What works in undergraduate mathematics?
Dave Rusin
I'm throwing this out to this newsgroup because I know there are several
faculty at mathematics departments who read this group from time to time.
I imagine this discussion will be unintelligible to those who work at
universities in countries with a healthy secondary-school system.
(Read: anywhere but the US.)
Colleagues:
I have recently been asked by faculty and administrators throughout
my university to comment on the low success rates in lower-division
mathematics courses.
We have in place a university-wide mathematics requirement which can
be achieved by passing a moderately meaty "quantitative literacy"
course, or by obtaining a C or higher in one of a few elementary
courses (usually Trig, Finite Math, Business Calculus, or Calculus I).
Unfortunately, only about 60% of the students taking these courses
get the grade they need on the first try.
Checking around at a few similar schools, I find that these numbers
are unremarkable; on the other hand, a few schools do claim a higher
success rate in these courses, at least with some populations.
Typically we place the problem in the students' lap -- poor prior
preparation or poor work habits -- but that response wears thin in the
face of demands to Do Something. And indeed, I note that we have already
set fairly restrictive entrance requirements for the courses, and
we already exhort the students to work hard. So it is time to look
at other options.
I have, I think, the support of my administration to try something
novel, even if takes some money (not too much of course!). I am
embarassed to respond to them that really I don't know what can be
done. I've seen the reform texts, the hi-tech teaching aids, new
scheduling plans, and so on -- as far as I can see, these don't seem
to promise any real improvement.
So now I'm shopping around for ideas. What new approaches have you
used which had a clear effect on student outcomes?
(If you would like simply to share your sob stories, I'd welcome
those too. It's nice to be able to respond to my bosses that we are
not alone, and even better to be able to say that various quick
fixes have been tried already and failed.)
dave
PS - for background: ours is a large state university, by some methods
of reckoning the second-best state school in a fairly large midwestern
state. Middle half of students have ACT scores in the 20-25 range.
Prof. David Rusin
Director of Undergraduate Studies
Department of Mathematical Sciences
Northern Illinois University
DeKalb, Illinois, 60115 USA
Email ru...@math.niu.edu
Web http://www.math.niu.edu/~rusin/
Telephone 1-815-753-6739
Fax 1-815-753-1112
Stone Jeremiah Ethan
I am graduating from a similar university this summer with a degree in
math and computer science and I have spent the last four years tutoring
students in the same classes that you describe. IMHO it comes down to one
thing: for the most part students that need to pass math classes in order
to satisfy degree requirements from the university *just don't care* Our
culture at large does not respect mathematics as much more than torturous
generalized nonsense. Why is it so surprising then that 18 and 19 year
old university students act the way that they do in remedial quantitative
reasoning courses? Additionally, with the current prevailing wisdom being
that intuition and "feeling" are more important than solid logical
reasoning it seems clear that we should expect such a dismal performance
from such students. Today is four days away from the end of the spring
semster here. We have a program called math mods which are independent
study courses for the ones in question. Suddenly the math building, which
is normally quiet and empty is *full* of undergraduates waiting in
hour-long lines to take their proctored math mod courses. I would be
willing to wager that 60% will fail. Why? They could not care less. The
thing is, math courses are not the only required courses that students do
not care about. They are however, some of the only required courses that
actually fail students. So, combine grade inflation in less rigorous
classes with general math apathy and you get the current situation. In
the face of this, I wish any educator in your position luck.
-Jeremiah
ru...@vesuvius.math.niu.edu (Dave Rusin) writes:
>Colleagues:
>dave
--
---------------------------------------------
Jeremiah Stone
sto...@colorado.edu
---------------------------------------------
Adam Atkinson
>We have in place a university-wide mathematics requirement which can
>be achieved by passing a moderately meaty "quantitative literacy"
>course, or by obtaining a C or higher in one of a few elementary
>courses (usually Trig, Finite Math, Business Calculus, or Calculus I).
May I ask why?
You can't be too surprised if people don't do well in things they're
forced to do against their will.
If I were forced to attend lessons in a language I had no interest in
learning, or a business studies course, I might very well do extremely
badly beause I Just Didn't Want To Be There.
--
Adam Atkinson (gh...@mistral.co.uk)
A hollow voice says "PLUGH"
Allan Adler
This seems to fall into the class of questions of the form, "Doc, it
hurts when I go like this," and the answer is "Don't go like this."
"Like this" is the control freak mentality which, not content with
knowing that an electron will somehow manage to get through one or
the other slit to hit the screen, insists on measuring which slit
the electron goes through. This changes everything.
One of the psychological manifestations of this tendency in individual
teachers is the depression that comes from the apparent uselessness of
their efforts to educate more than a certain percentage of the students.
The simple fact, however, is that the benefits and appreciation of what
a student is taught may not be apparent for years or decades after the
student has left the classroom. To some extent, this depression is more
about the needs of the teacher than those of the student.
Those asking the questions have their own control freaks to appease,
the ones who control their funding, and they in turn have their control
freaks, and so on. I think it is fair to say that from the standpoint
of funding agencies, the only legitimate activity is administration.
What they are really paying for is for someone to assume fiscal responsibility,
and once that team has been chosen, education and research become merely
the incidental costs of administering a university or research institute.
It is absolutely incredible that a list of assumptions so long that it
takes at least a whole college catalogue to state them is treated as
too obvious to mention and that the discussion instead focuses on
a few little details that one is thinking of changing.
You can't fix it. It was never meant to work. It is not a solution to
the problems of education or scholarship. It is merely the only wheel
in town.
What I think is that it should stop being the only wheel in town. This
is difficult as long as everyone is persuaded only by the one rule of
inference (money) that pays their bills. If the people who brought us
the Scopes Trial only did what they were paid to do, they would be
in the same fix as the people trying to keep evolution in the curriculum.
I say, "Out of the universities and into the streets!". Work where you must,
but also leave the workplace behind and teach and learn in society itself.
There is a need for adult role models to participate in intellectual
activity for its own sake and to take it seriously. A math professor
who never thinks about anything but math or mathematicians or the politics
of the math department is not setting a good example.
How to do this is a matter for continued experimentation. Some people will
talk about "outreach" and I'm sure they have good intentions and maybe also
some good effects. But what I have seen of outreach is that it is one
bureaucracy reaching out to another bureaucracy. There needs to be something
else, something more personal, something that is not a clone of or a fix for
or an extension of the only wheel in town. More individuals have to commit
themselves to looking for one and experimenting.
I don't pretend to have much success in this area. My primary student is
myself and I'm trying to succeed with that student where the system failed.
One of my experiments is my sporadic journal Labyrinths
http://www.swiss.ai.mit.edu/~adler/LABYRINTHS/labyrintro.html
Another is a set of activities I am trying to get off the ground in
Bowling Green, KY. For some current information on that, see:
http://www.accessky.net/wwwwwww (there are 7 w's)
For me, the question is not how to get the great bureaucracies to work;
there are already enough people working on that. I see the question as
how to nourish the neglected area of non-bureaucratic education. This is
a concept in search of a definition, and for the right to be called education
even if it isn't funded. One can get a glimpse of what it might mean by
considering the example of libraries and museums, which pretty much
leave people free to follow their own curiosity. The institutions
themselves might have their own bureaucracies, but patrons are largely
shielded from them, unlike in schools where the bureaucracies are as
much a part of the problem as a part of the solution.
Allan Adler
a...@zurich.ai.mit.edu
****************************************************************************
* *
* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Morever, I am nowhere near the Boston *
* metropolitan area. *
* *
****************************************************************************
Steven James Forsberg
: Colleagues:
: I have recently been asked by faculty and administrators throughout
: my university to comment on the low success rates in lower-division
: mathematics courses.
If I may inject a note of pessimism, the problem may be out of your
hands. One possible alternative - seriously look at the minimal requirements
for non-tech majors and consider lowering them. Otherwise, there may not be
much you can do.
As others have stated, the root reason could be explained as "the
students don't care." In my experience, there is another reason, the students
just don't have the time.
My background is more with the humanities, but a stats course heavily
taken (and failed) by social science students will serve as a good example.
The "management" wanted to know why so many students were failing. Well, the
way the course is set up and the amount of content are all built around the
assumption (made long ago) that a student will spend approx 2 hours of time
outside class for every hour inside class. I.E. for a 3 credit class like this
a student should spend about 6 hours a week outside class. The voluntary class
evaluations indicated that the average student spent under 2 hours per week
outside class on the class, however.
