| Topic: |
Sociology > Education |
| User: |
"Mark Shapiro" |
| Date: |
17 Nov 2003 11:19:55 PM |
| Object: |
Another Route to Grade Inflation. |
In the past two decades American colleges and universities have softened
their policies on withdrawing from courses to the point where students at
many colleges and universities can drop courses without penalty until
shortly before the final exam. These policies have helped to contribute to
the grade inflation that is rampant on American college campuses.
Our guest commentator, Tina Blue, from the University of Kansas shares her
experiences in this regard in her essay "Another Route to Grade Inflation".
Read it in its entirety at:
http://irascibleprofessor.com/comments-11-18-03.htm
Sincerely,
--
Dr. Mark H. Shapiro
Editor and Publisher
The Irascible Professor
http://irascibleprofessor.com
.
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| User: "Herman Rubin" |
|
| Title: Re: Another Route to Grade Inflation. |
18 Nov 2003 03:04:47 PM |
|
|
In article <%Zhub.1373$i24.1273444@news3.news.adelphia.net>,
Mark Shapiro <mshapiro2@nospm-adelphia.net> wrote:
In the past two decades American colleges and universities have softened
their policies on withdrawing from courses to the point where students at
many colleges and universities can drop courses without penalty until
shortly before the final exam. These policies have helped to contribute to
the grade inflation that is rampant on American college campuses.
Our guest commentator, Tina Blue, from the University of Kansas shares her
experiences in this regard in her essay "Another Route to Grade Inflation".
Read it in its entirety at:
http://irascibleprofessor.com/comments-11-18-03.htm
THIS type of "inflation" does not bother me; I believe it
only bothers those who have an unreasonable opinion of the
validity of grades. This causes courses to be dumbed down,
and concepts to be avoided, and trivia examined. What is
important about a course is what is known years later, not
at the time of the final exam, and certainly not what can
be done for homework.
Some universities do not, or at least did not, but grades
below "C" on the student's record. As came up when this
was discussed informally, we do not put our rejected papers
on our bibliographies.
From a very old Usenet posting:
I can't resist providing this little tidbit at a time
when all of academia are involved in assessing the
semester's accomplishments.
"A GRADE is an inadequate report
of an inaccurate judgement by a
biased and variable judge of the
extent to which a student has
attained an undefined level of
mastery of an unknown proportion
of an indefinite amount of material."
George W. Tauxe
University of Oklahoma
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
|
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|
| User: "Alberto Moreira" |
|
| Title: Re: Another Route to Grade Inflation. |
19 Nov 2003 07:18:37 AM |
|
|
Said (Herman Rubin) :
In article <%Zhub.1373$i24.1273444@news3.news.adelphia.net>,
Mark Shapiro <mshapiro2@nospm-adelphia.net> wrote:
In the past two decades American colleges and universities have softened
their policies on withdrawing from courses to the point where students at
many colleges and universities can drop courses without penalty until
shortly before the final exam. These policies have helped to contribute to
the grade inflation that is rampant on American college campuses.
Our guest commentator, Tina Blue, from the University of Kansas shares her
experiences in this regard in her essay "Another Route to Grade Inflation".
Read it in its entirety at:
http://irascibleprofessor.com/comments-11-18-03.htm
THIS type of "inflation" does not bother me; I believe it
only bothers those who have an unreasonable opinion of the
validity of grades. This causes courses to be dumbed down,
and concepts to be avoided, and trivia examined. What is
important about a course is what is known years later, not
at the time of the final exam, and certainly not what can
be done for homework.
Some universities do not, or at least did not, but grades
below "C" on the student's record. As came up when this
was discussed informally, we do not put our rejected papers
on our bibliographies.
From a very old Usenet posting:
I can't resist providing this little tidbit at a time
when all of academia are involved in assessing the
semester's accomplishments.
"A GRADE is an inadequate report
of an inaccurate judgement by a
biased and variable judge of the
extent to which a student has
attained an undefined level of
mastery of an unknown proportion
of an indefinite amount of material."
George W. Tauxe
University of Oklahoma
Grades are irrelevant. One either knows what's needed to move on, or
one doesn't. I'm almost getting to the point where my grade is either
pass or fail, and nothing else - therefore, you might get to find that
my grade sheets will either have A's or F's.
And I don't call it grade "inflation", I call it rather grade
"disregard". If you use your grade for boasting or comparison
purposes, your problem, just don't bother me with it.
Alberto.
.
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| User: "Mark Shapiro" |
|
| Title: Re: Another Route to Grade Inflation. |
19 Nov 2003 08:16:00 AM |
|
|
While I would agree that an individual grade is a very imperfect
measurement, in the aggregate the grades a student achieves are quite
meaningful in my opinion.
The only problem with your A grades is that they probably are closer to a C
grade in my book. In other words, your A does not mean "outstanding
performance", it means more or less "average" performance. That's grade
inflation, whether you admit it or not.
--
Dr. Mark H. Shapiro
Editor and Publisher
The Irascible Professor
http://irascibleprofessor.com
"Alberto Moreira" <junkmail@moreira.mv.com> wrote in message
news:3fbf6d1c.3284002@news.mv.net...
Said (Herman Rubin) :
In article <%Zhub.1373$i24.1273444@news3.news.adelphia.net>,
Mark Shapiro <mshapiro2@nospm-adelphia.net> wrote:
In the past two decades American colleges and universities have softened
their policies on withdrawing from courses to the point where students
at
many colleges and universities can drop courses without penalty until
shortly before the final exam. These policies have helped to contribute
to
the grade inflation that is rampant on American college campuses.
Our guest commentator, Tina Blue, from the University of Kansas shares
her
experiences in this regard in her essay "Another Route to Grade
Inflation".
Read it in its entirety at:
http://irascibleprofessor.com/comments-11-18-03.htm
THIS type of "inflation" does not bother me; I believe it
only bothers those who have an unreasonable opinion of the
validity of grades. This causes courses to be dumbed down,
and concepts to be avoided, and trivia examined. What is
important about a course is what is known years later, not
at the time of the final exam, and certainly not what can
be done for homework.
Some universities do not, or at least did not, but grades
below "C" on the student's record. As came up when this
was discussed informally, we do not put our rejected papers
on our bibliographies.
From a very old Usenet posting:
I can't resist providing this little tidbit at a time
when all of academia are involved in assessing the
semester's accomplishments.
"A GRADE is an inadequate report
of an inaccurate judgement by a
biased and variable judge of the
extent to which a student has
attained an undefined level of
mastery of an unknown proportion
of an indefinite amount of material."
George W. Tauxe
University of Oklahoma
Grades are irrelevant. One either knows what's needed to move on, or
one doesn't. I'm almost getting to the point where my grade is either
pass or fail, and nothing else - therefore, you might get to find that
my grade sheets will either have A's or F's.
And I don't call it grade "inflation", I call it rather grade
"disregard". If you use your grade for boasting or comparison
purposes, your problem, just don't bother me with it.
Alberto.
.
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|
| User: "Bob LeChevalier" |
|
| Title: Re: Another Route to Grade Inflation. |
19 Nov 2003 12:03:15 PM |
|
|
"Mark Shapiro" <mshapiro2@nospm-adelphia.net> wrote:
While I would agree that an individual grade is a very imperfect
measurement, in the aggregate the grades a student achieves are quite
meaningful in my opinion.
The only problem with your A grades is that they probably are closer to a C
grade in my book. In other words, your A does not mean "outstanding
performance", it means more or less "average" performance. That's grade
inflation, whether you admit it or not.
From Alberto's prior writings, I don't think this is so. He wants
only students who will earn an A in his class, sets his standards
high, and then flunks anyone who does not meet his A standards.
