[math-fun] grade school/jr high arithmetic
I've been going through the Khan Academy math exercises to see what math kids are learning. www.khanacademy.org While I am very impressed with the Khan Academy & its exercises, I am appalled by the time & effort in teaching fractions -- especially "mixed fractions". I realize that this is not the Khan Academy's fault -- KA is merely providing exercises to teach for the tests that the kids will have to pass. But who on Earth actually uses this stuff & why do we torture kids this way? No wonder people hate math. --- I think that the ability to do rudimentary programming is far more valuable to every kid than the ability to handle "mixed fractions". In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic. Yes, there is a place for summing fractions: when simplifying algebraic expressions, but not in basic arithmetic. --- The hours in every kid's life are valuable, and the hours in every teacher's day are even more valuable. Why do we want to waste these hours teaching them skills that bore them out of their minds, and that they will never use? If there is an educational crisis, it would appear to be caused by clueless adults.
A high school student, Julian Salazar, whom I've been coaching for the last year or so, put me on to the following, which should be required reading for everyone! R. http://www.maa.org/devlin/LockhartsLament.pdf On Fri, 28 Oct 2011, Henry Baker wrote:
I've been going through the Khan Academy math exercises to see what math kids are learning.
www.khanacademy.org
While I am very impressed with the Khan Academy & its exercises, I am appalled by the time & effort in teaching fractions -- especially "mixed fractions".
I realize that this is not the Khan Academy's fault -- KA is merely providing exercises to teach for the tests that the kids will have to pass.
But who on Earth actually uses this stuff & why do we torture kids this way?
No wonder people hate math.
---
I think that the ability to do rudimentary programming is far more valuable to every kid than the ability to handle "mixed fractions".
In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic. Yes, there is a place for summing fractions: when simplifying algebraic expressions, but not in basic arithmetic.
---
The hours in every kid's life are valuable, and the hours in every teacher's day are even more valuable. Why do we want to waste these hours teaching them skills that bore them out of their minds, and that they will never use?
If there is an educational crisis, it would appear to be caused by clueless adults.
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I'm a bit of two minds about drilling. I get how over-drilling can kill any creative spark a student may have for the beauty of math. Having taught it at the undergraduate level (which too often means, "at the middle-school/high-school level"), I've had to endure the scowls and sneers of those who didn't care a lick about math but had to do their calculations anyway, because that was part of the syllabus. However, I can also see how it certain facility with numbers and arithmetic operations is necessary to even begin to deal with math at anything more than a pure computational level. I had a buddy who also taught and was quite proficient in martial arts. In his class, he approached arithmetic drills as he would repetitive practice/warm-up in the martial arts context--do something relatively mundane so often that it becomes automatic, then move on to more sophisticated stuff. If there is an answer, it's probably the same one that it's always been--adjust the material with the level and goals of the student in mind. Kerry -- lkmitch@gmail.com www.kerrymitchellart.com
People write mixed fractions all the time: eg 9 1/2 weeks or whatever. I've had a couple of my own kids run this gauntlet at school and I just told them to immediately convert them to what I've taken to calling "fractions for grown ups" as a way of disparaging them and motivating my kids to not attempt to manipulate them in math homework, but to say that no one on Earth actually uses them is overstating the case in my opinion. On Fri, Oct 28, 2011 at 3:20 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I've been going through the Khan Academy math exercises to see what math kids are learning.
www.khanacademy.org
While I am very impressed with the Khan Academy & its exercises, I am appalled by the time & effort in teaching fractions -- especially "mixed fractions".
I realize that this is not the Khan Academy's fault -- KA is merely providing exercises to teach for the tests that the kids will have to pass.
But who on Earth actually uses this stuff & why do we torture kids this way?
No wonder people hate math.
---
I think that the ability to do rudimentary programming is far more valuable to every kid than the ability to handle "mixed fractions".
In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic. Yes, there is a place for summing fractions: when simplifying algebraic expressions, but not in basic arithmetic.
---
The hours in every kid's life are valuable, and the hours in every teacher's day are even more valuable. Why do we want to waste these hours teaching them skills that bore them out of their minds, and that they will never use?
If there is an educational crisis, it would appear to be caused by clueless adults.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
Henry Baker wrote:
In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic.
Actually I disagree about teaching GCD and LCM. These are the concepts where kids are genuinely introduced to thinking about the integers from the multiplicative point of view -- GCD and LCM are the thing that actually gets them to think about prime factorization. Most kids will never be taught any "number theory", but I think even rudimentary math education should make you think about why 15 and 16 and 17 are not all pretty much the same. --Michael -- Forewarned is worth an octopus in the bush.
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...... (Truth time: when was the last time you used "least common multiple", except on a test?) ......
A couple of days ago while explaining to my differential equations class how to integrate rational functions. We went on to discuss the Lotka-Volterra fox-rabbit equations. In preparation I went looking through Internet for some of the history and relevant discussion, and encountered a module on how to present the concepts to young children. Some of the discussions here came to mind, but mostly I was impressed by the possibility of substituting "teacher" for fox or "predator," and repacing "juicy young rabbits" or prey by "students." And as for the comparison with music theory, isin't it true that long ago, before they had middle schools, young boys were sent out to the fields to watch over the sheep. To relieve their boredom they got to cutting branches to make whistles and flutes, incidentally entertaining both the sheep and the wolves? Did counting the sheep have anything to do with Arithmetic? -hvm
participants (6)
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Henry Baker -
Kerry Mitchell -
mcintosh -
Michael Kleber -
Richard Guy -
Thane Plambeck