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Math is not a single linear path. EX: You don't need to know long division to get Algebra. You can even go the other way. If you say 4a + 8b + 4 = x, and a =

Math is not a single linear path. EX: You don't need to know long division to get Algebra. You can even go the other way. If you say 4a + 8b + 4 = x, and a = 10 * 10; b = 10. Now divide by 2b. Want to explain another base, say a = 16 * 16; b = 16. etc. PS: My father even taught a first grader long division that way. (Note: I think he used x1; x2, x3 and he soon move to the traditional form.) Edit: My point is if you want to build a house you can start with a foundation, or the windows. Keep studding math and there are plenty of opportunity's to review older concepts with new insights. Buy trying to focus on each little nibble in isolation it's harder to link concepts. EX: The sign rules are really just the associative property of addition and multiplication in another form. {-b + a = a + -b = a - b} {-b + -a = - ( a + b) } {-a * -b = (-1 * -1) * (a * b) = 1 * a * b}

hackinthebochs 15y ago
>My point is if you want to build a house you can start with a foundation, or the windows. This is exactly the reason why most people don't get math. If you start with the windows, the student asks "whats the point in learning this?". They can't see the house being built when you start with the windows. Without the foundation there is no intuitive understanding thus everything seems like meaningless rules. And in fact they are just that-meaningless.
kenjackson 15y ago
Long division is a bad example, as you don't need to know long division... for well... anything. But I did SAT tutoring when I was an undergrad for disadvantaged kids and I used to have serious trouble with a lot of basic concepts that made it really hard to go further. For example: 1) Some students didn't understand greater than vs less than symbols. They didn't know which direction indicated greater than. 2) Some students didn't know the relationship between the numerator and denominator. 3/2 and 2/3 would be routinely confused. Couple this confusion with (1) above and things get really weird. 3) Area, volume, circumference -- while they knew the concepts they didn't map the terms to the concepts. 4) The relationship between remainders and fractional parts was often completely unknown. 5) Percent to values often wasn't known. "60% off sales" often meant a bit more than half off. The right intuition, but you need an actual answer for the SAT. You're right, math is not linear. But if you only understand 50% of what is taught in elementary and junior high school, you're going to understand even less in high school.
- simpleTruth 15y ago
  you don't need to know long division... for well... anything On that we can more or less agree. Perhaps we could salvage some of that time and put it to more productive use. And then perhaps after a few years we can go back and look at it again. People think of math as a sort of tree structure where you need this long chain of tools to get to understand each new concept. I am simply suggesting it's closer to a graph where multiple approaches can reach the same concept and reinforce each other. As to the SAT it's mostly a middle school math test. I suspect after a while you build a little crib sheet of the basic concepts that people needed to understand. And yet considering people "studded" this stuff for ~5 hours a week, 36 weeks a year, for ~10 years I suspect the crib sheet was not all that long.
- jaredmck 15y ago
  the alligator is hungry, he wants to eat the bigger number.
  - ern 15y ago
    Another useful trick was taught to me in second grade: draw two dots for the bigger number, and one dot for the smaller one. Then join the dots.

hackinthebochs 15y ago

>My point is if you want to build a house you can start with a foundation, or the windows. This is exactly the reason why most people don't get math. If you start with the windows, the student asks "whats the point in learning this?". They can't see the house being built when you start with the windows. Without the foundation there is no intuitive understanding thus everything seems like meaningless rules. And in fact they are just that-meaningless.

kenjackson 15y ago

Long division is a bad example, as you don't need to know long division... for well... anything. But I did SAT tutoring when I was an undergrad for disadvantaged kids and I used to have serious trouble with a lot of basic concepts that made it really hard to go further. For example: 1) Some students didn't understand greater than vs less than symbols. They didn't know which direction indicated greater than. 2) Some students didn't know the relationship between the numerator and denominator. 3/2 and 2/3 would be routinely confused. Couple this confusion with (1) above and things get really weird. 3) Area, volume, circumference -- while they knew the concepts they didn't map the terms to the concepts. 4) The relationship between remainders and fractional parts was often completely unknown. 5) Percent to values often wasn't known. "60% off sales" often meant a bit more than half off. The right intuition, but you need an actual answer for the SAT. You're right, math is not linear. But if you only understand 50% of what is taught in elementary and junior high school, you're going to understand even less in high school.

simpleTruth 15y ago
you don't need to know long division... for well... anything On that we can more or less agree. Perhaps we could salvage some of that time and put it to more productive use. And then perhaps after a few years we can go back and look at it again. People think of math as a sort of tree structure where you need this long chain of tools to get to understand each new concept. I am simply suggesting it's closer to a graph where multiple approaches can reach the same concept and reinforce each other. As to the SAT it's mostly a middle school math test. I suspect after a while you build a little crib sheet of the basic concepts that people needed to understand. And yet considering people "studded" this stuff for ~5 hours a week, 36 weeks a year, for ~10 years I suspect the crib sheet was not all that long.
jaredmck 15y ago
the alligator is hungry, he wants to eat the bigger number.
- ern 15y ago
  Another useful trick was taught to me in second grade: draw two dots for the bigger number, and one dot for the smaller one. Then join the dots.