A Mathematician’ Lament: The Mathematics Curriculum

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Part 6 of “A Mathematician’s Lament” was about the mathematics curriculum of today, and how Lockhart, predictably, disagrees with it. Lockhart does not agree with the “ladder myth.” The ladder myth explains how math is arranged into subjects, each sequential subject more advanced than the previous, i.e.: Algebra to Geometry, Geometry to Algebra II, etc. The ladder myth creates math to be a race. The ladder myth creates a race, which in turn creates a  silent competition among students. How many math classes can you take before you graduate high school? How many formulas can you have memorized (because the ability to memorize certain formulas certainly dictates how smart a person is).

Because certain students may be more “advanced” in mathematics than others, parents may feel that their children are falling behind, when  in reality, they simply grasp math concepts (I will get to math concepts in a second) at a slower rate.

During the summer, I tutored two elementary-aged students in math. I covered multiplication and division facts with the younger student and decimals and fractions with the older student. I explained to the younger student that basic facts were important to know, but I presented this information by “drilling” the poor child with endless multiplication and division timed-tests. To the older student I gave definitions of mixed numbers and improper fractions. How I tutored these students is an excellent example of what Lockhart believes teachers should not do: give definitions, enforce the memorization of these definitions and facts (without prior exploration), allow no creativity. Teachers should allow students the freedom to explore certain areas of math and to make discoveries, while providing guidance along their mathematical journey.

“A Mathematician’s Lament” describes the crooked ways mathematics is approached in today’s society (of course, in the author’s opinion).  Reading the article is a bit overwhelming, as Lockhart discusses many, many “faults” in the math classroom. I may not have touched on all of his musings, but I hope that you can get a sense of the article from my reflections. Additionally, as I continue to delve into the article, my opinions change and develop.

Here is the link again if you wish to read the article.

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6 responses »

  1. I read “A Mathematician’s Lament” in only two sittings, but I think I’ll probably come back to it multiple times. Everything that this mathematician made sense to me. To tell you the truth, I am terrified of math… or the math that is being taught in our school system, at least. Because I haven’t been able to grasp the theorems and formulas presented, I was always considered “behind” in my class. Of course, I readily accepted this title. I mean, I’m more of a creative person, not math-orientated. Now that I look back on it, I think I just couldn’t get past the simple question of WHY? All those theorems and formulas and symbols just seemed too bizarre for me to follow. I couldn’t relate to them. Why was everyone throwing them at us, why was it so dang important to memorize the quadrilateral formula?! I wish I could say that I was just rejecting the mechanical mathematical curriculum, but I was truthfully just painfully confused. This lament has made me think a lot about the mathematical culture… maybe I’ll go home and try to theorize about some problems!
    Thank you so much for this intriguing read, it was truly enjoyable and through provoking.

    • Zabet-
      With your creative personality and way of going against the grain (that is a compliment), I can see why you have not fancied past math classes. Maybe you would feel differently if these math classes were presented in a different way; a way that promoted curiosity, inventiveness, and creativity…Lockhart’s ideal math class.

      I am glad you read the article! It is certainly a thought-provoker.

  2. I’m glad you both are finding the reading interesting. As a teacher, I had a really hard time with it. I knew that things weren’t right, and I knew that this is why I wanted to become a teacher. Now that I am one, I can feel all of the pressure that my teachers must have felt: we have to prepare you for the ACT, we have to prepare you to pass college math, we have to make sure you’re working really hard all of the time. The more I think about it, the more I wonder if the ACT didn’t exist, or if college math was a little more creative, would I teach half of the things that I do now?

    The story of students being turned off by math due to its cryptic almost cult-like characteristics is far too common, probably much more so than either of you realize. I’m not sure what to do about it.

    Abby, do you feel that Calculus has fostered creativity? Do I just beat a broken drum each day when I harp about thinking but then teach chapter x.xx? It’s hard, but I hope you guys at least find it entertaining.

  3. If you don’t mind me interjecting my thoughts, Mr. Cornally… Although it is certainly a valiant effort for a single teacher to strive to make a difference, I don’t think a difference can be made (at least large scale) without a large group of like-minded people. To change how our society thinks about math would be to change our whole education system. Perhaps this is why many teachers end up going with the flow, instead of fighting it. If you were to somehow convince other teachers at Solon High School that the education system must be changed, then gradually you might make a dent in the world of math. Granted, you might also lose your job. I am not part of your Calculus class, but I feel that if you are even mentioning the idea of math, then your students have a greatly improved chance of thinking creatively… possibly more than any other math class in the district. Just my thoughts.

  4. Mr. Cornally- I think you have a well-balanced combination of standard math, i.e.: preparing us for the ACT, college, etc., and creative math in Calculus. Yesterday’s lesson, I thought, was a perfect example of a balanced lesson, as it pushed us students into an unfamiliar, slightly uncomfortable territory, yet it prepared us for college.

    Even though you are only one teacher in a country, in a world, of thousands, the math movement has to begin somewhere. Maybe one day all of the teachers across the globe who are frustrated with today’s math education will come together and really begin to make a change.

  5. Sadly our present system of mathematics education is precisely this kind of nightmare. In.fact if I had to design a mechanism for the express purpose ofdestroying a child s natural.curiosity and love of pattern-making I couldn t possibly do as good a job as is currently being.done I simply wouldn t have the imagination to come up with the kind of senseless soul-.crushing ideas that constitute contemporary mathematics education…

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