Political Crossfire Forums

[ieatfood]

TwinkieDP wrote: ieatfood wrote:
I disagree--even in higher education, drilling is key. How do you learn to do calculus? Simply--you do hundreds of calculus problems. If you've done a thousand integration problems and still can't integrate, then you are beyond help.

As for learning that 2x3=2+2+2, that can be drilled too. Here's a drill--rewrite these 100 multiplications into addition, and visa versa...
Yes, for children who are new to math drilling is necessary. But different children have different skill levels. There comes a point where simple drilling saps the energy of students and doesn't really help them move forward.

People talk about higher math skills, its great and all if your kid can do all these types of math problems and ace them. But seriously, how often in real life do people use such skills? Unless you're in some kind of scientific research position, you probably won't have to use anything above calculus, or basic geometry. Most great inventions are created as a result of incorporating skills from multiple disciplines. The guy who sits around doing higher math, thinking about corollaries and theories about math alone won't have much of an impact on society.

"saps the energy of students??"
math is not for the lazy, actually doing well in school is not for the lazy
if you dont have the attention span to sit and do hundreds of math problems, then doing well in school is not for you

actually, all subjects in school require drilling. math is not alone. how do you do well on the english sat? do thousands of english problems--thats how.

as for useful skills, 90% of what you learn in school is useless for most people. That's because we give people a broad education--we teach them stuff from all fields so that students can be well rounded. A mechanical engineer is likely not going to need to know about shakespeare any more than an english teacher needs to know calculus. But everyone should learn both to be well rounded.

Bottom line, most people will never use math beyond basic additoin, subtration, multiplication, and division. The most common use of math for the average guy is calculating tip. But that doesn't mean that we shouldn't teach math beyond that. And the best way, actually the only way to teach math is to drill. That's for sure.

[F'losrix]

Drill first until they've learned the tried and true methods. Then introduce the shortcuts and explore creative approaches.

The discipline taught in doing things the hard way will serve them in other ways, whether or not they ever have a need to use the math itself again.

I'd frankly like to see a logic requirement in the curriculum as well, taught alongside language and math, as it has elements that relate to both.

[perdidochas]

F'losrix wrote: Drill first until they've learned the tried and true methods. Then introduce the shortcuts and explore creative approaches.

The discipline taught in doing things the hard way will serve them in other ways, whether or not they ever have a need to use the math itself again.

I'd frankly like to see a logic requirement in the curriculum as well, taught alongside language and math, as it has elements that relate to both.

Well, actually, concepts need to be taught first--like the example that kids need to know that 8x4 is the same as 8+8+8+8. Then drill, then shortcuts.

Things get a bit more complex in later math, when problems can legitimately be solved in more than one way. One method may be great for the way my mind is organized, but another method will be better for you. Regardless, we should get the same answer.

[F'losrix]

perdidochas wrote: Well, actually, concepts need to be taught first--like the example that kids need to know that 8x4 is the same as 8+8+8+8. Then drill, then shortcuts.
:tu: Good point!

[Random Evil Guy]

ieatfood wrote: In a recent nyt article, the subject of the nation's math curriculum was brought up. It is well known that the US s*cks at math--when compared to Asian countries, US students look like retards in math. Personally, I feel that most of it has to do with attitude--Americans simply don't care about math all that much. In any case, the new "reform" math curriculum isn't helping things. Reform math is a type of curriculum which works by "de-emphasizing basic drills and memorization in favor of allowing children to find their own ways to solve problems." In some curriculums, students are taught NOT to learn long division!!!

This is complete bullcrap. When I was growing up, I went to special summer school where every day, we took two tests, and were assigned copious homework which consisted of nothing but drills on top of drills. For many of the kids at the program, getting anything less than a full score on the SAT math would have been disappointing. You lean math by repetition, not creativity.

