[math-fun] Distributive law without +? (6th Grade)
You can pick a or c: 6*(9*1) or 6*(9+0)
why not b too? 6*(7+2)=6*(2+7) Not that I know much about educating children, but I suspect that demanding detailed educational standards about content is a waste of time. More effective might be to demand that the teachers actually know their topic. E.g. I had an elementary school teacher try to teach us that a/b + c/d = (a+c)/(b+d). Some parent, perhaps mine, later stepped in to try to correct her. So, maybe: don't test the children, test the teachers. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Of course, that's the ``right'' way to add fractions. Used much more frequently than the mathematicians' way. Batting averages (cricket or baseball), bowling averages (cricket), grade point averages, ... Both should be taught and carefully distinguished! R. On Tue, 26 Apr 2016, Warren D Smith wrote:
You can pick a or c: 6*(9*1) or 6*(9+0)
why not b too? 6*(7+2)=6*(2+7)
Not that I know much about educating children, but I suspect that demanding detailed educational standards about content is a waste of time. More effective might be to demand that the teachers actually know their topic. E.g. I had an elementary school teacher try to teach us that a/b + c/d = (a+c)/(b+d). Some parent, perhaps mine, later stepped in to try to correct her. So, maybe: don't test the children, test the teachers.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Warren D Smith writes:
I had an elementary school teacher try to teach us that a/b + c/d = (a+c)/(b+d). Some parent, perhaps mine, later stepped in to try to correct her.
Wow, that's just sad. I think we learned how to add fractions in 2nd or 3rd grade. It's hard to imagine how someone with such a weak understanding of basic arithmetic could be paid to teach it. You'd think the teachers would have to pass some basic competency test. Perhaps you could have used this to your advantage. Convince the teacher that a half dollar plus a quarter was in fact equal to (1+1)/(2+4) = 2/6 = 1/3 of a dollar, or 33 + 1/3 cents. Then offer to pay the teacher more than that, say 35 cents, in exchange for a half dollar plus a quarter. It would be a win-win: The teacher would think he/she was earning 1 + 2/3 cents, and you'd earn 40 cents. Rinse and repeat. I've always felt it was a student's responsibility to make unrepentant teachers pay for their ignorance. Tom
I had a math teacher in Junior High in NYC who would not admit making a mistake. We were discussing a problem in the textbook, and she asserted that the answer in the back of the book was correct. But as we all demonstrated, the answer was wrong. She wouldn't back down. Next class session, she claimed that she had discussed the problem with a Dr. So and So in the Math Dept, and that they agreed that the answer was correct; it was the question that was wrong. The Junior High was named after some famous American. I think it was Benedict Arnold. -- Gene From: Tom Karzes <karzes@sonic.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, April 26, 2016 1:38 PM Subject: [math-fun] Distributive law without +? (6th Grade) Warren D Smith writes:
I had an elementary school teacher try to teach us that a/b + c/d = (a+c)/(b+d). Some parent, perhaps mine, later stepped in to try to correct her.
Wow, that's just sad. I think we learned how to add fractions in 2nd or 3rd grade. It's hard to imagine how someone with such a weak understanding of basic arithmetic could be paid to teach it. You'd think the teachers would have to pass some basic competency test. Perhaps you could have used this to your advantage. Convince the teacher that a half dollar plus a quarter was in fact equal to (1+1)/(2+4) = 2/6 = 1/3 of a dollar, or 33 + 1/3 cents. Then offer to pay the teacher more than that, say 35 cents, in exchange for a half dollar plus a quarter. It would be a win-win: The teacher would think he/she was earning 1 + 2/3 cents, and you'd earn 40 cents. Rinse and repeat. I've always felt it was a student's responsibility to make unrepentant teachers pay for their ignorance. Tom
Yes, I've encountered that type before: People who just can't admit when they're wrong. To me, that's the real difference between a person who can learn and person who can't. It's the difference between science vs. dogma. Science is built on learning from mistakes, and adapting to correct them. Dogma is built on covering up mistakes under piles of more dogma. Tom Eugene Salamin via math-fun writes:
I had a math teacher in Junior High in NYC who would not admit making a mistake. We were discussing a problem in the textbook, and she asserted that the answer in the back of the book was correct. But as we all demonstrated, the answer was wrong. She wouldn't back down. Next class session, she claimed that she had discussed the problem with a Dr. So and So in the Math Dept, and that they agreed that the answer was correct; it was the question that was wrong.