He calls it pass/fail, but it could equally be called mastery
learning. In mastery learning, the passing level to move on to the
next topic is usually an A grade.
lojbab
--
lojbab
Bob LeChevalier, Founder, The Logical Language Group
(Opinions are my own; I do not speak for the organization.)
Artificial language Loglan/Lojban: http://www.lojban.org
.
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| User: "Alberto Moreira" |
|
| Title: Re: Another Route to Grade Inflation. |
19 Nov 2003 05:21:06 PM |
|
|
Said Bob LeChevalier <lojbab@lojban.org> :
"Mark Shapiro" <mshapiro2@nospm-adelphia.net> wrote:
While I would agree that an individual grade is a very imperfect
measurement, in the aggregate the grades a student achieves are quite
meaningful in my opinion.
The only problem with your A grades is that they probably are closer to a C
grade in my book. In other words, your A does not mean "outstanding
performance", it means more or less "average" performance. That's grade
inflation, whether you admit it or not.
From Alberto's prior writings, I don't think this is so. He wants
only students who will earn an A in his class, sets his standards
high, and then flunks anyone who does not meet his A standards.
He calls it pass/fail, but it could equally be called mastery
learning. In mastery learning, the passing level to move on to the
next topic is usually an A grade.
I actually have a bit of a nontraditional approach to grading. I set
up my courses in such a way that homework is an integral part of the
learning experience: my homework isn't there to test, but to force
students to do a minimum amount of additional work on the areas I feel
they should visit in order to complement what's examined in class.
Typically a student will get an A if he or she does the work to a
decent level. When I get substandard work, I bounce it back, and tell
the student why - the student fixes it, and resubmits. By the end of
the course, not only the student will have worked on the items I
wanted him or her to, but also he or she will have a portfolio of work
that can be shown to a prospective employer. My exams used to be take
home, but now I'm drifting away from exams altogether: I do without a
midterm, and my final is a presentation to the rest of the class on a
subject of the students' choice but it must be one that I did not
teach in class. Depending on the size of the class, I separate one or
maybe two days for this kind of thing, and I size the groups so that
they fit in the schedule. The presentation is live and oral, they
must have prepared a set of slides that can be shown in the computer
and passed to each individual student's computer, and if the project
was done in group, each group member must do a part of the
presentation.
I find traditional testing a hindrance and a nuisance, and I try to
avoid using it.
Alberto.
.
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| User: "Bob LeChevalier" |
|
| Title: Re: Another Route to Grade Inflation. |
20 Nov 2003 03:44:54 AM |
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(Alberto Moreira) wrote:
Said Bob LeChevalier < > :
From Alberto's prior writings, I don't think this is so. He wants
only students who will earn an A in his class, sets his standards
high, and then flunks anyone who does not meet his A standards.
He calls it pass/fail, but it could equally be called mastery
learning. In mastery learning, the passing level to move on to the
next topic is usually an A grade.
I actually have a bit of a nontraditional approach to grading. I set
up my courses in such a way that homework is an integral part of the
learning experience: my homework isn't there to test, but to force
students to do a minimum amount of additional work on the areas I feel
they should visit in order to complement what's examined in class.
Typically a student will get an A if he or she does the work to a
decent level. When I get substandard work, I bounce it back, and tell
the student why - the student fixes it, and resubmits. By the end of
the course, not only the student will have worked on the items I
wanted him or her to, but also he or she will have a portfolio of work
that can be shown to a prospective employer. My exams used to be take
home, but now I'm drifting away from exams altogether: I do without a
midterm, and my final is a presentation to the rest of the class on a
subject of the students' choice but it must be one that I did not
teach in class. Depending on the size of the class, I separate one or
maybe two days for this kind of thing, and I size the groups so that
they fit in the schedule. The presentation is live and oral, they
must have prepared a set of slides that can be shown in the computer
and passed to each individual student's computer, and if the project
was done in group, each group member must do a part of the
presentation.
You just described mastery learning to a "T". Thanks for agreeing
with me %^)
lojbab
--
lojbab
Bob LeChevalier, Founder, The Logical Language Group
(Opinions are my own; I do not speak for the organization.)
Artificial language Loglan/Lojban: http://www.lojban.org
.
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| User: "Alberto Moreira" |
|
| Title: Re: Another Route to Grade Inflation. |
20 Nov 2003 07:50:34 AM |
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|
Said Bob LeChevalier <lojbab@lojban.org> :
You just described mastery learning to a "T". Thanks for agreeing
with me %^)
One problem I have with this approach is, the current structure of
semester-by-semester courses is too rigid. There's a little bit of
cramping towards the end, where the students don't have time to fix
problems in the tail-end homework assignments, and I still don't have
a good answer to that. I tend to shape the difficulty of my
assignments as a bell curve: they're easy in the beginning, then they
ramp up towards the mid of the course, and then they ramp down so that
I increase the probability that they won't need to resubmit the last
couple of assignments, and plus, they'll have time to put together a
decent final presentation. But this is all in a state of flux, and
because I don't know too many professors who do it this way, it's very
hard to exchange ideas and to leverage on other people's experience to
improve and tune the process.
Alberto.
.
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| User: "Bob LeChevalier" |
|
| Title: Re: Another Route to Grade Inflation. |
20 Nov 2003 05:54:37 PM |
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|
(Alberto Moreira) wrote:
Said Bob LeChevalier < > :
You just described mastery learning to a "T". Thanks for agreeing
with me %^)
One problem I have with this approach is, the current structure of
semester-by-semester courses is too rigid. There's a little bit of
cramping towards the end, where the students don't have time to fix
problems in the tail-end homework assignments, and I still don't have
a good answer to that. I tend to shape the difficulty of my
assignments as a bell curve: they're easy in the beginning, then they
ramp up towards the mid of the course, and then they ramp down so that
I increase the probability that they won't need to resubmit the last
couple of assignments, and plus, they'll have time to put together a
decent final presentation. But this is all in a state of flux, and
because I don't know too many professors who do it this way, it's very
hard to exchange ideas and to leverage on other people's experience to
improve and tune the process.
The ideal of mastery learning is not to confine it to semesters, but
to have an orderly progression that the student proceeds on as s/he
masters it. The problem with variable rates of progression is that,
without a deadline, it takes pressure off the student to keep
progressing. Especially since the student is usually taking other
classes that DO have deadlines and tests, most students are motivated
to put off the mastery learning stuff without a deadline in favor of
the stuff that is due tomorrow.
One solution has been to let students move at the pace at which they
complete the assignments satisfactorily, and then to grade them on
whether they completed a sufficient number/level, giving a reduced
grade for coming close but not completing the minimum. I ended up
with a low grade in my one mastery learning class (formal logic)
because I couldn't stay focused on moving along in that class when
faced with daily pressure in other classes, and thus completed less of
the course than was expected (and struggled with it more than my other
subjects). Still I recognized that it was a good thing in concept
even while it did not work for me.
lojbab
--
lojbab
Bob LeChevalier, Founder, The Logical Language Group
(Opinions are my own; I do not speak for the organization.)
Artificial language Loglan/Lojban: http://www.lojban.org
.
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| User: "H. Reader" |
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| Title: Re: Another Route to Grade Inflation. |
20 Nov 2003 07:07:27 PM |
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|
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
Said Bob LeChevalier <lojbab@lojban.org> :
You just described mastery learning to a "T". Thanks for agreeing
with me %^)
One problem I have with this approach is, the current structure of
semester-by-semester courses is too rigid. There's a little bit of
cramping towards the end, where the students don't have time to fix
problems in the tail-end homework assignments, and I still don't have
a good answer to that. I tend to shape the difficulty of my
assignments as a bell curve: they're easy in the beginning, then they
ramp up towards the mid of the course, and then they ramp down so that
I increase the probability that they won't need to resubmit the last
couple of assignments, and plus, they'll have time to put together a
decent final presentation. But this is all in a state of flux, and
because I don't know too many professors who do it this way, it's very
hard to exchange ideas and to leverage on other people's experience to
improve and tune the process.
