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[P]
"Rotten teaching has made me lose most of my interest in math."

By Giant Space Hamster in MLP
Wed Mar 21, 2001 at 05:26:49 AM EST
Tags: You Know... (all tags)
You Know...

The title is a quote from a work report by Richard Hoshino, an undergraduate math student at the University of Waterloo. Last summer, Richard convinced professors in the math faculty to let him teach an undergraduate course, C&O 380: Mathematical Discovery and Invention. His work report details his goals, experiences, and results.


Richard's experience is interesting because he went into this course firmly believing that lectures are the wrong way to teach math. Rather than simply demonstrating proofs to the class, he had them work them out for themselves. In fact, Richard refers to himself not as a lecturer, but rather a tour guide.

Of course, Richard's experience has relevance in more areas than math. The lecture style of teaching is prevalent in most post-secondary education. Is there a better way to teach?

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How would you like to learn?
o Lectures 10%
o "Tours" 20%
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"Rotten teaching has made me lose most of my interest in math." | 30 comments (30 topical, editorial, 0 hidden)
So very true!!!! (2.50 / 2) (#1)
by anthrem on Tue Mar 20, 2001 at 10:40:46 PM EST

I can understand why this article was written. In the first line, I could instantly relate to the author's feelings about math teaching. After having teachers that got Ds in math in college teaching me math in junior high, and being taught geometry in high school by a genuine psychopath, I lost all of my interest. But really, it goes back to those damn color the balloons worksheets in grade school. If I had been paying attention 20 years ago when the teacher explained how to do those worksheets, I might have been a math whiz, or at least a math lover. Now, I avoid balancing my checkbook. <sigh>

However, I did have some good math teachers. They were simply few and far between. It comes down to paying teachers as they ought to be paid, instead of the mere pittance they receive on the average now



Disclaimer: I am a Buddhist. I am a Social Worker. Filter all written above throught that.
Professors ain't FaiB (Free, as in Beer) (3.50 / 2) (#2)
by Ludwig on Tue Mar 20, 2001 at 10:41:45 PM EST

I'm under the impression that Mr. Hoshino's discovery is pretty much common knowledge, arrogant and aloof lecturers notwithstanding: seminar-based learning has definite advantages over lectures, in mathematics or any other subject. If a professor doesn't even deign to take questions, why not just read a textbook? However, Hoshino neglects to take into account that seminars are far more resource-intensive. The high school course he taught had sixty students (and they were probably divided into two or three different classes rather than all being in one room at the same time.) It's not feasible to apply that teaching model to a 500 seat auditorium full of students.

The college I went to had no lectures at all; it was all seminars and independent studies. It was no coincidence that the school held the dubious honor of being the most expensive in the country.

Uhh...not high school... (none / 0) (#3)
by Giant Space Hamster on Tue Mar 20, 2001 at 10:45:52 PM EST

Third year university course. That's why it's interesting.

-------------------------------------------
The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts.
-- Bertrand Russell
[ Parent ]
my bad (none / 0) (#7)
by Ludwig on Tue Mar 20, 2001 at 11:11:41 PM EST

Must've been reading too fast. I thought he was teaching an undergraduate-level class to advanced high schoolers.

Doesn't really affect the point I was making, though.

[ Parent ]

Hampshire? (3.00 / 1) (#11)
by fuzzrock on Wed Mar 21, 2001 at 12:06:43 AM EST

Hey, a fellow Hampshire grad? Always nice to see others around! If you went to one of the other two most expensive, I have to apologize - the actual title switches around every couple of years.

Just to add something on-topic, it is important to note that while Hampshire (a college with few to no lecture classes) is one of the more expensive tuitions in the world, it also has a nearly-nonexistent endowment. Most schools have FAR more income, and could certainly afford to pay more professors to lead seminars instead of lecture. The reasons they don't have more to do with Tradition and inertia than money concerns. (caps intentional, for sarcasm)

[ Parent ]

Of Course (4.00 / 1) (#4)
by Osiris on Tue Mar 20, 2001 at 10:51:25 PM EST

Of course there are better ways to teach than just lecturing. Thing is, professors tend to not be good teachers, nor do they want to be.

