Oh, another interesting comment on math pedagogy - so, in high school, I took and understood calculus. I didn’t understand what it actually didi and was for until I read it in some Neal Stephenson book as an adult.
[QUOTE=Flipshod]
Slightly off topic, but I think kids should learn double-entry accounting as soon as they can add and subtract well. I learned it in my late 20s, and the whole time I was learning it I was wondering why they didn’t teach me this in 4th grade, when perhaps it might have been absorbed more naturally.
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Your school didn’t do that?
You know, I didn’t really get the whole math thing until I was doing calculus. Some of the trigonometry stuff was interesting, but it took a college math course before I realized exactly what all the algebra crap was about. That was the first time I really started to like math. Rote problem solving and arithmetic were so boring that I’d sometimes make mistakes just because I wasn’t paying attention. Calculus was where all the stuff I’d hated all that time came together and started making sense.
I totally agree that teaching some of the concepts and principles of calculus at younger ages would be a good thing. I’m kind of looking forward to having kids so that I can teach them some of the math principles I learned on my own through trying to figure out the why behind what I was just supposed to do by rote in class. I’m relatively bright, but I still didn’t really understand things well because of how they were taught. It’s no surprise to me that average to below average kids didn’t get it either. Teaching algebra in a different way, by teaching why you do it instead of just what to do, would be helpful. Even young kids can understand things like balance, and a lot of algebra is “balancing” equations. Teaching the principles of that shouldn’t be that hard.
(Upon looking at WhyNot’s link): Holy shit! Most of that page is stuff that I did to make basic math easier and faster to do in my head. The only thing I didn’t figure out was the partial sums thing, and that makes perfect sense. :smack: I should have thought of that. They didn’t teach me any of that in school, but once I figured out what was actually happening with adding/subtracting, multiplying/dividing, being lazy bastard that I am, I tried to look for easier ways of doing it. I used to get in trouble for not showing my work when I did things my way. I just didn’t know how to show it since my method was so different from the standard one.
Cool, they’re teaching my methods in school now! <singsong>Nya-nyaa, I was doing things the easy way.</singsong>
[QUOTE=WhyNot]
“But didn’t they give you the handbook? The answer to your question is on page 38!”
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Of COURSE! A Handbook! Why not have the parents teach the kids because the Chicago Math program is so wonderful… :rolleyes:
Completely amazing that the world survived without good old page 38… :smack:
As for my cites, I can only offer the past decade or so of personal observations of students in my community. If you want some other parental opinions, google for them. They are out there. :eek:
[QUOTE=Bippy the Beardless]
What does Grammar School mean to you?
For me (as a Brit) it means a secondary school (ages 13 to 18) with achademic rather than vocational leanings.
(they used to require students to pass a test at age 12 to get in)
Indeed Calculus is taught at Grammar Schools in UK.
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Traditionally a grammer school in the US would teach kindergarden to 8th grade.
[QUOTE=WhyNot]
This is totally different in pedagogy and methodology, at least. Kids still learn to add, subtract, multiply and divide, but at different rates and with different methods. They introduce functions and statistics in first grade (only they don’t call them that) and things are repeated over and over and over, but not in a rote way. There may be a page of three digit multiplication or fraction division review every few weeks even in the higher grades, where other books assume you remember how to do it - but there aren’t 10 pages to bore you out of your skull. There may be two pages of what looks like algebra, and then a page of geometry, and then two pages of arithmetic. Things are grouped by concept, not by modality.
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AFAIK, this is called integrated math.
I ran into it when I was helping teach a chemistry class in a high-rent neighborhood in 1999. I don’t know who was really right, but the charge was that there was not enough time for the kids to remember the operations of the functions, and they kept forgetting them because there wasn’t enough practice.
Personally, I think there was not enough tracking. The idea that you put the brightest in with the bottom half of the school angers me. There is no reason to pull down the acheivement of the top students unless you are sooooo liberal that you actually believe in equal results instead of equal opportunities. For God’s sake, even JFK is quoted as saying it’s the opportunities that are equal. At my HS, there was Math 92 (remedial 9th grade), 94 (average) 96 (college prep), and 98 (Honors).
Since there will always be the a couple kids who are placed to low accidently, there will always be those who get the point in about 10 minutes and can then tutor those around them. I’ve seen it in the chemistry classes I’ve taught, and even in the “Chemistry in the Community” class that was just an excuse to give 11th graders a science class so they could take the state exam at the end of the year.
OTOH, it’s possible the parents in that neighborhood saw disappointing results (so they thought) and reverted like we all do to what they had experienced as kids as “the norm”.
For what it’s worth, I had an excellent AP Bio/Chem teacher in high school who pointed out the limitations the current grade school math schedule in regards to advanced placement (AP) science classes. According to him, the logical order to take AP sciences is Physics, Chemistry, Biology. However, the main problem with teaching physics is that students in 9th/10th grade often do not have the math background for AP physics. He advocated teaching math earlier so that by the 10th grade, an AP physics teacher would not have to take time out to teach the math behind the physics.
Makes sense to me after going through the whole 9 yards of AP calc, physics, chem, bio… but I did it in reverse order (Bio, Chem, Physics/Calc).