Trigonometry and Logic
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Trigonometry and Logic
In my local school system, an average student completes Alebra I, Geometry, Algebra II, and Trigonometry classes (the Alg II and Geom classes sometimes are switched). In my opinion, the Trigonometry class ought be replaced by an Informal Logic / Argumentative Theory course. While Trig is a useful class for those going on to college, Logic is useful in all parts of life. It allows one to debate one's opinions and ensure they are sound. It would help those going to college and those not going to college. It would be used almost every day  compare that to how often you need to know what the trigonometric functions are!
So, xkcd forums, what say you? Is Logic more important than Trig?
So, xkcd forums, what say you? Is Logic more important than Trig?
Re: Trigonometry and Logic
Trig is essential for anyone who wants to take calculus and/or take classes in physics or other sciences. It just wouldn't make sense to replace trig with logic because it doesn't fit into the standard math sequence you need in order to learn calculus and then go into engineering or any physical science. If a school wants to teach logic and has the resources to do it, I'd say go for it, but any college department in a engineering/science field will expect you know trig, so they need to teach it.
Re: Trigonometry and Logic
I agree that logic (don't know why you call it informal logic though, understanding formal logic is just as important) is awfully important, and that it should be taught much earlier in the education systems.
But so are Trig, and unlike logic it is a requirement for further education systems after High school, and is necessary for Calculus.
But so are Trig, and unlike logic it is a requirement for further education systems after High school, and is necessary for Calculus.
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Re: Trigonometry and Logic
Calculus may be important for collegebound students, but logic is important even for those not continuing on to college. What I'd forgotten to mention is that most collegebound students take Alg I in their last year of middle school, so they would still have a chance to take trigonometry in high school. Since there are only so many classes one can take during high school (even if taking two online courses per year, that's still only thirtytwo courses, and online courses are an unusual option). Not all of those courses can be mathematics, so some tradeoffs must be made. To me, teaching everyone logic is worth the risk that students will need to catch up on trigonometry when they get to college.
Re: Trigonometry and Logic
Many high schools offer logic as an elective that interested students can choose to take. Even though it may be more useful in debate, the fact is that the vast majority of students do end up going onto college (about 70% http://www.bls.gov/news.release/hsgec.nr0.htm) and high schools need to prepare them for that by teaching trigonometry.
Re: Trigonometry and Logic
Parts of logic and proofs and such should simply be taught throughout students' math education. We teach calculation, not math.
I don't see how mathemtical logic/reasoning will be useful to people who don't go to college (these people are either smart and can make something of themselves without a formal class or they will end up being grunts for most of their lives).
Finally, taking calc in high school is importantnot only does it expose students to the subject before they get to a higherpressure environment but it makes their college application more competitive (of course, the issue of the value of the necessity of this competition is another matter entirely).
I don't see how mathemtical logic/reasoning will be useful to people who don't go to college (these people are either smart and can make something of themselves without a formal class or they will end up being grunts for most of their lives).
Finally, taking calc in high school is importantnot only does it expose students to the subject before they get to a higherpressure environment but it makes their college application more competitive (of course, the issue of the value of the necessity of this competition is another matter entirely).
 mmmcannibalism
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Re: Trigonometry and Logic
Parts of logic and proofs and such should simply be taught throughout students' math education. We teach calculation, not math.
Actually I have the worst example of this, were you ever taught why (a+b)x(c+d)=ac+ad+bc+bd?
Its really simple when viewed as a geometry problem, but just like the Pythagorean theorem the really simple explanation of why is neglected.
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Re: Trigonometry and Logic
Trig is not necessary for calculus (I mean, trig does not appear in the definitions and main theorems of calculus at all). You can restrict things to polynomials to start, and trig functions can be done with power series anyways (or use exponential functions with imaginary numbers, which ever one floats your boat).
Re: Trigonometry and Logic
Trigonometry is part of introductory analytic geometry, which is necessary for calculus. Unless you have sufficiently advanced geometry and algebra II classes that you can teach most of this analytic geometry, you need to have it in a seperate class. At any rate, precalculus classes are generally useful for transitioning students into more advanced math.