Yes, outlines are nice and kids want "just the needed stuff", but at
some point in time, if you don't put in some hours there is just no way that
people can pick up the material (until we invent the brain implant). Some
students just don't care, but a lot are torn by a need to work while attending
college or take part in
"career enhancing" activities. Gone are the days when the student body was
full time students and you KNEW that they had all afternoon every day to do
homework and study. People working and with families, in particular, can't
seem to put in the time to learn difficult material.
It's the same thing in history (more my field). The amount of reading
assigned to students (the ultimate arbiter of how much is learned) has gone
down drastically in the last 20 years, along with the amount of writing
expected. And still people are screaming about "too much". Well, at some point
the rubber hits the road and if people don't have time they simply won't pass
the course -- even IF their tuition check is good and the management wants
them happy.
My advice - have a serious study done as to how much time the typical
student is spending on the course outside of class. Compare it to how much
time they were expected to spend back when the syllabus was created. Even with
"improved teaching methods" and computers and such, the odds are that you simply
can not make up the ever decreasing amount of time being spent on your subject.
How do you get people to spend more time? Well, mandatory homework is a b*tch
and not like at the college level, but maybe it is needed. How about mandatory
study periods (i.e. labs)? Likewise, the management will see that as 'too
radical' and
'too much trouble'. Screening out students with too many other commitments
(like work)? That would be sacreligious. No easy answers.
Good luck,
steven j forsberg
----------------------------------------------
sjfo...@bayou.uh.edu wizard 87-01
Dave Rusin
Adam Atkinson <gh...@mistral.co.uk> wrote:
>On 01-May-00 18:03:59, Dave Rusin said:
>
>>We have in place a university-wide mathematics requirement which can
>>be achieved by passing a moderately meaty "quantitative literacy"
>>course, or by obtaining a C or higher in one of a few elementary
>>courses (usually Trig, Finite Math, Business Calculus, or Calculus I).
>
>May I ask why?
Do you mean, why require a math course at all?
The core competency requirements (math, English, and "communications") are
in place because these (1) reinforce skills necessary to survive other
college courses, and (2) impart some of the perspectives considered
essential for an educated citizenry. For (1), imagine students
trying to find science and social science classes which meet general
education requirements but require no skills with numbers, logical reasoning,
or problem solving! For (2), consider the loss to society when "college
educated" voters don't know the difference between a million dollars and
billion dollars, or between causality and coincidence.
Arguably, all students ought to take a fairly robust "mathematics for life"
course, but that's a little silly for future psychologists or engineers
who already have to work through comparatively more challenging courses.
On the assumption that a decent trigonometry class already involves a bit
of communicating with mathematics and so on, we grant dispensation from the
mathematics core course if the students get a C or better there.
If you mean, why require specific courses beyond the math core, I have
to say I don't really know. It makes sense to me that a physical therapy
student ought to learn a few facts about trigonometry in order to get
anything out of a kinesiology course; but our trig course is set up as
a calculus-preparatory course, much to the chagrin of those PT students.
I certainly can't argue with this:
>You can't be too surprised if people don't do well in things they're
>forced to do against their will.
Of course, one could begin debates about how much, really, ought to be
forced on the student. Internal motivation! Personal liberty! Students
as consumers! --- these sound quite attractive to students, and
(on occasions like this, at least) to faculty too. But there are also
questions about accreditation of schools, departments, and programs
(e.g. ABET will force engineers to take calculus, whether students
find it superfluous or not). And there are statewide norms, implied or
explicit, to which a public school must adhere (for example, we must be
fairly traditional if we hope to continue to attract the transfer students
who make up half our student population).
So, while a person of singular vision and intestinal fortitude might initiate
a dramatic change in the school requirements, I think the current set of
requirements is probably more or less a given. So too, sadly, are the
current admission requirements. We can tinker around the edges of those
constraints, but we really need to face the issue of how to help
students who, for example, arrive at college _not yet ready for a
precalculus course_, and yet are expected to work their way through,
say, a business calculus course. Everyone seems to agree that this
will take a couple of semesters; that the students and faculty will have
to work; that standards for passing ought not to be relaxed. We also
all agree that student failures are harmful to the students, frustrating
to the faculty, and dangerous for the institution. When we disagree
is when the administration says, "Don't let failures happen (so often)."
but the faculty say, "Hey, how much can I do? The kids failed."
[Faculty may insert here their own private collection of stories of
students who, given every opportunity to succeed, still managed
to fail spectacularly.]
dave
Bob Silverman
"Adam Atkinson" <gh...@mistral.co.uk> wrote:
> On 01-May-00 18:03:59, Dave Rusin said:
>
> >We have in place a university-wide mathematics requirement which can
> >be achieved by passing a moderately meaty "quantitative literacy"
> >course, or by obtaining a C or higher in one of a few elementary
> >courses (usually Trig, Finite Math, Business Calculus, or Calculus
I).
>
> May I ask why?
>
> forced to do against their will.
Then why are they in school??
A University has breadth requirements. This requires studying subjects
outside of one's major.
If they don't like this, then that is just too bad. They knew what
the University's requirements were before they entered.
>
> If I were forced to attend lessons in a language I had no interest in
> learning, or a business studies course, I might very well do extremely
> badly beause I Just Didn't Want To Be There.
Then leave. But don't expect to be granted a degree.
Reading, Writing, and Arithmetic. If one can't master these at a basic
level, or if one has no interest in doing so, then one does not DESERVE
a bachelor's degree.
--
Bob Silverman
"You can lead a horse's ass to knowledge, but you can't make him think"
Sent via Deja.com http://www.deja.com/
Before you buy.
Nico Benschop
>
> This seems to fall into the class of questions of the form, "Doc, it
> hurts when I go like this," and the answer is "Don't go like this."
> You can't fix it. It was never meant to work. It is not a solution to
> the problems of education or scholarship. It is merely the only wheel
> in town.
> What I think is that it should stop being the only wheel in town. This
> is difficult as long as everyone is persuaded only by the one rule of
>
> I say, "Out of the universities and into the streets!".
> Work where you must, but also leave the workplace behind and teach
> and learn in society itself.
> There is a need for adult role models to participate in intellectual
> activity for its own sake and to take it seriously. A math professor
> who never thinks about anything but math or mathematicians or the
> politics of the math department is not setting a good example.
>
> I don't pretend to have much success in this area.
> My primary student is myself and I'm trying to succeed with that
> student where the system failed.
> One of my experiments is my sporadic journal Labyrinths
> http://www.swiss.ai.mit.edu/~adler/LABYRINTHS/labyrintro.html
> Another is a set of activities I am trying to get off the ground in
> Bowling Green, KY. For some current information on that, see:
> http://www.accessky.net/wwwwwww (there are 7 w's)
>
> For me, the question is not how to get the great bureaucracies to
> work; there are already enough people working on that. I see the
> question as:
> how to nourish the neglected area of non-bureaucratic education.
This is the core of the matter, and in other countries called
(among others): "education parmanente" or "continued education"
It has to do with motivation: _why_ learn something of which you really
have not much (or any) clue about its applications & possibilities?
Only later in life an intelligent person gets the urge to learn what
others have learned & presented in books, theaters, musea, films, &c.
_Then_ you pick what you need , and who knows: something more, just for
the heck of it - just because it is interesting and fun.
Quote (Albert Einstein):
"It is a miracle that curiosity survives formal education."
Surely, there is a 'bootstrap' involved here: the chicken-and-egg
problem of what comes first? This is at the center of many problems of
learning & solving, especially in the Western world:
Creativity is NOT a linear thing, but cyclic (roughly;-)
That is: different/oppsoded aspects present themselves simultaneously,
and it is good to develop a multi-focus sensitivity to disparate but
essential aspects of a (any) whole... To bring analysied & linearized
material to a youngsters doorstep and expect him/her to study this for
the first 20 years or so is asking for trouble, really.
To study math for many years as a 'pure' discipline, _without_ the
benefit of doing/living a self-supporting life is a rather abstract
model of life, which is breaking-up any motivation of all but the
abnormally concentrated...
> This is a concept in search of a definition, and for the right to be
> called education even if it isn't funded. One can get a glimpse of
> what it might mean by considering the example of libraries and
> museums, which pretty much leave people free to follow their own
> curiosity. The institutions themselves might have their own
> bureaucracies, but patrons are largely shielded from them, unlike in
> schools where the bureaucracies are as much a part of the problem as
> a part of the solution. -- Allan Adler, a...@zurich.ai.mit.edu
The little I learned of discrete math (finite Semigroups & Arithmetic &
Boolean logic) is self-taught, as I needed it in my job (digital VLSI
design research), starting with sequential logic with the (Finite)
Internal State Model (FSM: Mealy/ Moore, Hartmanis/ Stearns, Birkhoff/
Bartee, Clifford/ Preston) and then _only_ those chapters that seemed
relevant. And not to forget my favourite "The development of
Mathematics" by E.T.Bell, a marvellous motivating & critical book [*],
with enough detail (upto mid last century;-) and A.Reny: "Dialogues in
Mathematics". [*] http://www.iae.nl/users/benschop/quotes.htm
My guess is that at least some of these writer pairs are a combination
of Math/Engineering (correct me if I'm wrong here;-), precisely what
I'm talking of: a multi-disciplinary outlook, a balance of form &
content, of semantics & syntax, of representation & abstraction.