For many professors, teaching an undergrad class is a necessary evil. They have no training in it, except the classes they TAed for when they were grad students maybe. They have to do it, so they can work with grad students, and do their own research. This attitude carries into the way they teach. If you stand in front of the class three hours a week, and then refer the reinforcement/questions to your TAs, you don't actually have to deal with the nasty little undergrads. You get the same attitude from the university administration, too: undergrads are an obnoxious obligation to us, who exist mainly to pay tuition so that we can pay for research.

Are all professors like this? Of course not. But you get this type especially in the lower echelon of classes, the "survey" or introductory topics that tons of people have to take. To be fair, a lot of the undergrads want to be in that class even less than the professor, but that's no excuse. Upper level classes aren't so bad, and you occasionally get a teacher who really likes the material he teaches, and it is a lot more fun to be in his class, and frankly you learn more. I try to take more classes from such profs.

So is there a better way to teach than just lecturing? Obviously. Do most professors want to do the extra work such a method would require? Hell no.



A few points... (5.00 / 1) (#5)
by scriptkiddie on Tue Mar 20, 2001 at 10:56:58 PM EST

  • There are doubtless much better ways to teach than are currently employed.
  • Some professors may be better at teaching a course seminar-style or teaching it lecture style. It's a combination of the teacher's personality and the nature of the subject.
  • None of this particularly matters in secondary education because the point of secondary education is not, and has never been, to expedite learning. In fact, I have argued that secondary education is as drawn-out as possible so that there aren't millions of 15-year-olds flooding into colleges.
  • In higher education, I doubt this will have the slightest bit of difference. College students are supposed to be able to figure things out on their own - if they need personal help, they should get it personally, rather than in class every day. Having a "tour guide" in college sounds more like a hinderance than a help to me. But that's just me.
  • There has been a ludicrously small amount of real study into how people actually learn. I mean, there are tons of experimental child psychologists, why can't they earn their keep by setting up 30 students with math teachers trained to teach in specific styles and test them all at the end of the year?
  • Lectures can be good. I'm in high school, and in my history class, there is basically no student-teacher interaction, and we have never had a class discussion. Yet the teacher has so much experience and is so good at discovering the important points in volumes of historical material that he really doesn't need his students' help. This teacher is the best I currently have, is the best any students who've I've asked have, and is officially recognized as the best teacher in our district (about 3,500 teachers).
  • Conversely, seminar classes can be absolutely terrible. I won't bore you with the details. However, I have never had a really stellar seminar class. I posit that this is because in seminar-style learning, much more of the direction for material studied in class is provided by the students, and students tend to average out to a fairly unflattering mean.

Hope that made sense, I'm half asleep and can hardly type....

Money talks... (5.00 / 2) (#6)
by _Quinn on Tue Mar 20, 2001 at 11:01:33 PM EST

   ... and it says to lecture. We need to pay teachers (and `primary care givers') in proportion to their import -- which is substantial -- and simultaneously reduce class size to make the methods known to work better than lecturing possible.

   (A personal aside: at my school, a post-doc doing research was asked to do a lecture, substituting for a professor who had to leave. The look of frustration on his face when he tried to involve the students, and they didn't respond, was simply amazing. I think many teachers want to do something more than just lecture, but inertia in the students, combined with the occasional real lack of understanding, make non-lecture courses difficult. It's strange, because only our non-humanities courses are normally taught as lectures, though they all have labs and/or recitations (== problem-solving sessions); the humanities courses are all discussion format.)

   I think a large part of the attraction of computer classrooms for many educators is the presumed ability to improve interaction -- along the lines of, `if a person isn't available, why don't we try substituting a computer?' (Phrased that way, the answer should be obvious. :))

   Sadly, any substantial change will be slow (about two decades), because the students taught in the new methods will need to grow up and become the professors teaching the new methods... the higher the education, the harder it is, (at least in the US) to enforce a teaching method/style and/or retrain the teachers (e.g. tentured faculty).