The ideal of mastery learning is not to confine it to semesters, but
to have an orderly progression that the student proceeds on as s/he
masters it. The problem with variable rates of progression is that,
without a deadline, it takes pressure off the student to keep
progressing. Especially since the student is usually taking other
classes that DO have deadlines and tests, most students are motivated
to put off the mastery learning stuff without a deadline in favor of
the stuff that is due tomorrow.
One solution has been to let students move at the pace at which they
complete the assignments satisfactorily, and then to grade them on
whether they completed a sufficient number/level, giving a reduced
grade for coming close but not completing the minimum. I ended up
with a low grade in my one mastery learning class (formal logic)
because I couldn't stay focused on moving along in that class when
faced with daily pressure in other classes, and thus completed less of
the course than was expected (and struggled with it more than my other
subjects). Still I recognized that it was a good thing in concept
even while it did not work for me.
What a couple of pansies. No wonder the image of educators
has been diminished over the past several decades. While you
boys are re-inventing the wheel, you might notice that your
students, as they flounder around to figure out your silly
rhymes and reasons, view you as barely tolerable twits.
Students want clarity and decisiveness. They want
their performances plainly and fairly measured.
They want measured, sensible steps and the time and
tools to accomplish them. The touchy feely flacidity of
poorly structured experimentation is not
what they want. You boys are viewed
either as flaky easy graders or a disasters
to be avoided. You'd do better at
real estate or wood chopping. Pick one.
.
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| User: "Donna Metler" |
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| Title: Re: Another Route to Grade Inflation. |
20 Nov 2003 07:45:37 PM |
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|
"H. Reader" <history.reader@verizon.net> wrote in message
news:jzdvb.697$Ul1.368@nwrddc01.gnilink.net...
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
Said Bob LeChevalier <lojbab@lojban.org> :
You just described mastery learning to a "T". Thanks for agreeing
with me %^)
One problem I have with this approach is, the current structure of
semester-by-semester courses is too rigid. There's a little bit of
cramping towards the end, where the students don't have time to fix
problems in the tail-end homework assignments, and I still don't have
a good answer to that. I tend to shape the difficulty of my
assignments as a bell curve: they're easy in the beginning, then they
ramp up towards the mid of the course, and then they ramp down so that
I increase the probability that they won't need to resubmit the last
couple of assignments, and plus, they'll have time to put together a
decent final presentation. But this is all in a state of flux, and
because I don't know too many professors who do it this way, it's very
hard to exchange ideas and to leverage on other people's experience to
improve and tune the process.
The ideal of mastery learning is not to confine it to semesters, but
to have an orderly progression that the student proceeds on as s/he
masters it. The problem with variable rates of progression is that,
without a deadline, it takes pressure off the student to keep
progressing. Especially since the student is usually taking other
classes that DO have deadlines and tests, most students are motivated
to put off the mastery learning stuff without a deadline in favor of
the stuff that is due tomorrow.
One solution has been to let students move at the pace at which they
complete the assignments satisfactorily, and then to grade them on
whether they completed a sufficient number/level, giving a reduced
grade for coming close but not completing the minimum. I ended up
with a low grade in my one mastery learning class (formal logic)
because I couldn't stay focused on moving along in that class when
faced with daily pressure in other classes, and thus completed less of
the course than was expected (and struggled with it more than my other
subjects). Still I recognized that it was a good thing in concept
even while it did not work for me.
What a couple of pansies. No wonder the image of educators
has been diminished over the past several decades. While you
boys are re-inventing the wheel, you might notice that your
students, as they flounder around to figure out your silly
rhymes and reasons, view you as barely tolerable twits.
Students want clarity and decisiveness. They want
their performances plainly and fairly measured.
They want measured, sensible steps and the time and
tools to accomplish them. The touchy feely flacidity of
poorly structured experimentation is not
what they want. You boys are viewed
either as flaky easy graders or a disasters
to be avoided. You'd do better at
real estate or wood chopping. Pick one.
Uh, this is how music is taught, at all levels. Exams are Juried-that is,
you play for a panel, and are evaluated, but it isn't a stopping point, just
a particular snapshot in time. Performances are essential, and are part of
the evaluation.
And there is one standard-PERFECTION. Every performance is only a step to
that goal. It is never "good enough", and there are no gentleman's C's. And
the goal is for the student to self-evaluate, not just expect to be
evaluated on the outside. I assure you that college music schools, or
conservatory programs are not "touchy feely flacidity of poorly structured
experimentation". Rather it is a tried and true methodology which has stood
the test of centuries.
Alberto has a very strong classical music background, and believes in the
same standard-perfection is the end goal, and that anything less is not
acceptable. And the only way to do this is to try, and try, and try again,
with frequent evaluation (preferably largely internal) and improvement.
.
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| User: "Alberto Moreira" |
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| Title: Re: Another Route to Grade Inflation. |
24 Nov 2003 08:00:11 AM |
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|
Said "Donna Metler" <dmmetler@bellsouth.net> :
Alberto has a very strong classical music background, and believes in the
same standard-perfection is the end goal, and that anything less is not
acceptable. And the only way to do this is to try, and try, and try again,
with frequent evaluation (preferably largely internal) and improvement.
Classical music has another litmus that lack in many other easier
fields: there are only so many places, hence, only the best survive.
Do you want a measured set of steps ? Keep dreaming, because if you
do, you won't make it.
Alberto.
.
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| User: "Herman Rubin" |
|
| Title: Re: Another Route to Grade Inflation. |
22 Nov 2003 02:42:21 PM |
|
|
In article <jzdvb.697$Ul1.368@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
.................
What a couple of pansies. No wonder the image of educators
has been diminished over the past several decades. While you
boys are re-inventing the wheel, you might notice that your
students, as they flounder around to figure out your silly
rhymes and reasons, view you as barely tolerable twits.
You sound like one of those educationists who
"think" that memorization and routine is what
matters. Neither of these is involved in real
thinking, and both of these can, and will, be
done by computers.
Students want clarity and decisiveness. They want
their performances plainly and fairly measured.
They want measured, sensible steps and the time and
tools to accomplish them.
It is clear that you do not understand any of
the key mathematical concepts, without which
most of science cannot be done. Nor can you
understand the scientific concepts; concepts
are not learned in "measured, sensible steps",
but when the light bulb comes on all at once.
Few of the college students now can handle
the basic mathematics courses, such as abstract
algebra and foundations of real analysis. This
was very definitely NOT the case a half century
ago; they came in with a better understanding
of mathematics than most leave with now.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
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| User: "H. Reader" |
|
| Title: Re: Another Route to Grade Inflation. |
22 Nov 2003 07:02:34 PM |
|
|
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpohnd$4alo@odds.stat.purdue.edu...
In article <jzdvb.697$Ul1.368@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
.................
What a couple of pansies. No wonder the image of educators
has been diminished over the past several decades. While you
boys are re-inventing the wheel, you might notice that your
students, as they flounder around to figure out your silly
rhymes and reasons, view you as barely tolerable twits.
You sound like one of those educationists who
"think" that memorization and routine is what
matters.
Certainly some of it does, though by what I wrote, my
views in that regard aren't even suggested.
Neither of these is involved in real
thinking, and both of these can, and will, be
done by computers.
So much can be written in response to those few words ...