Just some thoughts...
--
Ciao, Nico Benschop. -- http://www.iae.nl/users/benschop
gy...@post.com
> > If I were forced to attend lessons in a language I had no interest
> > in learning, or a business studies course, I might very well do
> > extremely badly beause I Just Didn't Want To Be There.
> Reading, Writing, and Arithmetic. If one can't master these at a
> basic level, or if one has no interest in doing so, then one does
> not DESERVE a bachelor's degree.
I believe the original poster is referring to learning a foreign
language. Also business studies does not figure in
"Reading, Writing, and Arithmetic.", neither does discrete mathematics
or calculus or college algebra for that matter.
I believe the basic skills you mention ought to be imparted at the
school-level,which they are,I believe. It is absurd to think a
college education is intended to impart the skill of "arithmetic".
Stone Jeremiah Ethan
>In article <755.156T2510T...@mistral.co.uk>,
> "Adam Atkinson" <gh...@mistral.co.uk> wrote:
>> On 01-May-00 18:03:59, Dave Rusin said:
>>
>> >We have in place a university-wide mathematics requirement which can
>> >be achieved by passing a moderately meaty "quantitative literacy"
>> >course, or by obtaining a C or higher in one of a few elementary
>> >courses (usually Trig, Finite Math, Business Calculus, or Calculus
>I).
>>
>> May I ask why?
>>
>> You can't be too surprised if people don't do well in things they're
>> forced to do against their will.
>Then why are they in school??
According to the students that I have come in contact with, to have the
time of their lives.
>A University has breadth requirements. This requires studying subjects
>outside of one's major.
>If they don't like this, then that is just too bad. They knew what
>the University's requirements were before they entered.
Wrong. Like it or not, students have the ability of change policies
through poor performance and ranting. At my university there is a push
under way to change the core requirements to allow students to test out of
the required math course but not out of the required english course
(anymore). The logic? Students get C's in the english course, which is
famous for giving *all* students C's, and fail the math courses. If the
math test is any easier than our current math mods which students fail at
an astonishing rate, we will be passing students with middle school math
skills (if that).
>>
>> If I were forced to attend lessons in a language I had no interest in
>> learning, or a business studies course, I might very well do extremely
>> badly beause I Just Didn't Want To Be There.
>Then leave. But don't expect to be granted a degree.
>Reading, Writing, and Arithmetic. If one can't master these at a basic
>level, or if one has no interest in doing so, then one does not DESERVE
>a bachelor's degree.
I agree, but unfortunately people who are well educated are not in the
administration. At my school, I would be willing to wager that the
administration is preoominately made up of former student who failed math
courses.
University Beauracracy: The revenge of the "C" student...
>--
>Bob Silverman
>"You can lead a horse's ass to knowledge, but you can't make him think"
>Sent via Deja.com http://www.deja.com/
>Before you buy.
Adam Atkinson
>> You can't be too surprised if people don't do well in things they're
>> forced to do against their will.
>Then why are they in school??
The "things" I'm referring to are things way outside what they could
reasonably be persuaded are part of their course of study
>A University has breadth requirements. This requires studying subjects
>outside of one's major.
This is not true of many universities. I happen to think being
_allowed_ to study things outside one's major is a brilliant idea. I
did Italian in my copious free time at university, and liked it so
much I went and spent six years in Italy immediately after graduation.
However, this had nothing to do with my degree.
Being allowed to do something is not the same as being forbidden to do
it or forced to do it, though.
>If they don't like this, then that is just too bad. They knew what
>the University's requirements were before they entered.
Now this _is_ a fair point. Is it possible to find universities in the
US without such requirements? If not, then people don't have much
choice in the matter.
>> If I were forced to attend lessons in a language I had no interest in
>> learning, or a business studies course, I might very well do extremely
>> badly beause I Just Didn't Want To Be There.
>Then leave. But don't expect to be granted a degree.
I shouldn't get a degree in (say) aerospace engineering because I
don't want to do (say) Sanskrit? I realise you're not talking about
Sanskrit, but making linguists, theologians and art historians do
calculus seems very nearly as perverse.
>Reading, Writing, and Arithmetic. If one can't master these at a basic
>level, or if one has no interest in doing so, then one does not DESERVE
>a bachelor's degree.
Whilst I tend to agree with you, I would have thought that this is
what admissions requirements are for. ISTR that the university I went
to required O-levels in English, Maths and a foreign language when I
went there. A few years earlier it required Latin.
I would be quite tempted to add "some knowledge of a foreign language"
to your list, but then I'm biased towards languages. Would I really
want to kick out promising physicists because they couldn't learn a
language?
--
Adam Atkinson (gh...@mistral.co.uk)
Never attribute to malice that which is adequately explained by
incompetence.
Adam Atkinson
>>May I ask why?
>Do you mean, why require a math course at all?
Yes
>For (2), consider the loss to society when "college
>educated" voters don't know the difference between a million dollars and
>billion dollars, or between causality and coincidence.
But isn't basic numeracy a high school issue?
>Arguably, all students ought to take a fairly robust "mathematics for life"
>course
Again, isn't this what high school is for? If someone is doing
theology or art history or something like that, making them do a year
of calculus (or whatever) seems a little perverse.
Perhaps my idea of this "core maths" couse is inaccurate.
>>You can't be too surprised if people don't do well in things they're
>>forced to do against their will.
>But there are also
>questions about accreditation of schools, departments, and programs
>(e.g. ABET will force engineers to take calculus, whether students
>find it superfluous or not).
I wasn't thinking of engineers doing calculus, or doctors doing
chemistry. I was thinking of linguists doing group theory or
mathematicians doing art history. If they want to do it, then that's
lovely, of course. I know a lot of linguists, and wouldn't feel very
comfortable making them do pre-calculus "for their own good".
>So, while a person of singular vision and intestinal fortitude might initiate
> a dramatic change in the school requirements, I think the current set of
>requirements is probably more or less a given. So too, sadly, are the current
>admission requirements.
I would _like_ to think that basic literacy and numeracy were
something that could be made an admission requirement. As I say
elsewhere, ISTR that the university I went to had a foreign language
admission requirement as well. In your "good for society" sense it's
probably a good thing for people to learn languages, but stopping
people from doing physics because they're dreadful at German seems
pretty odd.
Dave Rusin
You really must visit the US high school scene some time.
There is no legal requirement that students finish high school, although
the economic incentives convince some 70% or 80% of teens to do so.
There is no federal requirement that high school graduation actually
represent any particular accomplishment, although all states (as far as I
am aware) set up some minimal requirement.
In the state of Illinois, I believe high school graduates must finish
at least two years of "high school" mathematics. Depending on the school,
I think it's possible for a student to do so and _not yet have begun algebra_.
Even under ordinary circumstances, two years in high school would probably
mean just a first course in algebra and a first course in geometry.
I might as well add that state regulations mandate certain numbers and
course titles, but that beyond that, there is very little statewide
scrutiny of course quality and student mastery.
Entrance to our university requires, among other things, a high school degree
and "two or three" years of college-preparatory mathematics. There really
are students who have had only an algebra and a geometry course; indeed,
a result of certain social-engineering initiatives, some students are allowed
in with weaker backgrounds.
So no, I don't think I would agree that basic numeracy a high school issue.
Ought to be, yes. Usually is, yes. But universally, no.
(I hasten to add that _most_ students get a nearly adequate high school
education, that is, it's not as if almost no one is even taking trigonometry
any more. Your run-of-the-mill freshman college student has a decent chance
of mastering a cookbook calculus course, for example.)
>I would _like_ to think that basic literacy and numeracy were
>something that could be made an admission requirement.
Well, yes: basic as in "every 12-year-old ought to know this"; that's
likely true. But basic as in "this is enough to prepare you for an
introductory economcs course", no. We could not fill the dorms using
only those students who understand how to combine compound probabilities,
who could give a working definition of "slope", and who could give
the common log of the current US population with an error less than 2.0.
