7 ms·

It's silly to have churn in the publishing market with ever new approaches, all of which are known to be less effective than proven methods of learning math tha

It's silly to have churn in the publishing market with ever new approaches, all of which are known to be less effective than proven methods of learning math that have been known for hundreds of years. Just use the Singapore Math series for K-6 and be done with it. Sound pedagogy, known to work, has been debugged, no frivolous cutting edge theories from M.Eds who have never taught math successfully.

Angostura 15y ago
> all of which are known to be less effective than proven methods of learning math that have been known for hundreds of years. [Citation needed]. The methods my kids currently use, seem more effective that the ones I used at school. I am in my late 40s. edit: I'm based in the UK, however.
- droithomme 15y ago
  1. My personal experience as a teacher. 2. The average state of math knowledge of contemporary american high school graduates, coupled with statistics on needed remedial education for college entrants with high school diplomas. Teaching math is easy. I can teach any kid math. It's not a problem at all because we know how to do it. Many countries do it successfully. Observing what schools are doing, the textbooks, the approaches, and the level of math competency of elementary school teachers completely explains what is going wrong. It's not a mystery. Also explains why kids homeschooled by parents, even parents who were high school drop outs, end up with considerably better math skills than most public school graduates, and even many private school graduates. Typical high school graduates don't understand fractions, percentages or decimals. They can't do division. They don't understand algebra at all. We know this is true because of college placement tests. This is absurd. 100% of high school graduates should have passed differential and integral calculus. That should be the minimal acceptable standard. That it is not, and that graduates fail at even moderate arithmetic skills, shows the complete failure of the system. Downvote all you want while shouting "the dedicated teachers are not the problem, the students and their parents are!" That won't change a thing. Meanwhile, those who utilize proven approaches succeed and those who make excuses and follow fads fail.
  - graeme 15y ago
    What effect do you think calculators have? I do some SAT tutoring, and I find that students are helpless at basic arithmetic if they can't use a calculator. My suspicion is that calculators prevent students from developing mental math skills, and that this hurts conceptual understanding across the board. But I can only see the results of the system, so I don't know what actually produced the types of students I'm seeing. I may be wrong about calculators - from what you say, it could simply be that the system in general is bad.
    - tel 15y ago
      I grew up learning math from calculators. I still today am terrible at mental math, but having immediate, accurate graphing capabilities from precalc onward was an incredible boon. Even before that, mechanical skills such as polynomial factorization or algebraic reorganization ("fiddly symbol manipulation") were actually, in my opinion, aided by having a calculator which could perform them for me. By releasing the burden of actually performing the computations, I was focused on larger patterns which made the computation meaningful and possible. There are two camps here, of course. As an engineer or mathematician, doing mental arithmetic is a dead skill---all the effort comes from modeling and understanding the structure of math. However, "practical" math such as computing tips or adding up grocery bills---and this was the kind of math application stressed in my public school education---probably benefits much more from rapid mental sums. So, ironically, I'd support the heavy involvement of calculators (even ones as powerful as Mathematica itself) in education if it's to be aimed to produce engineers, scientists, or mathematicians. Otherwise, they're probably damaging.
      - moped 15y ago
        WolframAlpha is a good visual tool also, and I often use it when I tutor math.
      - lnguyen 15y ago
        The issue is whether you learned the actual skill (graphing, factorization, etc.) or just learned how to get the calculator to do it for you. In many cases, the end results appear identical. However, I'd rather the upcoming engineers, scientists and mathematicians be banned from using calculators for anything more than basic arithmetic until they prove they do understand the concepts.
- keithpeter 15y ago
  UK note: a lot of work has been done in primary especially over the last 20 years to teach the reasons behind arithmetic and to lay foundations for algebra &c. I'm beginning to see this filter through to College level. Education differs significantly between countries, international comparison is hard.
- gaius 15y ago
  Maths education in the UK is mostly about how numbers "feel" when you subtract from them, and how this is related to rainforests and/or the third world. It's why 25% of the population is now innumerate.
aik 15y ago
How is this different than saying "paper and pen has been known to work, has been debugged, and doesn't suffer from frivolous cutting edge theories... so why build typewriters... so why build computers... so why innovate from that which already works?" Your argument is the antithesis of the reason for hackernews!
- quanticle 15y ago
  The difference is that typewriters and computers are better than pen and paper in many ways. The "new math" being taught at many middle and high schools in the US is not better, from a pedagogical perspective, than the existing math. In many schools today, math is taught as a "holistic" subject, where algebra, geometry, trigonometry are intermixed and taught as a "integrated" whole. In theory, this would let students appreciate that there are many ways to approach a problem and that the same theorem can be proven via many methods. In practice, all it ensures is that students have an insufficient background in three subjects rather than thorough knowledge in one. Bruce Lee said, "I do not fear the man that has practiced 10,000 kicks once. I fear the man that has practiced one kick 10,000 times." What our schools are doing is teaching different "kicks" (mathematical skills) but without following it up with the necessary practice required for students to achieve mastery of those skills. What we end up with are kids that know of mathematical theorems and mathematical results without knowing the results themselves.
  - aik 15y ago
    Yes but I doubt the first, second, or even 100th typewriter was less applicable to most situations than pen and paper. Same goes with computers. And same goes with new innovations/theories within education. Maybe the issue isn't with the "frivolous" theories but rather with the treatment of them. As in depend on empirical evidence through studies prior to applying them to a wide student base. The first +-10000 light bulbs weren't released to the public. Why are new educational methods?
    - tygorius 15y ago
      Heh. The ghost of Sam Clemens might beg to differ: "Among the first users was Mark Twain, who fiddled around with it before putting it aside. Yes, Twain did become the first person to submit a novel in typed form to the publisher, but that wasn't until much later ("Life on the Mississippi,"1883) , and he didn't type it himself... it was a typed copy of his handwritten manuscript."[1] That manuscript was produced at least 8 years after the first Remington model appeared. Although Clemens was clearly a technophile (and pal of Tesla), he considered the first models to be curiosities rather than immediate replacements for pen or pencil and paper. [1] http://home.earthlink.net/~dcrehr/firsttw.html http://home.earthlink.net/~dcrehr/firsttw.html
kleiba 15y ago
How can "ever new approaches" be already "known to be less effective"?
- deleted 15y ago
  [deleted]
SkyMarshal 15y ago
Or this little gem: Calculus Made Easy http://www.gutenberg.org/ebooks/33283 http://www.gutenberg.org/ebooks/33283 An oldie but a goodie.
- aptwebapps 15y ago
  Thanks! I just read the first few pages and I'm liking it already. I also like the Ancient Simian Proverb in the dedication. Looks like a keeper. Edit: This prefigures the For Dummies books by what, 80 years?
  - SkyMarshal 15y ago
    Yeah, it was written back in the day when education was education, not training.
cdf 15y ago
As a singaporean parent, i find it appalling that the world puts our maths textbook on the pedestal. The current textbooks are nothing like what I used as a child, and the techniques used to solve problems, extremely contrived. I see it exactly as products of M.Eds, who at best has experience teaching maths ONLY to gifted kids.

