as to make mathematics a trivial subject.  This seems far from accurate.  Where would our world be without mathematics? Computers, medicine, science, technology, business and more wouldn’t even exist without mathematics.  So yes, Lockhart, mathematics is fun, but it is also vital to the world we live in.


  1. Good argument! You have strong points and express them well. Do you feel like his point of view could add anything to your teaching?

  2. Kerry, your review of this essay brings up a lot of interesting points which I agree with; when I read Lockhart's book last year, I thought of it more as a challenge to bring more exploration into the traditional curriculum rather than throw everything out. I especially found Lockhart's views about teaching proof in Geometry compelling. I love geometry, and I love proof. But I also have seen the vast majority of students turned off to geometry because of the way it is currently taught in most high schools. Since reading this book, I have tried to keep Lockhart's perspective in mind when planning, always trying to consider how best to engage the students in the study of one of my favorite subjects without 'enslaving them' with formal structures which may be irrelevant in the long run.

    I'm glad you wrote this review!

    1. Thank you for your comment! Your effort to take the book as a challenge to bring more exploration into the classroom seems like a great idea. I will definitely try to do the same!

  3. Kerry-

    This may not be fair since I taught with Paul and have a more nuanced view of both his philosophy and his actual teaching than he divulged in his book (this may also not be balanced for the same reason). That said, I don't think Paul believes that there shouldn't be any structure in a math class. To use his metaphor, giving students a blank canvas in art doesn't mean that an art class is void of any structure. I DO think he would passionately argue that middle school students (and younger) have the capacity to work on mathematics for hours without, as you put it, "guidance or instruction." I actually think Paul might argue that younger kids have a greater capacity for this than older kids since they have spent less time doing "school mathematics."

    As for needing a base to start from, there are lots of examples of great math problems, puzzles, and games that young children can access without any formal training, in the same way that young kids can finger paint without formal art classes. The game of Nim is just one example.

    As for your other points in terms of curricula, tests, and real world applications: your view of Paul's position is spot on, for better or for worse.

    1. Avery-

      Thank you for your comment! It's very cool to hear from someone who knows him personally and has taught with him! I am sure you have a more well rounded view of his philosophy than me. I only know and analyzed what I read from this book.

      As someone entering my teaching career, I would be curious to see how he runs his classroom. There is little detail mentioned of what types of structure he provides his students.

      I am also interested in checking out the game you suggested. I do love the idea of teaching my students through games.

      Thank you again for your comment.