I don't claim the students could do these things after passing our
"core" course, but at least there's a chance they'd recognize the
words in the questions...
dave
jonathan miller
> In the state of Illinois, I believe high school graduates must finish
> at least two years of "high school" mathematics. Depending on the school,
> I think it's possible for a student to do so and _not yet have begun algebra_.
> Even under ordinary circumstances, two years in high school would probably
> mean just a first course in algebra and a first course in geometry.
And don't forget the students that have gotten nothing but A's in their history,
including high school calculus, and still place into College Algebra on the
placement exam. Why? Because they still believe that sqrt(a^2 + b^2) = a + b
(among other things).
Jon Miller
jonathan miller
> On 02-May-00 14:27:02, Bob Silverman said:
> >If they don't like this, then that is just too bad. They knew what
> >the University's requirements were before they entered.
>
> Now this _is_ a fair point. Is it possible to find universities in the
> US without such requirements? If not, then people don't have much
> choice in the matter.
> I shouldn't get a degree in (say) aerospace engineering because I
> don't want to do (say) Sanskrit? I realise you're not talking about
> Sanskrit, but making linguists, theologians and art historians do
> calculus seems very nearly as perverse.
Actually, this is the rationale (not just languages but other "general
education" courses as well) behind considering engineering degrees
"technical" and linguistics degrees "educated". As with all sweeping
generalizations, there is a germ of truth to it that is blown out of
proportion by the generalization.
> I would be quite tempted to add "some knowledge of a foreign language" to
> your list, but then I'm biased towards languages. Would I really want to
> kick out promising physicists because they couldn't learn a language?
If they (physically) couldn't, they wouldn't be there. But what if they
educationally, socially, psychologically, . . . couldn't, what then?
Jon Miller
David C. Ullrich
know the material or not that would be Something you could Do.
But presumably you've thought of that and rejected it for some
reason. Short of that I doubt there's much you _can_ Do. The
problem is the students simply don't believe they actually
have to know this stuff - the idea of actually working on
it for several hours every day is just totally foreign to them.
Seriously. A few years ago someone here did a math-ed
Master's thesis(!) on Why Students Fail College Algebra. He
looked at some numbers - turned out that the students who
attend class and do the homework had relatively little problem
with the course.
At the time I said "yeah, that's a big surprise".
Later I decided it wasn't so silly, in terms of being something
a person could show to the administration. But that didn't help
much, the department was still supposed to Do Something. A few
people designed a brand-new course, "Functions", meant as a
more meaningful introduction to various mathematical concepts,
something the kids could pass. At the time I assumed it was
just supposed to be a way the kids could pass without knowing
anything, so I didn't approve. But it turns out the the
Functions guys actually do expect the kids to learn something.
And guess what: The kids who attend class and do the homework
have no problem with Functions, just like with college algebra.
The ones who don't attend class and don't do the homework flunk.
Good luck.
On 1 May 2000 18:03:59 GMT, ru...@vesuvius.math.niu.edu (Dave Rusin)
wrote:
>
>I'm throwing this out to this newsgroup because I know there are several
>faculty at mathematics departments who read this group from time to time.
>I imagine this discussion will be unintelligible to those who work at
>universities in countries with a healthy secondary-school system.
>(Read: anywhere but the US.)
I just read this article in an old Notices about the
guy observing a math class in Taiwan. The students were paying
attention, when the bell rang they waited for him to finish what
he was saying before thanking him and walking out... Sounds like
a bunch of Asian zombies. But no, during recess they were running
around screaming just like regular kids, they just had these
strange notions about how to behave in class.
DU
gy...@post.com
> Would I really want to kick out promising physicists because they
> couldn't learn a language?
*couldn't learn* or *doesn't want to learn* ?
A "promising" physicist ought to be able to pick up the basics of
any language. There would be a problem if he *couldn't* learn...
Gyan
Adam Atkinson
>>But isn't basic numeracy a high school issue?
>You really must visit the US high school scene some time.
I've had some exposure to the "high school" scenes in the UK, US and
Italy. I get the impression that many of the problems are really quite
similar, although they get moved around a bit. In particular, Italy
has lots of different kinds of secondary schools, so it's quite
possible for people who went to the upper echelon versions to honestly
believe that illiteracy doesn't exist in Italy because everyone they
were at school with could read at 16.
>Entrance to our university requires, among other things, a high school degree
>and "two or three" years of college-preparatory mathematics. There really are
>students who have had only an algebra and a geometry course; indeed, a result
>of certain social-engineering initiatives, some students are allowed in with
>weaker backgrounds.
Well, ok. But if you're letting them in to do modern languages, then
isn't there some argument that their general education is now over and
they are now linguists?
>So no, I don't think I would agree that basic numeracy a high school issue.
>Ought to be, yes. Usually is, yes. But universally, no.
The tone of my original comment was supposed to be taken as "ought to
be". Of course, I realise things aren't that simple. Hence my "like
to" in the next bit you quoted:
>>I would _like_ to think that basic literacy and numeracy were
>>something that could be made an admission requirement.
>Well, yes: basic as in "every 12-year-old ought to know this"; that's
>likely true. But basic as in "this is enough to prepare you for an
>introductory economcs course", no. We could not fill the dorms using
>only those students who understand how to combine compound probabilities,
>who could give a working definition of "slope", and who could give
>the common log of the current US population with an error less than 2.0.
>I don't claim the students could do these things after passing our
>"core" course, but at least there's a chance they'd recognize the
>words in the questions...
But a case can be made for economists needing a maths course as part
of their degree, so whether they like it or not they can be told it's
really necessary for what they want to do. It's the "across the board"
element taking in art historians, theologians etc. that seems odder.
(Actually, I believe art historians do get told how perspective works,
but that's probably not a justification for making them do multiple
credits worth of trigonometry and who knows what else)
--
Adam Atkinson (gh...@mistral.co.uk)
We'll call him Shaun, eh? Come on, Shaun!
Adam Atkinson
>> Would I really want to kick out promising physicists because they
>> couldn't learn a language?
> *couldn't learn* or *doesn't want to learn* ?
Not quite sure. My impression in the US was that scientists could
(with resentment and bad grace, perhaps) get passing grades in arts
courses they considered a waste of time to satisfy some pointless
requirement. And most artists could (with resentment a bad grace,
perhaps) do the same in some science courses, perhaps ones created
specifically for the purpose. But for a moderate number of artists and
a tiny number of scientists it was a real problem.
> A "promising" physicist ought to be able to pick up the basics of
> any language. There would be a problem if he *couldn't* learn...
Well, I would agree. But if the languages department decides what
constitutes the "basics" and can cause students to disappear from your
faculty, the situation is rather similar to what the mathematics
faculty can do to (say) superb linguists. This seems unsettling.
Richard Carr
:Date: 3 May 2000 6:33:43 +0000
:From: Adam Atkinson <gh...@mistral.co.uk>
:Newsgroups: sci.math
:Subject: Re: What works in undergraduate mathematics?
:
:On 02-May-00 22:58:40, Dave Rusin said:
:
:>>But isn't basic numeracy a high school issue?
:
:>You really must visit the US high school scene some time.
:
:I've had some exposure to the "high school" scenes in the UK, US and
:Italy. I get the impression that many of the problems are really quite
:similar, although they get moved around a bit. In particular, Italy
Very different. There's no way you'd get a course in a UK university that
tells people how to add fractions (as does the Basic Mathematics course
here) etc..
:has lots of different kinds of secondary schools, so it's quite
:
:--
:Adam Atkinson (gh...@mistral.co.uk)
:We'll call him Shaun, eh? Come on, Shaun!
:
Best beware of the evil mechanical, terminator-like, dog.
Adam Atkinson
>:I've had some exposure to the "high school" scenes in the UK, US and
>:Italy. I get the impression that many of the problems are really quite
>:similar, although they get moved around a bit. In particular, Italy
>Very different. There's no way you'd get a course in a UK university that
>tells people how to add fractions (as does the Basic Mathematics course
>here) etc..
Actually, adding fractions (along with long multiplication and
division) disappeared from UK state schools about 10 years ago. They
were "Just Too Hard", "Ruined Lives", etc. I don't know if they've made a
reappearance since then.
(Source of this information: I was doing teacher training at the time.
I didn't complete it do to a combination of not being any good at it,
and not wanting to say "What is 100 share 20?" to sixteen year olds to
avoid using difficult words like "divide", not thinking adding
fractions was life-ruining, etc.)
--
Adam Atkinson (gh...@mistral.co.uk)
EXAKCIP
Warwick Dumas
Hello, people round here.
