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For lower level math, my kids seemed to revisit the same subjects over and over from k-9th grades. For example, mean, median and mode, year after year. The fi

For lower level math, my kids seemed to revisit the same subjects over and over from k-9th grades. For example, mean, median and mode, year after year. The first few years it was just robotic problem solving. After a few years, they started to get a broader understanding. Maybe some people need to take several passes through the higher level stuff too.I guess the problem is that there is not enough time.

cgag 10y ago
I believe there's decent support for the idea that you could just teach them nothing until they reached the age of understanding, and theyd pick it up pretty much just as quick without the years of rote.
- dredmorbius 10y ago
  Source?
  - abecedarius 10y ago
    A U.S. elementary school principal in the 20th C. got his school to try leaving out any math in the first three grades (iirc), and the kids reportedly came out fine. I can't remember his name, and I'd like to be reminded too.
    - asimeqi 10y ago
      It was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who experimented with teaching no math in the first five grades in the early 1930s. See for example https://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-school https://www.psychologytoday.com/blog/freedom-learn/201003/wh...
      - abecedarius 10y ago
        Thanks! There's also his own report: http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html
    - dredmorbius 10y ago
      Interesting. I've been thinking about education and a few dynamics of it, including human cognitive development and individual differences. 1. Young children seem to have the biggest capability in learning languages. 2. There's the John Stuart Mill example -- homeschooled by his father in the classics and philosophy. Interesting biography (Wikipedia has a fair account). 3. There are children who are naturally skilled in art, storytelling, maths, sciences, music, etc. An opportunity to work to those strengths might be useful. I've also noticed that a short period of instruction at the appropriate time often seems disproportionately effective.
      - abecedarius 10y ago
        My guess is that math teaching can be a benefit to anyone at any age, but the usual curriculum on average mainly teaches people to hate math. (That's what's happening with my niece in grade school right now.) For some kids arithmetic may be boring, but at least it's easy, and they suffer less of this damage. If you start it later when they're readier, more of them will be open to learning a little actual math, not just gritting through baffling seemingly-arbitrary procedures. Montessori schools are said to be better on this score, though I haven't looked into them.
        dredmorbius 10y ago
        I've been looking at John Cleese's presentations on creativity, and suspect he's very much on to something with the idea of play and humour as key to real learning. I also think that there are approaches which take this too far (video games and such), though I've learned a number of things from unexpected places. Neal Stephenson's Cryptonomicon, The Baroque Cycle, and Anathem, for example, are all explorations of ideas. The first two of business, banking, and money, in contemporary and historical times, respectively. The latter covers a great deal of historical thought. Better authors of topics often incorporate humour in their writing -- someting the past few generations of academic literature would do well to consider. OTOH, it's a cure for insomnia.
      - lacampbell 10y ago
        > 1. Young children seem to have the biggest capability in learning languages. Is there any evidence that this is actually due to their capability? I would say it's far more likely it's their environment. IE, people are constantly talking to young kids. They simplify what they say to make themselves understood. And children have a huge incentive to learn to communicate - to get what they want from parents, or just understand the world around them. The same isn't true for a grown adult trying to learn a second language, in isolation, that they don't really need in their day to day lives. Disclaimer: this is pure conjecture.
douche 10y ago
What infuriates me, looking back on it, was simply how much of my time the educational system was allowed to waste. Thousands and thousands of lost hours, some of them filled with pointless busy-work, but many more just squandered on inanity. At least some of the teachers would let you finish the daily penance quickly, and sit quietly in the corner reading something interesting. Too few, though.
- pirocks 10y ago
  Learning cursive comes to mind.
- pdm55 10y ago
  I look at this way: early education focuses on learning to read and write and do arithmetic. The basic purpose is to give you tools whereby they can continue to educate yourself throughout your life. So basically, our early education aims to put our future education into our own hands. Let me qualify the above a little. You might ask, well what are the purpose of high-school teachers or university lecturers? Once we are given these tools shouldn't we just be given the books to progress on our own? Hopefully, teachers are people who can take a complex subject and guide us towards an understanding of that subject. To me teachers are like guides through a jungle of knowledge. We need a guide so that we don't get lost. For me, a teacher is part guide and part "composer of problems". I consider teaching to be guided problem-solving. When I am teaching a course, I pose problems, whether it be in Math or Chemistry, and guide the students as they try to solve those problems. And as for your comment about "wasted time", I am not sure what to think about this. The difficulty with learning is that we need repetition and reinforcement. Yes, I see a lot of pointless repetition, but we do need some repetition. I am presently struggling with improving my chess skills, as well as trying to learn to program an Arduino. Mastering these skills require a lot of repetition in order to cement that knowledge. Wish me luck.

