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The Teaching of Math

post #1 of 100
Thread Starter 
I'm curious to hearespecially from people who are currently students in high school or universityhow math is taught by the various faculty at your school. I ask for a variety of reasons, but mostly because it seems to me that math instruction is typically little more than a person at the front of the room showing how problems are solved on the chalkboard or overhead.

I was speaking to a math professor the other day, and I asked if she ever did any group work (i.e. students working together to solve problems and teach one another) and the answer was sheer astonishment at the idea.

So I ask: how is math taught these days? Is it effective? Can you imagine better ways to do it?
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post #2 of 100
Qualifications first: I am not a student, I am 43 years old, I was educated not in Canada, but in India. So, these will cloud my reply

I find that at least at high school levels in North America (both USA and Canada), maths skills seems to be non-existent, judging purely by the arithmentic skills of check-out clerks at grocery stores (or any other store).

(BTW in the commonwealth countries we abbreviate Mathematics to Maths, not Math)

I wonder if it has anything to do with a similar lack of English skills, especially with relation to the total lack of grammar or spelling skills. I have heard that teachers no longer correct spelling or grammar "in the interest of cultivating creativity". Bollocks I say. Maybe the same thing is happening with Maths?

Teachers, would you kindly comment and tell me I am full of shit and a reasonable justification of why you consider me so?

Cheers
post #3 of 100
Math is not taught effectively.

The problem is that the fundamentals of math are taught much too late -- the theory which is only presented in the most advanced undergrad courses. We teach children vocational or applied math in school and most approaches are strict following the method exactly laid out by the teacher. The issue of course is that there are people (like myself) who just get math, and the teachers couldn't teach me anything -- within a minute of college lectures, I could have completed the day's advances (and this was the way it was for me from 4th or 5th grade on). Of course, this is one of the reasons why I didn't go into math, and certainly have no aptitude for teaching it.

I have struggled teaching Upward Bound students that the rigorous methods they are given in high school are not the only way to look at problems. The blank stares and subsequent questions as to the exact mechanics of problems always bothered me because I could understand the fundamentals behind the problems first and the mechanics always came second.

I think that this points to the way math should be taught -- I think we should spend the early years of elementary school building up the conceptual frameworks to understand the real number system ending in algebra/calculus in eighth grade. High school can introduce advanced topics like analysis, and topology etc. To teach this though, would require more number play than we currently do, and I agree that groups may be the best way to do this.

This is rambling, I know... I apologize. Tomorrow I have to deal with a Grad student who has a BS in chemistry who doesn't understand some pretty basic fundamentals...
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post #4 of 100
Thread Starter 
Quote:
Originally Posted by tilt

I wonder if it has anything to do with a similar lack of English skills, especially with relation to the total lack of grammar or spelling skills. I have heard that teachers no longer correct spelling or grammar "in the interest of cultivating creativity". Bollocks I say. Maybe the same thing is happening with Maths?

Teachers, would you kindly comment and tell me I am full of shit and a reasonable justification of why you consider me so?

Cheers

What you're hearing is a kind of bastardized version of what's called "the writing process," which was advanced by Donald Murray and others in the 1970s. The idea is pretty simple: treat writing as a process, not as a product, and teach it that way. Teach the process. In this model, grammar and punctuation get shifted to the end of the process, since it's important that you have all your ideas out there before you go fixing comma splices.

Some (weak, in my opinion) teachers misunderstand this and think that the process is all there is or that they're de-emphasizing mechanics in favor of creativity. But this is incorrect.

Cheers
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post #5 of 100
Math is interesting because different people tend to learn it best in different ways, geniuses of science and engineering even tend do approach it differently from one another, but, as far as I know, it's taught in a fairly consistent manner at least through the 300 level at a certain, northeastern university with a long history of math and science credentials. The consistency I speak of is a thorough evaluation of theory built on nomenclature and logical/sequential methods of problem solving. It was very unsupportive to so-called visual thinkers, but then again I'm not sure if it's even possible to cram that much theory into an undersized semester without sticking to a strictly propositional foundation.