On 3 May 2000, Adam Atkinson wrote:
> On 03-May-00 05:51:28, Richard Carr said:
>
> >:I've had some exposure to the "high school" scenes in the UK, US and
> >:Italy. I get the impression that many of the problems are really quite
> >:similar, although they get moved around a bit. In particular, Italy
>
> >Very different. There's no way you'd get a course in a UK university that
> >tells people how to add fractions (as does the Basic Mathematics course
> >here) etc..
>
> Actually, adding fractions (along with long multiplication and
> division) disappeared from UK state schools about 10 years ago. They
> were "Just Too Hard", "Ruined Lives", etc. I don't know if they've made a
> reappearance since then.
I don't think anything can ever quite be said to disappear; one thing is
certain, nothing has *appeared*, at least not while I was there.
> (Source of this information: I was doing teacher training at the time.
> I didn't complete it do to a combination of not being any good at it,
> and not wanting to say "What is 100 share 20?" to sixteen year olds to
> avoid using difficult words like "divide", not thinking adding
> fractions was life-ruining, etc.)
Good for you, I'd have done likewise. On which note, school led me to
believe that most maths teaching is woefully misguided anyway. No one
(within reason) really needs to go over all that stuff at secondary
school. Curricula should move on as if it is all well-known, and any
missing pieces will turn up of their own accord.
The problem is (and I think, from report, that it is fairly
universal) that anyone not in top set is faced with a very dull sort of
mathematics which treats them as if they cannot handle *thought*. One
might be forgiven for thinking that (part and parcel with the rest of
school education) its main purpose is to keep people in their place, make
sure they learn to fear understanding.
Warwick Dumas
"If Adolf Hitler were here today
They'd send a limousine anyway." The Clash
My website:
www.warwick.ac.uk/~ecuqe
Charles H. Giffen
Worse than that -- they appear in Calculus II thinking that
1/(A+B) = 1/A + 1/B
and, recently, that
(A^2+B^2)/(A+B)^2 = (A^2+B^2)/(A^2+2AB+B^2) -- correct
= 1/(2AB) -- "cancel the A^2's and the B^2's"
... Grrrr!
--Chuck Giffen
Dave Rusin
Adam Atkinson <gh...@mistral.co.uk> wrote:
>>Entrance to our university requires, among other things, a high school degree
>>and "two or three" years of college-preparatory mathematics. There really are
>>students who have had only an algebra and a geometry course; indeed, a result
>>of certain social-engineering initiatives, some students are allowed in with
>>weaker backgrounds.
>
>Well, ok. But if you're letting them in to do modern languages, then
>isn't there some argument that their general education is now over and
>they are now linguists?
Yes, I agree: once you're on your way to being a linguist, general
education is over, and you ought to specialize. This argument works with
graduate education, and for undergraduate education at, perhaps, Caltech.
Some here want to use this argument with our students too, but I think
I'm in the camp which maintains general education is _not_ over for
the undergraduates at this institution. Let me explain.
Realistically, our students have no chance of becoming
linguists any time soon. They have a good chance at becoming a
translator for Sony, producing VCR manuals which are not full of
comical English errors. Or perhaps they won't be able to find such a
job but will work in some large business which from time to time has
customers whose only working language is German. In any event, it's
clear that they will have to spend a significant portion of their
time really immersed in some other pursuit besides languages.
Since we cannot tell, when they are 18 years old, what that other
pursuit will be, we consider it a service to them to insist that
they continue a fair amount of general education.
We take the same perspective with our mathematics majors, by the way.
Even beyond the university requirements, I regularly counsel the
students to consider taking particular extra courses outside
mathematics -- according to student interest, this might mean
more science courses, business courses, or foreign languages, for example.
(To be precise, out of approximately 40 college classes taken for
graduation, about 3 will be taken to meet a "core competency" requirement,
another 8 or so will meet "general education" requirements, about
15 will be specified individually or from a short menu by the
department of the major degree, and about a dozen more will be
"electives", possibly organized for the completion of a professional
certification -- in education, nursing, engineering, and the like --,
or the completion of a second major, or a minor, or simply for
more general education.)
dave
PS -- I located the minimum Illinois high school graduation requirements.
Here is our local high school's web page, describing state requirements:
http://dist428.dekalb.k12.il.us/dhs/profile.htm
Here is a list of our school's mathematics course offerings. (The list
reflects the nearly linear ordering of the topics by complexity. The
most common entry point at age 14 is Algebra):
http://dist428.dekalb.k12.il.us/dhs/depts/math/courses.htm
Here is the website of our school's most famous valedictorian :-)
http://www.cindycrawford.com/about/biography/index.html
Dave Rusin
Charles H. Giffen <ch...@virginia.edu> wrote:
>>
>> Why? Because they still believe that sqrt(a^2 + b^2) = a + b
>
>
>1/(A+B) = 1/A + 1/B
These are simply examples of the theorem "All functions are linear".
It really speeds up various calculations, e.g. sin(x+y)=sin(x)+sin(y),
and in particular sin(2x)=2sin(x), so that lim sin(2x)/x = 2 lim sin(x)/x
=2. You got a problem with that?
>and, recently, that
>
>(A^2+B^2)/(A+B)^2 = (A^2+B^2)/(A^2+2AB+B^2) -- correct
>
> = 1/(2AB) -- "cancel the A^2's and the B^2's"
Oh yes. Every quotient rule problem involves
(g f' - f g')/g^2 = (f' - f g')/g
Over-cancellation is another general "theorem" which I can't quite
state with precision. You see it in "sin(x)/x = sin", which leads
me to ask whether "tan(x) = sin(x)/cos(x) = sin/cos" should be continued
to "... = in/co" (cancel the s's). Or whether we should accept
16/64 = 1/4 by cancelling the 6's (hey, wait a minute...)
>... Grrrr!
Now, now --- semester's almost over...
Adam Atkinson
>> (Source of this information: I was doing teacher training at the time.
>> I didn't complete it do to a combination of not being any good at it,
>> and not wanting to say "What is 100 share 20?" to sixteen year olds to
>> avoid using difficult words like "divide", not thinking adding
>> fractions was life-ruining, etc.)
>Good for you, I'd have done likewise.
It wasn't entirely my decision. I got into a lot of trouble for being
fairly direct about thinking "What are you doing to stop the bright
ones from getting ahead?" was a criminal thing to ask.
> On which note, school led me to
>believe that most maths teaching is woefully misguided anyway. No one
>(within reason) really needs to go over all that stuff at secondary
>school.
My impression is that based on what I saw at junior and secondary
schools during the course, a fair number of 16 year olds learn less
than no maths in 5 years of secondary education.
>The problem is (and I think, from report, that it is fairly
>universal) that anyone not in top set is faced with a very dull sort of
>mathematics which treats them as if they cannot handle *thought*. One
>might be forgiven for thinking that (part and parcel with the rest of
>school education) its main purpose is to keep people in their place, make
>sure they learn to fear understanding.
This is more or less what I said at the time, and I was accused of
being a _right_-wing extremist.
--
Adam Atkinson (gh...@mistral.co.uk)
We know Jesus must have been Italian for 3 reasons: he lived at home
until he was 30, he thought his mother was a virgin, and she thought
he was God.
Herman Rubin
Dave Rusin <ru...@vesuvius.math.niu.edu> wrote:
>I'm throwing this out to this newsgroup because I know there are several
>faculty at mathematics departments who read this group from time to time.
>I imagine this discussion will be unintelligible to those who work at
>universities in countries with a healthy secondary-school system.
>(Read: anywhere but the US.)
>Colleagues:
>I have recently been asked by faculty and administrators throughout
>my university to comment on the low success rates in lower-division
>mathematics courses.
>We have in place a university-wide mathematics requirement which can
>be achieved by passing a moderately meaty "quantitative literacy"
>course, or by obtaining a C or higher in one of a few elementary
>courses (usually Trig, Finite Math, Business Calculus, or Calculus I).
>Unfortunately, only about 60% of the students taking these courses
>get the grade they need on the first try.
>Checking around at a few similar schools, I find that these numbers
>are unremarkable; on the other hand, a few schools do claim a higher
>success rate in these courses, at least with some populations.
>Typically we place the problem in the students' lap -- poor prior
>preparation or poor work habits -- but that response wears thin in the
>face of demands to Do Something. And indeed, I note that we have already
>set fairly restrictive entrance requirements for the courses, and
>we already exhort the students to work hard. So it is time to look
>at other options.