   Which brings up a truly cute point about America. Instead of deciding to improve our high schools (and primary eductation) to the point where they can produce the kind of workers the economy needs, the collective decision was to make the (potential) workers (or their parents, and usually via loans (sometimes funded by the taxpayers)), for the opportunity to become white-collar drones. It's really brilliant capitalism, but I fear it's not too hot for society; it wouldn't suprise me if America actually imported more researchers than produced domestically. (Ouch. Now /I/ sound like a capitalist!)

   (Insert tie-in to previous K5 story about the dearth of innovation here.)

-_Quinn
Reality Maintenance Group, Silver City Construction Co., Ltd.
I'm pro-lecture.... (4.00 / 1) (#8)
by daystar on Tue Mar 20, 2001 at 11:37:26 PM EST

After all, a lot of INFORMATION needs to get passed, and that's a pretty pure way to do it. Now, I had the same horrible (high school) math teachers as everyone else, and I agree that math is taught horribly, but I don't think the problem is in the lecture format. In my school it was just that the math teachers didn't like math that much. They mostly had degrees in biology or english, and were just marking time waiting for the old bio teacher to die (small town).

The best math teacher I ever had was in calc 1. Mr. Grant (mesa community college). He was a strict lecturer, and had a vicious homework ethic and he got his point across brilliantly. He was also someone with a degree in math (and one in history, which didn't hurt his story-telling skills. Lotta good stories in math history...) and he had the kind of love for the subject that a lot of geeks have. I will be grateful to him for a loooong time. Great guy. I can't rave enough about him.

--
There is no God, and I am his prophet.

Really? (none / 0) (#9)
by Giant Space Hamster on Tue Mar 20, 2001 at 11:42:12 PM EST

In a math course, is there really a lot of material to be passed on? For example, when studying for my Calculus III midterm, I realized that all the important information fit on a single sheet. The entire course had been taken up with the proofs for every theorem.

While proofs are important, I think proving for oneself is a far better way of learning them than lectures.

-------------------------------------------
The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts.
-- Bertrand Russell
[ Parent ]

how to teach math.. (2.00 / 1) (#10)
by rebelcool on Tue Mar 20, 2001 at 11:44:21 PM EST

i despised (and still do), math. And i'm a CS major. The main reason, it's never interested me in the slightest. Mostly because I learn best by relation..and this is true for the majority of people. Most of the examples given in math courses are either non-existant, or irrelevant.

And of course, once you get to the higher disciplines, many of the examples simply dont have real world equivalence.

It's one of those elite things, where unless you're very interested in it, it's difficult stuff to learn. Even if you're very good at related fields (such as CS).

COG. Build your own community. Free, easy, powerful. Demo site

Really good? (5.00 / 1) (#12)
by darthaya on Wed Mar 21, 2001 at 12:08:06 AM EST

You won't be "REALLY GOOD" in CS if you have no interests whatsoever in Mathematics, let's put it this way.

[ Parent ]
rather presumptious (none / 0) (#14)
by rebelcool on Wed Mar 21, 2001 at 12:18:52 AM EST

certainly, were I interested in cryptology, this would be true.

But i'm not.

Were I interested in statistical analysis of data and scientific programming.

But i'm not.

CS has branched to many fields now, and what I do is primarily networking. I love to write server software, clients, protocol design and the like. And indeed, this is what I do. Both in my free time and what I get paid to do. Coding server software itself, backend processing... and none of it, has ever, not once, required beyond basic algebra.

COG. Build your own community. Free, easy, powerful. Demo site
[ Parent ]

not CS (none / 0) (#18)
by jkominek on Wed Mar 21, 2001 at 11:02:26 AM EST

none of what you say you do is computer science. it is in the domain of software engineering and programming.

do you even make use of the data structures you were taught, or do you just abuse arrays into doing everything you need?
- jay kominek unix is all about covering up the fact that you can't type.
[ Parent ]

oh my (none / 0) (#19)
by rebelcool on Wed Mar 21, 2001 at 11:13:50 AM EST

of course i use the data structures. it would foolish not to.

The CS (data structure, design and what not) side of it all has been very beneficial to the work I do beyond that. Yet I still don't use any of the math i'm forced to chug, even in the CS classes.

The math isn't too valuable in my experience, except for the CS-related fields that are of course, math based. That's a kind of obvious answer, but it's true.

