The case against teaching math • Hacker News Board

Re: The case against teaching math

#41

Post by derefr » Sun, Mar 28, 2010, 1:50 AM UTC

Just a slight quibble:

> R–recitation. He wrote that by "recitation" he meant, "speaking the English language." He did "not mean giving back, verbatim, the words of the teacher or the textbook." The children would be asked to talk about topics that interested them–experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he thought, would help them develop the capacity to reason and communicate logically.

He means "rhetoric." That's what the second "R" of the "Three Rs" (a.k.a. the Trivium) is supposed to mean.

Re: The case against teaching math

#42

Post by derefr » Sun, Mar 28, 2010, 1:57 AM UTC

This occurred to me when I took my first college psych course, and we were talking about "operational stages." The whole lecture was about how kids can't work with disconnected mental abstractions until they reach a certain level of cognitive development (the Formal Operational Stage.) It was also enforced that moving between stages of cognitive development just takes time, not more or better prerequisite education. In that light, it's kind of obvious that young children shouldn't be being taught math, any more than they should be being taught first-order logic.

Re: The case against teaching math

#43

Post by epochwolf » Sun, Mar 28, 2010, 4:26 AM UTC

buckler wrote: post #28

epochwolf wrote: post #26

Earlier quoted context omitted.

Sadly, I'm graduating in 6 weeks. I think I'll have to figure it out on my own.

May be you've seen these HN threads about self-learning maths already... if not, hopefully you'll find these textbooks useful. Here's a little HN link dump, in the order of time at which the discussions took place (from the oldest to the most recent): - http://news.ycombinator.com/item?id=108723 - http://news.ycombinator.com/item?id=201913 - http://news.ycombinator.com/item?id=458926 - http://news.ycombinator.com/ite…

Thanks for the list. Saves me from cluttering HN with a another similar thread. :)

Re: The case against teaching math

#44

Post by psawaya » Sun, Mar 28, 2010, 5:26 AM UTC

marze wrote: post #16

teilo wrote: post #6

This story is dead on. I know this from personal experience and from teaching my own children. I could not add until I was 10. It was painful. I still remember it vividly. Suddenly everything clicked, and I rocketed through all the material I was behind on. I have six children, five of which are old enough to be in school. We have been home schooling them, I believe I have some creds on this. Two of them (both girls)…

It sounds like you are suggesting teaching children only the things they are interested in and ready for at the time. Compared to teaching on arbitrary set of topics at arbitrary times, you should have big gains in learning efficiency and enjoyment, since it is inefficient to spend time attempting to convey a concept the child is not ready for or is uninterested. The child will be spending a greater fraction of the t…

There are actually schools (http://en.wikipedia.org/wiki/Sudbury_school) that attempt to teach K-12 this way. It would be interesting to read a study of how Sudbury alumni perform after they graduate, but I can't find one right now.

Re: The case against teaching math

#45

Post by hkuo » Sun, Mar 28, 2010, 7:05 AM UTC

This is silly. He's on his way to make a good point, but fails when his main points become 1) no math 2) focus on stories and language early on.

The good point he could have arrived at is to put less emphasis on things a child is not immediately acquiring. It would be like trying to force-feed mashed potatoes down a drinking straw. Perhaps sometimes it's math. Perhaps sometimes it's music.

Instead, he just says, stories and language are the important part! Leave math for later!

What a buffoon. He started with a bigger picture that ended with a close-minded detail.

To the original author, remind yourself that "not everyone is you." Kids can grow up to be scientists, artists, doctors, lawyers, even gasp mathematicians! And we all take different paths, even at a young age.

Re: The case against teaching math

#46

Post by Qz » Sun, Mar 28, 2010, 8:08 AM UTC

teilo wrote: post #6

This story is dead on. I know this from personal experience and from teaching my own children. I could not add until I was 10. It was painful. I still remember it vividly. Suddenly everything clicked, and I rocketed through all the material I was behind on. I have six children, five of which are old enough to be in school. We have been home schooling them, I believe I have some creds on this. Two of them (both girls)…

I agree with you, even though math was never a problem for me.