Re: Trigonometry and Logic
Why is this true? I thought calculus is all about limits, which involves: For all [imath]\epsilon[/imath], there exists [imath]\delta[/imath] such that blah if you want to be technical, or about slopes and areas if you aren't that technical, or plugging in 0.9, 0.99, 0.9999, etc on the calculator if you are really informal. Besides, even if you want analytic geometry, trig isn't essential, conics are quadratic equations, to start.nash1429 wrote:Trigonometry is part of introductory analytic geometry, which is necessary for calculus.
Edit: Fixed a stupid mistake.
Last edited by achan1058 on Mon Aug 16, 2010 3:43 pm UTC, edited 2 times in total.
Re: Trigonometry and Logic
The limits are used in analytic geometry: those deltas and epsilons (which you have backwards) are usually referring to accuracy levels around coordinates on axes. And trigonometry is just as essential to analytic geometry as conics (these topics are usually taught in the same course anyway), yet I could see it being even more useful to daily life than formal reasoning.
Re: Trigonometry and Logic
maxh wrote:To me, teaching everyone logic is worth the risk that students will need to catch up on trigonometry when they get to college.
That would be doing a serious disservice to people who want to go into technical fields. Trig is more important than addition and subtraction in my field.
maxh wrote:It would be used almost every day  compare that to how often you need to know what the trigonometric functions are!
Is that a joke?
I do think logic ought to be taught, but 1) it's much better off being taught as a part of English, where you make (and, very easily if the teacher wishes, study) arguments every day and 2) high school graduates don't really need it. I don't think your average plumber or mechanic is going to be hamstrung by a lack of formal instruction on why, if x implies y that does not mean y implies x. Logic can formalize the thought processes that already go on in our heads, but if we don't have a "logical sense" (based on experience) to start with, a bunch of abstract instruction isn't going to fix that, at least not for the average Joe.
Edit: if you want to kill something, kill Physical Education. The actually important parts of that subject can be taught in about a month, the rest of the time is spent learning the rules of various random games. Definitely not suitable for an academic environment.
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
Re: Trigonometry and Logic
Replacing trigonometry with logic is a great idea!Without understanding logic you do not have any hope of understanding college level mathematics (with or without trig) anyway. And you do not need more than two weeks to teach trigonometry, so those weeks can easily be incorporated into another subject. The fact that trigonometry has its own course is absurd.
 KestrelLowing
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Re: Trigonometry and Logic
I must agree with all the people who say you cannot eliminate trig.
In my school system, the progression (for honors college bound students) went algebra I (taught in 8th grade), geometry, algebra II, precalc, calc. Some people opted for AP Stat instead of AP calc  especially if they weren't considering a major that required calc. The nonhonors (but many still college bound) group had the same classes, but they started with algebra I in 9th grade and made it to precalc.
While there wasn't a particular class called Trigonometry, it was covered mainly in precalc, and a little in geometry. Trig is essential for any respectable college math courses. (I don't believe you even get credit for a trig class at my college  you pay for it and take it, but it doesn't count for anything. I believe the first math class you get credit for is calc I.) If trig was eliminated for logic  something many college bound students understand quite easily  you would completely mess up any hope they had for getting college done in four years.
The majority of colleges start their curriculum at calc I. If the math schedule is pushed back, other classes are also pushed back because of prereqs. You can't take physics if you haven't taken calc. You can't take dynamics if you haven't taken physics and so on. You'd probably be adding on another year to school.
For those who don't think trig is needed in calc, you obviously haven't taken it yet. It's fairly important.
Logic is a great elective, but it shouldn't take the place of trig. If you want it to be mandatory, make it take the place of yet another literary analysis class.
In my school system, the progression (for honors college bound students) went algebra I (taught in 8th grade), geometry, algebra II, precalc, calc. Some people opted for AP Stat instead of AP calc  especially if they weren't considering a major that required calc. The nonhonors (but many still college bound) group had the same classes, but they started with algebra I in 9th grade and made it to precalc.
