Re: [math-fun] NYTimes: How to Fix Our Math Education
Wasn't there a math course at MIT in which you could score 200% if you got _all_ the answers wrong? Needless to say, you had to be pretty sure about your answers before turning in a test booklet like this! At 02:19 PM 8/28/2011, Eugene Salamin wrote:
Here's a news article [ http://news.yahoo.com/ind-vouchers-prompt-thousands-change-schools-170216446... ] with headline "Indiana vouchers prompt thousands to change schools". It looks like, given the freedom to choose and take their money with them, people will desert the public schools.
Not all families have this freedom. Sometimes, it is reserved for economically or scholastically poor students. Here's an idea. A gifted student will normally strive for 100% on these performance exams that have become so important in recent times. Public schools like smart students since the high grades help their rating score and bring increased funding. But suppose instead these students conspire to achieve 0%. Say there are fifty 5-choice questions, 0.8^50 = 1.4e-5, so there's a subtle message in that zero score.
-- Gene
Prof. Ambrose did this. He always gave true false exams -- some of the hardest exams I have ever taken. +1 for correct answers, -1 for incorrect, 0 for not answering, except for all incorrect. Class averages were in the low 20's. There was a rumor that negative class averages had once occurred, but I never saw it. On Aug 29, 2011, at 10:39 AM, Henry Baker wrote:
Wasn't there a math course at MIT in which you could score 200% if you got _all_ the answers wrong? Needless to say, you had to be pretty sure about your answers before turning in a test booklet like this!
At 02:19 PM 8/28/2011, Eugene Salamin wrote:
Here's a news article [ http://news.yahoo.com/ind-vouchers-prompt-thousands-change-schools-170216446... ] with headline "Indiana vouchers prompt thousands to change schools". It looks like, given the freedom to choose and take their money with them, people will desert the public schools.
Not all families have this freedom. Sometimes, it is reserved for economically or scholastically poor students. Here's an idea. A gifted student will normally strive for 100% on these performance exams that have become so important in recent times. Public schools like smart students since the high grades help their rating score and bring increased funding. But suppose instead these students conspire to achieve 0%. Say there are fifty 5-choice questions, 0.8^50 = 1.4e-5, so there's a subtle message in that zero score.
-- Gene
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Why even bother, with a true/false exam? Only two choices makes it clear that "all wrong" and "all right" are equivalent. Paul Vojta gave exams to his graduate math classes with true/false statements of relevant lemmas: +5 for a correct answer, 0 for blank, -2 for saying something was false when it was true, -7 for saying something was true when it was false. If you merely aren't aware that a lemma is true, all that happens is that you need to do the work to rediscover it. If you think a lemma is true but it's not, then you end up proving incorrect theorems! --Michael On Mon, Aug 29, 2011 at 12:41 PM, Thomas Knight <tk@csail.mit.edu> wrote:
Prof. Ambrose did this. He always gave true false exams -- some of the hardest exams I have ever taken. +1 for correct answers, -1 for incorrect, 0 for not answering, except for all incorrect. Class averages were in the low 20's. There was a rumor that negative class averages had once occurred, but I never saw it.
On Aug 29, 2011, at 10:39 AM, Henry Baker wrote:
Wasn't there a math course at MIT in which you could score 200% if you got _all_ the answers wrong? Needless to say, you had to be pretty sure about your answers before turning in a test booklet like this!
At 02:19 PM 8/28/2011, Eugene Salamin wrote:
Here's a news article [ http://news.yahoo.com/ind-vouchers-prompt-thousands-change-schools-170216446...] with headline "Indiana vouchers prompt thousands to change schools". It looks like, given the freedom to choose and take their money with them, people will desert the public schools.
Not all families have this freedom. Sometimes, it is reserved for economically or scholastically poor students. Here's an idea. A gifted student will normally strive for 100% on these performance exams that have become so important in recent times. Public schools like smart students since the high grades help their rating score and bring increased funding. But suppose instead these students conspire to achieve 0%. Say there are fifty 5-choice questions, 0.8^50 = 1.4e-5, so there's a subtle message in that zero score.
-- Gene
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
But if you think a lemma is false when it's actually true, you can prove anything by contradiction. So you still get to prove incorrect theorems. --ms On 8/29/2011 12:46 PM, Michael Kleber wrote:
Why even bother, with a true/false exam? Only two choices makes it clear that "all wrong" and "all right" are equivalent.
Paul Vojta gave exams to his graduate math classes with true/false statements of relevant lemmas: +5 for a correct answer, 0 for blank, -2 for saying something was false when it was true, -7 for saying something was true when it was false. If you merely aren't aware that a lemma is true, all that happens is that you need to do the work to rediscover it. If you think a lemma is true but it's not, then you end up proving incorrect theorems!
--Michael
On Mon, Aug 29, 2011 at 12:41 PM, Thomas Knight<tk@csail.mit.edu> wrote:
Prof. Ambrose did this. He always gave true false exams -- some of the hardest exams I have ever taken. +1 for correct answers, -1 for incorrect, 0 for not answering, except for all incorrect. Class averages were in the low 20's. There was a rumor that negative class averages had once occurred, but I never saw it.