Another factor that could play into this is the learned frustration that comes with the increasing force of the teaching attempts. Some people might be bad at math when they're young, but then because it gets pushed on them so much they then acquire a personal dislike for the subject, so even if later they might be in a spot where they could learn the subject easily, they'll still have in their head that they suck at math and don't like it. It's a really hard thing to unteach.

Re: The case against teaching math

#47

Post by Qz » Sun, Mar 28, 2010, 8:15 AM UTC

greenlblue wrote: post #37

Completely False. I started to learn mathematics starting in preschool and when I arrived in the US I was shocked by what passed as mathematics education in the US. The stuff American students where doing in 6th grade I had already done in 3rd grade. It might be that starting later is a good idea but the exact opposite was true for me. If I had been forced to learn mathematics the way American students learn it, well…

The American education system is constantly changing. I don't even know how they teach math to kids these days but I would probably think it was completely foolish. Apparently they changed the way they teach spelling and vocabulary and I think the new method is complete nonsense.

But the point of the article is that the current mantra seems to be that if 'kids aren't good at math in grade X' then 'teach even more math at grade X-1', which has diminishing returns when you start getting down to kindergarten and such.

Re: The case against teaching math

#48

Post by olliesaunders » Sun, Mar 28, 2010, 9:36 AM UTC

bobbin wrote: post #27

bmj wrote: post #17

Earlier quoted context omitted.

As another homeschooler, there is a fine line between gauging interest and imparting self-discipline. Of course, such "hard work" looks radically different at home than it does in the classroom. It's important to teach your children that there are times when they need to focus on things that don't necessarily interest them, but, again, how this is carried out in the home would likely be more positive than a classroom…

> It's important to teach your children that there are times when they need to focus on things that don't necessarily interest them Why do you need to teach them that? life does that when you pursue something you are interested in. Whenever I want to achieve something there are things I don't want to do that are necessary to do what I want.

I completely agree with this. Just cultivate an attitude of ambition in them. The environment will show them what skills are necessary to achieve their ambitions. I don't believe you should teach anything without demonstrating it's use; the environment does this more effectively than any teacher can.

Re: The case against teaching math

#49

Post by bmj » Sun, Mar 28, 2010, 1:27 PM UTC

bobbin wrote: post #27

bmj wrote: post #17

Earlier quoted context omitted.

As another homeschooler, there is a fine line between gauging interest and imparting self-discipline. Of course, such "hard work" looks radically different at home than it does in the classroom. It's important to teach your children that there are times when they need to focus on things that don't necessarily interest them, but, again, how this is carried out in the home would likely be more positive than a classroom…

> It's important to teach your children that there are times when they need to focus on things that don't necessarily interest them Why do you need to teach them that? life does that when you pursue something you are interested in. Whenever I want to achieve something there are things I don't want to do that are necessary to do what I want.

But if a child is never exposed to work (that is, focusing on things that don't necessarily interest them rather than simply floating between things they find fun), he may not be equipped to make the proper decisions later in life.

Don't misinterpret what I'm saying--I'm not suggesting that children are simply forced to learn things, especially without any sort of context. I am suggesting that sometimes children needed to be nudged to get over the "I don't want to think hard about this" hump. We've seen this in our own kids. Our older son didn't particular like to put forth the effort to read himself, but we asked him to do it just a bit each day, and quickly he realized this opened up a whole world of stuff that he could do on his own.

Re: The case against teaching math

#50

Post by cabalamat » Sun, Mar 28, 2010, 4:56 PM UTC

euroclydon wrote: post #35

cabalamat wrote: post #20

Earlier quoted context omitted.

You don't need any geometry to understand algebra. Though graphs (and therefore cartesian co-ordinates) certainly help).

To understand calculus, not algebra.

Well corrected. |You don't need geometry to understand calculus, either.