The Junior High was named after some famous American. I think it was Benedict Arnold.
-- Gene
From: Tom Karzes <karzes@sonic.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, April 26, 2016 1:38 PM Subject: [math-fun] Distributive law without +? (6th Grade)
Warren D Smith writes:
I had an elementary school teacher try to teach us that a/b + c/d = (a+c)/(b+d). Some parent, perhaps mine, later stepped in to try to correct her.
Wow, that's just sad. I think we learned how to add fractions in 2nd or 3rd grade. It's hard to imagine how someone with such a weak understanding of basic arithmetic could be paid to teach it. You'd think the teachers would have to pass some basic competency test.
Perhaps you could have used this to your advantage. Convince the teacher that a half dollar plus a quarter was in fact equal to (1+1)/(2+4) = 2/6 = 1/3 of a dollar, or 33 + 1/3 cents. Then offer to pay the teacher more than that, say 35 cents, in exchange for a half dollar plus a quarter. It would be a win-win: The teacher would think he/she was earning 1 + 2/3 cents, and you'd earn 40 cents. Rinse and repeat.
I've always felt it was a student's responsibility to make unrepentant teachers pay for their ignorance.
Tom
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Great story, Gene. I had a math teacher in 8th grade who asked us to each invent a new calendar. Mine was a 364-day year, of 13 months of 28 days each, so that the same date always fell on the same day of the week. It seemed like a good idea at the time. Every 28 years there was a 14th month — of 35 days — to help catch up. The seasons had slid by almost a month. [35 = 28(365-364) + 28/4.] Maybe not the most brilliant idea, but Mrs. Lewis insisted that by not compensating sooner for the 1/4 day per year that was normally compensated for with leap years, my calendar meant we would soon all be waking up in the middle of the night. I knew that whatever its flaws, that wasn't one of them. But I could not convince her despite repeated attempts. (Then they moved me to the 9th grade math class for a month, then to the 10th grade class.) —Dan
On Apr 26, 2016, at 2:15 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
I had a math teacher in Junior High in NYC who would not admit making a mistake. We were discussing a problem in the textbook, and she asserted that the answer in the back of the book was correct. But as we all demonstrated, the answer was wrong. She wouldn't back down. Next class session, she claimed that she had discussed the problem with a Dr. So and So in the Math Dept, and that they agreed that the answer was correct; it was the question that was wrong.
The Junior High was named after some famous American. I think it was Benedict Arnold.
I also remember one time on a chemistry test being asked which has greater density: sodium or potassium I looked at the giant periodic table on classroom wall, and correctly answered sodium. The teacher graded me as "wrong" since I presumably didn't "understand the principle" that higher atomic weight, same column of table, implies greater density. No amount of protest and consultation of databooks availed. :) Later I noticed that a lot of questions on "IQ tests" simply do not have unique objectively correct answers. This did not appear to bother the psychologists devising those tests, who just chose one answer which according to them was "the only right answer"! A lot of the questions are not really about finding correct answer, they are about finding out whether the testee thinks in the same manner as the problem-creator. If does, then has "greater intelligence." If you gave really-maximally-correct answers to IQ test questions, they might be "answers a,b and c all may be justified, by the following reasoning xxxx" -- and you would then be graded as having "low intelligence" despite objectively doing a better job than all the other test-takers and the test creators! And then, the psychology community determined (in one of their "greatest discoveries") that "intelligence" was a pretty one-dimensional thing. I.e. you might think you are good at French and poor at crosswords, but according to the shrinks there is only one quantity "g" describing your "general intelligence" and hence your abilities at everything are all high or all low. The fact that the most-favored IQ tests today are largely not about correctness, but rather about consensus, was of course not discussed at all, and surely couldn't have anything to do with that "great discovery" could it? Shut up, critics. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