But I'll settle for this: "real thinking" requires some knowledge
of real facts. Further, encouraging people to become in
effect merely manipulators or extensions of machines
summons images of humanity diminishing into some
kind of automatonistic nightmare.
Students want clarity and decisiveness. They want
their performances plainly and fairly measured.
They want measured, sensible steps and the time and
tools to accomplish them.
It is clear that you do not understand any of
the key mathematical concepts, without which
most of science cannot be done. Nor can you
understand the scientific concepts; concepts
are not learned in "measured, sensible steps",
but when the light bulb comes on all at once.
In teaching a classroom full of people, it helps
to construct the material with the aim of having
the light bulb come on all at once for everyone.
For a few the lights don't come on, but that's
what office hours and tutors are for.
Few of the college students now can handle
the basic mathematics courses, such as abstract
algebra and foundations of real analysis. This
was very definitely NOT the case a half century
ago; they came in with a better understanding
of mathematics than most leave with now.
No doubt. Many of them in History and Literature
classes are unfamiliar with knowledge that 50 years
ago was considered generally to be common knowledge.
I had a guy in class in his early 20s who looked at
me and asked in all sincerity, "George Washington
was the first president, right?"
.
|
|
|
| User: "Herman Rubin" |
|
| Title: Re: Another Route to Grade Inflation. |
24 Nov 2003 06:13:23 PM |
|
|
In article <KGTvb.2837$Pm4.2559@nwrddc03.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpohnd$4alo@odds.stat.purdue.edu...
In article <jzdvb.697$Ul1.368@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
.................
What a couple of pansies. No wonder the image of educators
has been diminished over the past several decades. While you
boys are re-inventing the wheel, you might notice that your
students, as they flounder around to figure out your silly
rhymes and reasons, view you as barely tolerable twits.
You sound like one of those educationists who
"think" that memorization and routine is what
matters.
Certainly some of it does, though by what I wrote, my
views in that regard aren't even suggested.
Neither of these is involved in real
thinking, and both of these can, and will, be
done by computers.
So much can be written in response to those few words ...
But I'll settle for this: "real thinking" requires some knowledge
of real facts.
Not the ones you think it does. The development of
the ordinal properties of the integers from the
Peano Postulates, without which there is at best a
crude understanding of the integers, introduces the
"facts" in the axioms.
Further, encouraging people to become in
effect merely manipulators or extensions of machines
summons images of humanity diminishing into some
kind of automatonistic nightmare.
What do you think is accomplished by teaching how to
add and multiply strings of decimal digits? Or by
any of the other memorize and regurgitate procedures.
Students want clarity and decisiveness. They want
their performances plainly and fairly measured.
They want measured, sensible steps and the time and
tools to accomplish them.
It is clear that you do not understand any of
the key mathematical concepts, without which
most of science cannot be done. Nor can you
understand the scientific concepts; concepts
are not learned in "measured, sensible steps",
but when the light bulb comes on all at once.
In teaching a classroom full of people, it helps
to construct the material with the aim of having
the light bulb come on all at once for everyone.
For a few the lights don't come on, but that's
what office hours and tutors are for.
For a VERY few, the light bulb can come on that
quickly, or on a precise schedule. A study on
the formation of mathematical concepts in children
seemed to indicate that the concept comes on all
at once, and in agreement with previous studies,
the trial involved seems to have a geometric
distribution. That means that if it takes a
certain length for a particular student to get
the concept with probability .5, it will take
about 3.3 times that long to have a 90% chance
of getting it. I suggest that much of this be
done outside of class.
Note that I was not saying 50% of a class; the
class variation was not even considered. With
that much uncertainty in how long it will take
an individual to get it, what you are asking for
is impossible. It takes work outside of class,
and doing enough exercises until the light dawns,
and no more after that.
Few of the college students now can handle
the basic mathematics courses, such as abstract
algebra and foundations of real analysis. This
was very definitely NOT the case a half century
ago; they came in with a better understanding
of mathematics than most leave with now.
No doubt. Many of them in History and Literature
classes are unfamiliar with knowledge that 50 years
ago was considered generally to be common knowledge.
I had a guy in class in his early 20s who looked at
me and asked in all sincerity, "George Washington
was the first president, right?"
In mathematics, it is not a knowledge of facts,
but of the logical thinking processes. It seems
that in history the Politically Correct view is
not to pay attention to the major figures, but
to study how the families in the various colonies
cooked their meals, etc.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
|
|
|
| User: "H. Reader" |
|
| Title: Re: Another Route to Grade Inflation. |
25 Nov 2003 02:47:01 PM |
|
|
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpu6r3$3avu@odds.stat.purdue.edu...
In article <KGTvb.2837$Pm4.2559@nwrddc03.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpohnd$4alo@odds.stat.purdue.edu...
In article <jzdvb.697$Ul1.368@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
.................
What a couple of pansies. No wonder the image of educators
has been diminished over the past several decades. While you
boys are re-inventing the wheel, you might notice that your
students, as they flounder around to figure out your silly
rhymes and reasons, view you as barely tolerable twits.
You sound like one of those educationists who
"think" that memorization and routine is what
matters.
Certainly some of it does, though by what I wrote, my
views in that regard aren't even suggested.
Neither of these is involved in real
thinking, and both of these can, and will, be
done by computers.
So much can be written in response to those few words ...
But I'll settle for this: "real thinking" requires some knowledge
of real facts.
Not the ones you think it does.
Are you omniscient or clairvoyant?
The development of
the ordinal properties of the integers from the
Peano Postulates, without which there is at best a
crude understanding of the integers, introduces the
"facts" in the axioms.
Further, encouraging people to become in
effect merely manipulators or extensions of machines
summons images of humanity diminishing into some
kind of automatonistic nightmare.
What do you think is accomplished by teaching how to
add and multiply strings of decimal digits? Or by
any of the other memorize and regurgitate procedures.
Adding and multiplying is to "memorize and regurgitate?"
And what do you have against memorizing? It seems to
be a useful skill.
Students want clarity and decisiveness. They want
their performances plainly and fairly measured.
They want measured, sensible steps and the time and
tools to accomplish them.
It is clear that you do not understand any of
the key mathematical concepts, without which
most of science cannot be done. Nor can you
understand the scientific concepts; concepts
are not learned in "measured, sensible steps",
but when the light bulb comes on all at once.
In teaching a classroom full of people, it helps
to construct the material with the aim of having
the light bulb come on all at once for everyone.
For a few the lights don't come on, but that's
what office hours and tutors are for.
For a VERY few, the light bulb can come on that
quickly, or on a precise schedule. A study on
the formation of mathematical concepts in children
seemed to indicate that the concept comes on all
at once, and in agreement with previous studies,
the trial involved seems to have a geometric
distribution. That means that if it takes a
certain length for a particular student to get
the concept with probability .5, it will take
about 3.3 times that long to have a 90% chance
of getting it. I suggest that much of this be
done outside of class.
Note that I was not saying 50% of a class; the
class variation was not even considered. With
that much uncertainty in how long it will take
an individual to get it, what you are asking for
is impossible. It takes work outside of class,
and doing enough exercises until the light dawns,
and no more after that.
So your disagreement is ... what? That everyone
should learn math from a tutor?
Few of the college students now can handle
the basic mathematics courses, such as abstract
algebra and foundations of real analysis. This
was very definitely NOT the case a half century
ago; they came in with a better understanding
of mathematics than most leave with now.
No doubt. Many of them in History and Literature
classes are unfamiliar with knowledge that 50 years
ago was considered generally to be common knowledge.
I had a guy in class in his early 20s who looked at
me and asked in all sincerity, "George Washington
was the first president, right?"
In mathematics, it is not a knowledge of facts,
but of the logical thinking processes. It seems
that in history the Politically Correct view is
not to pay attention to the major figures, but
to study how the families in the various colonies
cooked their meals, etc.
