Article on the case against teaching math

[dna]

http://ordinary-gentlemen.com/blog/2010/03/25/the-chloroformed-mind-the-case-against-teaching-math/

Any thoughts on this argument?

[fma001]

The problem is not that we teach math too early. The problem is that we teach it so badly. Elementary kids aren't given enough time to master what they are learning. It is better to teach less and teach it very well. Asians tend to be good at math because they spend far more time on mastering foundational concepts. American students are rushed from one concept to the next and often don't under Concept A before being rushed onto Concept B. We absolutely should teach math to young kids. But we should teach fewer concepts at a time and make sure students master what they are learning before moving on. Math is such a linear subject. If you don't develop a good foundation, you can't do it at a higher level. Math education is US schools is one more reason why I homeschool.

[drummerboy]

For a really interesting perspective on how math should be taught see if you can find anything on Richard Feynman's thoughts.

Maths and physics genius he finds the way we approach the teaching of math abhorrent.

It is our approach to the subject that is wrong not our timing. Hence the children in the experimental group being able to do problem solving it wasn't that they hadn't been taught as they had been they had been taught with a much better approach.

Let's face it what skill would you rather your child have - the ability to think logically and work things out for themselves or the ability to apply an algorithm the origins of which they have no understanding and the applicability of which to the real world being almost zero?

[happymomof5]

it is very important to really comprehend the concepts, understanding being the key
i am a math teacher - it's not the route memorization that is important, it's the logic & the understanding

by the way, pls note in the above mentioned article the author also says that the experimental children had regular experiences with measuring, counting, etc - the second key point to successful math learnign - practical application - so they did have math, actually the way it should be taught, life math!  They experienced math in a natural way, not memorized some facts that were disconnected from their life! That is the best way to teach kids math, through practical experiences.

and of course, teaching several languages & the story telling - absolutely!!! YES!!! And i also do agree that good language skills do improve your thinking ability & problem solving skills - actually that would be pretty logical, wouldn't it

[MummyRoo]

I agree that the way maths is being taught is wrong, not the teaching of it. We would not expect primary school children to sit and drill verb declensions and come out with perfect literacy, so why do we expect the memorising of facts in maths to create a perfect understanding of numeracy?

Learning the facts is important, but learning them in a real-life context is what makes them stick! 

[DadDude]

If a superintendent tried it in 1929, it's good enough for me!

Just kidding :-)

[fma001]

I'm always concerned when people say that math should be relevant or based on real life. That is important to some extent. But isn't teaching children abstract thinking important too? Literature, philosophy, critical thinking and math can be very effective in helping children build abstract thinking skills. If we always try to teach these things in a way that seems relevant or real life, wouldn't we create a bunch of students who are incapable of abstract thought?

[DadDude]

I'm always concerned when people say that math should be relevant or based on real life. That is important to some extent. But isn't teaching children abstract thinking important too? Literature, philosophy, critical thinking and math can be very effective in helping children build abstract thinking skills. If we always try to teach these things in a way that seems relevant or real life, wouldn't we create a bunch of students who are incapable of abstract thought?

You're onto something there.  I was just writing a blog post (haven't decided whether & how to finish it) in which I argue that much of what we learn in school is best learned in books, precisely because it is abstract.

There is definitely a general movement afoot against abstract thinking in all its forms.  Everything has to be applied, experiential, hands-on.  Which is, of course, complete nonsense, if you think about it.

[DadDude]

OK, I finished reading the article all the way through.  This is very weak.  Let me sum up my thoughts:

1. Well, that's a neat trick--kids learning seven years' worth of math (well, maybe) in one year.  It's worth more study.  Maybe I too would agree that we should defer all math until much later.  We defer plenty of other things that could be introduced in a simple way earlier, such as logic.

2. But I'm looking for the argument for why we shouldn't teach math in elementary school.  It goes like this: "Uhhhhh...like, so, there was this superintendent in 1929, see...who did this experiment, like, and the kids weren't taught math until the sixth grade, you know?  And uh...they were able to do simple math word problems better than the other kids at the start of the year, and by the end of the year, they were doing the rest of the math problems as well as the others.  Like, WHOA!"  (OK, that's what I read, even if he didn't say exactly that.)  That's it?  One study, done 82 years ago?  I'm not even going to list the problems here.  Suffice it to say that this is a shockingly thin basis on which to make such a radical proposal.  A responsible scholar should know better.  Psychology Today should know better.

3. Suppose some children we were to do both recitation and math--not just one or the ohter.

4. There is no reason given to think that the late-educated kids would not come to hate math just as much as the early-educated kids.  It is a hypothesis that there is something wrong with teaching math to younger kids that explains why children don't like math.  The author didn't even establish that the late-educated kids liked math in the sixth grade, let alone when they were in the ninth.