In high school and below, the only problem I can think of is that schools don't do a good enough job at sorting out those who get it and those who don't, and more importantly, understandinging that different kids mature at different rates. These are of course extremely difficult aspects to judge, particularly the case of a gifted mathematical mind who happens to be a late-bloomer. I had a bunch of friends who were always a little bit behind the curve until late in high school when they suddenly made names for themselves as apex students.

Needless to say, I am a so-called visual thinker and I like to "stop and smell the roses" when it comes to the mathematic progression of a concept. I finished with a BSE in Electrical Engineering (focusing on the more mathy "signals" branch of it), and I didn't enjoy my academic experience much, which apparently makes me a serious outlier given the recent data from US News on this particular school. But after four years of smelling roses -- which ironically lead many profs into thinking I was a slacker -- I managed to teach myself how to teach myself, and have cultivated it since. When I graduated two years ago, I had no desire to ever go back to school, because I hated the experience. Now, I see no reason.
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post #6 of 100
We all know you went to Princeton, spliny.

Your mock humility makes it all the worse. If you readily admit that you went to Princeton and then describe your experience, you wouldn't come off as such a condescending fuck.

Regardless, there are those amongst the posters here who have attended more prestigious schools.

Edit:

I should say that this is by no means an attack on you Spliny. But your post doesn't accomplish what I believe you set out for it to accomplish, mostly because the tone that follows statements (that you often make) about that elite north eastern school you attended...
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post #7 of 100
The problem with teaching these days is that teachers assume (at least at the grade school level) to a much higher degree than in the past, that kids only need to know what the answer is, and not know why that's the answer and/or how to arrive at that answer on their own. Answers are taught, not theories or thought processes.

The way that maths are taught is by memorizing multiplication tables and formulas. It's not until students get into calculus that they are asked to derive even the simplest formulas for themselves. Let me qualify my take on the significance of this: I got an 800 on the SAT math when I took it in my Junior year of high school. For those of you not familiar, that's a perfect score. Now the reason I got an 800 was not that I memorized the formulas or studied countless hours solving problems over and over again or was some superadvancedhighmathgenius. The reason I got an 800 was that I was taught in a way that made me understand why a formula makes sense, and not just what that formula is. I'm sure that during the test there were formulas I forgot, and was able to derive during the test.

I think there are definite parallels between the theaching of math (maths) and the teaching of reading. Why the hell did phonics fall out of favor in schools? It works! Kindergarten reading regime should exist 100% of Dr. Seuss. If bright kids read, and study Dr. Seuss in kindergarten (and by bright I mean the top 90%), their reading and spelling skills are set for life, guaranteed.

Likewise, if bright kids learning multiplication are taught that 3x3 = 3+3+3, 3x4 = 3+3+3+3 and not 3x3 = 9, 3x4 = 12, then their math skills will be significantly better.

Memorization is by it's nature temporary. Theoretical reasoning sticks.
post #8 of 100
Thread Starter 
Quote:
Originally Posted by tonton

Why the hell did phonics fall out of favor in schools?

It got displaced by "whole language learning."
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post #9 of 100
I'm still waiting for an english speaking math teacher at my university... \
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post #10 of 100
Thread Starter 
Quote:
Originally Posted by Guybrush Threepwood

I'm still waiting for an english speaking math teacher at my university... \

Your math teachers don't teach in English?
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post #11 of 100
Quote:
Originally Posted by midwinter

Your math teachers don't teach in English?

I bet he is making a snyde/racist remark about their Indian (or other) accent, though I could be wrong, in which case I apologise for making that assumption...
post #12 of 100
Quote:
Originally Posted by tilt


I find that at least at high school levels in North America (both USA and Canada), maths skills seems to be non-existent, judging purely by the arithmentic skills of check-out clerks at grocery stores (or any other store).

Bad metric: I ran into a high school classmate last week at the super market and he told me that he dropped out of HS and so did a lot of others in the store...