Along with the color and sex and degree of oppression
suffered by those who did the cooking.
.
|
|
|
| User: "Herman Rubin" |
|
| Title: Re: Another Route to Grade Inflation. |
27 Nov 2003 09:33:51 AM |
|
|
In article <9dPwb.2985$f32.1257@nwrddc02.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpu6r3$3avu@odds.stat.purdue.edu...
In article <KGTvb.2837$Pm4.2559@nwrddc03.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpohnd$4alo@odds.stat.purdue.edu...
In article <jzdvb.697$Ul1.368@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
.................
So much can be written in response to those few words ...
But I'll settle for this: "real thinking" requires some knowledge
of real facts.
Not the ones you think it does.
Are you omniscient or clairvoyant?
Neither. However, I am knowledgeable about the sort
of approach advocated by those who do not understand
abstract concepts, and have the mistaken idea that
they need to come from abstraction of the concrete.
The development of
the ordinal properties of the integers from the
Peano Postulates, without which there is at best a
crude understanding of the integers, introduces the
"facts" in the axioms.
Further, encouraging people to become in
effect merely manipulators or extensions of machines
summons images of humanity diminishing into some
kind of automatonistic nightmare.
What do you think is accomplished by teaching how to
add and multiply strings of decimal digits? Or by
any of the other memorize and regurgitate procedures.
Adding and multiplying is to "memorize and regurgitate?"
And what do you have against memorizing? It seems to
be a useful skill.
It may or may not be. I have nothing against developing
useful skills when the concepts are known. Pushing them
before this makes it harder to learn the concepts. It does
show up in the lack of success in teaching mathematical
concepts to present and prospective schoolteachers. It is
extremely difficult to get someone who has had statistical
methods to realize that the computer package does not do
what is wanted, but that instead one has to shuck the
methods and get down to formulating the problem, without
even assuming that the formulator has the mathematical
knowledge to understand any reasonably correct methods.
.....................
In teaching a classroom full of people, it helps
to construct the material with the aim of having
the light bulb come on all at once for everyone.
For a few the lights don't come on, but that's
what office hours and tutors are for.
For a VERY few, the light bulb can come on that
quickly, or on a precise schedule. A study on
the formation of mathematical concepts in children
seemed to indicate that the concept comes on all
at once, and in agreement with previous studies,
the trial involved seems to have a geometric
distribution. That means that if it takes a
certain length for a particular student to get
the concept with probability .5, it will take
about 3.3 times that long to have a 90% chance
of getting it. I suggest that much of this be
done outside of class.
Note that I was not saying 50% of a class; the
class variation was not even considered. With
that much uncertainty in how long it will take
an individual to get it, what you are asking for
is impossible. It takes work outside of class,
and doing enough exercises until the light dawns,
and no more after that.
So your disagreement is ... what? That everyone
should learn math from a tutor?
What I am saying is that, except for the really bright,
or those who have already done the right exercises,
different for different students, one is not going to
understand the concept at some specified time in class.
..................
In mathematics, it is not a knowledge of facts,
but of the logical thinking processes. It seems
that in history the Politically Correct view is
not to pay attention to the major figures, but
to study how the families in the various colonies
cooked their meals, etc.
Along with the color and sex and degree of oppression
suffered by those who did the cooking.
Did this make any difference? How do you measure the
degree of oppression? The factory workers in England
in the 19th century felt less oppressed than when they
were working their own farms. Even Marx recognized the
importance of entrepreneurs in business and industry.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
|
|
|
| User: "H. Reader" |
|
| Title: Re: Another Route to Grade Inflation. |
29 Nov 2003 03:21:32 AM |
|
|
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bq55gv$1ipg@odds.stat.purdue.edu...
In article <9dPwb.2985$f32.1257@nwrddc02.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpu6r3$3avu@odds.stat.purdue.edu...
In article <KGTvb.2837$Pm4.2559@nwrddc03.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bpohnd$4alo@odds.stat.purdue.edu...
In article <jzdvb.697$Ul1.368@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Bob LeChevalier" <lojbab@lojban.org> wrote in message
news:9jkqrv0rg88ge9e6lh3c4ov12a8cr5gbic@4ax.com...
junkmail@moreira.mv.com (Alberto Moreira) wrote:
.................
So much can be written in response to those few words ...
But I'll settle for this: "real thinking" requires some knowledge
of real facts.
Not the ones you think it does.
Are you omniscient or clairvoyant?
Neither. However, I am knowledgeable about the sort
of approach advocated by those who do not understand
abstract concepts, and have the mistaken idea that
they need to come from abstraction of the concrete.
So facts then are unnecessary in education. Fascinating.
The development of
the ordinal properties of the integers from the
Peano Postulates, without which there is at best a
crude understanding of the integers, introduces the
"facts" in the axioms.
Further, encouraging people to become in
effect merely manipulators or extensions of machines
summons images of humanity diminishing into some
kind of automatonistic nightmare.
What do you think is accomplished by teaching how to
add and multiply strings of decimal digits? Or by
any of the other memorize and regurgitate procedures.
Adding and multiplying is to "memorize and regurgitate?"
And what do you have against memorizing? It seems to
be a useful skill.
It may or may not be. I have nothing against developing
useful skills when the concepts are known. Pushing them
before this
This?
makes it harder to learn the concepts. It does
show up in the lack of success in teaching mathematical
concepts to present and prospective schoolteachers.
At least that's your theory. Also, and I mention this
in the most friendly way, you might omit so many pronouns
and instead name the thing you're referring to. Specifically,
the word *it* is a problem.
It is
extremely difficult to get someone who has had statistical
methods to realize that the computer package does not do
what is wanted,
Statistical methods somehow narrow the mind?
but that instead one has to shuck the
methods and get down to formulating the problem,
I'm no expert, but I always figured the problem
came first and the method of solving it came second.
without
even assuming that the formulator has the mathematical
knowledge to understand any reasonably correct methods.
I'm not sure what you mean by that.
In teaching a classroom full of people, it helps
to construct the material with the aim of having
the light bulb come on all at once for everyone.
For a few the lights don't come on, but that's
what office hours and tutors are for.
For a VERY few, the light bulb can come on that
quickly, or on a precise schedule. A study on
the formation of mathematical concepts in children
seemed to indicate that the concept comes on all
at once, and in agreement with previous studies,
the trial involved seems to have a geometric
distribution. That means that if it takes a
certain length for a particular student to get
the concept with probability .5, it will take
about 3.3 times that long to have a 90% chance
of getting it. I suggest that much of this be
done outside of class.
Note that I was not saying 50% of a class; the
class variation was not even considered. With
that much uncertainty in how long it will take
an individual to get it, what you are asking for
is impossible. It takes work outside of class,
and doing enough exercises until the light dawns,
and no more after that.
So your disagreement is ... what? That everyone
should learn math from a tutor?
What I am saying is that, except for the really bright,
or those who have already done the right exercises,
different for different students, one is not going to
understand the concept at some specified time in class.
Some will and some won't. That's the nature of
teaching a class.
In mathematics, it is not a knowledge of facts,
but of the logical thinking processes. It seems
that in history the Politically Correct view is
not to pay attention to the major figures, but
to study how the families in the various colonies
cooked their meals, etc.
Along with the color and sex and degree of oppression
suffered by those who did the cooking.
Did this make any difference?
No. It's all pretty much nonsense in the service of
recognizing or creating victims to enshrine.
How do you measure the
degree of oppression?
By the shovel-full, usually.
The factory workers in England
in the 19th century felt less oppressed than when they
were working their own farms.