While there wasn't a particular class called Trigonometry, it was covered mainly in precalc, and a little in geometry. Trig is essential for any respectable college math courses. (I don't believe you even get credit for a trig class at my college  you pay for it and take it, but it doesn't count for anything. I believe the first math class you get credit for is calc I.) If trig was eliminated for logic  something many college bound students understand quite easily  you would completely mess up any hope they had for getting college done in four years.
The majority of colleges start their curriculum at calc I. If the math schedule is pushed back, other classes are also pushed back because of prereqs. You can't take physics if you haven't taken calc. You can't take dynamics if you haven't taken physics and so on. You'd probably be adding on another year to school.
For those who don't think trig is needed in calc, you obviously haven't taken it yet. It's fairly important.
Logic is a great elective, but it shouldn't take the place of trig. If you want it to be mandatory, make it take the place of yet another literary analysis class.
Re: Trigonometry and Logic
That is definitely embarrassing. I guess that's why I am in combinatorics instead of analysis.nash1429 wrote:which you have backwards
Referring to accuracy level isn't the best way to describe it. I agree coordinate geometry is used for the intuition of calculus, but I am still failing to see why trig is essential for it, other than historical reasons. I maintain that they can all be done with polynomial.nash1429 wrote:The limits are used in analytic geometry: those deltas and epsilons (which you have backwards) are usually referring to accuracy levels around coordinates on axes. And trigonometry is just as essential to analytic geometry as conics (these topics are usually taught in the same course anyway), yet I could see it being even more useful to daily life than formal reasoning.
I am a grad student in mathematics, so I think I have taken calculus. To answer your point directly though. Yes, trig is a chapter in calc, but it does not have to be, especially since that chapter (like the log/exp chapter) is really just introduce a few formulas, then plug and chug anyways. It's not really calculus. It might be needed for the engineers out there, true, but that's not necessary the best reason in the world.KestrelLowing wrote:For those who don't think trig is needed in calc, you obviously haven't taken it yet. It's fairly important.
Anyways, it is not necessary to eliminate all of trig, since informal logic isn't all that large, but certain things like trig proofs can be removed or delayed. I do have an alternative. Speed up the curriculum. The Asian schools usually have gone through calculus, logic, and more, by the time high school is finished. Surely we can squeeze a bit more out of the North American ones.
 KestrelLowing
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Re: Trigonometry and Logic
achan1058 wrote:I am a grad student in mathematics, so I think I have taken calculus. To answer your point directly though. Yes, trig is a chapter in calc, but it does not have to be, especially since that chapter (like the log/exp chapter) is really just introduce a few formulas, then plug and chug anyways. It's not really calculus. It might be needed for the engineers out there, true, but that's not necessary the best reason in the world.KestrelLowing wrote:For those who don't think trig is needed in calc, you obviously haven't taken it yet. It's fairly important.
Anyways, it is not necessary to eliminate all of trig, since informal logic isn't all that large, but certain things like trig proofs can be removed or delayed. I do have an alternative. Speed up the curriculum. The Asian schools usually have gone through calculus, logic, and more, by the time high school is finished. Surely we can squeeze a bit more out of the North American ones.
Oops, sorry about that. I knew something would come and bite me in the butt when I wrote that! (Not saying you did, just my general ‘not thinkingness’.)
The most vivid thing I remember about calc was taking the derivatives and integrals of trig functions and having to deal with half and double angle formulas and just hating the crap out of it. It could be just different focuses. I know I'll be using trig functions and calc in vibrations this year, so maybe it does have to do with discipline.
As for the speeding up curriculum, I'm fully with that. I think the biggest failing is doing nothing in middle school (in the US). Middle school is a joke. If subjects were introduced earlier in middle school, there would be more time for more subjects. Elementary school could probably also use a boost.
Re: Trigonometry and Logic
Mcxz wrote:The fact that trigonometry has its own course is absurd.