Also, having worked retail, I can tell you that I knew almost instantly how much change to give, and whatever else dealing with numbers, but we CANT do or say anything untill the computer spits out the totals, if your cost $7, gave me $10, I know that $3 is your change, but I couldnt say that or give you the money untill i pushed 10->cash on the register and got the thing to say it too.
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post #13 of 100
Quote:
Originally Posted by midwinter

Your math teachers don't teach in English?

No, but in high school I was taught pre-calc by an English teacher. That's about as far as I managed to go, mathematically :P

Next year I decided to just take statistics instead of calculus.
post #14 of 100
Quote:
Originally Posted by Guybrush Threepwood

I'm still waiting for an english speaking math teacher at my university... \

amen to that -- it's good to see things haven't changed much in 20 years!








midwinter, check out the Saxon math program. I think this is the silver bullet. A rotation of concepts that seems at first pointless and painfully redundant, but it will have your 8-year old doing algebraesque operations.

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

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In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

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post #15 of 100
I teach stats (granted, not real math), and don't really do any group work, but my impression is that students naturally talk to each other about issues more than in other classes.

I teach it in a computer classroom, and I just do examples on the board, and then we use computers to run them too. One of the things I've noticed is that we go through the different methods, and everyone does fine, but when I have a final where they have to choose which method to use for a given data set, they can't do it. It's like they can easily learn how to plug in numbers, but not apply them in practical situations. We've been playing with different ideas, but we're not sure how to try to improve it.
post #16 of 100
Thread Starter 
Quote:
Originally Posted by BRussell

I teach stats (granted, not real math), and don't really do any group work, but my impression is that students naturally talk to each other about issues more than in other classes.

I teach it in a computer classroom, and I just do examples on the board, and then we use computers to run them too. One of the things I've noticed is that we go through the different methods, and everyone does fine, but when I have a final where they have to choose which method to use for a given data set, they can't do it. It's like they can easily learn how to plug in numbers, but not apply them in practical situations. We've been playing with different ideas, but we're not sure how to try to improve it.

Do you give them consistent instruction in the class about applying these methods? I ask only because Friday a colleague in another department called me up and said "THESE DAMNED KIDS ARE DRIVING ME NUTS!" When I asked why, she revealed that her students had just turned in a small "essay" (really more of a "response") and they hadn't done well. I asked what kind of instruction they'd been given. She said "Write a critical analysis." When I asked if she'd explained to them what a "critical analysis" is, she said "No. It's a critical analysis. What more do they need to know than that?"

At that point I just decided to make fun of the assignment, because, you know, a "critical analysis" is waaaay harder than an "uncritical analysis." And just a plain "analysis"? Feh. 10 minutes. Tops.
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post #17 of 100
Quote:
Originally Posted by hardeeharhar

We all know you went to Princeton, spliny.

I covered it up because there are other elements I liked about the Princeton experience, and I didn't want to create worry for the random passerby who may happen to be a freshman at Princeton. If in turn I come across as condescending, then I guess that's a problem we'll both have to live with.

The reason why I hinted in the first place is because I want people to realize that disinterested math instruction is not just a problem at the low or middle end of the educational spectrum. You assume too much. As indicated by my last post, I place very little value on the formalities of my college education, and whether or not various posters here have won Nobel prizes, it doesn't really mean all that much to me. I'm much more concerned with actual success than feigned academic accolades.
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post #18 of 100
Quote:
Originally Posted by midwinter

Do you give them consistent instruction in the class about applying these methods? I ask only because Friday a colleague in another department called me up and said "THESE DAMNED KIDS ARE DRIVING ME NUTS!" When I asked why, she revealed that her students had just turned in a small "essay" (really more of a "response") and they hadn't done well. I asked what kind of instruction they'd been given. She said "Write a critical analysis." When I asked if she'd explained to them what a "critical analysis" is, she said "No. It's a critical analysis. What more do they need to know than that?"

