The Teaching of Math
I'm curious to hear?especially from people who are currently students in high school or university?how 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?
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?
Comments
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
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...
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
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.
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...
Why the hell did phonics fall out of favor in schools?
It got displaced by "whole language learning."
I'm still waiting for an english speaking math teacher at my university...
Your math teachers don't teach in English?
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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.
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.
Now that's dmz's kind of algebra.