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Another thing is that even very basic math concepts can be hard to explain in a way that makes sense to kids. For example, if you have to explain why multiplyin

• atroyn 11y ago
  A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures. Most adults don't even remember any procedures, since they have no need to in daily life. This condemns children to repeat the cycle. They (completely rationally) decide that they're just 'not math people' because they can't follow lists of arbitrary seeming steps to do something that no one they have ever met ever actually does in daily life. And some of them grow up to be teachers themselves.
  • Thriptic 11y ago
    > A deeper problem is that math is almost always taught as a list of rules in the first place, frequently by teachers who do not themselves understand the underlying concepts. Teachers who only remember the procedures can of course only teach procedures Sigh, your statement reminds me of one time when I was in 6th grade geometry and was asked to complete this one proof. The problem was intended to get us to apply a concept we had been taught verbatim, but I couldn't remember it well and so I completed the proof a different way by extrapolating other basic concepts we had gone over into a method we had not been taught. I remember feeling very proud of myself when I finished, as I had created something which in my 12 year old eyes was a "novel proof". I ended up being given 0 points on the problem because I did not complete my proof using cookie cutter methods we had been taught (even though my proof was correct and it was not specified that I use a particular concept in the instructions). I remember complaining to my teacher about how this was unfair and she kept saying something akin to "well you didn't do the problem the right way". The incident pretty much killed any interest I had in math, which wasn't rekindled until I stumbled upon machine learning recently in my 20s.
    • Xcelerate 11y ago
      That kind of story makes me irrationally upset. That's horrible — killing a child's interest in math because they didn't do the problem the "right way". It's completely antagonistic to the spirit of the field. Teachers shouldn't be teaching subjects if they don't understand them.
      • Kluny 11y ago
        Same - I vow to make sure that never happens to my kids, even if I have to homeschool them.
        • _rpd 11y ago
          We had to homeschool for a year because of this (substitute teacher just going through the motions). My son has been a year ahead in math ever since. We've had to supplement to keep him challenged.
      • 11y ago
  • bitwize 11y ago
    This itself explains the worship of the Standard Algorithm, and why people see a New World Order conspiracy behind every attempt to reform math education. Not helping matters is the fact that most of the reformers are themselves ignorant chuckleheads who identify the heuristics that skilled arithmeticians use and codify them as a NEW set of rules to be memorized...
    • stdbrouw 11y ago
      FWIW, this is certainly not what people who do research into how to teach math advocate. In fact, one of the recommendations for teachers is that they should try to get students to come up with the algorithms themselves, or to "guide" them to these algorithms, and then let students use whichever they prefer, because that's the only way to get students to really understand and use them. That said, I've definitely seen some of that "let's just replace method X with method Y" – how harmful that is depends on whether it is just presented as a default or as The New Standard Algorithm, I guess.
      • bitwize 11y ago
        > FWIW, this is certainly not what people who do research into how to teach math advocate. Of course it isn't, because such lunacy wouldn't be supported by competent research. But the people who do education research, the administrators making curriculum decisions, and the concerned parents trolling about the dangers of "Common Core" on Facebook are distinct sets with little overlap.
    • milspec 11y ago
      Standard algorithms are standard for very good reasons. They are 100% reliable and at least reasonably fast, if not the fastest. Failure to learn the standard algorithms impedes progress. You are unlikely to do well in the next course if you are slow and can't handle numerous cases. Learning alternate algorithms is great... once you have the standard algorithms down solid and are ready to prove equivalence.
