Math Education: An Inconvenient Truth

[nightning]

It's an interesting idea you brought up pt... math and drilling... Drilling yourself with it until it's automatic. Undoubtedly it makes a difference... there's also the other side of wanting/seeing the necessity of doing it. Is being forced to do it until you are competent worth it against hate and resistance to use it?

[ptgatsby]

Originally Posted by nightning

It's an interesting idea you brought up pt... math and drilling... Drilling yourself with it until it's automatic. Undoubtedly it makes a difference... there's also the other side of wanting/seeing the necessity of doing it. Is being forced to do it until you are competent worth it against hate and resistance to use it?

Well, I hated brushing my teeth, going to bed, learning to read, playing the piano. Yet 15 years later, I don't have cavities, still hate going to bed, read extremely well and wish I still played the piano... that is, outside of even trying to get good marks in my courses, or just plain understand it so I can perform well at work, almost everything I can do now is related to things I didn't want to do as a child.

It's not a side effect, honestly... parents just need to force their kids to do it, just like anything else. I fought and fought and came up with all sorts of ways of getting around it... thinking back, if I had just done it for the 15-30 minutes it takes 4-5 times a week, plus the one day of going in, I'd probably have saved myself a lot of time. Towards the end, 15-30 minutes is probably way higher - around K (I think?) or so it slows down, but doing it in 5-10 wasn't unusual until then. Hell, some of the tests (F?) had to be done in under 13 minutes.

[nightning]

Originally Posted by ptgatsby

Well, I hated brushing my teeth, going to bed, learning to read, playing the piano. Yet 15 years later, I don't have cavities, still hate going to bed, read extremely well and wish I still played the piano... that is, outside of even trying to get good marks in my courses, or just plain understand it so I can perform well at work, almost everything I can do now is related to things I didn't want to do as a child.

No, it has nothing to do with marks nor understand... I was more referring to interest. I'm just going to use reading and piano for example because you brought those up. Reading... I didn't have to be forced to learn to read simply because I enjoyed it on my own. I'm a decent reader... well my reading speed is probably faster than an average person and comprehension is up there as well. I continue with leisure reading, fiction and non-fiction alike even now. Where as with piano, I just stopped because I couldn't take it. Perhaps it was incompatibility between the teachers and myself, or perhaps it was just that I can't stand the rigidity of it all. The final ending comments people had of my playing was "it conveys the atmosphere, but lacks precision". Maybe the insistence of drilling would have made a difference, but you kill the spirit of things. I didn't touch the piano back then unless I had to. Nowadays, I visit it say once in a blue moon. It's certainly not enough to regain skills. I couldn't help but think maybe if a different method was used, things would be different.

I don't mean to go off on a tangent like that... but just illustrating the point. The Kumon method isn't for everybody, but darn if I know what works for people like me.

[ptgatsby]

Originally Posted by nightning

I don't mean to go off on a tangent like that... but just illustrating the point. The Kumon method isn't for everybody, but darn if I know what works for people like me.

Maybe not, but you can take away Kumon and replace it with anything... as simple as homework - say, writing essays or doing math homework... working on projects... drawing. In the end, if you want the skill, you need to do it. If, as a parent, you know your child needs the skill, you force them to do it. Course, I agree that in theory there may be another way to learn, or a different way of getting someone to work through problems... but how do you get around the doing? If the child doesn't want to do... then what?

I know of no other way of learning the skills you need than by actually going through the motions. I regret realising this in my mid twenties, being a miserable student my entire life... but I am fortunate that my "love" was computers - it got me a good job. But it was luck - and a combination of being forced to do things that I really didn't like doing. My parents were too easy going - they were wise to force the math and english, but they really let me slide on the school side. They also thought that if I understood it I would be fine... as it turns out, the discipline might of seen me through my college drop out years.

In the end, I'm saying that skill comes down to doing it. Kumon is a distilled version of that - maybe not the best or only one - but the one I am familiar with. It's just not enough to know "how".

[GZA]

I didn't bother watching that because I currently don't have sound.

So is this going to infect Canada as well?

I'm going to assume it isn't, because if its truely a stupid idea, it won't make it in. Maybe I'm getting ahead of myself.

You know how every graduating class has that kid who never really learned how to read and write proporly and should probably go back to grade 9 english? Well, I'm that kid, but with math. I can't do mental math, and I'm poor at other kinds of math, and I'm hoping to just kind of shove it under the carpet after I pass this math class (Grade 11 math -they condensed the cirriculum so that the essential things that used to be in the grade 12 math are now in grade 11 so that people who do not plan on studying math or math related things don't have their average blown down). Thanks Governemnt of Ontario

[ygolo]

I don't know why I missed this the first time it came up.

There is nothing wrong with teaching the focus and cluster methods. Just because parents don't understand them doesn't mean they are bad. They are especially useful for "ball-parking" an answer to check against what a calculator or computer (or your own application of the standard algorithm) spits out.

Both these methods, along with a few other ways, are useful for me to do mental math. I didn't have names for them, I was simply using my reasoning skills. Admittedly, the way I do math when I take pencil to paper are the standard ways (though sometimes I do it the way shown in Everyday Math.)

I think the standard algorithm is a good one, and should be taught while making sure the students actually understand the concept of numbers (non-negative integers), instead of thinking of them as just being part of some algorithms.

It may come as a surprise to many who are proficient at math, but just knowing the algorithm makes the step to algebra very difficult. It also makes the understanding of logarithms and trigonometry more difficult. I've seen it in many students. I was baffled--how could they do basic math but find it so incredibly hard to take the next steps? I finally realized that all they knew were the route methods, with no conceptual understanding.

I believe spending time on applications and learning to use a calculator are very important skills in the modern world. But frankly, students ought to be forced to memorize the times table to 10*10, at least. You can't even use the cluster and focus methods for much without those memorized.

The standard algorithms are easy enough, and some practice is needed as well. But how long do you really need for them?

Also, even in the days when they only taught the standard algorithm, there were people who didn't know how to multiply 6*4. In all base ten algorithms, that just needs to be memorized. I suppose you can cluster 4 times if you know how to add...but that is cumbersome.

People like to criticize what is new or different. But I think people have been bad at math for a while. No need to blame it on the new methods.

Mocking group work is another thing that seemed like easy fodder. Frankly, I think people have been checking against other peoples answers for a long time.

The claims made in the video were presented without evidence, and the people in the college course with the presenter could have been educated with different methods than the ones she criticized.

Also, the lattice method that seemed "so stupid" to some IS the standard algorithm, just placed diagonally on a grid allowing for a higher place value to be placed right next to each other. Also, the base-2 version of that is how a computer does multiplication (well with a lot of "compression" and optimization for speed, but it is important to have the basic idea taught by the lattice method).

Being able to get an answer in multiple ways is absolutely essential for checking your answers, absolutely. The fact that the presenter mocked this, I found outrageous. Just because 36/6 is easy for you doesn't mean that the concept is well placed for you. Having a student come up with multiple ways to solve such a basic thing is something very important to understanding numbers...something that will be build upon for algebra,word problems, etc.

Here is an actual math professor's response (not the hearsay of someone)
Note: I typed out my response before watching these videos. The similarities in responses came from our similar backgrounds.
YouTube - Math Education: A response to "An Inconvenient Truth" Part1

+ "Math Education: A response to "An Inconvenient Truth" Part 1" via YouTube

YouTube - Math Education: A response to "An Inconvenient Truth" Part2

+ "Math Education: A response to "An Inconvenient Truth Part 2"" via YouTube