Your entrance requirements may LOOK restrictive. I do not
believe you have any idea of how little mathematics, other
than routine calculation, has even been presented to the
students in their K-12 "education". Most of the high school
courses labeled "algebra" spend little time on the general
problem of formulating word problems, but almost all on the
drill of routine manipulation. Most of the courses labeled
"geometry" are little more than memorizing figures and
formulas, and the practice of studying for tests and
forgetting the next day is not learned in the universities.
You cannot even tell them that variables are pronouns,
because most of them do not understand pronouns. They
see mathematics solely as memorizing formulas to be
forgotten after the course, and "plug and chug".
What is needed is understanding. Mathematical literacy,
being able to read and write the equivalent of declarative
sentences, not to solve complicated problems, requires
being able to use symbols, to translate, and to know at
least intuitively what is a valid argument. Notice that
I have not included calculation or the production of
proofs in this; one can understand without being able to
carry out performances.
Even those courses which do a fair amount of word problems
make it rather difficult by starting out with the idea of
using one, or at most few, variables. This, together with
asking for solutions rather than formulations, confuses
the issue completely.
I suggest you consider remediation of this type, and
also test to see if they can handle mathematical ideas,
not manipulations. Multiple choice questions will not
find this out, especially under time pressure.
>I have, I think, the support of my administration to try something
>novel, even if takes some money (not too much of course!). I am
>embarassed to respond to them that really I don't know what can be
>done. I've seen the reform texts, the hi-tech teaching aids, new
>scheduling plans, and so on -- as far as I can see, these don't seem
>to promise any real improvement.
These do not. Teaching manipulation does not produce
understanding, and may even make it harder to learn. You
should consider that your students may even have been
handicapped by their pre-college manipulatory courses.
As far as I know, this has not been tried. Mathematicians
are people who have managed at least use understanding in
spite of the way they have been taught. The material I
am suggesting belongs in elementary school, but it will
not be taught there, as the teachers would have to learn
it as a new subject. It is language, including some of
the language of logic.
>So now I'm shopping around for ideas. What new approaches have you
>used which had a clear effect on student outcomes?
--
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, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Herman Rubin
Dave Rusin <ru...@vesuvius.math.niu.edu> wrote:
>In article <755.156T2510T...@mistral.co.uk>,
>>>We have in place a university-wide mathematics requirement which can
>>>be achieved by passing a moderately meaty "quantitative literacy"
>>>course, or by obtaining a C or higher in one of a few elementary
>>>courses (usually Trig, Finite Math, Business Calculus, or Calculus I).
>>May I ask why?
>Do you mean, why require a math course at all?
>The core competency requirements (math, English, and "communications") are
>in place because these (1) reinforce skills necessary to survive other
>college courses, and (2) impart some of the perspectives considered
>essential for an educated citizenry. For (1), imagine students
>trying to find science and social science classes which meet general
>education requirements but require no skills with numbers,
This is overrated. It is important to know what it means
to compute, but hand computation is not that important.
They SHOULD be able to handle rational numbers, however;
there are few calculators or computer languages which do so.
logical reasoning,
Again, they need to know what a proof it, but not necessarily
to be able to produce them.
>or problem solving!
Problem solving has TWO parts; the first, and most important,
is problem FORMULATING. This is poorly taught, and not
emphasized. The engineer needs to be able to formulate the
differential equations, without consideration of whether he
can solve those. This should be taught without limitation
on the number of variables.
We do not teach the conceptual part of anything until far
too late in the curriculum. Knowing how to calculate is
not of much importance, if any, in understanding. The
linear algebra course was supposedly put in as a step
toward understanding algebra; it has become an obstacle
instead. Unlearning is painful at best.
For (2), consider the loss to society when "college
>educated" voters don't know the difference between a million dollars and
>billion dollars, or between causality and coincidence.
Nor can they distinguish between reasoning and wishful
thinking, nor can they even consider the manifold
consequences of actions.
>Arguably, all students ought to take a fairly robust "mathematics for life"
>course, but that's a little silly for future psychologists or engineers
>who already have to work through comparatively more challenging courses.
>On the assumption that a decent trigonometry class already involves a bit
>of communicating with mathematics and so on, we grant dispensation from the
>mathematics core course if the students get a C or better there.
What is TESTED in our courses? Memorization and routine
computation! Someone can learn the concepts in a trigonometry
course, and set up a problem covering a new situation, without
being able to calculate anything by hand, with tables or with
canned programs. Someone can memorize the definitions and
formulas, compute rapidly, and have no idea of what it means.
We are testing the latter; we are teaching the latter; and
the former does not get learned.
Statistics has been called the religion of medicine. It is
also the religion of education and psychology, and is badly
misused. Students come to learn statistics, without the
mathematical background, and want to learn it in one term.
Now one can have them memorize definitions and methods, but
are they any closer to understanding what they are doing?
Very definitely not. They need about three other courses
before learning about statistical methods, just as the students
having problems need courses in mathematical concepts before
getting into more computation.
Herman Rubin
Bob Silverman <bo...@my-deja.com> wrote:
>In article <755.156T2510T...@mistral.co.uk>,
> "Adam Atkinson" <gh...@mistral.co.uk> wrote:
>> On 01-May-00 18:03:59, Dave Rusin said:
>> >We have in place a university-wide mathematics requirement which can
>> >be achieved by passing a moderately meaty "quantitative literacy"
>> >course, or by obtaining a C or higher in one of a few elementary
>> >courses (usually Trig, Finite Math, Business Calculus, or Calculus
>I).
>> May I ask why?
>> You can't be too surprised if people don't do well in things they're
>> forced to do against their will.
>Then why are they in school??
>A University has breadth requirements. This requires studying subjects
>outside of one's major.
>If they don't like this, then that is just too bad. They knew what
>the University's requirements were before they entered.
They did not know what these meant. They are only exposed
to courses adjusted to the level of those in the classroom,
no matter how low that is.
>> If I were forced to attend lessons in a language I had no interest in
>> learning, or a business studies course, I might very well do extremely
>> badly beause I Just Didn't Want To Be There.
>Then leave. But don't expect to be granted a degree.
>Reading, Writing, and Arithmetic. If one can't master these at a basic
>level, or if one has no interest in doing so, then one does not DESERVE
>a bachelor's degree.
The problem started when the educationists decided that
EVERYONE should get a high school education, and not only
that, they should be getting the same education at any
given age as everyone else of that age group. This
started more than 60 years ago; while a few of the early
excesses have been corrected, this philosophy has not.
So the teachers, who understand NO mathematical concepts,
are teaching only mechanics to the children, and are
also dumbing down their courses so that all can pass.
This continues into the high schools. Our President
has proposed than anyone who gets a B average in high
school be guaranteed at least two years of college; now
what is the result of this? In elementary school and
high school, if a teacher maintains standards, that
teacher may well be fired for that. We have this also
in the universities, where student evaluations are used
for tenure decisions.
jonathan miller
> Very different. There's no way you'd get a course in a UK university that
> tells people how to add fractions (as does the Basic Mathematics course
> here) etc..
Does this get college credit now? Although 25 years ago, it got approx. 1/2 credit
(i.e. 5 contact hours per week for 2-3 credits) at a large public midwestern
university. Applies only to credit requirements, not to math (and nothing below
"college algebra" counted toward degree requirements, although sometimes that
did). Have things changed?
Jon Miller
Jeremy Boden
<gh...@mistral.co.uk> writes
>On 03-May-00 05:51:28, Richard Carr said:
>
>>:I've had some exposure to the "high school" scenes in the UK, US and
>>:Italy. I get the impression that many of the problems are really quite
>>:similar, although they get moved around a bit. In particular, Italy
>
>>tells people how to add fractions (as does the Basic Mathematics course
>>here) etc..
>
>division) disappeared from UK state schools about 10 years ago. They
>were "Just Too Hard", "Ruined Lives", etc. I don't know if they've made a
>reappearance since then.
It would seem so.
My son (age 10) has learnt the basics of these procedures (in Junior
school).
--
Jeremy Boden
ame...@my-deja.com
"Adam Atkinson" <gh...@mistral.co.uk> wrote:
> My impression is that based on what I saw at junior and secondary
> schools during the course, a fair number of 16 year olds learn less
> than no maths in 5 years of secondary education.
I think the problem largely starts at the top. In high school, you
have high ranking administrators (and some math teachers) telling
students it's ok to take geometry before algebra. Then they wonder why
so many students flunk geometry. Another thing I see is that they are
starting to expand courses (i.
e. algebra 1A and 1B in two years). I wouldn't be suprised if they
have geometry 1A & 1B and algebra 2A & 2B. The next thing you know,
we'll see algebra 1A, 1B, 1C, 1D completed after 4 years in high
school. Well I guess it's better than nothing.