      • keithpeter 11y ago
• DanBC 11y ago
  Amazon.com: http://www.amazon.com/Help-Your-Kids-Math-problem/dp/075664979X http://www.amazon.com/Help-Your-Kids-Math-problem/dp/0756649... http://www.amazon.com/Math-Power-Child-Dover-Mathematics/dp/0486491811 http://www.amazon.com/Math-Power-Child-Dover-Mathematics/dp/... http://www.amazon.com/What-Help-Child-Math-Myself/dp/0974168904 http://www.amazon.com/What-Help-Child-Math-Myself/dp/0974168... Amazon.co.uk http://www.amazon.co.uk/Help-Your-Kids-Math-Problem/dp/075664979X http://www.amazon.co.uk/Help-Your-Kids-Math-Problem/dp/07566... http://www.amazon.co.uk/Math-Power-Child-Dover-Mathematics/dp/0486491811 http://www.amazon.co.uk/Math-Power-Child-Dover-Mathematics/d... http://www.amazon.co.uk/What-Help-Child-Math-Myself/dp/0974168904 http://www.amazon.co.uk/What-Help-Child-Math-Myself/dp/09741... My favourites are the Rob Eastaway / Mike Askew books: http://www.amazon.com/More-Maths-Mums-Askew-Eastaway/dp/0224095315 http://www.amazon.com/More-Maths-Mums-Askew-Eastaway/dp/0224... http://www.amazon.com/Maths-Mums-Dads-Rob-Eastaway-ebook/dp/B003ULP3NA http://www.amazon.com/Maths-Mums-Dads-Rob-Eastaway-ebook/dp/... http://www.amazon.co.uk/Maths-Mums-Dads-Mike-Askew/dp/0224086359 http://www.amazon.co.uk/Maths-Mums-Dads-Mike-Askew/dp/022408... http://www.amazon.co.uk/More-Maths-Mums-Dads-Askew/dp/0224095315 http://www.amazon.co.uk/More-Maths-Mums-Dads-Askew/dp/022409... (Amazon: Please have some really easy way to give me a clean url for sharing. I am literally sending potential customers to your website.)
  • pboutros 11y ago
    They do! For the .com links, concatenate: "amzn.com/",[10 character string in URL, aka ASIN] For the .co.uk links, concatenate: "amazon.co.uk/dp/",[10 character string in URL, aka ASIN] So, your first link would be "amzn.com/075664979X"
    • brewdad 11y ago
      That seems even less user friendly though. At least the original links give some clue to the text's title and subject.
      • ZeroGravitas 11y ago
        http://www.amazon.co.uk/this-text-is-arbitrary/dp/0224086359 http://www.amazon.co.uk/this-text-is-arbitrary/dp/0224086359
• marcosdumay 11y ago
  Not much, but for your example I'd draw two circles (or bars), fill 1/3 of one, 1/2 of the other, and ask the child to sum those. Then, add the missing divisions to the circles, so that both are divided in 6, and ask the child to sum. I don't know how to draw a multiplication (and I think I'm not alone), but get some physical tokens that you can divide in 2 or 3 (like matches), and you can do all kinds of fraction multiplication and division with them.
  • stdbrouw 11y ago
    You could draw the multiplication of e.g. 1/2 and 1/2 by dividing half a pie into another half. But you're right, it's harder in many cases and impossible in some.
• shas3 11y ago
  The problem starts when the curriculum attaches needless importance to fractions. 'Mixed fractions', wth curriculum-authors? Similarly with adding and multiplying fractions. The emphasis is more on the procedure and getting the student to be able to implement certain procedures, rather than understand the underlying intuition. Let's take two examples: 1/2 + 1/4 and 3/4 + 1/7. For the former there is a heavy intuitive reason for kids to understand adding half to a fourth. If you think about the latter, you are just adding two mathematical entities with little physical relevance. Equivalent entities are 0.75 and 0.142857, there is no good reason why one should stick to fractions when you are dealing with hairy numbers like 1/7. Kids aren't told this, and it complicates issues. The answer that kids are forced to look for is -1-1-/-1-4- 25/28, which is as unintuitively clunky as 1/7. They are challenged to add increasingly hard fractions like 13/37 + 22/7, etc. At this point, kids who can grasp abstract concepts do well, and those that can't get discouraged. I think physically intuitive math and abstract math should be explicitly identified and treated differently in curricula. Else, the result will be clumsy contrived attempts to find physical relevance to abstract concepts and weaker students falling behind. Dreary contrived problems must be replaced with fun puzzles. Puzzles share the attribute of abstractness-and-apparent-uselessness with portions of the math curriculum. Somehow teachers and parents find it hard to accept that some topics in math curricula are purely in the abstract realm. The other meta problem and perhaps a big cause of math anxiety is that the curriculum and system doesn't have much wiggle room to fail at understanding something. The most important quality for success in later life is perseverance when you're stuck or when you hit a wall. The education system teaches the exact opposite: "it is not ok to hit a wall or fail to understand something, you have to learn this right now, else you're done for!" There is very little flexibility to allow students to fail, persevere, and repeat. This is worsened by the needlessly frenetic pace of the academic year. Edit: D'oh, got 3/4 + 1/7 wrong, it should be 25/28