Ain't That the Truth?
Before I close the book on this, I'd like to mention that Denise has a wonderful post on the distinction between repeated addition and multiplication.
Go check it out.
Some folks over here are still somewhat desperately trying to defend the practice of teaching children that multiplication is the same thing as repeated addition. (And, mysteriously, no more of my comments are getting through, mysteriously.) Their latest tack—and one that's actually been taken by various people ever since the debate started—is to ignore or write off any potential difficulties blurring or removing the distinction causes by trotting out their success stories (or their children's success stories) or their Ph.D.'s and saying, "Look, I learned it as repeated addition; my kid gets it as repeated addition. I did fine in math. My kid is doing well in math. What's the problem?"
First, let me just clarify for what seems like the billionth time that Devlin is NOT arguing that repeated addition never ever be spoken of again in relation to multiplication. Some people have been all over the Web arguing about Devlin's articles for nearly a month and continue to pretend that this is what Devlin is saying. It's not. Second, my answer to the "What's the problem?" question is usually "Doesn't matter. Wrong is wrong. Please rewrite it and have it on my desk tomorrow morning."
However, when you step back and look at it, the "What's the problem?" question is based on a remarkably ugly and arrogant assumption—that every kid in the world is just as capable as I and my kids are. The truth is that many children (see Denise's post linked above) have difficulties discerning between multiplicative and additive situations—an important skill when solving problems in elementary mathematics. And that may very well be just the tip of the iceberg.
My defense of the main idea in Devlin's articles does not come from my having known it all along. I haven't. Before I read his first article, I did not give much thought to the very important distinction between repeated addition and multiplication.
My defense of Devlin's articles comes from the very same defense I have had to muster for the last twelve years in writing and editing textbooks—and the same defense I used to start this blog.
I wrote long ago that there was one incident in my career in educational publishing that directly pushed me to start this blog. I had noticed an error with one of the problems in a textbook I was working on. And, as I had just started with the company, I was asked to clear any major changes with the author. So I called her. The problem was something very similar to this:
I'll never forget her response: "But kids aren't going to get that. Let's leave it."
It is the instinctive response that many educators and what seems like every non-educator offer to the challenge of repairing the discontinuity between the truth and what we teach as the truth: The kids aren't going to get that. Let's leave it.
This kind of response presented itself throughout the various online debates over the distinction between repeated addition and multiplication, as commenters seriously argued that it is okay to teach kids something that is wrong because it matches students' intuitions better. Such an argument would justify teaching kids that the Sun orbits the Earth, since it pretty much seems that way. And, hey, in a sense, if kids start off thinking that the Sun orbits the Earth, that's just an "incomplete understanding" that we could later "extend" into the truth.
It would be nice to see more people like Devlin—people engaged in critically analyzing that disparity between the truth and what we teach as the truth. The discussion we're surrounded with now sounds more like two old buddies on a park bench talking about their day. There's a lot of head-nodding and "Ain't that the truth," but nothing is really being said.
Go check it out.
Some folks over here are still somewhat desperately trying to defend the practice of teaching children that multiplication is the same thing as repeated addition. (And, mysteriously, no more of my comments are getting through, mysteriously.) Their latest tack—and one that's actually been taken by various people ever since the debate started—is to ignore or write off any potential difficulties blurring or removing the distinction causes by trotting out their success stories (or their children's success stories) or their Ph.D.'s and saying, "Look, I learned it as repeated addition; my kid gets it as repeated addition. I did fine in math. My kid is doing well in math. What's the problem?"
First, let me just clarify for what seems like the billionth time that Devlin is NOT arguing that repeated addition never ever be spoken of again in relation to multiplication. Some people have been all over the Web arguing about Devlin's articles for nearly a month and continue to pretend that this is what Devlin is saying. It's not. Second, my answer to the "What's the problem?" question is usually "Doesn't matter. Wrong is wrong. Please rewrite it and have it on my desk tomorrow morning."
However, when you step back and look at it, the "What's the problem?" question is based on a remarkably ugly and arrogant assumption—that every kid in the world is just as capable as I and my kids are. The truth is that many children (see Denise's post linked above) have difficulties discerning between multiplicative and additive situations—an important skill when solving problems in elementary mathematics. And that may very well be just the tip of the iceberg.
My defense of the main idea in Devlin's articles does not come from my having known it all along. I haven't. Before I read his first article, I did not give much thought to the very important distinction between repeated addition and multiplication.
My defense of Devlin's articles comes from the very same defense I have had to muster for the last twelve years in writing and editing textbooks—and the same defense I used to start this blog.
I wrote long ago that there was one incident in my career in educational publishing that directly pushed me to start this blog. I had noticed an error with one of the problems in a textbook I was working on. And, as I had just started with the company, I was asked to clear any major changes with the author. So I called her. The problem was something very similar to this:
How many line segments are in the figure below?
I'll never forget her response: "But kids aren't going to get that. Let's leave it."
It is the instinctive response that many educators and what seems like every non-educator offer to the challenge of repairing the discontinuity between the truth and what we teach as the truth: The kids aren't going to get that. Let's leave it.
This kind of response presented itself throughout the various online debates over the distinction between repeated addition and multiplication, as commenters seriously argued that it is okay to teach kids something that is wrong because it matches students' intuitions better. Such an argument would justify teaching kids that the Sun orbits the Earth, since it pretty much seems that way. And, hey, in a sense, if kids start off thinking that the Sun orbits the Earth, that's just an "incomplete understanding" that we could later "extend" into the truth.
It would be nice to see more people like Devlin—people engaged in critically analyzing that disparity between the truth and what we teach as the truth. The discussion we're surrounded with now sounds more like two old buddies on a park bench talking about their day. There's a lot of head-nodding and "Ain't that the truth," but nothing is really being said.
Labels: education, mathematics, textbooks