COG. Build your own community. Free, easy, powerful. Demo site
[ Parent ]

Sorry. I really can't resist. (none / 0) (#13)
by kwsNI on Wed Mar 21, 2001 at 12:09:10 AM EST

i despised (and still do), math. And i'm a CS major.

And you repeat yourself.

kwsNI
I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they'd never expect it. -Jack Handy
[ Parent ]

Hey, now... (4.50 / 2) (#17)
by fluffy grue on Wed Mar 21, 2001 at 04:55:38 AM EST

I love math. I took CS291 (Calculus III) my second semester just for the hell of it, because I wanted to. It was a fun class, even though the grad student who was teaching it was almost incomprehensible due to his heavy Chinese accent. I've always grokked math, and I see the relationship between math and CS very clearly. Then again, I'm also one of the (apparently few) computer scientists who can juggle between functional and imperative without a problem, and can see everything in both an abstract and low level. To me, the mathematics is the words composing the poetry of CS.

Granted, most CS majors can't grasp math at all, but those tend to be the ones who are getting a CS degree for the sake of getting a CS degree. Note to people everywhere: CS is about the science of computation, NOT about programming. Programming is a tool used to test theories in computer science; it is not the means to the end. That is NOT to say that purely-practical programmers are any lesser of people than computer scientists, just as how mechanical engineers and physicists both have their place in the world, but although they deal in the same sorts of things, they are not the same sorts of people. It is unfortunate that most universities have a computer science program but not a software engineering program, because most of the people in a CS major really should be in a software engineering major.

One of the profs in the CS department here, Frank Harary, recently celebrated his 80th birthday. He has been around longer than computers. He has been doing "computer science" since before there was such a thing; his research was in graph theory, which is very closely related to computation theory (ever heard of a finite automaton?) but is obscenely mathematical in its nature. I don't think he even has a computer in his office, nor does he need one. Yet he's a very distinguished professor in Computer science, even though it's highly unlikely he's ever even touched a compiler, much less written an actual piece of software.

Computer science helps the world of software engineering, just as chemistry helps the world of photography, but nobody would ever go up to a chemistry researcher and ask, "So, would you recommend Agfa or Kodachrome?" So why do people ask computer scientists how they'd write an accounting package?

</rant> (heh, past my bedtime)
--
"Is not a quine" is not a quine.
I have a master's degree in science!

[ Hug Your Trikuare ]
[ Parent ]

well said (none / 0) (#22)
by rebelcool on Wed Mar 21, 2001 at 12:45:06 PM EST

Computer Science here at UT is about programming mainly. Of course, there is alot of underlying theory and what not. It's not just about "learning the language" of course, but rather the programmatic concepts and structures which apply to every language, as well as good design.

I suppose you could consider the mathematical concepts behind computing belong more on the mathematics side than the actual computer hardware/software side, since programming has little to do with math, unless you're writing equations into your code, which isn't what this is about.

The comparison between physicists and mechanical engineers is an excellent one. The physicists develop the fundamental pieces to which stuff works, and the ME's put it to practical use.

COG. Build your own community. Free, easy, powerful. Demo site
[ Parent ]

That's not quite true either (none / 0) (#26)
by fluffy grue on Wed Mar 21, 2001 at 01:55:54 PM EST

Mathematics and the fundamental low-level algorithmic bits of CS are actually quite different. Like, I've rarely needed calculus in any algorithmic stuff (certainly never calculus III), and even then that was for pretty specialized things, such as complexity proofs and various things in graphics. However, a lot of the specific CS-specific stuff is similar to mathematics - axiomatic proofs have nothing to do with "real" mathematics, but they're very mathematical in nature; lambda calculus has nothing whatsoever to do with real math, but writing and "executing" a lambda calculus program both involve very algebraic things (but not algebra).

CS isn't just an offshoot of math, and it's not just math rearranged. It's just that a lot of the theoretical concepts are very similar to a lot of the concepts in math, and math can be used in order to solve a lot of the single problems. But CS being similar to math doesn't mean that a "good CS-mindset program" is just a string of equations, one after another, because that's not CS either, that's scientific computation - computation for other forms of science, not the science of computation.
--
"Is not a quine" is not a quine.
I have a master's degree in science!