It doesn't have its own course, it is taught as part of an introductory analytic geometry course, and it is just as much a part of the subject as conics, differentiation, and integration.
achan1058 wrote:nash1429 wrote: wrote:which you have backwardsThat is definitely embarrassing. [/qoute]I guess that's why I am in combinatorics instead of analysis.
Not really, there is absolutely no reason to remember that.
Speeding up math and introducing it earlier in the US is definitely a good idea, the pace is rather absurd at the moment. It may just be me, but I never formalize my logical processes in day to day life, but I find myself considering the trigonometric relationships around me rather frequently. It is more important to teach than logic because it cannot be utilized if it isn't taught, but anybody (at least, most people) can use reason.
Re: Trigonometry and Logic
There is, since we can make jokes about the TA's intelligence being epsilon. Besides, after multiple analysis course, it should have been ingrained into you. Somehow my mind just slipped when I was making the original post.nash1429 wrote:achan1058 wrote:nash1429 wrote: wrote:which you have backwardsThat is definitely embarrassing. [/qoute]I guess that's why I am in combinatorics instead of analysis.
Not really, there is absolutely no reason to remember that.
I doubt that one very much. There are too many logical fallacy going around in informal arguments, like denying the antecedent.nash1429 wrote:It is more important to teach than logic because it cannot be utilized if it isn't taught, but anybody (at least, most people) can use reason.
 lu6cifer
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Re: Trigonometry and Logic
Like everyone else posting, I think it'd be a terrible mistake to replace trigonometry with calculus. As mentioned, a lot of trigonometric formulas pop up a lot in calculus (a simple example, taking the derivative of 2sinxcosx is much simpler if you know that 2sinxcosx = sin(2x)), plus it adds to the student's mathematical maturity, and serves as good preparation for a calculus course. And for anyone going into engineering/physics/almost any science/math field, calculus is important.
I agree that logic is important, but it's really under the realm of discrete mathematics, and doesn't really fit with the standard math courses taught in secondary schools (not that it shouldn't). Although, I do recall our high school teaching formal logic right before a geometry course, as an introduction to the flow of geometric proofs.
I agree that logic is important, but it's really under the realm of discrete mathematics, and doesn't really fit with the standard math courses taught in secondary schools (not that it shouldn't). Although, I do recall our high school teaching formal logic right before a geometry course, as an introduction to the flow of geometric proofs.
lu6cifer wrote:"Derive" in place of "differentiate" is even worse.
doogly wrote:I'm partial to "throw some d's on that bitch."
Re: Trigonometry and Logic
achan1058 wrote:I doubt that one very much. There are too many logical fallacy going around in informal arguments, like denying the antecedent.
Well certainly when people try to formalize their logic it turns out rather ugly, I always thought of it more as a symptom of general ignorance and stupidity in society. But it still seems to me that the sort of "formal" logic that people use would be better taught in literature and history classes becuase they are the areas where people usually seem to use "logic" and becuase the type of reasoning they teach is the type of reasoning people use.
To clarify though: I DO think formal logic and proofs should be taught as part of math, but I don't think they should replace precalculus until more advanced math is introduced earlier, leaving more room for a course.
Re: Trigonometry and Logic
achan1058 wrote:I agree coordinate geometry is used for the intuition of calculus, but I am still failing to see why trig is essential for it, other than historical reasons. I maintain that they can all be done with polynomial.
I agree with you conceptually but you are making a completely pointless argument. If you go out of your way to teach calculus without trig great, your students will know calculus without trig but you'll have created a generation of engineers and physicists who have no idea what's going on. Trig may not be strictly necessary but it is important that students get introduced to trig before calculus for the purpose of conceptual harmony. The most popular way to represent continuous time signals is with the sine function, and so to do anything with that you need to be able to apply calculus to it. Not to mention, trig is used in first semester college physics because without it you can only do statics and dynamics in one dimension.