5. It's well known that many teachers are very poorly educated themselves.  But that is quite possibly because of the anti-intellectualism that runs rampant in our education departments; anyone who is firmly committed to the life of the mind is disgusted by what passes for pedagogy today.  Anyway, what's the point of saying that elementary school teachers don't know math?  Oh, they can't teach math if they don't know it?  Well,

6. My guess--and the author provides no reason to think this is not the case--is that in the long run, the students who started earlier, and especially the ones like the Doman kids who started thinking about and memorizing facts about numbers as very young children, will be quicker with math, generally speaking.  It's not implausible that poor math pedagogy could turn kids off to math in K-6 grades, and get them thinking about it all the wrong way.  But it's a long leap from that to the conclusion that we should not teach math in K-6.

[DadDude]

My more complete response: http://larrysanger.org/2011/06/should-we-teach-math-in-elementary-school/

[Frukc]

In the link above, author writes:
He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.


Here http://www.livingmath.net/
I read:
Ways to Learn Math Naturally
Count, count, count objects. Young children love to count. Counting seems simple, but when you do it with your child, you begin to see just how rich counting activities can be. 


So I think the author does not know what he is speaking about. I believe that math must be started early. And experimental groups always perform better because they get better teachers who are open and creative.

[fma001]

Larry,

I don’t think people often consider side benefits of certain things. Many people may consider learning poetry to be a waste of time. It isn’t something practical that most people use in real life. But it’s very possible that poetry builds a lot of useful skills, such as abstract thinking, analytical, memory and concentration skills.

A lot of educators once thought that teaching grammar was a waste of time. Students were memorizing a lot of useless facts. But linguists say that learning grammar is necessary to have good writing skills. They say even if you don’t remember the difference between a pronoun or a proper noun, you actually internalize grammar rules and use them when you write. Now that many students, including MBA graduates, can no longer write well, there is a push to bring grammar back to schools.

Learning a musical instrument is a perfect example of this. Musical training builds other skills, such as logic and spatial reasoning. Kids who learn music learn many math concepts much more easily than non-musically trained children. This has even been found in studies where children were assigned to a group to either study music or study something else like drama. So, it is not a case of more intelligent and more privileged kids taking music at a higher rate. Better math ability is a very real outcome of musical training.

A lot of the hands on, problem solving and collaborative “real world” learning in schools is actually nothing like the real world. The kinds of problem solving done in schools is often trial and error. In the real world, if you are put in charge of a million dollar project, you’d better not use trial and error. In the real world, you have to study a problem and get it right the first time.

Collaborative learning in the real world usually isn’t sitting around a table working on a problem together. It is having a meeting, getting assigned your part, working alone on your part of the project and then meeting again to update each other. I’m sure the kind of collaborative learning commonly done in schools does happen, but it isn’t the norm.

I think schools teach kids a lot of things they don’t need and avoid teaching them things they do need based on misguided views about what is useful in the “real world” and what isn’t.

[MummyRoo]

I like the Living Math website!

I stick by my earlier comment that it is important to make maths understandable in a real life context, but I also agree that it is important to learn the abstract.

It strikes me that teachers are too focused on the fact that children must learn all the abstract facts to be able to do maths. Surely it is better at an elementary level to introduce the fundamental mathematical ideas in a way that relates to real life and things that children can understand, then once these basics are understood, start introducing the abstract ways of thinking.

Maybe I'm wrong, but I think that if children don't understand the fundamentals because it is all presented in an abstract manner, then they can't progress to understanding abstract concepts later because they won't know the basics!

[fma001]

Frukc,

It is true that a lot of educational methods that were very successful in trials, often were failures when put into widespread use. One reason is that educators in trials are often very well trained in those methods and much more dedicated. More resources tend to be put into trials as well. When put into widespread use, teachers tend to lack the training, time and resources to successfully implement those methods that worked well in trials.

[fma001]

MummyRoo,

I think you need to do both the concrete and abstract at the same time. When teaching a child to add, it is very important to use real world examples. There is one bird on a branch. Two more birds land on the branch. How many birds are on the branch now? However, it is important to also introduce more abstract concepts like place value and carrying as well. One problem with the focus on everything being real life is that it often leads to extremes, like introducing calculators in 1st grade because it is considered pointless to have children work out algorithms.

So, I don't disagree with you to a certain extent. The more relevant you can make math in the early years the better. But it is also important to train children in abstract thinking early. Schools should not avoid the abstract and only focus on real life examples. They should also avoid teaching only the abstract and avoid real life examples. If a child has only been trained in the concrete, they will be lost once they start learning abstract math like algebra. On the other hand, if everything is abstract, children may not have a good conceptual understanding. It really has to be both together. I think schools have a tendency to go from one extreme to another rather than using a more balanced approach.

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