[ Hug Your Trikuare ]
[ Parent ]

I'm a student at UWaterloo... (4.00 / 1) (#15)
by HoserHead on Wed Mar 21, 2001 at 12:45:39 AM EST

...and Richard, in some respects, is dead-on. I'm only in my second term but I already know exactly how bad teachers can be. I've got a CS prof who couldn't teach her way out of a bag - but in person she's a lovely, very intelligent person.

But I also know how good teachers can be. UW this year is performing a sort of experiment: I am one of 45 students taking a modified Calculus 2 course, with a heavy emphasis on the development of calculus and applications of it to real physical problems. Instead of learning things which seem to come right out of left field, we learn how Taylor took Newton's interpolating polynomial, and extended it to create the Taylor polynomial. We learn that MacLaurin did the same thing, around the same time, using a completely different method. And then, we try to increase the accuracy of this polynomial - we take it to the limit - and poof! out comes the Taylor Series for sine, or the exponential.

This class has truly been an eye-opener for me. Calc 1 was fun, but that was because I had a really irreverant, funny grad student as a teacher. Calc 2 has ignited the true passion for math I know is in there - and I'm a CS student. It's made me want to take a minor in applied math. Why?

I can only attribute it to my professor, Dr. G. Tenti. He's enthusiastic, he truly knows what he's doing -- and he knows how to teach. He said to us on the first day of the course 'I'm not going to give you my e-mail address or phone extension. I don't like those things, they tend to make things impersonal. If I can't look into your eyes, I can't see if you actually understand.' I'd take another course taught by Dr. Tenti in an instant.

Now, as for my CS professor? Well, I try to defend her, because I like her as a person. People have a tendency to ridicule her because she's just not at home in front of a crowd teaching. She's at home researching - which, not so incidentally, is why she's a member of the faculty.

The simple fact is that professors, in this day and age, are there to do research, and they have to teach, because it's part of their duties. And really, (there has been a lot of complaining -- particularly in those taking a BMath here at UW), there's nothing that can be done about it. Good researchers are not necessarily good teachers. There are those like Dr. Tenti who are, but then there are those like my CS professor, who simply can't teach. And that's unfortunate - undergrads in particular find themselves learning more out of a textbook than in lectures.

I don't know - but is there any way of motivating professors to learn to teach more? Any way to get universities to encourage better teachers?

creating better teachers (none / 0) (#28)
by eudas on Thu Mar 22, 2001 at 01:11:26 AM EST

when you hire those professors to come over and do research at your university, and then turn around and require them to teach,:

step 1:
TEACH THEM ENGLISH. not just passable 'can understand a 5-minute conversation if you listen really carefully, pay close attention, and have them repeat things a few times' english, but real true english. make them take 1-2 years of the university's remedial english classes or something. you're really not doing anybody any good if they can't be understood.

step 2:
if you're going to require them to teach, TEACH THEM HOW TO TEACH. again, make them spend some time in whatever you've got that can help them with this. Education department maybe? Show them how to be teachers. That's not what they're there for, you say? THEN WHY ARE YOU REQUIRING THEM TO TEACH UNDERGRADS? If they're brilliant researchers but the worst teachers in the world, you're just crippling the next generation, including the next generation of potential researchers.

those are my two major bitches. UT has a bad habit of hiring professors who are, i'm sure, brilliant in their field, but who have the worst accents and/or have no clue how to teach a class. When your undergrads rely more on the TA's than the professor for learning (and the TA's are grad students paying to go to the university too), then there's a real problem.

eudas
"We're placing this wood in your ass for the good of the world" -- mrgoat
[ Parent ]
Cheers to Waterloo (5.00 / 1) (#16)
by yuri on Wed Mar 21, 2001 at 01:00:51 AM EST

As someone who has experienced Wednesday nights at the Bomber and poor lectures by faculty at Waterloo, Math 115 (shite) and 116 (great) circa 1985/6 I can relate to this story and the work term report by Richard.

Obviously Richard must be one of the best undergrads at Waterloo or the faculty would not have let him teach an advanced course for his work term otherwise. I applaud Richard's attitude and approach to teaching as he sounds like someone who could truly inspire his students and has some great ideas for interactive teaching.