In reality, all this talk of "reform math" is a fundamental misunderstanding of what math is. Math is a skill--like playing tennis, like playing the violin, like playing video games--a skill. Skills have certain properties. Here they are:

#1--some people are just better at certain skills than others, this is genetics and there's nothing you can do about it. Some people will never be good at math no matter what you do.
#2--skills are learned by repetition. You don't see champion tennis players say they perfected their tennis through "creativity" and "exploration." No--they perfected it by hitting 200,000 forehands followed by 200,000 backhands in 95 degree heat. That's how you get good at a skill--drill.
#3--Skills are cumulative--you can't learn how to hit a slice backhand before you learn how to hit a normal one. Stop trying to skip important skills like long-division. You need to learn how to divide in order to do other things in the future. If you skip the basic fundamentals, how can you expect to master anything down the line?

http://www.nytimes.com/2006/11/14/education/14math.html

Anyone who thinks that we should stop drilling and testing in math doesn't know a thing about math and should not be in the business of teaching it.

ah, it is so funny reading bullcrap like this. people commenting on things they know very little about. the classic 'it worked for me, then it should work for everyone else'. i suggest you actually read up on the issue before commenting on it. for example take a look at the timms and pisa studies.

reason why finland, netherlands, singapore, japan, hong kong etc are all doing well in math is because they are able to combine problem solving with the more traditional math education in which they practice procedures. they also employ inductive learning and a more vertical(instead of a horizontal) approach to math.

for instance, in japan, which is one of the countires scoring the highest in the timms study, they spend more than 40% of the time working on how to solve mathematical problems. by that, i mean how you solve problems that aren't 'straight forward'. often you must use a combination of knowledge from a number of different subjects to solve the problems. they work on being intuitive and creative. how to actually apply math to complicated problems. in the us, they spend less than 6% of time on this.

furthermore, they spend more than 10% of the time working on fundamental concepts in math, not just procedures and skill, but they focus on developing a real and genuine understanding of the mathematical definitions. classes in the us spend less than 4% of the time learning and understanding concepts.

these are just a couple of issues surrounding this issue. this is a very complicated issue, but what is definately certain is that the old, traditional way of teaching math is definately not the most efficient method. you need to drill algorithms and math skills, but devolping a deeper understanding of mathematical concepts and an intuitive 'feeling' for math is just as important. this is something every big study shows and all prominent scientists in the field of math didactics agree on.

[Random Evil Guy]

for example, when teaching kids that (x+n)^2 = x^2 + 2nx + n^2

you can give them a square (X^2) which is x*x, a rectangle (X) which is x*1 and a square (1) which is 1*1. then you ask them if they can arrange new squares using the given figures. then, with a little help, they might be able to see the pattern themselves and they will, according to studies, develop a much better understanding of the formula.

(x+2)^2 would for example be the X^2, then four X and finally another four 1.

[ieatfood]

Random Evil Guy wrote:

ah, it is so funny reading bullcrap like this. people commenting on things they know very little about. the classic 'it worked for me, then it should work for everyone else'. i suggest you actually read up on the issue before commenting on it. for example take a look at the timms and pisa studies.

reason why finland, netherlands, singapore, japan, hong kong etc are all doing well in math is because they are able to combine problem solving with the more traditional math education in which they practice procedures. they also employ inductive learning and a more vertical(instead of a horizontal) approach to math.

for instance, in japan, which is one of the countires scoring the highest in the timms study, they spend more than 40% of the time working on how to solve mathematical problems. by that, i mean how you solve problems that aren't 'straight forward'. often you must use a combination of knowledge from a number of different subjects to solve the problems. they work on being intuitive and creative. how to actually apply math to complicated problems. in the us, they spend less than 6% of time on this.

furthermore, they spend more than 10% of the time working on fundamental concepts in math, not just procedures and skill, but they focus on developing a real and genuine understanding of the mathematical definitions. classes in the us spend less than 4% of the time learning and understanding concepts.

