Tuesday, May 17, 2011

Math is Not about Numbers

Today, I came across an article today in Education Week entitled "Researchers Probe Causes of Math Anxiety."  It was a decent article.  There were a few insights I found interesting.

When I finished the article, I read the comments.  Michael P. Goldenberg, a math coach in Ann Arbor, Michigan said this:
The way most US teachers present the subject in K-12, it's about only or primarily the following: calculation, arithmetic, and speed (with accuracy, of course). None of those things are particularly what mathematicians deal with. No mathematician is judged by speed of calculations - arithmetic or otherwise. Calculation may not even be a particular strength of a professional mathematician. Mathematicians by and large deal with abstractions, patterns, connections. Of course, some deal with applications of mathematics to sciences and engineering and other "real world" problems and situations. But when it comes to pure calculation, it's hard to beat a computer for speed and accuracy. What the computer won't give is insight, leaps of heuristic thinking that connects seemingly unrelated ideas in two or more areas of mathematics, the recognition of underlying structural similarities, etc. Computers don't think.
I had been thinking of writing a post entitled "Math is Not about Numbers" for a while.  I actually started this post a week ago, and saved it as a half-completed draft.  I don't know, however, that I can say it any better than Michael P. Goldenberg did. 

In a few years all of my fifth grade students will be using a calculator and/or computer to do their calculations.  I refuse to spend an entire school year teaching them procedures to calculate.  I'm going to spend the majority of the time in my math classes teaching them to make connections, recognize patterns, and make predictions.  I'm going to teach them to do what computers can't - think.  I'm going to teach them math.


  1. I always did wonder why we tested them on speed with math facts? I never really saw the point.

  2. I agree that speed is not as important as accuracy, but being familiar with the "math facts" is. Having a good number sense of how each number is made up of endless possibilities of other numbers is extremely crucial. You simply can't do long division with confidence without knowing your multiplication facts. There is a need for students to understand why the calculations work on a machine and whether or not the answer they get makes sense. Without a doubt, how Math is taught (generally) is just too intense, boring and irrelevant to students today... of all ages. I can't seem to get a very good answer as to why students have to be ready for Algebra in 8th grade. I think we rush them through each concept as quickly as possible trying to get to that goal. Every year from 4th to 8th grade they add fractions, and they know the trick -but how many truly understand that you are combining parts. I applaud you for wanting to teach them to think. That will apply to all areas of study and Math is a great instrument to teach it with.

  3. I'm flattered by the link to my post. I would like to add that this is a complex issue, but most people seem to approach it emotionally rather than rationally. It's heresy in many quarters to suggest, as I do, that while knowing math facts is useful, teaching them as a major focus of class time in elementary school is not a good expenditure of instructional/learning time.

    The best resource I know for elementary school math methods is the various books by the late John van de Walle. His approach to teaching/ learning "the facts" seems far more sane to me than what most teachers do and traditionalists insist upon. I also can't recommend strongly enough the value of games and play to help kids gain facts, number sense, etc., though in the case of the latter, well-constructed lessons should engage students in thoughtful activities that build and promote their deep thinking about the workings of the whole numbers and arithmetic operations. The emphasis should be on understanding, concepts, connections, etc., not rote. There are, in fact, more ways to "memorize" than rote repetition, something that seems to have eluded an awful lot of traditionalists. A few good activities that lead to understanding are far more valuable than a thousand worksheets that ask students to do nothing more than drill mindlessly.

    For more of my ranting and raving, see my blog, Rational Mathematics Education (http://rationalmathed.blogspot.com)