The problem is that math faculty (or any science/technical faculty at research focussed universities) are not hired for their ability as teachers. This is irrelevant, they are hired for their research ideas and they are promoted for their research ideas.

Of course many undergrads suffer because of this, but Richard is not among them. At major research universities, students like Richard can learn on their own and may get the opportunity to teach advanced courses (pretty rare) or more commonly get research experiences in industry or at the university that are hard to come by any other route. These types of experience are worth far more than any course you will ever take. For the best students, the sacrifice in quality instruction is more than made up for in experience/opportunity at research universities. For the vast majority of students, a private/undergraduate education-focussed university would be a better choice provided you can afford them.

Richard's idealism with teaching is admirable but somewhat naive. Suppose he was required to teach a course he was not interested in teaching (or didn't know a lot about the subject?), would he be so excited about the course? Would his course be the greatest thing since sliced bread? Probably not. This situation happens all the time to faculty members at universities everywhere. Is it a shame? you bet ya! What can we do about it?....

How about a system where we have research profs (who just do research) and teaching profs (who primarily teach), tenure decisions (10 year rolling horizons) are based on the primary focus of the person involved allowing great teachers to excel even in research focussed universities (and the reverse).

The above approach may sound fine to the undergrads but it is the research profs who raise the grant money that provides the overhead costs that pays for the classrooms. The current funding structure leads to a vicious cycle of poor teachers because the teachers do not have access to federal grant sources, only the researchers have direct access to significant quantities of federal money.

We need a government that will provide a source of funds for good teachers to tap into. This would attract the better teachers to teaching and greatly improve the quality of education in our schools.

My three cents,

Cheers,

Y

Al's Kids? (none / 0) (#20)
by Alik on Wed Mar 21, 2001 at 11:58:24 AM EST

I can comprehend the first two problems, but how on earth does one work out the ages of Al's kids? After pondering, I can come up with the following:

  1. Product of ages three kids is 36. This means that the oldest is no older than 18.
  2. Mentioning of a youngest child suggests that the two youngest are not twins. The two oldest could both be 6 years old.

Beyond this, I am lost.

Bob knows (none / 0) (#23)
by dbowden on Wed Mar 21, 2001 at 12:57:25 PM EST

We can assume that Bob knows how long he & Al have been friends, and he states that knowing the product and sum of their ages is not enough information to determine the ages.

Therefore, we can assume from this that there is more than one possible solution to the product & sum.

The algebra involved is too much of a pain for me to solve at work, but I was able to come up with some likely answers by guessing:

The important ones , which yielded the same sum (13) and product (36) were 9,2,2 and 6,6,1.

As you already pointed out, the mention of a youngest child suggests that the youngest two are not twins, which leaves their ages as 6,6, and 1.

That's a pretty good brain bender, huh?

David

[ Parent ]

Use the fact that knowing was enough (none / 0) (#24)
by kallisti on Wed Mar 21, 2001 at 01:00:05 PM EST

The total age is known to Bob, the possible choices of total are: 18+2+1=21, 12+3+1=16, 9+2+2=13, 9+4+1=14, 6+6+1=13, 3+3+4=10, 2+3+6=11. Since knowing the product and sum was not enough, the total must have been 13. The fact that there is a youngest indicates the ages are 6,6,1.

[ Parent ]
Math should be taught like philosophy (4.00 / 1) (#21)
by bluesninja on Wed Mar 21, 2001 at 12:29:59 PM EST

I half-agree with the story, and I know how frustrating math courses can be (at the University of Waterloo, no less). I think the major problem is that math courses from high-school through undergrad are taught as an "applied" discipline. Meaning, it is taught in the form of "these are the properties of X, and from this we can arrive at Y". This is no different from studying physics or biology -- someone is telling you what the "observable" properties of mathematics are.

The problem is that most people, even math undergraduates, don't really get what math is. This is never taught. It's just taken for granted.

I didn't understand why mathematics was interesting until i took a philosophy of mathematics course. (If you're at U of W in math, TAKE THIS COURSE!!! You will not regret it.)If I'd learned that stuff in highschool, I might not have dropped CS for Philosophy.