these are just a couple of issues surrounding this issue. this is a very complicated issue, but what is definately certain is that the old, traditional way of teaching math is definately not the most efficient method. you need to drill algorithms and math skills, but devolping a deeper understanding of mathematical concepts and an intuitive 'feeling' for math is just as important. this is something every big study shows and all prominent scientists in the field of math didactics agree on.

interestingly, education is one of those areas where experience does matter and where studies don't

the problem with doing education studies is bias--you cannot do blinded studies in education and thus any study you do will be subject to all sorts of bias making any conclusions meaningless.

the reason why asians are good at math is cultural--asians simply care more about math than nonasians
thats it
there's no special educational trick--no special magic technique for learning math

I grew up in an asian community, went to an asian summer school, and saw the methods they employ. I assure you, its just drilling, day after day after day. They just sit in a basement, with no windows, doing problem after problem under timed conditions and knowing that beating the person next to them brings them tremendous accolade from teachers, parents, and their peers.

with a country like japan or CHina, you can't even compare to the US. The culture is just very different. They actually RESPECT their teachers--a concept that is quite foreign to us Americans. The cultural differences are so great that the teaching technique itself is almost secondary.

the magic is hard work--drill drill drill. You can do studies till your blue in the face, but the fundamentals will still hold true.

[ieatfood]

Random Evil Guy wrote: for example, when teaching kids that (x+n)^2 = x^2 + 2nx + n^2

you can give them a square (X^2) which is x*x, a rectangle (X) which is x*1 and a square (1) which is 1*1. then you ask them if they can arrange new squares using the given figures. then, with a little help, they might be able to see the pattern themselves and they will, according to studies, develop a much better understanding of the formula.

(x+2)^2 would for example be the X^2, then four X and finally another four 1.

uh, are you kidding?
that is the most confusing way to learn this i have ever seen.
hell, i am already confused and I know the topic.

this topic is so simple, an idiot can teach it--it is just a simple algorithm, remember the algorithm and you can do any problem in no time. There's really nothing to understand--an algorithm is an algorithm. You are making it so much more difficult than it is. Just have them memorize the formula, then plug and chug.

I have taught this to many kids and it never takes me more than a few minutes. It's all memorization. Actually, if you really want to teach concepts, you can show them the derivation of the formula from (x+y)(x+y). Of course, the students should already know how to do (x+y)(a+b) in their sleep.

using triangles and crap is a waste of time--you'd be far better off just having them drill the formula until they can do the problems in their sleep. Then teach some applications (eg do some word problems). Then move on to advanced topics like graphing.

Having to use geometry to solve a simple algorithm tells me that these kids aren't having problems with the algorithm itself. THey're having problems with actually solving the computation part. They're having problems with exponents and order of operations. These topics must be drilled and mastered way way way before you even think about trying to teach (X+y)^2. As I have said before, math is cumulative. If you don't master the basics, you will be completely overwhelmed by more advanced topics, no matter how many geometrical shapes you employ.

[Random Evil Guy]

ieatfood wrote: Random Evil Guy wrote:

ah, it is so funny reading bullcrap like this. people commenting on things they know very little about. the classic 'it worked for me, then it should work for everyone else'. i suggest you actually read up on the issue before commenting on it. for example take a look at the timms and pisa studies.

reason why finland, netherlands, singapore, japan, hong kong etc are all doing well in math is because they are able to combine problem solving with the more traditional math education in which they practice procedures. they also employ inductive learning and a more vertical(instead of a horizontal) approach to math.

for instance, in japan, which is one of the countires scoring the highest in the timms study, they spend more than 40% of the time working on how to solve mathematical problems. by that, i mean how you solve problems that aren't 'straight forward'. often you must use a combination of knowledge from a number of different subjects to solve the problems. they work on being intuitive and creative. how to actually apply math to complicated problems. in the us, they spend less than 6% of time on this.

furthermore, they spend more than 10% of the time working on fundamental concepts in math, not just procedures and skill, but they focus on developing a real and genuine understanding of the mathematical definitions. classes in the us spend less than 4% of the time learning and understanding concepts.