I won't repeat my previously posted opinions concerning public education, as it would pretty much be a political tirade. But I will remark about a positive experience with a teacher, but one that was not in public education. In my freshman year at MIT, I took an honors chemistry class taught by J. S. Waugh (a great guy). A question on a quiz asked whether a certain reaction occurred. If you calculated the change in Gibbs free energy, you would conclude that the reaction was thermodynamically favored. However, having been a chemical hacker as a kid, I knew that in fact the reaction did not happen, and that was the official answer to the question. In the post-quiz discussion, a student complained that he should be credited for answering that the reaction does proceed, because being thermodynamically favored, it should proceed however slowly. The prof said he would give him the credit when the reaction completes. As for IQ, I dismiss the whole concept. IQ is the score on an IQ test, and nothing more. -- Gene From: Warren D Smith <warren.wds@gmail.com> To: math-fun@mailman.xmission.com Sent: Tuesday, April 26, 2016 1:38 PM Subject: Re: [math-fun] Distributive law without +? (6th Grade) I also remember one time on a chemistry test being asked which has greater density: sodium or potassium I looked at the giant periodic table on classroom wall, and correctly answered sodium. The teacher graded me as "wrong" since I presumably didn't "understand the principle" that higher atomic weight, same column of table, implies greater density. No amount of protest and consultation of databooks availed. :) Later I noticed that a lot of questions on "IQ tests" simply do not have unique objectively correct answers. This did not appear to bother the psychologists devising those tests, who just chose one answer which according to them was "the only right answer"! A lot of the questions are not really about finding correct answer, they are about finding out whether the testee thinks in the same manner as the problem-creator. If does, then has "greater intelligence." If you gave really-maximally-correct answers to IQ test questions, they might be "answers a,b and c all may be justified, by the following reasoning xxxx" -- and you would then be graded as having "low intelligence" despite objectively doing a better job than all the other test-takers and the test creators! And then, the psychology community determined (in one of their "greatest discoveries") that "intelligence" was a pretty one-dimensional thing. I.e. you might think you are good at French and poor at crosswords, but according to the shrinks there is only one quantity "g" describing your "general intelligence" and hence your abilities at everything are all high or all low. The fact that the most-favored IQ tests today are largely not about correctness, but rather about consensus, was of course not discussed at all, and surely couldn't have anything to do with that "great discovery" could it? Shut up, critics. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
And then, the psychology community determined (in one of their "greatest discoveries") that "intelligence" was a pretty one-dimensional thing. I.e. you might think you are good at French and poor at crosswords, but according to the shrinks there is only one quantity "g" describing your "general intelligence" and hence your abilities at everything are all high or all low.
I think the whole idea of g is that that's substantial correlation between (a certain group of) different abilities, more particularly, the largest linear component explains a relatively large portion of the variance. I don't think anyone claims that all other components are 0 or negligible. (I've seen studies suggesting g accounts for 40-50% of total variance, though of course this can only be as good as the tests used.) Actually, I'm curious as to what the next few components are... Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Apr 26, 2016 at 4:38 PM, Warren D Smith <warren.wds@gmail.com> wrote:
I also remember one time on a chemistry test being asked which has greater density: sodium or potassium
I looked at the giant periodic table on classroom wall, and correctly answered sodium.
The teacher graded me as "wrong" since I presumably didn't "understand the principle" that higher atomic weight, same column of table, implies greater density. No amount of protest and consultation of databooks availed. :)
Later I noticed that a lot of questions on "IQ tests" simply do not have unique objectively correct answers. This did not appear to bother the psychologists devising those tests, who just chose one answer which according to them was "the only right answer"! A lot of the questions are not really about finding correct answer, they are about finding out whether the testee thinks in the same manner as the problem-creator. If does, then has "greater intelligence." If you gave really-maximally-correct answers to IQ test questions, they might be "answers a,b and c all may be justified, by the following reasoning xxxx" -- and you would then be graded as having "low intelligence" despite objectively doing a better job than all the other test-takers and the test creators!
And then, the psychology community determined (in one of their "greatest discoveries") that "intelligence" was a pretty one-dimensional thing. I.e. you might think you are good at French and poor at crosswords, but according to the shrinks there is only one quantity "g" describing your "general intelligence" and hence your abilities at everything are all high or all low.
The fact that the most-favored IQ tests today are largely not about correctness, but rather about consensus, was of course not discussed at all, and surely couldn't have anything to do with that "great discovery" could it? Shut up, critics.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (6)
-
Charles Greathouse -
Dan Asimov -
Eugene Salamin -
rkg -
Tom Karzes -
Warren D Smith