I think math should be taught more like an arts course: they always begin with at least one week's worth of background into the discipline as a whole, and why it's useful/interesting/important to study in a very general sense. I never got this in math, and I suspect this is true of nearly everybody else in a North American school system. Nobody really has any idea what it is exactly you're studying when you study mathematics.

/bluesninja

Just like tutoring (4.00 / 1) (#25)
by tnt on Wed Mar 21, 2001 at 01:08:03 PM EST

When I was tutoring Math (not too long ago when I was back school) I always got the students to do everything I explained. I found this to be necessary for them to do because: (1) it proves they really understand it, and (2) it helps them remember it. [And I guess (3) ] it also makes them faster at doing it,... which is something that is often needed to pass some of the tests that students get [... you've got to be fast enough, to finish the test, to get a good grade].

This seems to be basically what he's doing. (Alot of tutors would have told you that this is necessary to teach things well. Unfortunately Universities aren't really known for teaching,... they're known lecturing.)



--
     Charles Iliya Krempeaux, B.Sc.
__________________________________________________
  Kuro5hin user #279

It all depends on the teacher (none / 0) (#27)
by joshv on Wed Mar 21, 2001 at 07:38:45 PM EST

Let's face it, a bad teacher is a bad teacher - their teaching modality is not going to compensate for an inadequate ability to communicate the basic underpinning of mathematics to students.

I was taught almost entirely in a lecture format by guys (and a gal) who knew their shit cold. Their lectures were lucid, enthusiastic, and dare I say - fun. But, I went to a small liberal arts school that *gasp* emphasized teaching ability in the faculty. In fact a very brilliant mathematician, who was the most prolific of all the faculty in terms of published material, didn't make tenure because he had a very poor rapport with students.

I suggest anyone looking for a good undergraduate mathematical education think twice before going to one of the larger 'publish or parish' institutions. Schedule a meeting with the Calc I professor if you can when you visit the school. The kind of person he or she is will tell you a lot about the school's attitudes towards mathematical education.

-josh

Explains my experience well (none / 0) (#29)
by vasi on Fri Mar 23, 2001 at 03:39:38 AM EST

When I met Richard, I was at one of the math seminars he refers to in his work report, and he dead-on explains some of my feelings about that math camp.

Some things I found well donw. Every day, they'd distribute some problems, and encourage solutions, which they'd correct and post on a wall. We could go over people's solutions, and see what mistakes we made and how to improve our proofs. But most importantly, they made us clearly present our proofs. We had to *understand* what we wrote well enough to explain them, they wouldn't accept just a lot of equation mangling ending in a solution.

Other things weren't as great, at least from my point of view. All of us were there because of having done well in competitions, so some of the classes being taught were very "memorize this stuff"-oriented, and I couldn't stand it.

But although I'm the type who usually has to deeply grok something to use it, I frankly wouldn't want to be taught only in an understanding-oriented way. I've noticed on competitions, and at that seminar, that those who do best are often those who memorize the right things. This isn't to say that we should tailor the courses to that small fraction of the population which can memorize enough to ace competitions. Because what helped them wasn't that they memorized the solutions to problems, but that the little steps--those that I had to derive from first principles, all over again--they consolidated better, once they learned them.

In other words, I think it works best if first I fully understand where a theorem/technique comes from; then commit it to memory so that I can move on to more advanced topics which incorporate that technique/theorem. Does this sound reasonable? Or am I missing something?

vasi

'loo (none / 0) (#30)
by Kinthelt on Wed Apr 04, 2001 at 04:16:30 PM EST

I'm also a University of Waterloo student. I suppose I am a bit of an odd-ball. I happen to like all of the mathematics taught in first and second year (so much so that I took Calculus 3 as an elective). I do agree that for most people, having the professor sit in front of the class and drone about limits can be tiresome. I suggest to them to just stick through it and take some later-year courses. It is amazing how the professors get more lively when they're teaching something they are interested in. I took PMATH 370 with Gilbert last fall and it was one of the most exciting courses I ever took (along with CS 360 with Biedl).

"Rotten teaching has made me lose most of my interest in math." | 30 comments (30 topical, 0 editorial, 0 hidden)
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