these are just a couple of issues surrounding this issue. this is a very complicated issue, but what is definately certain is that the old, traditional way of teaching math is definately not the most efficient method. you need to drill algorithms and math skills, but devolping a deeper understanding of mathematical concepts and an intuitive 'feeling' for math is just as important. this is something every big study shows and all prominent scientists in the field of math didactics agree on.

interestingly, education is one of those areas where experience does matter and where studies don't

the problem with doing education studies is bias--you cannot do blinded studies in education and thus any study you do will be subject to all sorts of bias making any conclusions meaningless.

the reason why asians are good at math is cultural--asians simply care more about math than nonasians
thats it
there's no special educational trick--no special magic technique for learning math

I grew up in an asian community, went to an asian summer school, and saw the methods they employ. I assure you, its just drilling, day after day after day. They just sit in a basement, with no windows, doing problem after problem under timed conditions and knowing that beating the person next to them brings them tremendous accolade from teachers, parents, and their peers.

with a country like japan or CHina, you can't even compare to the US. The culture is just very different. They actually RESPECT their teachers--a concept that is quite foreign to us Americans. The cultural differences are so great that the teaching technique itself is almost secondary.

the magic is hard work--drill drill drill. You can do studies till your blue in the face, but the fundamentals will still hold true.

:lol:

i guess that means that the finnish and the dutch are also culturally predisposed to 'like math'. you enjoy your anecdotal evidence. i think i'll go with the actual science on this one. if you are interested, i recomend reading the pisa and timms study. there you will find the numbers that matters and they are explained and conculsions are drawn. if you can get your hands on it, i also recomend the video study from timms. in which they recorded and documented classroom activities from a number of schools in germany, the us and japan. the differences are very interesting and probably shocking to someone like yourself.

[Random Evil Guy]

ieatfood wrote: Random Evil Guy wrote: for example, when teaching kids that (x+n)^2 = x^2 + 2nx + n^2

you can give them a square (X^2) which is x*x, a rectangle (X) which is x*1 and a square (1) which is 1*1. then you ask them if they can arrange new squares using the given figures. then, with a little help, they might be able to see the pattern themselves and they will, according to studies, develop a much better understanding of the formula.

(x+2)^2 would for example be the X^2, then four X and finally another four 1.

uh, are you kidding?
that is the most confusing way to learn this i have ever seen.
hell, i am already confused and I know the topic.

this topic is so simple, an idiot can teach it--it is just a simple algorithm, remember the algorithm and you can do any problem in no time. There's really nothing to understand--an algorithm is an algorithm. You are making it so much more difficult than it is. Just have them memorize the formula, then plug and chug.

I have taught this to many kids and it never takes me more than a few minutes. It's all memorization. Actually, if you really want to teach concepts, you can show them the derivation of the formula from (x+y)(x+y). Of course, the students should already know how to do (x+y)(a+b) in their sleep.

using triangles and crap is a waste of time--you'd be far better off just having them drill the formula until they can do the problems in their sleep. Then teach some applications (eg do some word problems). Then move on to advanced topics like graphing.

Having to use geometry to solve a simple algorithm tells me that these kids aren't having problems with the algorithm itself. THey're having problems with actually solving the computation part. They're having problems with exponents and order of operations. These topics must be drilled and mastered way way way before you even think about trying to teach (X+y)^2. As I have said before, math is cumulative. If you don't master the basics, you will be completely overwhelmed by more advanced topics, no matter how many geometrical shapes you employ.

sorry to say, but you're making a complete fool of yourself. you're talking about something you know absolutely nothing about. you're talking from your own, very limited experience. that is per defination anecdotal evidence. all of which is very strange, as most of your earlier posts i've read have shown that you're an intelligent poster and, probably, educated poster. have you even ever tried using inductive learning concepts when teaching? i have, in everything from junior high school to college and university level.

