<p>I don’t recall do that many proofs in Geometry but actually memorizing and knowing those relationships and formulas has been one of the useful math tools I have had on a regular basis. For most people in real life I think advanced level math is the most useless thing that schools waste time on and students get very little bang for the buck.</p>
<p>I’m saying that learning to try things out intuitively and use the results to draw generalizations is a useful skill in math classes. There are times when teaching students to try things out for themselves provides more benefits than lessons in rigor and proofs do. I disagree with the way the geometry class in the OP’s post is run, but I also don’t think it’s quite as bad as people are making it out to be, since higher-level math courses often use similar techniques to provide insight into what can later be formally developed into a theorem. This is quite honestly a technique I wish my geometry class had employed more, as a good portion of the proofs in my own course went over my head because the teacher didn’t encourage experimentation of this sort.</p>
<p>So my point is that even without the proof part, these are still valuable skills. Geometry might lend itself well to the basics of proofs, but I don’t believe that it’s helped me at all in any of my proof-based courses, since everything is at such a low level. On the other hand, the concepts of guessing and generalizing has served me well in multiple fields. One’s mileage will vary, of course, and every student is different, but I feel that a logic or philosophy course is more beneficial for cultivating the type of critical thinking for constructing sound arguments than a basic Euclidean geometry class.</p>
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<p>Probably true, depending on what exactly counts as advanced math. The problem is that not taking enough math freezes people out of some fields that might later interest them. Advanced science can be pretty useless too.</p>
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<p>I agree that logic classes are probably more useful for constructing arguments than Euclidean Geometry. Developing intuition in math is also useful, but it’s dangerous without the discipline to check that intuition with general proof.</p>
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And here we have an exemplar on why America is 25th in the world in math/science scores these days. People think it’s a waste of time. Society finds mathematical illiteracy acceptable - in fact, it’s “geeky :(” to be “good” at math. Sexier to be an airhead. </p>
<p>It’s supposed to be about thinking, barrons. And yes, people get little bang for the buck, because thinking is hard and they are too lazy to bother doing more than the bare minimum to get by.</p>
<p>…climbs down…</p>
<p>I did not say not to learn basic math through algebra, geometry and stats. But that is all you need for most professional jobs in the USA. The rest is just not needed in most real life professions. Lawyers and doctors and business owners do not need math beyond those levels. They are fine just actually knowing the basics–which few people actually retain into the workplace. So, yes, going beyond those levels is a waste of time and money unless you plan to go into engineering and some sciences, (most bio-science also requires little math beyond the basics). We can still produce plenty of engineers and physicists without forcing everyone to waste time on advanced math. Math thinking is not the only thinking out there. All the economists with all their advanced math skills can’t figure out a way to get the economy moving. Why–many of the reasons are not subject to math–they are feelings and attitude related. That’s why the consumer confidence data are more important than all the other equations anyone can render.</p>
<p>“All the economists with all their advanced math skills can’t figure out a way to get the economy moving”</p>
<p>Au contraire, we know exactly how, using math skills and models. We just can’t get the congress to pass what the majority of economists know is needed. The climate scientists, who also have math skills and models, are in the same boat these days.</p>
<p>I DO think that for folks not going on into science, engineering, or econ, it might be more useful to take probability and statistics than trig/precalc and calc.</p>
<p>No, at least according to NPR today the leading economist in the administration had few ideas within current constraints. The problems are more behavioral than mathematical. Also the entire leading climate models are proving highly inaccurate at predicting the future and contain massive errors due to faulty fundamental assumptions on how climate really works. They tried to force it all on CO2 which was just wrong.</p>
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<p>Is this what you’re talking about? I’m thinking not.</p>
<p>[Economists:</a> Extend Bush tax cuts for wealthy, middle class - Sep. 19, 2010](<a href=“http://money.cnn.com/2010/09/19/news/economy/what_to_do_economists_survey/index.htm]Economists:”>http://money.cnn.com/2010/09/19/news/economy/what_to_do_economists_survey/index.htm)</p>
<p>“within current constraints.”</p>
<p>Within current political constraints, which rule out another round of needed fiscal stimulus.</p>
<p>This is offtopic. If you really want to know what are best economists think, I recommend [Economics</a> and Politics - Paul Krugman Blog - NYTimes.com](<a href=“http://krugman.blogs.nytimes.com/]Economics”>http://krugman.blogs.nytimes.com/) Read that regularly and you will learn a lot about the state of the econ profession today, about math and models, etc.</p>
<p>You are also incorrect about climate science. However this is also off topic.</p>
<p>I think we can drop the idea that “math is not important” though. If you’re talking to a flat earther, its hard to make the case that navigation skills helped Magellan.</p>
<p>"Is this what you’re talking about? I’m thinking not.</p>
<p>Economists: Extend Bush tax cuts for wealthy, middle class - Sep. 19, 2010 "</p>
