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The case against teaching math

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Re: The case against teaching math

#21

Post by flatline »

abstractbill wrote: post #19
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)…

Just adding my own experience to this: Until the age of 15, maths was considered a real "problem subject" for me. At every parent-teacher conference it was generally accepted that I would never be good at it (and I had no problem with that at all - I found the whole subject very boring and difficult). Then one day, at age 15, a classmate showed me how to do quadratic equations. I have no idea why, but that day a real…

I came out of Algebra I with a C or a D and didn't feel like I understood any of it. Geometry came next and it was fun, I really liked proofs and somehow by the time I got to Algebra II, everything made sense.

From that point forward, however, math just seemed like rote memorization without any meaning or elegance. I shied away from it for years, only just returning to school to learn more math recently, in my 30s. I still feel like there's something fundamentally lacking in the way the whole math curriculum is set up, as I didn't see much that I really enjoyed in the period between 9th grade Geometry and Calculus II. I understand the need to build a solid foundation before learning more advanced material, but it seems very one-sided when there is such a breadth of interesting material out there.

Re: The case against teaching math

#22

Post by jrp »

epochwolf wrote: post #15
jerf wrote: post #7

Bear with me here, I have to lay down some foundation to get to my point. Bias has a specialized definition in machine learning; in a (really thin) nutshell, it represents the set of concepts a given technique can represent. If your banana vs. ball classifier can only represent "roundness" and "yellowness", the bias will prevent it from seeing a yellow cube as anything but a banana. (If you really dig in, I find this…

Think about it; how many adults have downright childish issues with math? Childish misunderstandings, childish opinions, childish beliefs? Coincidence? Bad motivation? Right here. I taught myself programming and I got pointers (references, same difference) within the first week I started reading about php. I enjoy learning new concepts except for math. I really want to learn math but I am so afraid of just opening a…

I would try to find a book that balances managable and brain stretchy. _Calculus made easy_ was good for me at a certain level of understanding (yes algebra and geometry, no calculus). Try things at a library, and get recommendations, until you find one that turns you on. There's no penalty for trying a book and aborting after 1 page ;)

Re: The case against teaching math

#23

Post by rw »

epochwolf wrote: post #15
jerf wrote: post #7

Bear with me here, I have to lay down some foundation to get to my point. Bias has a specialized definition in machine learning; in a (really thin) nutshell, it represents the set of concepts a given technique can represent. If your banana vs. ball classifier can only represent "roundness" and "yellowness", the bias will prevent it from seeing a yellow cube as anything but a banana. (If you really dig in, I find this…

Think about it; how many adults have downright childish issues with math? Childish misunderstandings, childish opinions, childish beliefs? Coincidence? Bad motivation? Right here. I taught myself programming and I got pointers (references, same difference) within the first week I started reading about php. I enjoy learning new concepts except for math. I really want to learn math but I am so afraid of just opening a…

Are you in school? Get an independent study going with a professor on a topic she likes and you wouldn't mind learning. Emphasize that you want to get your training wheels for autodidactic math education.

Re: The case against teaching math

#24

Post by rw »

Tichy wrote: post #2

I learned maths AND was able to solve "story problems" in elementary school. Looking back, the maths taught in elementary school is very basic, too. Just multiplication and division of integers, not even fractions yet. To be honest, I don't care that much anymore if somebody doesn't want to learn maths. It's just their loss. But maths was one of the few things I enjoyed at school, so I absolutely see no point in remo…

"Everyone generalizes from one example. At least, I do."

Re: The case against teaching math

#25

Post by lotharbot »

Tichy wrote: post #2

I learned maths AND was able to solve "story problems" in elementary school. Looking back, the maths taught in elementary school is very basic, too. Just multiplication and division of integers, not even fractions yet. To be honest, I don't care that much anymore if somebody doesn't want to learn maths. It's just their loss. But maths was one of the few things I enjoyed at school, so I absolutely see no point in remo…

In Montessori, there is some emphasis on choosing what you're interested in, but I think the more important part (when it comes to math) is that it's typically taught using strong visuals, manipulation of number blocks/cubes, etc. Instead of focusing on rote memorization of algorithms, the focus is on patterns and sensory experience. Kids "get" patterns; what they struggle with is algorithms applied to symbols.