Angostura 15y ago

> all of which are known to be less effective than proven methods of learning math that have been known for hundreds of years. [Citation needed]. The methods my kids currently use, seem more effective that the ones I used at school. I am in my late 40s. edit: I'm based in the UK, however.

droithomme 15y ago
1. My personal experience as a teacher. 2. The average state of math knowledge of contemporary american high school graduates, coupled with statistics on needed remedial education for college entrants with high school diplomas. Teaching math is easy. I can teach any kid math. It's not a problem at all because we know how to do it. Many countries do it successfully. Observing what schools are doing, the textbooks, the approaches, and the level of math competency of elementary school teachers completely explains what is going wrong. It's not a mystery. Also explains why kids homeschooled by parents, even parents who were high school drop outs, end up with considerably better math skills than most public school graduates, and even many private school graduates. Typical high school graduates don't understand fractions, percentages or decimals. They can't do division. They don't understand algebra at all. We know this is true because of college placement tests. This is absurd. 100% of high school graduates should have passed differential and integral calculus. That should be the minimal acceptable standard. That it is not, and that graduates fail at even moderate arithmetic skills, shows the complete failure of the system. Downvote all you want while shouting "the dedicated teachers are not the problem, the students and their parents are!" That won't change a thing. Meanwhile, those who utilize proven approaches succeed and those who make excuses and follow fads fail.
- graeme 15y ago
  What effect do you think calculators have? I do some SAT tutoring, and I find that students are helpless at basic arithmetic if they can't use a calculator. My suspicion is that calculators prevent students from developing mental math skills, and that this hurts conceptual understanding across the board. But I can only see the results of the system, so I don't know what actually produced the types of students I'm seeing. I may be wrong about calculators - from what you say, it could simply be that the system in general is bad.
  - tel 15y ago
    I grew up learning math from calculators. I still today am terrible at mental math, but having immediate, accurate graphing capabilities from precalc onward was an incredible boon. Even before that, mechanical skills such as polynomial factorization or algebraic reorganization ("fiddly symbol manipulation") were actually, in my opinion, aided by having a calculator which could perform them for me. By releasing the burden of actually performing the computations, I was focused on larger patterns which made the computation meaningful and possible. There are two camps here, of course. As an engineer or mathematician, doing mental arithmetic is a dead skill---all the effort comes from modeling and understanding the structure of math. However, "practical" math such as computing tips or adding up grocery bills---and this was the kind of math application stressed in my public school education---probably benefits much more from rapid mental sums. So, ironically, I'd support the heavy involvement of calculators (even ones as powerful as Mathematica itself) in education if it's to be aimed to produce engineers, scientists, or mathematicians. Otherwise, they're probably damaging.
    - moped 15y ago
      WolframAlpha is a good visual tool also, and I often use it when I tutor math.
    - lnguyen 15y ago
      The issue is whether you learned the actual skill (graphing, factorization, etc.) or just learned how to get the calculator to do it for you. In many cases, the end results appear identical. However, I'd rather the upcoming engineers, scientists and mathematicians be banned from using calculators for anything more than basic arithmetic until they prove they do understand the concepts.
keithpeter 15y ago
UK note: a lot of work has been done in primary especially over the last 20 years to teach the reasons behind arithmetic and to lay foundations for algebra &c. I'm beginning to see this filter through to College level. Education differs significantly between countries, international comparison is hard.
gaius 15y ago
Maths education in the UK is mostly about how numbers "feel" when you subtract from them, and how this is related to rainforests and/or the third world. It's why 25% of the population is now innumerate.