<p>any stimulus would help. The science indicates that the biggest bang for the buck is from spending and tax cuts aimed at the poor (to understand why, we would need to discuss “marginal propensity to consume”) and after that tax cuts to the middle class, and then tax cuts to the upper class - most of which will be saved, for precisely the reasons those economists most skeptical of keynsian solutions think no fiscal stimulus will be effective. </p>
<p>I cannot vouch for the economists CNN money selected. I am not going to summarize Krugman here, but I think the evidence is very strong that the keynsian models have been confirmed by the events of the last two years.</p>
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<p>No need. I think everyone is aware of Krugman’s position - he’s not shy and doesn’t keep it a secret. I know he’s got a Nobel Prize. But he’s still only one economist, not “most economists”. And I’m not sure I disagree with him, I don’t really know enough. I don’t even think there’s necessarily consensus on this, let alone total agreement.</p>
<p>But you’re right, this is off-topic.</p>
<p>The profession is divided, but IIUC theres rather more consensus than you’d imagine from the reading the pundits and pols. But no, not nearly the degree of consensus you would see in climate science. </p>
<p>I would conclude that for anyone considering either climate science or econ (and most work in econ is micro, not macro, but the public tends to forget that) higher math is a good idea.</p>
<p>“No need. I think everyone is aware of Krugman’s position - he’s not shy and doesn’t keep it a secret.”</p>
<p>I wasn’t thinking of his position, so much as his evidence. I tend NOT to enjoy his more political pieces, esp on areas that veer from macroeconomics. But his moderately technical pieces are a JOY to read. There are certainly economists who disagree with him (and you will certainly see that in his blog) (and while there is no consensus, I think the majority of macroeconomists are keynsians - its certainly not a fringe view) but for a good explanation of the issue barrons raised - what econ models and maths can tell us, and the things they tell us are constrained by real world politics - I dont think you can do better.</p>
<p>Certainly if someone is saying math is useless in econ, cause econs cant find a solution, it may be interesting to look at economists who actually believe they have a solution. Even the ones who are not keynsians, dont seem to think that math is not intensely useful to economics. Indeed, they seem MORE focused on math.</p>
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At the risk of one more derailment I’ll say that this sounds reasonable.</p>
<p>From what I read and see I think there’s agreement that there needs to be more money out in the economy and it needs to be flowing around more freely (duh). Most of the debate I see is at the edges -whether it should be done with fiscal policy, monetary policy, tax policy, regulation, whatever. It is all pretty nuanced, and a good deal is probably beyond me.</p>
<p>In fact here is a piece ESPECIALLY about the topic at hand - the role of math and models, in which Krugman specifically argues that the problem with those who disagree with him is that they are too limited to a mathematical approach, without appreciating the implications of the equations. I think (ON TOPIC NOW) it shows precisely that economists, to make sense of the world, need mathematics AND need to go beyond mathematics - math isn’t enough. [Math</a>, Models, and Mystification - NYTimes.com](<a href=“http://krugman.blogs.nytimes.com/2010/10/04/math-models-and-mystification/]Math”>Math, Models, and Mystification - The New York Times)</p>
<p>Back on the OP’s topic…</p>
<p>I am reading it thinking who takes Geometry in the 8th grade???<br>
Back in the day, I took it in 10th grade after Algebra I in 9th grade. My kids took Algebra I in 8th grade in Geometry in 10th grade. I have no idea if they did proofs or not - it was a while ago. I wonder if kids who take Geometry in the 8th grade know what a real number is.
My Dad was my Geometry teacher back in the 70’s. He taught us both deductive and inductive reasoning. I remember him telling me that a lot of kids who don’t do well in Geometry just don’t have a mature brain. It’s not necessarily a matter of cognitive ability but maturity in the thinking process.</p>
<p>this by the OP really gets to me though -
One of my pet peeves. I happen to believe that the work produced by a student belongs to them and not their lazy teacher.</p>
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<p>Except tax policy IS fiscal policy.</p>
<p>The idea that cutting taxes is, in terms of being a “stimulus” a different species of action from increasing spending, is, again, an idea from pundits and pols. I dont think any macroeconomist, even at UChicago, would make that false distinction.</p>
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<p>I’d guess that there are lots of kids that study geometry in the 8th grade. You could probably find many at The Art of Problem Solving. There are a lot of ways to convey math but generating interest may be the hardest part. I found that the best way to do that was with casual conversation and a few extra special math books like the Aha! series from Gardner.</p>
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I know. More correctly, tax policy is PART of fiscal policy. But they are not identical, there is more to fiscal policy than just taxes. I didn’t know I was going to be proofread.</p>
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<p>How the government chooses to spend and the mix it uses to fund that spending are significant issues, for one thing because they affect which segments of the population the “stimulus” is directed at. I’m sure you would agree that’s important, since you basically stated so in a previous post.</p>
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<p>Unless you meant to say you disagree with the science.</p>