They did have a more reliable income, which led to a more
predictable life, but then they also lived in slums, tended to
die young, and had few means of advancing. I have no
idea how they felt about it.
Even Marx recognized the
importance of entrepreneurs in business and industry.
Apparently the Soviets and the Maoists didn't
get the word.
.
|
|
|
| User: "Herman Rubin" |
|
| Title: Re: Another Route to Grade Inflation. |
29 Nov 2003 09:37:41 AM |
|
|
In article <wyZxb.17432$785.277@nwrddc01.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:bq55gv$1ipg@odds.stat.purdue.edu...
In article <9dPwb.2985$f32.1257@nwrddc02.gnilink.net>,
H. Reader <history.reader@verizon.net> wrote:
.................
So much can be written in response to those few words ...
But I'll settle for this: "real thinking" requires some knowledge
of real facts.
Not the ones you think it does.
Are you omniscient or clairvoyant?
Neither. However, I am knowledgeable about the sort
of approach advocated by those who do not understand
abstract concepts, and have the mistaken idea that
they need to come from abstraction of the concrete.
So facts then are unnecessary in education. Fascinating.
This is a misinterpretation, at best. Learning to read
does not require memorization of many words. Learning
the properties of the integers does not require skill
in carrying out the computations; what does the ability
to do base 10 arithmetic have to do with understanding?
Why not base 2 or base 16 or base 60?
Some things need to be memorized, but not too many. There
was a recent article in the _Science Times_ section of the
_New York Times_ on dyslexia, and it made that very point;
pushing the problem onto the memory part of the brain, as
determined by MRI, was far from optimal.
The development of
the ordinal properties of the integers from the
Peano Postulates, without which there is at best a
crude understanding of the integers, introduces the
"facts" in the axioms.
Further, encouraging people to become in
effect merely manipulators or extensions of machines
summons images of humanity diminishing into some
kind of automatonistic nightmare.
What do you think is accomplished by teaching how to
add and multiply strings of decimal digits? Or by
any of the other memorize and regurgitate procedures.
Adding and multiplying is to "memorize and regurgitate?"
And what do you have against memorizing? It seems to
be a useful skill.
It may or may not be. I have nothing against developing
useful skills when the concepts are known. Pushing them
before this
This?
Before the concepts are known. Children seem to
be able to learn concepts far more easily than the
bulk of the teaching profession.
makes it harder to learn the concepts. It does
show up in the lack of success in teaching mathematical
concepts to present and prospective schoolteachers.
At least that's your theory. Also, and I mention this
in the most friendly way, you might omit so many pronouns
and instead name the thing you're referring to. Specifically,
the word *it* is a problem.
Agreed; that is why we need to teach the general
use of variables early. This is purely linguistic.
One of the posters here claimed to have no problem
in learning to use variables for numbers, but got
thrown when they were used for functions. It is
true that this was first done by Euler, about 150
years after Viete had come up with the essentially
modern use for arbitrarily many numbers. But they
can be used for anything, and we need to use them
in "ordinary" language.
It is
extremely difficult to get someone who has had statistical
methods to realize that the computer package does not do
what is wanted,
Statistical methods somehow narrow the mind?
It seems to be the case. Statistics does not do what
most think it can do, largely because that is not even
possible. It is necessary to understand this. Even
statistical theorists have problems with this.
but that instead one has to shuck the
methods and get down to formulating the problem,
I'm no expert, but I always figured the problem
came first and the method of solving it came second.
It should, but if it is not carefully and correctly
formulated, the wrong method can get used. The
engineer who formulates a real problem using a linear
differential equation when a nonlinear one is needed
is likely to build a failure. In engineering, the
failures tend to be seen easily. In statistics, when
one rarely can be close to sure, not so.
without
even assuming that the formulator has the mathematical
knowledge to understand any reasonably correct methods.
I'm not sure what you mean by that.
A common example of this is the educational practice
of converting to normality and then using bad linear
methods without even considering their appropriateness.
It is WRONG; there is NO justification for either.
Also, the belief that "statistical significance" is
a measure of truth is totally false. Few statistical
methods courses give a good idea of probability.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
|
|
|
| User: "Alberto Moreira" |
|
| Title: Re: Another Route to Grade Inflation. |
30 Nov 2003 07:13:05 AM |
|
|
Said (Herman Rubin) :
This is a misinterpretation, at best. Learning to read
does not require memorization of many words. Learning
the properties of the integers does not require skill
in carrying out the computations; what does the ability
to do base 10 arithmetic have to do with understanding?
Why not base 2 or base 16 or base 60?
Because, Herman, we have 5 digits on each hand, not 1, 8 or 30.
The way we write numbers is decimal because people used hands: One
hand, two hands, three hands, plus four fingers, that's 34. It took a
little bit of lateral thinking to realize that, well, we can give a
number for 10 hands, and for 10 of those, and so on, and the concept
of recursion was born.
The fact that we can count in base 2, or base 16, is crystal clear to
a musician, for example, but not to many other people: because there's
no solid, intuitive prop like one's hands to recourse to.
And then, using base 2 or 16 or 60 adds no understanding whatsoever to
the basic issue that arithmetic is about counting - and screw the
base. It's not that 12 + 15 = 27, it's that twelve plus fifteen equals
twenty-seven, and here we have a fundamental truth: ARITHMETIC IS
INDEPENDENT OF THE CONVENTIONS WE USE TO WRITE OUR NUMBERS. So, I find
it a mistake to teach arithmetic based on number bases, because number
bases help us WRITING numbers, but they don't really help us handling
the CONCEPT of addition or multiplication. Number bases are thus well
downstream, and I think it would be a mistake to burden beginners
with that kind of thing.
One of the posters here claimed to have no problem
in learning to use variables for numbers, but got
thrown when they were used for functions. It is
true that this was first done by Euler, about 150
years after Viete had come up with the essentially
modern use for arbitrarily many numbers. But they
can be used for anything, and we need to use them
in "ordinary" language.
You see, any senior computer programmer does that as a matter of fact,
and many of us can't even handle high school math. Point being,
there's got to be an upstream layer that's been ignored when many of
us teach mathematics, and that layer is not conceptual but intuitive.
If you look at a computer program, a function is way more than just a
rule: very few functions we deal with are as simply stated as those we
bump into in your typical mathematics book. Our functions require a
language to be stated, they have conditionals, loops, quantifiers,
complex binding rules, scoping, recursion, typing, and what not - and
yet most programmers can handle it, even those who don't know any
math. Some functions are stated in terms of tables, and it's not that
hard to grok that, down below, any function does nothing but to create
the elements of that table, and the choice then is merely whether we
write the table at compile time or whether we let it be computed
dynamically at run time: and any programmer who deserves his stripes
knows how an array, a structure and a function basically end up being
the same thing.
Moreover, the way we program today, there's no such thing as a
function f, there's rather a function o.f, where o is an object or a
hierarchy of namespaces, and f is no longer called a "function" but a
"method", and it exists not by itself, but inside a hierarchy of
namespaces. Also, merely stating "function f", or even "function o.f"
is not enough because of polymorphism: we may have function f(x) and
it'll be different from f(x,y): two functions, not one. Also, f(int x)
is not the same function as f(char x), neither is "int f(int x)" the
same as "boolean f(int x)": it's no longer enough to identify
functions by names or even by hierarchy of names, we MUST take their
domain and range well into consideration: to a computer man, a
function is always a triple: a domain, a method and a range. The
method may collapse to zero if we know the pairs upfront and are able
to substitute an array or a structure for the triple (domain, method,
range), and that leaves us with the traditional concept that a
function is a set of pairs.
None of that is taught in our K12 mathematics courses, yet programmers
handle it naturally and many don't know any of the underlying math.
