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Joined: Feb 2013
Posts: 40
Junior Member
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Junior Member
Joined: Feb 2013
Posts: 40 |
Devlin seems to believe that math is all abstract and the goal of math education is to study the abstractness, whereas other people try to relate math to the real world to make math concrete and useful.
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Joined: Sep 2008
Posts: 1,898
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Joined: Sep 2008
Posts: 1,898 |
Devlin's often interesting, but he doesn't half have some strange ideas, and I say that as a mathematician.
Email: my username, followed by 2, at google's mail
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Joined: Mar 2013
Posts: 1,453
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Joined: Mar 2013
Posts: 1,453 |
I read the articles along with some of his other stuff and concluded that he thinks that the goal of maths education ought to be in adequately preparing people for being able to think with rigour and to abstract the essential principles at work in any given situation.
While I don't particularly agree with everything that he writes, I do like the pithy way that he expresses it.
Become what you are
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Joined: Apr 2011
Posts: 1,694
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Joined: Apr 2011
Posts: 1,694 |
I have just started homeschooling math with my 7 yr old, who is not super "mathy" at all. She's about 18-24monthd ahead of appropriate grade (she's skipped), so she's certainly not struggling, she's just not rocketing along naturally the way many kids here do. I'm finding it interesting that she is far better conceptually and at problem solving than she is at facts/arithmetic, it's hard at times to balance what she understands against the fact that she doesn't "just know" things that seem like they should be "self evident" (like addition and subtraction within 10). So she has struggles with fairly simple problems that are not about the concept or the idea of the method so much as the calculation, even when broken down to simplest facts.
She can be faced with "81-20" and mutter out loud "8-2...5...50..51" so no trouble getting that she should knock the zeros off, or deal with the ones later, but stumbles with the most basic computation.
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Joined: Apr 2011
Posts: 1,694
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Joined: Apr 2011
Posts: 1,694 |
I've been reading Liping Ma's book "knowing and teaching elementary mathematics" and finding it fascinating, I'm planning I read the articles above too. It seems like there are endless trends about how to best teach basic math that make little or no difference when the people teaching have no more understanding of the concepts than they did during the previous fad. There are some startling examples in the book of manipulative or concrete examples being hopelessly counter productive.
My DDs teacher has just sent home the class newsletter and has apparently been at a conference on teaching math and is now convinced that its detrimental for young students to learn math by writing down algorithms before they can do double digit addition and subtraction in their heads... So now she's all about making sure she avoids writing things out with her 2nd graders... Whih will suit some kids really well, but seriously why do schools follow each new trend with such reckless abandonment? Where is the middle ground and balanced multi pronged approach?
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Joined: Feb 2011
Posts: 5,181
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Joined: Feb 2011
Posts: 5,181 |
This seems timely-- Devlin just had a Coursera course go live. Probably not suitable for the youngest kiddos here, but could be a good fit for the 10y+ set. Intro to Mathematical ThinkingIt looked interesting, so I thought I'd give it a whirl. I'd really like for my DD to take a look at it if it is a good course, as the ideals espoused in the mission seem positive. The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.
The primary audience is first-year students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind. If that is you, you will need mathematical thinking to succeed in your major. Because mathematical thinking is a valuable life skill, however, anyone over the age of 17 could benefit from taking the course. There is fairly extensive coverage of proofs, which makes me pretty pleased.
Schrödinger's cat walks into a bar. And doesn't.
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Joined: Feb 2013
Posts: 1,228
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Joined: Feb 2013
Posts: 1,228 |
I was parodying Devlin's gratuitous smartypantedness.
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Joined: Mar 2013
Posts: 161
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Joined: Mar 2013
Posts: 161 |
I was parodying Devlin's gratuitous smartypantedness. I know, I was parodying yours.
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Joined: Oct 2011
Posts: 2,856
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Joined: Oct 2011
Posts: 2,856 |
How timely. After reading Devlin go on and on about addition and multiplication being different operations, DD brought home some vocabulary homework from her math class, and needed help looking up the various properties of operations, since they don't show up in her dictionaries.
And so we came to "identity property," and I immediately exclaimed, "Which one?"
Addition: n + 0 = n
Multiplication: n x 1 = n
They're totally different rules. Here was an immediate illustration of how thinking of them as totally different operations can help make sense of them.
Product and divisor were on the word list, addend and sum were not, so I assumed they wanted the properties of multiplication.
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