The Rule of Reason :: The Weblog of Edward Cline
Boy, that got me angry! Watching those needlessly complicated and sloppy methods of doing mathematical calculations actually began to give me a headache.Because I learned mathematics the old-fashioned way, I am able to do most of my calculations in my head. Often, I find it to be much faster than using a calculator. The other advantage of being able to do it in my head is that when I do use a calculator, I have a feel for what the number should be. Therefore, I know when I have made a mistake on the calculator. (Of course, when a calculator isn't handy, I can pick up a pencil and quickly solve the math problem!)The mathematical illiteracy promoted by the methods described in the video reminds me of the reading and spelling illiteracy produced by the "look-say" method of learning reading. A student is asked to spell "apple" and writes "elephant". He lacks even an approximate sense of the correct spelling because he never learned how to spell phonetically.These modern math students are slaves to their calculators, and yet they lack an earned "feel" for the numbers that comes from doing many math problems the right way by hand. As a result, they won't even be able to use their calculators properly, because they will fail to recognize errors. Their arithmetic skills are likely to be as good as their spelling skills.
Can someone trace this horrendous approach to math instruction back to the philosophical school (as well as leading philosophers) that is responsible? What branch of Postmodernism is causing this?
Since I haven’t studied the philosophy of education beyond the basics, I can’t comment with much authority. Any other takers?
Hmmmm...I have very mixed emotions about this piece. Mostly, I think we're watching a tempest in a teapot here.I'm a computer programmer with a Ph.D. science background (nuclear physics, to be exact). I run numbers in my head all the time. And yes, I multiply and divide by parts. 21*36 done conventionally in my head is tedious, but I can recon 20*36 and then add another 36 to it almost instantly. The methods this woman is railing against is not all bad.I suspect part of the disparity is that some of us are visual learners and some of us are auditory learners. In spite of all the diagrams I've drawn working problems, I'm definitive an auditory learner... and I know it. I suspect this lady is a visual learner. That's fine, but it doesn't mean that the new techniques are bad either.Confused parents aren't a new problem either. It's called progress. One would hope that students today would learn concepts that weren't available to their parents. So what?I'm the first to critique education in this country. I'm the first to tell stories about students lacking in basic skills. But I suspect that it has more to do with bad teachers and unmotivated students (and parents) than curriculum.In academe, we'd call this a red herring.
> 21*36 done conventionally in my head is tedious, but I can recon 20*36 and then add another 36 to it almost instantly. The methods this woman is railing against [are] not all bad.I think they are for establishing mastery. The example you give is a neat trick that one can do on the fly (I sometimes do it myself), but I would argue that to understand numerical relationships as such, one must first understand the traditional method.> I'm the first to tell stories about students lacking in basic skills. But I suspect that it has more to do with bad teachers and unmotivated students (and parents) than curriculum.I would argue that these bad teachers and unmotivated students are the tragic outcome of the misbegotten ideas in education which impact both the curriculum and how the curriculum is taught. After all, teachers and students don’t become bad in a vacuum. In this case, I see it as a benighted attempt to make math easier for students, while in fact increasing its complexity and leaving students unable to master the work as necessary.
I suspect that to do math calculations well in one's head, it is first necessary to become fluent with a good, efficient method of doing calculations by hand. The "old math" method appears better.When I do the calculations in my head, my method is definitely similar to the "new math" methods described. I just cannot imagine beginning my learning of math that way.In any case, if a bright student can put down the correct answers without going through any particular steps (whether "old math" or the "new math" kind), he should be told he got the right answer.
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