aik 15y ago

How is this different than saying "paper and pen has been known to work, has been debugged, and doesn't suffer from frivolous cutting edge theories... so why build typewriters... so why build computers... so why innovate from that which already works?" Your argument is the antithesis of the reason for hackernews!

quanticle 15y ago
The difference is that typewriters and computers are better than pen and paper in many ways. The "new math" being taught at many middle and high schools in the US is not better, from a pedagogical perspective, than the existing math. In many schools today, math is taught as a "holistic" subject, where algebra, geometry, trigonometry are intermixed and taught as a "integrated" whole. In theory, this would let students appreciate that there are many ways to approach a problem and that the same theorem can be proven via many methods. In practice, all it ensures is that students have an insufficient background in three subjects rather than thorough knowledge in one. Bruce Lee said, "I do not fear the man that has practiced 10,000 kicks once. I fear the man that has practiced one kick 10,000 times." What our schools are doing is teaching different "kicks" (mathematical skills) but without following it up with the necessary practice required for students to achieve mastery of those skills. What we end up with are kids that know of mathematical theorems and mathematical results without knowing the results themselves.
- aik 15y ago
  Yes but I doubt the first, second, or even 100th typewriter was less applicable to most situations than pen and paper. Same goes with computers. And same goes with new innovations/theories within education. Maybe the issue isn't with the "frivolous" theories but rather with the treatment of them. As in depend on empirical evidence through studies prior to applying them to a wide student base. The first +-10000 light bulbs weren't released to the public. Why are new educational methods?
  - tygorius 15y ago
    Heh. The ghost of Sam Clemens might beg to differ: "Among the first users was Mark Twain, who fiddled around with it before putting it aside. Yes, Twain did become the first person to submit a novel in typed form to the publisher, but that wasn't until much later ("Life on the Mississippi,"1883) , and he didn't type it himself... it was a typed copy of his handwritten manuscript."[1] That manuscript was produced at least 8 years after the first Remington model appeared. Although Clemens was clearly a technophile (and pal of Tesla), he considered the first models to be curiosities rather than immediate replacements for pen or pencil and paper. [1] http://home.earthlink.net/~dcrehr/firsttw.html http://home.earthlink.net/~dcrehr/firsttw.html

kleiba 15y ago

How can "ever new approaches" be already "known to be less effective"?

deleted 15y ago
[deleted]

SkyMarshal 15y ago

Or this little gem: Calculus Made Easy http://www.gutenberg.org/ebooks/33283 http://www.gutenberg.org/ebooks/33283 An oldie but a goodie.

aptwebapps 15y ago
Thanks! I just read the first few pages and I'm liking it already. I also like the Ancient Simian Proverb in the dedication. Looks like a keeper. Edit: This prefigures the For Dummies books by what, 80 years?
- SkyMarshal 15y ago
  Yeah, it was written back in the day when education was education, not training.

cdf 15y ago

As a singaporean parent, i find it appalling that the world puts our maths textbook on the pedestal. The current textbooks are nothing like what I used as a child, and the techniques used to solve problems, extremely contrived. I see it exactly as products of M.Eds, who at best has experience teaching maths ONLY to gifted kids.