memorization is not understanding. problem is, they can memorize this until their face is blue, but, most of them, will never truly understand the formula in itself. they will just apply it whenever they see a similar problem. however, when they are supposed to use the formula in combination with other skills and topics, they get confused and herein lies the problem. they don't understand what they're doing. using visual aids such as this first and then moving on to symbolic representation is proven to have much better results than the classic memorization model.

the biggest difference between japan and the us, is how much time they spend on learning concepts and developing a deeper understanding of solving mathematical problems. the us(as norway) focuses almost exclusively on memorizing algorithms and mathematical skills. how to solve very structured and straight forward excercises. working on your skills is important, but it is near useless for most people unless you work on developing an intuitive understanding of math as well.

finally, i suspect you're basing your entire line of reasoning on the fact that it worked on you, which is a logical fallacy. it worked on me as well, but people are different and, in fact, the traditional model doesn't work at all for most people. that is why countries such as netherlands, finland, singapore, japan etc are doing on average so well. they are able to get the most out of each and every student.

btw, there is a lot of strong evidence to suggest that the example given, gives a better understanding of the formula than just telling the kids/students the formula up front. it illustrates the difference between inductive learning(going from examples to general rule/formula) and deductive learning(going from formula to examples). learning things on your own, leads to a much better and deeper understanding of something. not to mention, it is how science(and math) works on a higher level...

[ieatfood]

Random Evil Guy wrote:

memorization is not understanding. problem is, they can memorize this until their face is blue, but, most of them, will never truly understand the formula in itself. they will just apply it whenever they see a similar problem. however, when they are supposed to use the formula in combination with other skills and topics, they get confused and herein lies the problem. they don't understand what they're doing. using visual aids such as this first and then moving on to symbolic representation is proven to have much better results than the classic memorization model.
the issue with (x+y)^2, however, is that there is no understanding to be done. the only understanding that you need possibly is the derivation of the forumula (x+y)(x+y)= x*x+x*y+y*x+y*y=x^2+2xy+y^2. But that's it. THere's nothing more to understand. So the fact that kids aren't able to grasp this simple formula tells me not that they don't understand this concept, because there really is nothing to understand. It tells me that they don't understand something more fundamental--like order or operations or how to take squares of numbers or how to use the distributive property. It tells me that they have skipped over topics that should have previously been mastered.

I have nothing against using visual aids, but in this case, it is quite unnecessary except as a memory aid. I, too have used shapes to teach (x+y)^2 but only as a way to help them easier remember the formula, not becuase I think they gain any greater understanding of something so basic.


Random Evil Guy wrote: the biggest difference between japan and the us, is how much time they spend on learning concepts and developing a deeper understanding of solving mathematical problems. the us(as norway) focuses almost exclusively on memorizing algorithms and mathematical skills. how to solve very structured and straight forward excercises. working on your skills is important, but it is near useless for most people unless you work on developing an intuitive understanding of math as well.

i disagree--the biggest difference is still cultural. Doing studies among countries is especially useless since countries differ in so many factors. It's impossible to isolate all the different factors cultural and otherwise and to ascribe differences to simply teaching technique, which itself is extremely variable across the nation. Demographics matter a lot--for example, the differences between poor blacks and rich asians in this country is vast despite the fact that they are all "americans." Thus, studies comparing "americans" versus "chinese" students are really meaningless--it depends which subpopulation you are talking about.

I agree that intuition is extremely important in math. But you develop intuition through repetition. You develop intuition by solving a whole variety of problems so you can adapt to any situation. But you need a good foundation. You can't expect to solve hard problems unless you have mastered the easy ones.

Random Evil Guy wrote: finally, i suspect you're basing your entire line of reasoning on the fact that it worked on you, which is a logical fallacy. it worked on me as well, but people are different and, in fact, the traditional model doesn't work at all for most people. that is why countries such as netherlands, finland, singapore, japan etc are doing on average so well. they are able to get the most out of each and every student.

