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The problems he suggests overall seem too difficult for the average non-mathematically inclined student. And they also require quite a skilled teacher to teach.

The problems he suggests overall seem too difficult for the average non-mathematically inclined student. And they also require quite a skilled teacher to teach. I'm not sure stuff beyond "algebra 1" needs to be taught to everyone in high school. Even the concept of using "x" to stand for an unknown is very difficult for some to grasp. Instead, schools should make sure all students can properly understand how to use addition, subtraction, multiplication, and division, with applications to things like personal finance. In my experience, even many college graduates have trouble understanding when to multiply, divide, etc...

ghaff 10y ago
At the risk of being sarcastic, the suggestion seems to be that mathematics is best taught through stereotypical management consulting interview questions. Or the apocryphal (?) Google interview questions like how many ping pong balls can fit on a bus. ADDED: I also suspect that the average high school student lacks the world knowledge to come up with meaningful guestimates for the inputs to many of those questions. A lot of the high school mathematics that I learned such as geometric proofs and trig are not all that useful. And it seems as if things that would be more generally useful like probability and stats are not that broadly taught--and are often taught in a very theoretical way when they are.
- blahblah3 10y ago
  Unfortunately, probability and stats are not easy to teach, and even many professional scientists / researchers have major confusions about the subjects. Common sense actually provides a decent enough guide for most people (i.e a baseball player with a high batting average is more likely to hit the ball). Euclidean geometry as taught in school does seem rather archaic and out of place though. Some people say it's an introduction to "proofs/rigorous thinking", but it seems to me that that purpose could be better served with a first order logic class.
  - inimino 10y ago
    First-order logic is much more abstract. I think a major benefit of geometry is that it introduces visual thinking and is very grounded and real because you can see and draw the proofs. This foundation of visual/spatial intuition seems to be very useful in higher math, as a counterpart to the exclusively symbolic manipulation of algebra or first-order logic.
    - ghaff 10y ago
      As an anecdote, I actually had a fair bit of trouble with geometry in high school even though I did very well throughout high school in math/science generally and went on to major in engineering in college. I'm not so sure about the visual thinking part but wrt symbolic representations at least you're probably right as I've never felt a particular connection to higher level math and theoretical physics.
      - inimino 10y ago
        By the way, what I mean by "geometry" is basically reading Euclid and working out the proofs with a straightedge and compass. What I see in the high school geometry homework I've come across is something else altogether.
  - Koshkin 10y ago
    How is learning facts about the space we all live in is "out of place"? Geometry continues to be extremely useful. In fact, in its generalized forms it is one of the most important parts of the modern mathematical thought. If anything, for a mathematically inclined student learning geometry, I imagine, would be much more both instructive and fun, than some "first order logic".
    - blahblah3 10y ago
      well I can only speak to my own experience. personally I really enjoyed geometry but can't say the same for most students
  - 10y ago

ghaff 10y ago

At the risk of being sarcastic, the suggestion seems to be that mathematics is best taught through stereotypical management consulting interview questions. Or the apocryphal (?) Google interview questions like how many ping pong balls can fit on a bus. ADDED: I also suspect that the average high school student lacks the world knowledge to come up with meaningful guestimates for the inputs to many of those questions. A lot of the high school mathematics that I learned such as geometric proofs and trig are not all that useful. And it seems as if things that would be more generally useful like probability and stats are not that broadly taught--and are often taught in a very theoretical way when they are.

blahblah3 10y ago
Unfortunately, probability and stats are not easy to teach, and even many professional scientists / researchers have major confusions about the subjects. Common sense actually provides a decent enough guide for most people (i.e a baseball player with a high batting average is more likely to hit the ball). Euclidean geometry as taught in school does seem rather archaic and out of place though. Some people say it's an introduction to "proofs/rigorous thinking", but it seems to me that that purpose could be better served with a first order logic class.
- inimino 10y ago
  First-order logic is much more abstract. I think a major benefit of geometry is that it introduces visual thinking and is very grounded and real because you can see and draw the proofs. This foundation of visual/spatial intuition seems to be very useful in higher math, as a counterpart to the exclusively symbolic manipulation of algebra or first-order logic.
  - ghaff 10y ago
    As an anecdote, I actually had a fair bit of trouble with geometry in high school even though I did very well throughout high school in math/science generally and went on to major in engineering in college. I'm not so sure about the visual thinking part but wrt symbolic representations at least you're probably right as I've never felt a particular connection to higher level math and theoretical physics.
    - inimino 10y ago
      By the way, what I mean by "geometry" is basically reading Euclid and working out the proofs with a straightedge and compass. What I see in the high school geometry homework I've come across is something else altogether.
- Koshkin 10y ago
  How is learning facts about the space we all live in is "out of place"? Geometry continues to be extremely useful. In fact, in its generalized forms it is one of the most important parts of the modern mathematical thought. If anything, for a mathematically inclined student learning geometry, I imagine, would be much more both instructive and fun, than some "first order logic".
  - blahblah3 10y ago
    well I can only speak to my own experience. personally I really enjoyed geometry but can't say the same for most students
- 10y ago