I went through "normal" school and was always way ahead in math. My Montessori-educated sister, 3 years younger than me and not particularly mathematically inclined, could intelligently converse with me about my algebra homework when I was in sixth grade and she was in third. She wasn't as familiar with the symbols as I was, but she recognized many of the patterns (like difference of squares) in physical form.

The Montessori math approach is outlined at http://www.infomontessori.com/mathematics/introduction.htm

Re: The case against teaching math

#26

Post by epochwolf »

rw wrote: post #23
epochwolf wrote: post #15

Earlier quoted context omitted.

Think about it; how many adults have downright childish issues with math? Childish misunderstandings, childish opinions, childish beliefs? Coincidence? Bad motivation? Right here. I taught myself programming and I got pointers (references, same difference) within the first week I started reading about php. I enjoy learning new concepts except for math. I really want to learn math but I am so afraid of just opening a…

Are you in school? Get an independent study going with a professor on a topic she likes and you wouldn't mind learning. Emphasize that you want to get your training wheels for autodidactic math education.

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

Re: The case against teaching math

#27

Post by bobbin »

bmj wrote: post #17
marze wrote: post #16

Earlier quoted context omitted.

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…

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.

Re: The case against teaching math

#28

Post by buckler »

epochwolf wrote: post #26
rw wrote: post #23

Earlier quoted context omitted.

Are you in school? Get an independent study going with a professor on a topic she likes and you wouldn't mind learning. Emphasize that you want to get your training wheels for autodidactic math education.

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/item?id=755043

- http://news.ycombinator.com/item?id=1058359

- http://news.ycombinator.com/item?id=1193352

One caveat is that many of these textbooks do not come with a solutions manual. So, in terms of practice, I think that's where the dearth of uploaded lecture materials could come in. Sometimes, there might be no e-learning/opencourseware material for the topic you're interested in. In such cases, I found that if you look through universities' Websites closely enough, professors upload a lot of course materials on their personal pages. You can do this by finding a random university's math dept. page, then searching from course/faculty listings.

Last of all, I'm pretty certain you've heard of this site already, as it's being circulated quite a lot lately, but many have professed that videos from khanacademy.org to be quite helpful when grasping basic mathematical concepts.

Re: The case against teaching math

#29

Post by xiaoma »

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 was very different. I learned basic addition as a toddler, and then demanded that my uncle teach me whatever was "next". Bless his heart, he made me a basic math game on his commodore 64 with flashing lights, progressively harder levels, time limits and hints. Through his patient instruction and a lot of free time on that game, I learned to multiply before entering elementary school and passed a college calculus class before entering high school.

Then, somehow after going to high school I got really into sports and less nerdy subjects and never progressed much further in terms of math than where I was at the age of 14 or 15. I regret it and OpenCourseWare beckons.

Re: The case against teaching math

#30

Post by [deleted] »

lotharbot wrote: post #25
Tichy wrote: post #2

I learned maths AND was able to solve "story problems" in elementary school. Looking back, the maths taught in elementary school is very basic, too. Just multiplication and division of integers, not even fractions yet. To be honest, I don't care that much anymore if somebody doesn't want to learn maths. It's just their loss. But maths was one of the few things I enjoyed at school, so I absolutely see no point in remo…

In Montessori, there is some emphasis on choosing what you're interested in, but I think the more important part (when it comes to math) is that it's typically taught using strong visuals, manipulation of number blocks/cubes, etc. Instead of focusing on rote memorization of algorithms, the focus is on patterns and sensory experience. Kids "get" patterns; what they struggle with is algorithms applied to symbols. I wen…

[deleted]
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