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
Re: Trigonometry and Logic
I do not see why trig is "conceptual harmonious" with calculus, not even if I am to take a practical approach instead of a theoretical one. More importantly, not everyone is going to be an engineer and physicist, but everyone is going to watch the news. (or at least significantly more people, so I hope) They can have an introductory course on trig later, like how the first year CS students have an intro course to discrete math. Simply push calculus back a bit if you insist on teaching trig before calc. That is, of course, assuming you couldn't speed up the curriculum to fit everything in.Solt wrote:I agree with you conceptually but you are making a completely pointless argument. If you go out of your way to teach calculus without trig great, your students will know calculus without trig but you'll have created a generation of engineers and physicists who have no idea what's going on. Trig may not be strictly necessary but it is important that students get introduced to trig before calculus for the purpose of conceptual harmony. The most popular way to represent continuous time signals is with the sine function, and so to do anything with that you need to be able to apply calculus to it. Not to mention, trig is used in first semester college physics because without it you can only do statics and dynamics in one dimension.
My opinion is this: Logic, especially informal logic (ie. not all symbols and all, but more word based), is so important that I am willing to sacrifice most of the number crunching topics in mathematics in high school, with the exception of probability and statistics.
Re: Trigonometry and Logic
nash1429 wrote:Mcxz wrote:The fact that trigonometry has its own course is absurd.
It doesn't have its own course, it is taught as part of an introductory analytic geometry course, and it is just as much a part of the subject as conics, differentiation, and integration.
Maybe you should read the maxh's post again:
maxh wrote:In my local school system, an average student completes Alebra I, Geometry, Algebra II, and Trigonometry classes
Emphasis mine.
 lu6cifer
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Re: Trigonometry and Logic
Mcxz wrote:nash1429 wrote:Mcxz wrote:The fact that trigonometry has its own course is absurd.
It doesn't have its own course, it is taught as part of an introductory analytic geometry course, and it is just as much a part of the subject as conics, differentiation, and integration.
Maybe you should read the maxh's post again:maxh wrote:In my local school system, an average student completes Alebra I, Geometry, Algebra II, and Trigonometry classes
Emphasis mine.
You do realize that, in general, a high school 'trigonometry' course involves much more than just triangles? In my district, trigonometry is synonymous with a general precalc course.
lu6cifer wrote:"Derive" in place of "differentiate" is even worse.
doogly wrote:I'm partial to "throw some d's on that bitch."
 KestrelLowing
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Re: Trigonometry and Logic
lu6cifer wrote:You do realize that, in general, a high school 'trigonometry' course involves much more than just triangles? In my district, trigonometry is synonymous with a general precalc course.
As I mentioned in a previous post somewhere, my school doesn't have trig as a separate class, it's just precalc. Some of the trig is covered in geometry. This track is for average and above average students. (Above average continue onto calc)
For slightly below average (at math), they take FST or Functions, Stats and Trig. This class is basically a combination of Alg. II and trig. (The students have already taken Alg. II, it's more or less review partly) It also has a few concepts one would typically find in pre calc.
For this type of class  meant typically only for students who will not be pursuing a math/science related field but still quite possibly going to college (there's a tier of math below that  alg. II takes two years), it might make a little since for them to have the option of taking a logic course instead of FST.
Re: Trigonometry and Logic
achan1058 wrote:My opinion is this: Logic, especially informal logic (ie. not all symbols and all, but more word based), is so important that I am willing to sacrifice most of the number crunching topics in mathematics in high school, with the exception of probability and statistics.
I don't see how they are the same field then. Why can't logic be taught in English?
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
Re: Trigonometry and Logic
Because logic is math, not English. Even if it is in a relatively informal setting, one can transition to a more formal one, or perhaps teach it formally, then applying it to current news casts. Besides, the topic is whether logic is more important than trig, not whether logic is more important than Shakespeare. (which I also think it is)Solt wrote:achan1058 wrote:My opinion is this: Logic, especially informal logic (ie. not all symbols and all, but more word based), is so important that I am willing to sacrifice most of the number crunching topics in mathematics in high school, with the exception of probability and statistics.