At that point I just decided to make fun of the assignment, because, you know, a "critical analysis" is waaaay harder than an "uncritical analysis." And just a plain "analysis"? Feh. 10 minutes. Tops.

That's pretty funny.

But it's tough. Normally the way stats is taught is that you present the methods and show how they're used. But in the real world, you have some problem - some data that you want to analyze - and then you need to figure out which method to use. It's as if you teach it backwards from the way you really use it. But it's not clear how to teach it the other way around. Perhaps a class could be completely problem-oriented (or data-oriented): Here are some data from a study, now how should we deal with it? But still, at some point you have to teach how to use the method.
post #19 of 100
Quote:
Originally Posted by midwinter

Your math teachers don't teach in English?

No. Have yet to find a fluent English speaking math teacher at my university. Some may think I'm exaggerating, but I'm not.

Quote:
Originally Posted by tonton

I bet he is making a snyde/racist remark about their Indian (or other) accent, though I could be wrong, in which case I apologise for making that assumption...

As a matter of fact tonton, none of them are Indian.

Those are the engineering instructors...
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post #20 of 100
Quote:
Originally Posted by midwinter

I ask for a variety of reasons, but mostly because it seems to me that math instruction is typically little more than a person at the front of the room showing how problems are solved on the chalkboard or overhead.

What other things are there? Unless your field of research is Math itself and you're taking a high level graduate course, Math is nothing more than a tool, like a hammer. You'd like to know when and how to use it. That's it.

Quote:
I was speaking to a math professor the other day, and I asked if she ever did any group work (i.e. students working together to solve problems and teach one another) and the answer was sheer astonishment at the idea.

That's what homeworks and study groups are for. Using class time for these type of activities is useless. If a student has a problem that him and his peers can't solve, you come to see the prof. at office hours.

Then there is the type of math - math for scientists, math of engineers, math economists... all different.
post #21 of 100
Thread Starter 
Quote:
Originally Posted by skatman

That's what homeworks and study groups are for. Using class time for these type of activities is useless. If a student has a problem that him and his peers can't solve, you come to see the prof. at office hours.

I find it difficult to believe that the most effective way to teach math is to have someone at the front of the room writing things on the blackboard.
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post #22 of 100
Quote:
Originally Posted by midwinter

I find it difficult to believe that the most effective way to teach math is to have someone at the front of the room writing things on the blackboard.

...before college, it's known as homeschooling.

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

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In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

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post #23 of 100
Holy trinity - holy ghost = 2*JesusGod

Now that's dmz's kind of algebra.
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post #24 of 100
At my high school all math classes I have been in have a lot of said group work after a short lecture about the material.
post #25 of 100
Quote:
Originally Posted by hardeeharhar

Holy trinity - holy ghost = 2*JesusGod

Now that's dmz's kind of algebra.

Actually, it's the one-on-one with the kids, some are ready to read at 3, some not till 6. It's a good thing.

In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

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In our desire to impose form on the world we have lost the capacity to see the form that is there;
and in that lies not liberation but alienation, the cutting off from things as they really are. --...

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post #26 of 100
You should do that AND send them to socialize/learn with other children; but seeing as you live in a town of ~3500, I can see where you can rationally argue that your family constitutes the only source of children for the school system.
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post #27 of 100
midwinter here's an article about elementary math education that might interest you.
post #28 of 100
Quote:
Originally Posted by a_greer

Bad metric: I ran into a high school classmate last week at the super market and he told me that he dropped out of HS and so did a lot of others in the store...

Also, having worked retail, I can tell you that I knew almost instantly how much change to give, and whatever else dealing with numbers, but we CANT do or say anything untill the computer spits out the totals, if your cost $7, gave me $10, I know that $3 is your change, but I couldnt say that or give you the money untill i pushed 10->cash on the register and got the thing to say it too.

Ah, high school is a little too late to be taught basic arithmetic. Basic arithmetic like addition, subtraction, multiplication and division are covered (and one is expected to do the sums in their heads) by the time one passes 4th or 5th standard (grade in North American parlance).