I base my knowledge on how the best math students do things. I went to a school full of math geniuses and everyone looks at math the same way. All the smartest math students all grew up on drilling, not wasting their time on shapes and the such.

I would be quite wary of relying on "studies"
most education studies are quite susceptible to bias, especially if they're retrospective.

Random Evil Guy wrote: btw, there is a lot of strong evidence to suggest that the example given, gives a better understanding of the formula than just telling the kids/students the formula up front. it illustrates the difference between inductive learning(going from examples to general rule/formula) and deductive learning(going from formula to examples). learning things on your own, leads to a much better and deeper understanding of something. not to mention, it is how science(and math) works on a higher level...

except that drilling is inductive learning. At first, the person may not memorize the formula and may need to have a study aid to solve the first 5-10 problems. But by the 100th-150th problem, the formua itself is now second nature because that person has done it so many times. If you had the formula perfectly memorized the first time, you wouldn't need to do the drills.

[Random Evil Guy]

ieatfood wrote:
the issue with (x+y)^2, however, is that there is no understanding to be done.

in this example, (x+y) is the length of a side in a square. (x+y)^2 is the area. by displaying this both geometrically and algebraically kids and students devlop a better understanding of the concept and how the different aspects of it relate to each other. it's all part of developing a deeper knowledge of math. which in turn leads to a better chance of solving more complex and intricate mathematical problems.

ieatfood wrote:
I agree that intuition is extremely important in math. But you develop intuition through repetition. You develop intuition by solving a whole variety of problems so you can adapt to any situation. But you need a good foundation. You can't expect to solve hard problems unless you have mastered the easy ones.

you have to do both, which is what they are doing in mentioned countries. work on understanding concepts, devlop mathematical skills and devlop a deeper and intuitive understanding of math.

in the timms video study, they recorded what was happening in 100 german, 81 american and 50 japanese math classes for 15 year olds. the goal was to observe and note differences and similarities. fact of the matter is, that on the surface, things were very similar. similar class rooms, similar classes and number of students etc. difference was in the teaching methods and in more particular, how much time they spent on different issues. the researchers divided the activity into three categories: a)excercises and procedures. b)problem solving and reflect. c)understanding concepts. the results and how much time they spent on each category:
--------------a-------b-------c
japan-----42,5%--42,8%-13,8%
the us----94,9%--0,2%---4,9%
germany-89,2%--4,5%---6,3%

so, do you see any significant results here...? point is, students in japanese classrooms spend as much time in solving problems and discussing mathematical concepts as they do practising skills. that is what is meant by the teaching gap, or cultural differences. this study also blows away the misconceptions that the japanese students are doing so well because they are constantly practicing skills.

ieatfood wrote:
i disagree--the biggest difference is still cultural. Doing studies among countries is especially useless since countries differ in so many factors. It's impossible to isolate all the different factors cultural and otherwise and to ascribe differences to simply teaching technique, which itself is extremely variable across the nation.

based on what, you're own 'feelings'? can you provide any form of peer reviewed research that actually support these claims?

you keep going on and on about 'culture' and refer to the differences between american culture and easter asian culture, but you seem to be ignoring/forgetting that there are other countries doing very well in for instance the pisa study. in the 2003 report, the 6 top countries were:
1.hongkong
2.finland
3.korea
4.netherlands
5.japan
6.canada

(the us finished in 27th out of 38).

as you can see, a wide range of different 'cultures', more than one of which are quite similar to the us. so please, don't give me the culture excuse.

ieatfood wrote:
I base my knowledge on how the best math students do things. I went to a school full of math geniuses and everyone looks at math the same way. All the smartest math students all grew up on drilling, not wasting their time on shapes and the such.

exactly and that is the way of thinking that will keep the us(and norway) lagging far behind the likes of netherlands, japan, finland and hongkong. if it works for some students, why change it? point is, the teaching methods in said countries are far more wide reaching. they get the best out of far more students, which in turn leads to a massive improvement in their average results. not only do they have far fewer drop outs, but they also have a lot more potential candidates for higher education.