The conclusion is obvious: there's go to be something out of focus in
the way we teach the stuff in our K12 classes.
Alberto.
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| User: "Herman Rubin" |
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| Title: Re: Another Route to Grade Inflation. |
30 Nov 2003 04:07:00 PM |
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In article <3fcbe73e.1479797@news.mv.net>,
Alberto Moreira <junkmail@moreira.mv.com> wrote:
Said (Herman Rubin) :
This is a misinterpretation, at best. Learning to read
does not require memorization of many words. Learning
the properties of the integers does not require skill
in carrying out the computations; what does the ability
to do base 10 arithmetic have to do with understanding?
Why not base 2 or base 16 or base 60?
Because, Herman, we have 5 digits on each hand, not 1, 8 or 30.
The Sumerians counted to 12 on one hand; they used the
segments of the fingers. Is the thumb a digit? They also
came up with the use of base 60, and base 60 calculations
done by them and the Babylonians were more advanced than
any Western base 10 calculations until after Greek times.
Our use of minutes, seconds, etc., for fractions comes from
that.
The way we write numbers is decimal because people used hands: One
hand, two hands, three hands, plus four fingers, that's 34. It took a
little bit of lateral thinking to realize that, well, we can give a
number for 10 hands, and for 10 of those, and so on, and the concept
of recursion was born.
See the above. The oldest arithmetic records we have were
base 60, not base 10. More than 4000 years ago, they had
the arithmetic operations, a symbol for 0 in a place, division
with remainder, and sexagesimal fractions to many places.
This does not mean that base 10 was not used by many peoples.
Also, the Mayans seem to have used base 20.
The fact that we can count in base 2, or base 16, is crystal clear to
a musician, for example, but not to many other people: because there's
no solid, intuitive prop like one's hands to recourse to.
And then, using base 2 or 16 or 60 adds no understanding whatsoever to
the basic issue that arithmetic is about counting - and screw the
base. It's not that 12 + 15 = 27, it's that twelve plus fifteen equals
twenty-seven, and here we have a fundamental truth: ARITHMETIC IS
INDEPENDENT OF THE CONVENTIONS WE USE TO WRITE OUR NUMBERS.
Agreed; I still suggest that anyone teaching arithmetic be
conversant with a good development from the Peano Postulates,
and if a person cannot read the first part of Landau's book,
that person cannot understand arithmetic.
So, I find
it a mistake to teach arithmetic based on number bases, because number
bases help us WRITING numbers, but they don't really help us handling
the CONCEPT of addition or multiplication. Number bases are thus well
downstream, and I think it would be a mistake to burden beginners
with that kind of thing.
On this, we are in agreement, but requiring mastery of base 10
manipulations does not help this understanding.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
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| User: "Alberto Moreira" |
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| Title: Re: Another Route to Grade Inflation. |
02 Dec 2003 07:33:54 AM |
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Said (Herman Rubin) :
The Sumerians counted to 12 on one hand; they used the
segments of the fingers. Is the thumb a digit? They also
came up with the use of base 60, and base 60 calculations
done by them and the Babylonians were more advanced than
any Western base 10 calculations until after Greek times.
Our use of minutes, seconds, etc., for fractions comes from
that.
As far as mathematics go, we're neither Sumerian nor Babylonian. We're
kind of Greek, but their mathematics, considered from our modern
viewpoint, were a bit incipient. As far as mathematics go, our true
origins are Arabic, we inherited the decimal system from them and
that's what made the transition from antiquity to modernity possible.
And you don't have to look twice to see that our hour/minute/second
system of measuring time is a baroque anachronism.
See the above. The oldest arithmetic records we have were
base 60, not base 10. More than 4000 years ago, they had
the arithmetic operations, a symbol for 0 in a place, division
with remainder, and sexagesimal fractions to many places.
Yet that's not where our mathematics comes from. We're deep rooted in
the Arabic tradition.
Agreed; I still suggest that anyone teaching arithmetic be
conversant with a good development from the Peano Postulates,
and if a person cannot read the first part of Landau's book,
that person cannot understand arithmetic.
That may be true to math majors - it isn't true to the rest of us. The
Peano Postulates aren't but a formalization of our counting intuition,
and our own intuitive machinery is well more suited to learn
elementary arithmetic than Peano's formalization. I do not find the
need for any kind of formalization before 5th grade or so ! Time will
come when the formalization can be introduced naturally and as a
consequence of the need to look at things with a more critical eye -
but that's probably not the most efficient way to teach the stuff to
young children.
On this, we are in agreement, but requiring mastery of base 10
manipulations does not help this understanding.
It makes it possible, because, again, we have ten fingers. Unless of
course you're willing to do it the Japanese way and use the abacus,
but then, you're bound to the number representation enforced by the
abacus. The point is, the basic concept is masked by the manipulation,
and it must be brought out slowly and in a way that doesn't interfere
with intuition; only mathematicians and mathematically gifted kids can
start from a bare definition and build on top, and even then, I'm not
sure that's the best way of teaching either.
Alberto.
.
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| User: "Herman Rubin" |
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| Title: Re: Another Route to Grade Inflation. |
03 Dec 2003 01:16:28 PM |
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In article <3fcc930a.243880@news.mv.net>,
Alberto Moreira <junkmail@moreira.mv.com> wrote:
Said (Herman Rubin) :
The Sumerians counted to 12 on one hand; they used the
segments of the fingers. Is the thumb a digit? They also
came up with the use of base 60, and base 60 calculations
done by them and the Babylonians were more advanced than
any Western base 10 calculations until after Greek times.
Our use of minutes, seconds, etc., for fractions comes from
that.
As far as mathematics go, we're neither Sumerian nor Babylonian. We're
kind of Greek, but their mathematics, considered from our modern
viewpoint, were a bit incipient. As far as mathematics go, our true
origins are Arabic, we inherited the decimal system from them and
that's what made the transition from antiquity to modernity possible.
And you don't have to look twice to see that our hour/minute/second
system of measuring time is a baroque anachronism.
We did not get the idea of using a decimal system to
calculate from the Indians through the Arabs; all that
we got from them in this direction was the use of the
same characters in all places, with a "0" character to
indicate no term with that power of 10. Otherwise,
there is no difference between arithmetic using Egyptian,
Greek, or Roman numerals. In fact, it might be best
from a pedagogic standpoint to start with Egyptian, which
(at least as I read it in the encyclopedia) just used a
symbol for each power of 10, repeated the appropriate
number of times.
See the above. The oldest arithmetic records we have were
base 60, not base 10. More than 4000 years ago, they had
the arithmetic operations, a symbol for 0 in a place, division
with remainder, and sexagesimal fractions to many places.
Yet that's not where our mathematics comes from. We're deep rooted in
the Arabic tradition.
We are accustomed to doing it that way; it is important that
we recognize that it is no more than that. The Greeks used
9 symbols for 1-9, another 9 for 10-90, and another 9 for
100-900, and indicated multiplying by 1000 by a bar over the
symbol. Other than having more symbols, their arithmetic
was no different from ours.
And this is arithmetic, not mathematics.
Agreed; I still suggest that anyone teaching arithmetic be
conversant with a good development from the Peano Postulates,
and if a person cannot read the first part of Landau's book,
that person cannot understand arithmetic.
That may be true to math majors - it isn't true to the rest of us. The
Peano Postulates aren't but a formalization of our counting intuition,
and our own intuitive machinery is well more suited to learn
elementary arithmetic than Peano's formalization. I do not find the
need for any kind of formalization before 5th grade or so !
VERY wrong! The need for formalization is before too much
is learned essentially by rote. Variables, as used in
mathematics and its applications, but not in computers, are
formal extensions of language, and are needed for concise
precise communication. With variables, word problems
become much more trivial.
