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.

 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.
 >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).I'm not sure how much I agree.Sure, the math and the principles involved in designing scientific studies etc. can get pretty complicated. But there are a number of fairly basic ideas that could be usefully taught. And I'd argue that many people don't have a great common sense view of stats and probability. Sure, they have some idea of what batting average means--though there are lots of interesting sabermetric discussions to be had around baseball measurements--but there are also many well-known and consistent biases that many people have. For example, around ideas like streaks.I've argued before and continue to believe that a semester long intro-level course on stats and probability that didn't get overly wrapped up in a lot of complex equations would be more useful at the high school level than some of the ways that time is used today.
 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".
 well I can only speak to my own experience. personally I really enjoyed geometry but can't say the same for most students
 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.
 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.
 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.

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