ieatfood wrote:
except that drilling is inductive learning. At first, the person may not memorize the formula and may need to have a study aid to solve the first 5-10 problems. But by the 100th-150th problem, the formua itself is now second nature because that person has done it so many times. If you had the formula perfectly memorized the first time, you wouldn't need to do the drills.

no, you don't understand the difference between inductive and deductive learning. as i said, the former goes from specific examples to a general rule/formula. the latter from a general rule which is applied to specific examples. studies have shown which is more effective and it is not the deductive method. deductive learning is basically being told what to do and then just replicating someone else's work. it is as far from science as you could possibly get. it is intellectually lazy. jerome s.bruner has written some interesting papers on the concept of discovery learning.

[ieatfood]

Random Evil Guy wrote: ieatfood wrote:
the issue with (x+y)^2, however, is that there is no understanding to be done.

in this example, (x+y) is the length of a side in a square. (x+y)^2 is the area. by displaying this both geometrically and algebraically kids and students devlop a better understanding of the concept and how the different aspects of it relate to each other. it's all part of developing a deeper knowledge of math. which in turn leads to a better chance of solving more complex and intricate mathematical problems.

oh, ok--i didnt know that's what you meant
sure, that's a good idea, but only if you've mastered both (X+y)^2 and how to take the area of a square. Thus, if drilling 100 problems, this problem might be one of the later ones I'd introduce. But definitely not one of the first few problems. It's very easy to get confused trying to combine squaring with computation with geometry. You can't teach kids to swim before they've learned how to tread water.


Random Evil Guy wrote: tical skills and devlop a deeper and intuitive understanding of math.

in the timms video study, they recorded what was happening in 100 german, 81 american and 50 japanese math classes for 15 year olds. the goal was to observe and note differences and similarities. fact of the matter is, that on the surface, things were very similar. similar class rooms, similar classes and number of students etc. difference was in the teaching methods and in more particular, how much time they spent on different issues. the researchers divided the activity into three categories: a)excercises and procedures. b)problem solving and reflect. c)understanding concepts. the results and how much time they spent on each category:
--------------a-------b-------c
japan-----42,5%--42,8%-13,8%
the us----94,9%--0,2%---4,9%
germany-89,2%--4,5%---6,3%

so, do you see any significant results here...? point is, students in japanese classrooms spend as much time in solving problems and discussing mathematical concepts as they do practising skills. that is what is meant by the teaching gap, or cultural differences. this study also blows away the misconceptions that the japanese students are doing so well because they are constantly practicing skills.

multiple problems with this study
one--its retrospective--there are multiple problems with all retrospective studies, which I wont get into
two--its not representative. Students in Mississippi, are very different than students in New york based on a whole variety of demographic factors--you would have to control for them all, which is impossible
three--its a study that proves correlation, not causation

we have no idea how much homework there kids are doing, how much support they are getting from their parents, etc. We also have no idea what kind of education these kids had before and after the video portion (which is an very very insignificantly small subsegment of the child's education).

I could do a similar study and chart the number of times children were allowed to go out for a drink of water. Likely, there would be major differences between countries. I could come up with a chart just like yours and start to draw outrageous conclusions. It doesn't mean anything. Studies like this are complete bunk.

The only way to learn how to educate kids is by personal experience. Doing flawed studies doesn't help and is a waste of time and money.


