“For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory. Their trust in writing, produced by external characters which are no part of themselves, will discourage the use of their own memory within them. You have invented an elixir not of memory, but of reminding; and you offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with, since they are not wise, but only appear wise.”(Phaedrus 274c-275b)
The above quote is Socrates complaining about the invention of the written word. He claimed that allowing students to write down facts instead of memorizing them would weaken their minds.
I’m reminded of this when I see some of the reactions to suggestions that we embrace the use of computer technology in the way we teach math. The most noted advocate for this is Conrad Wolfram, who described his philosophy in a 2010 TED Talk.
My first introduction to technology-assisted math was in my high school chemistry class, where we learned how to use a slide rule. (Yes, I’m thatold.) We didn’t have them in math class (or calculators for that matter) so all calculations was done by hand. I didn’t get my first calculator until I went off to college. As this technology got cheaper and more readily available, it began to filter down towards K-12, where I recall a lot of controversy over allowing their use in class. It was felt at the time that it would make students unable to do arithmetic by hand and therefore become dependent entirely on machines to do it for them.
Back in 1957, Isaac Asimov wrote a short story “The Feeling of Power”, about just that kind of future and how society had to rediscover the technique of doing arithmetic by hand. The comments at this page about this story are…..okay, I’m trying to think of how to say this….well, let’s just say there’s a certain ‘you kids get off of my lawn’ quality to them.
Please don’t misunderstand. I absolutely believe that grade school kids should learn how to do arithmetic by hand, to start. But I don’t believe that it’s as simple as we either do all of our math by hand or become completely dependent on machines.
First of all, I have no problem doing arithmetic using a machine. Arithmetic is a very mechanical activity, which is one of the reasons why teaching it involves so much memorization. It isn’t something that comes naturally to us humans. However, we should be comfortable with arithmetic so that we can visualize what our answer should look like and to make sure the problem was entered correctly. (I prefer using a text editor to writing by hand. This doesn’t make me illiterate.)
Math, on the other hand, involves intuition, creativity, imagination and logical thinking. Machines can make the arithmetic part of it easier but you still need to understand the problem well enough to explain it to the machine. We teachers don’t have to fear the use of calculators or computers in a math class if we use them intelligently. Where these machines can be used to our advantage is to reduce student anxiety about the mechanical parts of the problem so they can focus on the part requiring human-based thinking.
In my experience, students hate math because they fear arithmetic. They are so scarred by their grade school arithmetic classes where the slightest error in a long chain of arithmetic would ripple down and cause them to get the problem wrong (and fail the test) that they don’t want to be anywhere near any class that reminds them of that.
I encourage the use of calculators (and spreadsheets and Wolfram Alpha) in my college math class. They take away fear and give us more time to actually talk about math.
We Hate Math 