It is a major problem to teach students formal concepts
after they have gotten poor intuitive ideas, or just
learned methods. It is the opposite of the way
educationists have it; one needs certain abilities to
replace miscellaneous garbled intuitions with structure or
formalism; one does need to keep not only the formalism,
but the concepts, in mind as well. We had much less of a
problem of teaching good formal mathematics in high school
a half century ago than we have in teaching it to college
students who have had more facts and computational
procedures today.
Time will
come when the formalization can be introduced naturally and as a
consequence of the need to look at things with a more critical eye -
but that's probably not the most efficient way to teach the stuff to
young children.
Formalization is natural for children; it is after they
learn in a sloppy manner that it becomes difficult.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
.
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| User: "Alberto Moreira" |
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| Title: Re: Another Route to Grade Inflation. |
04 Dec 2003 07:52:23 AM |
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Said (Herman Rubin) :
We did not get the idea of using a decimal system to
calculate from the Indians through the Arabs; all that
we got from them in this direction was the use of the
same characters in all places, with a "0" character to
indicate no term with that power of 10. Otherwise,
there is no difference between arithmetic using Egyptian,
Greek, or Roman numerals. In fact, it might be best
from a pedagogic standpoint to start with Egyptian, which
(at least as I read it in the encyclopedia) just used a
symbol for each power of 10, repeated the appropriate
number of times.
Herman, the Iberic peninsula was dominated by Arabs before the
Renaissance. The Eastern Roman Empire was overrun by Ottomans. The
Western Roman Empire was taken over by tribes of ignorant barbarians,
so, the transition between Rome and Renaissance was filled up with
Arabic knowledge. That knowledge was kept in monasteries for a few
centuries before it could sprout again, in Italy and elsewhere.
It is best, from a pedagogical point of view, to start with a solid
contemporary western culture. We're not Egiptians either.
We are accustomed to doing it that way; it is important that
we recognize that it is no more than that. The Greeks used
9 symbols for 1-9, another 9 for 10-90, and another 9 for
100-900, and indicated multiplying by 1000 by a bar over the
symbol. Other than having more symbols, their arithmetic
was no different from ours.
That is irrelevant today except to historians. The arithmetic may not
have been different, but the algorithms were, and it's a terrible idea
to revert to Greek or Roman ways when we have evolved way past it.
And this is arithmetic, not mathematics.
Arithmetic is a part of mathematics, and much mathematics exists to
build up the number system and the arithmetic around it. There's more
to mathematics than arithmetic, but mathematics must include
arithmetic.
VERY wrong! The need for formalization is before too much
is learned essentially by rote. Variables, as used in
mathematics and its applications, but not in computers, are
formal extensions of language, and are needed for concise
precise communication. With variables, word problems
become much more trivial.
It's not variables that make word problems trivial, but the ability to
parse loose English into algebraic formalism. And we're not dealing
with "variables" in algebra, but with SYMBOLS - a letter like "x" or
"y" doesn't stand for something that "varies", but for a quantity that
has a value that we don't care to know what it is. Symbols are LABELS,
they just stand for quantities that we don't care to measure - and
then, who cares if they are variables or not. When you go to computer
usage, the best way to look at it is the Lambda Calculus way: we have
functions and symbols that stand for functions, and nothing else -
numbers are built as a sequence of functions and are called "Church
Numerals" for that very reason.
So, no, the concept of "variable" is not only not central, but
probably not that important to be made either. Inside a computer we
have labels for quantities: some are writable, some are not, and the
difference between a constant and a variable is merely a question of
an attached attribute, that's hardly important or central to the
concept.
Furthermore learning by rote IS necessary, because that rote generates
skill, and a lot of fields that depend on applied mathematics requires
an intense amount of mathematical skill. Skill comes first, concept is
a far second, if it is at all needed: it's like driving a car, nobody
needs to know the internals of a car to drive one.
It is a major problem to teach students formal concepts
after they have gotten poor intuitive ideas, or just
learned methods.
No intuitive idea is poor. What becomes "poor" is the attempt to force
on students a set of formalisms that does not respond to their
intuition. I contend that it is hardly ever necessary to bother about
infinity in K12, and hence much of the need for anything beyond
intuition disappears in a puff of smoke - finite sets are pretty well
behaved, thank you, and they match intuition like a glove. So much so
that a lot of the problem students have learning modern math for the
first time is that it all looks like mental masturbation, a lot of
pseudobabble gobbledigook that ends up not saying anything that cannot
be reached by intuition or by other means.
It's only when we put infinity into the equation that the need for
formalism arrives, and that doesn't come but much later in the
process. Meanwhile, it's way better to rely on intuition than on
formalism.
It is the opposite of the way
educationists have it; one needs certain abilities to
replace miscellaneous garbled intuitions with structure or
formalism; one does need to keep not only the formalism,
but the concepts, in mind as well.
One needs neither if the intuition is well rooted. Again, number is an
intuitive notion and we don't need any formalism or any axioms to
inculcate them into our students - again, it's only when we deal with
infinities that we will need the formalism. The concept is very
pedestrian: we have addition, which is counting, which is intuitive.
The rest of arithmetic is basically addition in disguise. Algebra is
arithmetic in disguise. Geometry needs a little bit of spacial common
sense - not formalism - and then it's all about the application of
arithmetic to measurement. It's only when we get to calculus that we
bump into the need to explain limits to them, and then we hit the
issue of infinity; however, a careful preparation would have taught
them set theory and logic, so that by the time they get there they can
see that the concept of accumulation point can be easily handled by
drawing open sets around that point and counting how many elements are
inside it, and so on: and nowhere did we need to resort to Peano
postulates or any other arithmetic formalism. Now, calculus is just
about as much math as most of us will ever use, outside math majors
and computer science, so, pray, what's the use of the formalism ? I
believe in rooting it on intuition, not on formalism, and using
formalism to complement intuition and to allow going into areas where
intuition cannot.
We had much less of a
problem of teaching good formal mathematics in high school
a half century ago than we have in teaching it to college
students who have had more facts and computational
procedures today.
We don't need that kind of mathematics in college, nor do we need it
in high school. But while high school students will take anything,
college students are adult and many know what they want, and they're
worried about learning physics and engineering and computer science,
and they don't have time for any mathematics that doesn't directly
support their courses and helps them earn a passing grade. Again,
formalism should COMPLEMENT intuition, not replace it.
Formalization is natural for children; it is after they
learn in a sloppy manner that it becomes difficult.
Formalization is NOT natural for anyone, because it requires us to
restrict our inference process to a very restricted set of rules. This
is the basic problem with mathematical proof, a formal proof is rather
difficult to be handled because it requires the inference steps to be
COMPUTED, rather than reasoned out. I find it important to teach this
difference, but not as a mainstream way of teaching arithmetic and
geometry. The road to formalism and abstraction must be gradual, it
must start with intuition, and it must slowly but surely wean them out
of naive reasoning and into formalized reasoning. But it's a mistake
to replace one with the other altogether, or to start with formalism
and forget intuition, because that's not the way our minds work, nor
is it what's needed for most of the use of mathematics that our
students will face.
'
Alberto.
.
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| User: "Herman Rubin" |
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| Title: Teaching arithmetic concepts and operations |
06 Dec 2003 11:20:41 AM |
|
|
In article <3fd1367d.661150@news.mv.net>,
Alberto Moreira <junkmail@moreira.mv.com> wrote:
Said (Herman Rubin) :
We did not get the idea of using a decimal system to
calculate from the Indians through the Arabs; all that
we got from them in this direction was the use of the
same characters in all places, with a "0" character to
indica | | | | | | | | | | | | | | | | | | | | | | |