As for not being permitted to do anything till the computer spits out the totals, I beg to differ. I have had times when I hand out $21.25 for a $15.25 charge and had the kid look at me totally confused as to why I am offering that kind of money. All I want is a $5 bill instead of a lot of coins in change! I am doing this calculation in my head while they are staring at me with their mouths wide open and waiting for theit "computer" to tell them what kind of change to make!

Edited to correct a lot of typos resulting from fat fingers and fast mind
post #29 of 100
Quote:
Originally Posted by tonton

I bet he is making a snyde/racist remark about their Indian (or other) accent, though I could be wrong, in which case I apologise for making that assumption...

I think he was trying to be funny Tonton. I have not known Midwinter to be prejudiced when it comes to race.

BTW, I wonder - why is it that when Americans can put up with French accents, Spanish accents, Russian accents, British accents, Southern accents and New York accents that they cannot put up with Indian accents? It is just another accent.

Cheers
post #30 of 100
Thread Starter 
Quote:
Originally Posted by tilt

I think he was trying to be funny Tonton. I have not known Midwinter to be prejudiced when it comes to race.

BTW, I wonder - why is it that when Americans can put up with French accents, Spanish accents, Russian accents, British accents, Southern accents and New York accents that they cannot put up with Indian accents? It is just another accent.

Cheers

I think Tonton was playing straightman to my sarcasm.

That's a good question about Indian accents. I wonder if the issue is that MANY people in America have little experience with Indian accents, and so they don't fall into expected patterns. The other problem is that many, many students in the flyover states have never heard anyone with a real accent, and because they're young and entitled, they have a redneck response of "I CAIN'T UNNERSTAN' A GAWL DANG WURD HE'S UH SAYIN'!! AHM DRAWPIN' THIS CLASS!!!"

When I was in grad school, the university instituted a policy of "no rookies on rookies," which, while it sounded nice and honorable, I read as a code for "No Indian or Chinese people in the classroom before they've been felt out and develop some conversational skills!"

I was horrified and appalled.
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post #31 of 100
Southerner's should learn to speak English, too.






post #32 of 100
Thread Starter 
Quote:
Originally Posted by ShawnJ

Southerner's should learn to speak English, too.

At least we know how to use an apostrophe.
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post #33 of 100
lol..
post #34 of 100
Thread Starter 
Quote:
Originally Posted by ShawnJ

lol..

And the period, apparently. You really shouldn't just toss them around like that. There could be a shortage, and then where would you be?
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post #35 of 100
*cough*
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post #36 of 100
Quote:
Originally Posted by tilt

As for not being permitted to do anything till the computer spits out the totals, I beg to differ. I have had times when I hand out $21.25 for a $15.25 charge and had the kid look at me totally confused as to why I am offering that kind of money. All I want is a $5 bill instead of a lot of coins in change!

Well, they were probably looking at you confused cause that's 6 dollars change
post #37 of 100
Quote:
Originally Posted by tilt

I think he was trying to be funny Tonton. I have not known Midwinter to be prejudiced when it comes to race.

BTW, I wonder - why is it that when Americans can put up with French accents, Spanish accents, Russian accents, British accents, Southern accents and New York accents that they cannot put up with Indian accents? It is just another accent.

Cheers

All those accents (except Southern ones) are sexy.
post #38 of 100
Quote:
Originally Posted by gregmightdothat

All those accents (except Southern ones) are sexy.

Russian accents?
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
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"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
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post #39 of 100
Come on...

Xenia Onatopp?
Anna K...
Sharapova...
post #40 of 100
Quote:
Originally Posted by ShawnJ

Come on...

Xenia Onatopp?
Anna K...
Sharapova...

Come on...

Natrilova?
Boris the Bullet-Dodger?
The Russian from Rocky IV?
"If I had played my career hitting singles like Pete (Rose), I'd wear a dress." - Mickey Mantle
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