On Aug 29, 2011, at 10:39 AM, Henry Baker wrote:
Wasn't there a math course at MIT in which you could score 200% if you got _all_ the answers wrong? Needless to say, you had to be pretty sure about your answers before turning in a test booklet like this! At 02:19 PM 8/28/2011, Eugene Salamin wrote:
Here's a news article [ http://news.yahoo.com/ind-vouchers-prompt-thousands-change-schools-170216446...] with headline "Indiana vouchers prompt thousands to change schools". It looks like, given the freedom to choose and take their money with them, people will desert the public schools. Not all families have this freedom. Sometimes, it is reserved for economically or scholastically poor students. Here's an idea. A gifted student will normally strive for 100% on these performance exams that have become so important in recent times. Public schools like smart students since the high grades help their rating score and bring increased funding. But suppose instead these students conspire to achieve 0%. Say there are fifty 5-choice questions, 0.8^50 = 1.4e-5, so there's a subtle message in that zero score. -- Gene
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Monday 29 August 2011 17:46:33 Michael Kleber wrote:
Why even bother, with a true/false exam? Only two choices makes it clear that "all wrong" and "all right" are equivalent.
The 200% thing provides students with a way to say "I am very confident that all my answers are correct". Having that level of confidence and being right presumably correlates with knowing the material very well indeed -- better than can be identified merely by having got everything right, on a true/false exam -- so the exam gains a little bit of extra dynamic range. -- g
On 29 Aug 2011 at 12:41, Thomas Knight wrote:
Prof. Ambrose did this. He always gave true false exams -- some of the hardest exams ... I have ever taken. +1 for correct answers, -1 for incorrect, 0 for not answering, except for all incorrect.
I don't remember the professor but I believe that that course was Real Analysis II (it was course 18.22, I think). As I recall it was open- book, open-end. And I think that the class average the year I took it was, indeed, right around 20. /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
Yes, I remember that scheme, and the first quiz. A student finished early, handed in his quiz and ran out. The professor looked it over, laughed, and said, "He just got -19. I warned you." Chuckle, chuckle. The lessons in homomorphisms were valuable, but more longlasting was the lesson in human nature. Hilarie Quoting Bernie Cosell <bernie@fantasyfarm.com>:
On 29 Aug 2011 at 12:41, Thomas Knight wrote:
Prof. Ambrose did this. He always gave true false exams -- some of the hardest exams ... I have ever taken. +1 for correct answers, -1 for incorrect, 0 for not answering, except for all incorrect.
I don't remember the professor but I believe that that course was Real Analysis II (it was course 18.22, I think). As I recall it was open- book, open-end. And I think that the class average the year I took it was, indeed, right around 20.
/Bernie\
-- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Around 1962 I took a physics class at Stanford. The class was large and the professor, Wolfgang Panofsky, if I remember correctly, gave one of those +1, -1 true/false exams. There were lots of counter intuitive questions and indeed the class average was negative. I have no recollection what my score was. I probably blanked it for good reason! On Mon, Aug 29, 2011 at 11:41 AM, Thomas Knight <tk@csail.mit.edu> wrote:
Prof. Ambrose did this. He always gave true false exams -- some of the hardest exams I have ever taken. +1 for correct answers, -1 for incorrect, 0 for not answering, except for all incorrect. Class averages were in the low 20's. There was a rumor that negative class averages had once occurred, but I never saw it.
On Aug 29, 2011, at 10:39 AM, Henry Baker wrote:
Wasn't there a math course at MIT in which you could score 200% if you got _all_ the answers wrong? Needless to say, you had to be pretty sure about your answers before turning in a test booklet like this!
At 02:19 PM 8/28/2011, Eugene Salamin wrote:
Here's a news article [ http://news.yahoo.com/ind-vouchers-prompt-thousands-change-schools-170216446... ] with headline "Indiana vouchers prompt thousands to change schools". It looks like, given the freedom to choose and take their money with them, people will desert the public schools.
Not all families have this freedom. Sometimes, it is reserved for economically or scholastically poor students. Here's an idea. A gifted student will normally strive for 100% on these performance exams that have become so important in recent times. Public schools like smart students since the high grades help their rating score and bring increased funding. But suppose instead these students conspire to achieve 0%. Say there are fifty 5-choice questions, 0.8^50 = 1.4e-5, so there's a subtle message in that zero score.
-- Gene
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Yes, I did this once in Ankeny's algebra class. And I blew it. To make up for the large negative score, he let me (but only me) try again on another test, in exchange for tutoring his daughter in physics. I even remember the T/F question I got wrong: All groups of order 15 are Abelian. --ms On 8/29/2011 10:39 AM, Henry Baker wrote:
Wasn't there a math course at MIT in which you could score 200% if you got _all_ the answers wrong? Needless to say, you had to be pretty sure about your answers before turning in a test booklet like this!
At 02:19 PM 8/28/2011, Eugene Salamin wrote:
Here's a news article [ http://news.yahoo.com/ind-vouchers-prompt-thousands-change-schools-170216446... ] with headline "Indiana vouchers prompt thousands to change schools". It looks like, given the freedom to choose and take their money with them, people will desert the public schools.
Not all families have this freedom. Sometimes, it is reserved for economically or scholastically poor students. Here's an idea. A gifted student will normally strive for 100% on these performance exams that have become so important in recent times. Public schools like smart students since the high grades help their rating score and bring increased funding. But suppose instead these students conspire to achieve 0%. Say there are fifty 5-choice questions, 0.8^50 = 1.4e-5, so there's a subtle message in that zero score.
-- Gene
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (8)
-
Bernie Cosell -
Gareth McCaughan -
Henry Baker -
hilarie＠xmission.com -
James Buddenhagen -
Michael Kleber -
Mike Speciner -
Thomas Knight