Random Evil Guy wrote: ieatfood wrote:
i disagree--the biggest difference is still cultural. Doing studies among countries is especially useless since countries differ in so many factors. It's impossible to isolate all the different factors cultural and otherwise and to ascribe differences to simply teaching technique, which itself is extremely variable across the nation.

based on what, you're own 'feelings'? can you provide any form of peer reviewed research that actually support these claims?

you keep going on and on about 'culture' and refer to the differences between american culture and easter asian culture, but you seem to be ignoring/forgetting that there are other countries doing very well in for instance the pisa study. in the 2003 report, the 6 top countries were:
1.hongkong
2.finland
3.korea
4.netherlands
5.japan
6.canada

(the us finished in 27th out of 38).

as you can see, a wide range of different 'cultures', more than one of which are quite similar to the us. so please, don't give me the culture excuse.




actually, international comparisons are by themselves, flawed to begin with. The US is an incrediblly heterogeneous country many times the size of any of these other countries. YOu're really comparing apples to oranges from the getgo.

however there are different attitudes towards education in many countries and the US happens to have one of the worst attitudes. How does this not make sense? Similarly, if you ranked support for peace in Iraq, the US would also rank among the bottom. You could do the same timms retrospective study and find all sorts of correlates to greater likelihood to support war. But that study would be just as flawed as the timms study.

Random Evil Guy wrote:
ieatfood wrote:
I base my knowledge on how the best math students do things. I went to a school full of math geniuses and everyone looks at math the same way. All the smartest math students all grew up on drilling, not wasting their time on shapes and the such.

exactly and that is the way of thinking that will keep the us(and norway) lagging far behind the likes of netherlands, japan, finland and hongkong. if it works for some students, why change it? point is, the teaching methods in said countries are far more wide reaching. they get the best out of far more students, which in turn leads to a massive improvement in their average results. not only do they have far fewer drop outs, but they also have a lot more potential candidates for higher education.

the question is, why do they have fewer drop outs? YOu can't prove causation with a retrospective study. All we have is correlates.
Random Evil Guy wrote:
ieatfood wrote:
except that drilling is inductive learning. At first, the person may not memorize the formula and may need to have a study aid to solve the first 5-10 problems. But by the 100th-150th problem, the formua itself is now second nature because that person has done it so many times. If you had the formula perfectly memorized the first time, you wouldn't need to do the drills.

no, you don't understand the difference between inductive and deductive learning. as i said, the former goes from specific examples to a general rule/formula. the latter from a general rule which is applied to specific examples. studies have shown which is more effective and it is not the deductive method. deductive learning is basically being told what to do and then just replicating someone else's work. it is as far from science as you could possibly get. it is intellectually lazy. jerome s.bruner has written some interesting papers on the concept of discovery learning.

i never said that inductive reasoning should not be employed. You still need to master the fundamentals though, by drilling.

[californian conservative]

Well my 2 cents. I'm a senior in H.S. (private school) in calculus right now for some context as to where i'm coming from.

I would consider myself very good at math, not because I have a wide knowledge in the subject, but I can reason myself through just about any math problem (excluding calculus, alot of that has to be taken on faith for me) The teachers teaching me math (honors throughout all of high school) have had a wide variety of teaching styles. My favorite was my pre-cal teacher. She would teach one way to do something, usually by deriving the equations and such, first. Then she would often teach us another way to look at the problem. To this day I can often solve problems using several methods thanks to her.

Some math, especially the concepts, needs to be drilled in. as to your example of the (x+y)^2 the square thing you mentioned wouldn't help me at all. I just learned how to deal with powers, and it makes perfect sense to me. The secret to math is that, up to calculus, all math can be solved the exact same way. And yet some students are unable to do this because they don't know how to do the basics. For instance i've seen kids who don't know what the commutative property is or how to use it. Understanding how the numbers relate to each other is exceptionally important. I'm no expert in math or education, but i can tell you what has worked for me. 1st grade was addition and subtraction. 2nd and third was multiplication and basic division. 4th was long division. It was constantly drilled in how to do them, and how they related to everything else. That laid the foundation for everything that i learned later. I honestly can't remember what i did in math in 5th and 6th grade but in 7th i started algebra. Algebra was one of the easiest classes i had just because the fundamentals had already been taught to me. We fail to teach the fundamentals and then wonder why the kids fail.

my 2 cents, cya