BigGaayAl

First off, this was one of the best written posts I have ever read, Wulfyn.

While reading through it, noticing your convictions that young kids' brains are unable to think logically, I was expecting you to debunk the statement that started this thread.

However your own educational experience then seems to contradict your statements (specifically the ones about logic) as you state that your teachers were constantly trying to help you see the bigger picture:
"We also had really good teachers that took the effort to frame a problem".

I'll read it again when I have more time. I bet you are not contradicting yourself, but that I missed a turn somewhere.

I also wonder on what you base the assertion that "humans do not develop the capacity for logical thought until they are around 12 years". I think I remember some ethics research that indicates a certain kind/level of ethical logic only appears around the age of 12. I just wonder how logic is defined in the research you are thinking of.

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Santa

I think if my brother read what you wrote wulfyn (and ill show him next time i see him) that he would probably agree with you. Hes purely a mathematics/computer science guy. I dont think he ever took any kind of class that would have taught him about early childhood growth, so he probably assumed that children would be capable of abstract thinking but were simply not given the chance to think that way.

You bring up a good point about possibly teaching kids to think abstractly at a later age. Trying to think of what i was capable of years ago is difficult, but id say I was capable of understanding the theories behind mathematics when i was either taking pre-algebra or geometry. But of course i was not taught this way. I was taught how to work with polynomials (despite having little clue what they were), and what a point, line, and plane are.

I dont know how they do it in Britain, but the order of math classes here is algebra, geometry, algebra 2, pre-calc, so on. This order seems really flawed to me. Wouldnt it make more sense to go Geometry first, then algebra, then algebra 2, and so on? Geometry could be a kid's first experience at thinking abstractly, after all it is a new set of rules in a new framework. From there, you can learn algebra and algebra 2 in a more thoughtful, abstract way because you would have experience thinking this way.

Embiggener

I think its a shame that people have the attitude that we should only teach kids the math they need to get through life. We don't give this treatment to other subjects. You don't really need any history to go to function as an adult. Literature and art and music, we could do without them. We learn all sorts of stuff in school that is forgotten after we leave. The real purpose is to develop skills/thought processes that can be applied in the future, not to memorize facts. Mathematics develops problem solving skills that can be applied to any problem.

From my own experience with high school math, and science somewhat, I found that it was just preparation for higher learning. Meaning that students weren't told why they were learning things, just that they had to know them. Things like matrix algebra, I learned it in high school, I didn't know what good it was then or why anyone would need to know it. It makes for a really boring class. The other thing that bothered me was how some subjects were "simplified" for high school. The full picture may be too complicated to understand but you could still go over it briefly to give some motivation to students.

The problem is clear when you get to university level math courses, the concepts are emphasized rather than the calculations, students aren't used to this, they can crank out the math but they don't really know what they're doing.



I dont really know much about it myself, but just try looking up intellectual development in children and theres a general outline for brains developing. Like what age kids get a sense of self etc. I think logical thought/abstract thinking is the last one.

chaf3d

Oh good god, i remember the first time of two things: 1) How WAY to long the first Calc form is to do when you can look at a derivative and just KNOW that 3x^2 turns into 6x instead of the limits, and 2) the first time learning the calculus as to why 6/3 = 2... cause yes, you do technically need to the anti-derivatives for the division to 'make sense' as my calc prof used to say.

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All the forces of Evil need to Succeed is for enough Good men to do nothing.
-Edmund Burke

Santa

Oh jesus, tell me about it. Its amazing how ya can take a half page of work and turn it into nothing with a simple trick.

Relmar

Is our children learning?

VegaBond

I've had a horrible advanced match during high school, our teacher was Indian and all of us couldn't understand him half the time and all our grades went down and still effects us to this day on certain mathematical area's.. but college did get me back on track but still they ask about how my gpa went down due to language barriers...


Btw, MATH RULES EVERYDAY OF YOUR LIFE.

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sordavie

I have somewhat of a hard time understanding that awkward run-on sentence there.

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