Adam Atkinson
>>Actually, adding fractions (along with long multiplication and
>>division) disappeared from UK state schools about 10 years ago. They
>>were "Just Too Hard", "Ruined Lives", etc. I don't know if they've made a
>>reappearance since then.
>It would seem so.
>My son (age 10) has learnt the basics of these procedures (in Junior
>school).
Actually, my "learning less than nothing in 5 years" observation was
based on the difference between final year juniors and final year
(bottom set) secondary school students. The juniors were doing
drawings and then scaling them by various factors, including negative
fractional ones. But the bottom set fifth year secondary students
didn't appear to have every done anything with fractions at all in
their whole lives.
--
Adam Atkinson (gh...@mistral.co.uk)
ZOOGE
Herman Rubin
Jeremy Boden <jer...@jboden.demon.co.uk> wrote:
>In article <1072.158T1650...@mistral.co.uk>, Adam Atkinson
><gh...@mistral.co.uk> writes
>>On 03-May-00 05:51:28, Richard Carr said:
...................
>>Actually, adding fractions (along with long multiplication and
>>division) disappeared from UK state schools about 10 years ago. They
>>were "Just Too Hard", "Ruined Lives", etc. I don't know if they've made a
>>reappearance since then.
>It would seem so.
>My son (age 10) has learnt the basics of these procedures (in Junior
>school).
If the concepts had even been poorly taught, developing speed
in these might take time, but learning what it MEANS would not
take much time. As currently taught, it is the mechanics which
is drilled, with no understanding.
Jeremy Boden
<hru...@odds.stat.purdue.edu> writes
>In article <tSK+YDAK...@jboden.demon.co.uk>,
>Jeremy Boden <jer...@jboden.demon.co.uk> wrote:
>>In article <1072.158T1650...@mistral.co.uk>, Adam Atkinson
>><gh...@mistral.co.uk> writes
>>>On 03-May-00 05:51:28, Richard Carr said:
>
> ...................
>
>>>Actually, adding fractions (along with long multiplication and
>>>division) disappeared from UK state schools about 10 years ago. They
>>>were "Just Too Hard", "Ruined Lives", etc. I don't know if they've made a
>>>reappearance since then.
>
>>It would seem so.
>>My son (age 10) has learnt the basics of these procedures (in Junior
>>school).
>
>If the concepts had even been poorly taught, developing speed
>in these might take time, but learning what it MEANS would not
>take much time. As currently taught, it is the mechanics which
>is drilled, with no understanding.
For such basic operations you need to be able to do the mechanics first;
understanding comes later. If I am unable to add 2 fractions together
then I am unlikely to understand much about irrationals, for example.
Isn't this one of those areas where appreciation occurs at a number of
levels, so it is better if a child is gradually introduced to these
ideas.
Actually, a full understanding of addition surely requires a course in
logic and a study of computability...
--
Jeremy Boden
ame...@my-deja.com
ull...@math.okstate.edu wrote:
> If you want to decide to pass them all whether they
> know the material or not that would be Something you could Do.
> But presumably you've thought of that and rejected it for some
> reason. Short of that I doubt there's much you _can_ Do. The
> problem is the students simply don't believe they actually
> have to know this stuff - the idea of actually working on
> it for several hours every day is just totally foreign to them.
Good point, but most students don't have that kind of time.
Instructors and students rarely do something unless they are forced
to. You probably publish simply because you have to. Suppose you were
working at a small liberal arts college or a community college. Would
you still study mathematics outside of what you teach?
ull...@math.okstate.edu
[Actually he wrote this 5 days ago - he doesn't know
what the heck is eating his newsgroup posts lately...]
> > If you want to decide to pass them all whether they
> > know the material or not that would be Something you could Do.
> > But presumably you've thought of that and rejected it for some
> > reason. Short of that I doubt there's much you _can_ Do. The
> > problem is the students simply don't believe they actually
> > have to know this stuff - the idea of actually working on
> > it for several hours every day is just totally foreign to them.
>
> Good point, but most students don't have that kind of time.
Heh-heh. Must be that years ago there was more time in
the day. (Please don't bother explaining that kids today are
busier than they used to be - I understand that there was more
time in the day before MTV and WWW.)
> Instructors and students rarely do something unless they are forced
> to.
Um, right. But that's a restatement of the problem, says
nothing about the solution.
> You probably publish simply because you have to. Suppose you
were
> working at a small liberal arts college or a community college. Would
> you still study mathematics outside of what you teach?
Tee-hee. You're a few clues short here...
Herman Rubin
...................
You would find that few of the teachers of mathematics
understand the integers, let alone the rationals. It does
not take any facility with base 10 manipulation to acquire
understanding.
Also, there is a major difference between being able to
do the operation at all, possibly using a very slow method,
and using a memorized method which enables it to be done
quickly.
>Actually, a full understanding of addition surely requires a course in
>logic and a study of computability...
In one sense, a full understanding is not known to anyone,
especially when both addition and multiplication are used.
However, the Peano Postulate approach uses only concepts
at a very elementary level, and is understandable by small
children. It seems to get harder with the more manipulation
which has been learned.
It is not only here that this happens; I doubt that there
are many who can understand limits and derivatives after
being taught essentially how to calculate derivatives who
would not have understood it before; the results indicate
that the other direction is harder. The same holds for
abstract algebra; teach it as abstract, and then put in
the specialization to linear algebra.
Statistics is even more extreme; it is hard for someone
taught the classical religion to be able to consider the
problem of decision making under uncertainty.
Lynn Killingbeck
>
> In article <8f42rt$ik1$1...@nnrp1.deja.com>,
> ame...@my-deja.com wrote:
> > In article <390f1172.9724793@news>,
> > ull...@math.okstate.edu wrote:
>
> [Actually he wrote this 5 days ago - he doesn't know
> what the heck is eating his newsgroup posts lately...]
>
Only about the slow newsgroup posts, folks!
I ran into a delay of several days with posts in another newgroup. Turns
out the articles were being cross-posted to a moderated newsgroup, too.
Apparently the moderator only released stuff every few days. Meanwhile,
the articles don't show up on _any_ newsgroup until the moderator "Does
His Thing" to release them. Not all the moderated groups end with *.m.
So, if articles are being cross-posted, this might explain several days
delay in showing up, even in the unmoderated groups.
Lynn Killingbeck
Erik Max Francis
> I ran into a delay of several days with posts in another newgroup.
> Turns
> out the articles were being cross-posted to a moderated newsgroup,
> too.
Delays can occur due to down machines, misconfigured newsservers, etc.
Delays are an unfortunate but expected part of contriubting to Usenet.
--
\ Erik Max Francis / m...@alcyone.com / http://www.alcyone.com/max/
\ San Jose, CA, US / 37 20 N 121 53 W / ICQ16063900 / &tSftDotIotE
\ / Kepler's laws / http://www.alcyone.com/max/physics/kepler/
/ \ A proof of Kepler's laws.
/ Men live by forgetting -- women live on memories.
/ T.S. Eliot
ull...@math.okstate.edu
kill...@pointecom.net wrote:
> ull...@math.okstate.edu wrote:
> >
> > In article <8f42rt$ik1$1...@nnrp1.deja.com>,
> > ame...@my-deja.com wrote:
> > > In article <390f1172.9724793@news>,
> > > ull...@math.okstate.edu wrote:
> >
> > [Actually he wrote this 5 days ago - he doesn't know
> > what the heck is eating his newsgroup posts lately...]
> >
> >(snip)
>
> Only about the slow newsgroup posts, folks!
>
Turns
> out the articles were being cross-posted to a moderated newsgroup,
too.
Good point, and yes, I certain possess sufficient density
to cross-post a reply without realizing it, done so many times.
But that's not what the problem is (was?) here.
>
> Lynn Killingbeck
ull...@math.okstate.edu
Erik Max Francis <m...@alcyone.com> wrote:
> Lynn Killingbeck wrote:
>
> > I ran into a delay of several days with posts in another newgroup.
> > Turns
> > out the articles were being cross-posted to a moderated newsgroup,
> > too.
>
> Delays are an unfortunate but expected part of contriubting to Usenet.
Indeed. What's irritating here is I had no idea that things
were not appearing, since they appeared just fine on the local
server - Friday someone asked me why I hadn't had anything to
say in while.
Seems like a large number of posts from me have appeared
today, which is curious since today the local server is actually
down. Probably sent out my stuff with its dying breath.
