Thursday, August 11, 2005
The Problem with Education - Found!
I have a theory why primary education in the US does such a poor job. It is the fault of the kindergarten teachers.
Consider. The average high school teacher does a pretty good job educating his charges, considering the poor preparation of the incoming students in his class. Likewise, any middle school teacher will tell you that the kids coming into her classroom do not know the material they should -- otherwise, things would go much better. By induction, the problem starts at the beginning of the chain -- the kindergarten teachers.
This obviously facetious theory points out what I think is a real problem in mathematics education -- the failure of lower grades to impart basic arithmetic facts to the students. Many middle school students struggle with any sort of arithmetical algorithm -- for example, finding LCD, or prime factors, or long division -- not because they have trouble learning the steps, but because they are constantly getting stuck on simple facts. Ask them what 6 times 7 is. Long pause, long pause…. 42? Often you can see fingers moving under the table, counting the same way a Babylonian might have 3000 years ago.
I have another theory, this one in earnest. Years ago, we learned math facts by rote; endless drilling in addition tables and times tables. We chanted facts every day. And for the most part learned them.
At some point some educators (probably math morons themselves) decided since they hated all this rote they would replace it with a "better" way to teach math. Children would organically learn using flashcards. Guess what? That way works even less well than rote. And children rise through the academic system, crippled by the inability to add or multiply two single-digit numbers instantly and instinctively.
But we don't chant times tables anymore.
Consider. The average high school teacher does a pretty good job educating his charges, considering the poor preparation of the incoming students in his class. Likewise, any middle school teacher will tell you that the kids coming into her classroom do not know the material they should -- otherwise, things would go much better. By induction, the problem starts at the beginning of the chain -- the kindergarten teachers.
This obviously facetious theory points out what I think is a real problem in mathematics education -- the failure of lower grades to impart basic arithmetic facts to the students. Many middle school students struggle with any sort of arithmetical algorithm -- for example, finding LCD, or prime factors, or long division -- not because they have trouble learning the steps, but because they are constantly getting stuck on simple facts. Ask them what 6 times 7 is. Long pause, long pause…. 42? Often you can see fingers moving under the table, counting the same way a Babylonian might have 3000 years ago.
I have another theory, this one in earnest. Years ago, we learned math facts by rote; endless drilling in addition tables and times tables. We chanted facts every day. And for the most part learned them.
At some point some educators (probably math morons themselves) decided since they hated all this rote they would replace it with a "better" way to teach math. Children would organically learn using flashcards. Guess what? That way works even less well than rote. And children rise through the academic system, crippled by the inability to add or multiply two single-digit numbers instantly and instinctively.
But we don't chant times tables anymore.
// posted by Old Math @ 11:29 AM 
Comments:
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I actually can't do multiplcation from a times table for a handful of numbers. Having done it so many times, I can typically do them all, there are still various ones that I do the path on.
Ask me 6 * 7 and I will likely take 5 *7 = 35 and add 7. I have become pretty fast at this, the only problem is it makes my math very insecure. Even though I long learned it to be 42 I never yell "42."
In Canada, they start multiplication at 1st grade. My kindie kids are already starting multiplication. I started multiplication in 3rd grade. When would you start something like that?
Ask me 6 * 7 and I will likely take 5 *7 = 35 and add 7. I have become pretty fast at this, the only problem is it makes my math very insecure. Even though I long learned it to be 42 I never yell "42."
In Canada, they start multiplication at 1st grade. My kindie kids are already starting multiplication. I started multiplication in 3rd grade. When would you start something like that?
Starting while the child is in the womb seems about right. Shortly thereafter perhaps. Research has shown that newborn babies have a concept of number.
Many people have a problem with 6x7 by the way. You were only one step away from the solution, many kids are 6 steps away.
Many people have a problem with 6x7 by the way. You were only one step away from the solution, many kids are 6 steps away.
I know it's late, but I just found your site and I agree completely. I'm gonna add you to my blogroll right now.
3-24-06
Well, I'm WAY late to the party, but I'm stunned to learn that people have problems with 6x7.
6x7 is possibly the SOLE multiplication fact that has managed to trip me up for years. (I never chanted math facts as a kid - though now that you mention it, it sounds like a great idea - but I learned them all. I don't even know what "do the path on" means!)
Catherine's bad day
Vlorbik's bad day
Well, I'm WAY late to the party, but I'm stunned to learn that people have problems with 6x7.
6x7 is possibly the SOLE multiplication fact that has managed to trip me up for years. (I never chanted math facts as a kid - though now that you mention it, it sounds like a great idea - but I learned them all. I don't even know what "do the path on" means!)
Catherine's bad day
Vlorbik's bad day
# posted by 
: 7:02 AM
: 7:02 AM
oh, wait
Now that I re-read Matt, the meaning of "do the path" is obvious.
I was never taught to "do the path." I learned my math facts, and I learned them well.
otoh, I never noticed that multiplication is repeated addition. Nor did anyone point this out to me.
My fragmented but sturdy knowledge of math provides some justification for constructivist loathing of what they call "rote knowledge."
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Now that I re-read Matt, the meaning of "do the path" is obvious.
I was never taught to "do the path." I learned my math facts, and I learned them well.
otoh, I never noticed that multiplication is repeated addition. Nor did anyone point this out to me.
My fragmented but sturdy knowledge of math provides some justification for constructivist loathing of what they call "rote knowledge."
# posted by : 7:06 AM
: 7:06 AM << Home