cgag 10y ago

I believe there's decent support for the idea that you could just teach them nothing until they reached the age of understanding, and theyd pick it up pretty much just as quick without the years of rote.

dredmorbius 10y ago
Source?
- abecedarius 10y ago
  A U.S. elementary school principal in the 20th C. got his school to try leaving out any math in the first three grades (iirc), and the kids reportedly came out fine. I can't remember his name, and I'd like to be reminded too.
  - asimeqi 10y ago
    It was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who experimented with teaching no math in the first five grades in the early 1930s. See for example https://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-school https://www.psychologytoday.com/blog/freedom-learn/201003/wh...
    - abecedarius 10y ago
      Thanks! There's also his own report: http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html
  - dredmorbius 10y ago
    Interesting. I've been thinking about education and a few dynamics of it, including human cognitive development and individual differences. 1. Young children seem to have the biggest capability in learning languages. 2. There's the John Stuart Mill example -- homeschooled by his father in the classics and philosophy. Interesting biography (Wikipedia has a fair account). 3. There are children who are naturally skilled in art, storytelling, maths, sciences, music, etc. An opportunity to work to those strengths might be useful. I've also noticed that a short period of instruction at the appropriate time often seems disproportionately effective.
    - abecedarius 10y ago
      My guess is that math teaching can be a benefit to anyone at any age, but the usual curriculum on average mainly teaches people to hate math. (That's what's happening with my niece in grade school right now.) For some kids arithmetic may be boring, but at least it's easy, and they suffer less of this damage. If you start it later when they're readier, more of them will be open to learning a little actual math, not just gritting through baffling seemingly-arbitrary procedures. Montessori schools are said to be better on this score, though I haven't looked into them.
      - dredmorbius 10y ago
        I've been looking at John Cleese's presentations on creativity, and suspect he's very much on to something with the idea of play and humour as key to real learning. I also think that there are approaches which take this too far (video games and such), though I've learned a number of things from unexpected places. Neal Stephenson's Cryptonomicon, The Baroque Cycle, and Anathem, for example, are all explorations of ideas. The first two of business, banking, and money, in contemporary and historical times, respectively. The latter covers a great deal of historical thought. Better authors of topics often incorporate humour in their writing -- someting the past few generations of academic literature would do well to consider. OTOH, it's a cure for insomnia.
    - lacampbell 10y ago
      > 1. Young children seem to have the biggest capability in learning languages. Is there any evidence that this is actually due to their capability? I would say it's far more likely it's their environment. IE, people are constantly talking to young kids. They simplify what they say to make themselves understood. And children have a huge incentive to learn to communicate - to get what they want from parents, or just understand the world around them. The same isn't true for a grown adult trying to learn a second language, in isolation, that they don't really need in their day to day lives. Disclaimer: this is pure conjecture.

douche 10y ago

What infuriates me, looking back on it, was simply how much of my time the educational system was allowed to waste. Thousands and thousands of lost hours, some of them filled with pointless busy-work, but many more just squandered on inanity. At least some of the teachers would let you finish the daily penance quickly, and sit quietly in the corner reading something interesting. Too few, though.

pirocks 10y ago
Learning cursive comes to mind.
pdm55 10y ago
I look at this way: early education focuses on learning to read and write and do arithmetic. The basic purpose is to give you tools whereby they can continue to educate yourself throughout your life. So basically, our early education aims to put our future education into our own hands. Let me qualify the above a little. You might ask, well what are the purpose of high-school teachers or university lecturers? Once we are given these tools shouldn't we just be given the books to progress on our own? Hopefully, teachers are people who can take a complex subject and guide us towards an understanding of that subject. To me teachers are like guides through a jungle of knowledge. We need a guide so that we don't get lost. For me, a teacher is part guide and part "composer of problems". I consider teaching to be guided problem-solving. When I am teaching a course, I pose problems, whether it be in Math or Chemistry, and guide the students as they try to solve those problems. And as for your comment about "wasted time", I am not sure what to think about this. The difficulty with learning is that we need repetition and reinforcement. Yes, I see a lot of pointless repetition, but we do need some repetition. I am presently struggling with improving my chess skills, as well as trying to learn to program an Arduino. Mastering these skills require a lot of repetition in order to cement that knowledge. Wish me luck.