Seriously, how does Usenet work anyway? Trying to figure
out what the problem was(is?): Does the local server broadcast
the fact that it has new news (in which case the problem could
be just upstream) or does the local server wait for other
servers to request new news (in which case the problem must
have been here, there is no concept of "juist upstream")?
> --
> \ Erik Max Francis / m...@alcyone.com / http://www.alcyone.com/max/
> \ San Jose, CA, US / 37 20 N 121 53 W / ICQ16063900 / &tSftDotIotE
> \ / Kepler's laws / http://www.alcyone.com/max/physics/kepler/
> / \ A proof of Kepler's laws.
> / Men live by forgetting -- women live on memories.
> / T.S. Eliot
>
Erik Max Francis
> Seems like a large number of posts from me have appeared
> today, which is curious since today the local server is actually
> down. Probably sent out my stuff with its dying breath.
Sounds like the primary feeds came back online and then the server went
down for other reasons. If the server is configured properly, when the
feeds restore themselves your posted articles will be sent out
essentially all at once, but then some servers aren't configured very
well.
> Seriously, how does Usenet work anyway? Trying to figure
> out what the problem was(is?): Does the local server broadcast
> the fact that it has new news (in which case the problem could
> be just upstream) or does the local server wait for other
> servers to request new news (in which case the problem must
> have been here, there is no concept of "juist upstream")?
Usenet is a asynchronous network; each server gets or sends a feed to a
set of other servers, and the set of newsgroups that are exchanged for
each feed need not be the same (e.g., you can get an alt.* feed from one
peer, a rec.* and sci.* feed from another, and export your own ullrich.*
feed to three others).
Theoretically there is no primary server hub on which all news
originates, but there are quite a few de facto hubs (i.e., major servers
which have a good deal of bandwidth devoted to Usenet traffic that many
other servers directly or indirectly rely upon). Competent news admins
try to secure many feeds from a variety of sources, but even then a few
hubs going down or having queueing problems can throw a wrench into the
whole process -- for instance, it's not all that helpful to have two
feeds from servers A and B (intended for redundancy) if both higher up
the chain rely on the same server C for their primary newsfeed.
Occasionally goofs certainly can cause delays of a day or more in news
delvery, but by the nature of having a network of servers, things return
to normal operation rapidly enough.
--
Erik Max Francis / m...@alcyone.com / http://www.alcyone.com/max/
__ San Jose, CA, US / 37 20 N 121 53 W / ICQ16063900 / &tSftDotIotE
/ \ No man who needs a monument ever ought to have one.
\__/ Nathaniel Hawthorne
Physics reference / http://www.alcyone.com/max/reference/physics/
A physics reference.
Alberto
ame...@my-deja.com wrote:
> Good point, but most students don't have that kind of time.
I thought students were at college to learn ?
> Instructors and students rarely do something unless they are forced
> to. You probably publish simply because you have to.
I don't see students at that light. My students seem to be genuinely
interested in learning something useful, and are bent in making those three
or four semesters they take to get their master degree as profitable as
they can get, because they seem to realize that, like a good springboard,
the initial distance they'll cover in professional life will depend on it.
> Suppose you were
> working at a small liberal arts college or a community college. Would
> you still study mathematics outside of what you teach?
I do teach at a small liberal arts college, and yes, I still study a lot of
math outside of what I teach. Doing things because one's forced isn't as I
see it, a very good idea: the day this happens to me, I'll switch into
doing something more in line with what I want to do.
Alberto.
Alberto
"David C. Ullrich" wrote:
> I just read this article in an old Notices about the
> guy observing a math class in Taiwan. The students were paying
> attention, when the bell rang they waited for him to finish what
> he was saying before thanking him and walking out... Sounds like
> a bunch of Asian zombies. But no, during recess they were running
> around screaming just like regular kids, they just had these
> strange notions about how to behave in class.
You know, the strong majority of my classes is made up by Chinese people. And
they're far from being zombies. But they do know the difference between work
and fun, if you see what I mean. I have learned a whole lot from my Chinese
students, as far as what's the difference between being serious and being an
automaton, or about having fun and being irresponsible. Stereotyping is a
terrible thing!
Alberto.
ull...@math.okstate.edu
Yes, stereotyping is a terrible thing. I'm not sure whether
you saying I'm guilty of this terrible thing - if that _is_ your
point I don't see how you get that from what I wrote.
In any case it was certainly not my intention, far from it.
> Alberto.
ame...@my-deja.com
Alberto <junk...@moreira.mv.com> wrote:
>
>
> ame...@my-deja.com wrote:
>
> > Good point, but most students don't have that kind of time.
>
> I thought students were at college to learn ?
They are, but my point was that they also have other subjects not to
mention that they also waste a lot of time being jackasses.
>
> > Instructors and students rarely do something unless they are forced
> > to. You probably publish simply because you have to.
>
> I don't see students at that light.
So would you say that most of your students spend hours studying math
every day?
> My students seem to be genuinely
> interested in learning something useful, and are bent in making those
> three
> or four semesters they take to get their master degree as profitable
> as
> they can get,
I thought that we were talking about undergraduates.
> > Suppose you were
> > working at a small liberal arts college or a community college.
> > Would
> > you still study mathematics outside of what you teach?
>
> I do teach at a small liberal arts college, and yes, I still study a
> lot of
> math outside of what I teach.
Good for you.
> Doing things because one's forced isn't
> as I
> see it, a very good idea: the day this happens to me, I'll switch into
> doing something more in line with what I want to do.
Very few people work at jobs without being forced to do something in it
which they aren't particularly interested in. Most people with degrees
in mathematics like math, but many math majors go into other fields not
because they particularly like them, but because they are compelled to
choose something which pays more money.
Herman Rubin
>In article <391AB6C3...@moreira.mv.com>,
> Alberto <junk...@moreira.mv.com> wrote:
>> ame...@my-deja.com wrote:
>> > Good point, but most students don't have that kind of time.
>> I thought students were at college to learn ?
>They are, but my point was that they also have other subjects not to
>mention that they also waste a lot of time being jackasses.
Most are not; they are there to get degrees, and getting
grades and credits is part of the process. Why else would
students take courses which they essentially know, and why
would they deliberately take courses with massive overlap
rather than trying to get the most content?
ame...@my-deja.com
hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
>
> Most are not; they are there to get degrees, and getting
> grades and credits is part of the process. Why else would
> students take courses which they essentially know, and why
> would they deliberately take courses with massive overlap
> rather than trying to get the most content?
Most undergrads could care less about the content of the course, it's
just bull crap to them. It's all about getting good grades so they can
look good to employers (as if that matters). This is why the attrition
rate is very high for the upper level courses which require a lot
thought.
Alberto
ame...@my-deja.com wrote:
> I thought that we were talking about undergraduates.
My college routinely puts undergrads in M.Sc. classes. And it's more or less
the same thing, a senior undergrad is in his or her last leg before facing
the world, and they know it.
> Very few people work at jobs without being forced to do something in it
> which they aren't particularly interested in. Most people with degrees
> in mathematics like math, but many math majors go into other fields not
> because they particularly like them, but because they are compelled to
> choose something which pays more money.
I believe that if I'm good enough at something, the money will come.
Alberto.
ame...@my-deja.com
Alberto <junk...@moreira.mv.com> wrote:
> I believe that if I'm good enough at something, the money will come.
This is always a dangerous assumption. Being good at something
(especially at math) has little or nothing to do with how much money
you earn.
Anonymous
> I just read this article in an old Notices about the
> guy observing a math class in Taiwan. The students were paying
> attention, when the bell rang they waited for him to finish what
> he was saying before thanking him and walking out... Sounds like
> a bunch of Asian zombies. But no, during recess they were running
> around screaming just like regular kids, they just had these
> strange notions about how to behave in class.
A strange notion called "respect"...
Jim Nastos
For a similar story of how students in different countries behave in a
classroom, read Richard Feynman's first autobiography (I think it's the
first) when he tells the story of him having gone to a country in South
America - I believe Brazil - to teach physics, and he points out some
clear distinctions between North American classroom VS other classrooms.
When I took a course in linear algebra back in my earlier university
years, I had a professor V. Platanov who had taught in many countries in
Europe, Russia, and North America, and he feels that students here in
North America have a bigger sense of freedom in the classroom and they
feel they have a justified right in asking questions during lectures and
stuff. His reason is because here, students pay (a lot) of money for their
education. In most other countries abroad, the government provides the
education, so it is easy to see where discipline and respect comes from in
those cases.
Feynman pointed out (the autobiography is called "Surely, You're Joking,
Mr. Feynman!") that students choose not to ask questions in the lecture,
because the remainder of the students feel that the asking student is
wasting their (lecture) time.
Jim