I don't see how they are the same field then. Why can't logic be taught in English?
 cjmcjmcjmcjm
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Re: Trigonometry and Logic
KestrelLowing wrote:lu6cifer wrote:You do realize that, in general, a high school 'trigonometry' course involves much more than just triangles? In my district, trigonometry is synonymous with a general precalc course.
As I mentioned in a previous post somewhere, my school doesn't have trig as a separate class, it's just precalc. Some of the trig is covered in geometry. This track is for average and above average students. (Above average continue onto calc)
For slightly below average (at math), they take FST or Functions, Stats and Trig. This class is basically a combination of Alg. II and trig. (The students have already taken Alg. II, it's more or less review partly) It also has a few concepts one would typically find in pre calc.
For this type of class  meant typically only for students who will not be pursuing a math/science related field but still quite possibly going to college (there's a tier of math below that  alg. II takes two years), it might make a little since for them to have the option of taking a logic course instead of FST.
I also had the FST/PDF math curriculum. My school went Alg I in 7th grade, geometry, Alg II, FST, PDM, and calc BC to finish out you HS math experience. I think Alg2, FST, and PDM could easily be condensed into 2 years even with a large formal logic component. Way too much duplication there.
Because none of my English classes actually taught me any. I learned what I know about analyzing academic arguments through writing history papers. My English classes were about writing based on the literature we read. Those really wasted my timeachan1058 wrote:Why can't logic be taught in English?
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Re: Trigonometry and Logic
achan1058 wrote:Because logic is math, not English. Even if it is in a relatively informal setting, one can transition to a more formal one, or perhaps teach it formally, then applying it to current news casts.
Plenty of things that are "not English" are taught in English. In 9th grade English we had a unit on the holocaust and tolerance. In 10th grade we had mock debates. Hell, on the GRE its the writing section that has an argument construction section, not the quantitative. English class is a medium, not a subject (unless the class is actually called "English Literature" or "English Writing" etc). From what I've heard of logic and philosophy courses, they are very heavy on reading and writing. Seems like a perfect fit for English classes.
I don't see how a course in formal symbolic logic could possibly help the average high school student more than a logic unit in English. I see plenty of ways in which it would be inferior.
cjmcjmcjmcjm wrote:Because none of my English classes actually taught me any. I learned what I know about analyzing academic arguments through writing history papers. My English classes were about writing based on the literature we read. Those really wasted my time
You might have missed the point of those literary essays.
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
Re: Trigonometry and Logic
That's not what I have in my English classes. Maybe that's because I am in Canada?Solt wrote:Plenty of things that are "not English" are taught in English. In 9th grade English we had a unit on the holocaust and tolerance. In 10th grade we had mock debates. Hell, on the GRE its the writing section that has an argument construction section, not the quantitative. English class is a medium, not a subject (unless the class is actually called "English Literature" or "English Writing" etc). From what I've heard of logic and philosophy courses, they are very heavy on reading and writing. Seems like a perfect fit for English classes.
 KestrelLowing
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Re: Trigonometry and Logic
achan1058 wrote:That's not what I have in my English classes. Maybe that's because I am in Canada?Solt wrote:Plenty of things that are "not English" are taught in English. In 9th grade English we had a unit on the holocaust and tolerance. In 10th grade we had mock debates. Hell, on the GRE its the writing section that has an argument construction section, not the quantitative. English class is a medium, not a subject (unless the class is actually called "English Literature" or "English Writing" etc). From what I've heard of logic and philosophy courses, they are very heavy on reading and writing. Seems like a perfect fit for English classes.
Well, in my experience, the majority of English classes did mostly fuss about literature. Still, we had to learn how to write a persuasive paper, how to write an informative paper, how to write a comparison paper. After a while, you run out of literature topics and go to real world ones. It seems like integrating logic into an English class would be fairly easy. The actual topic and approach would be graded as well as the writing style and mechanics. Seems like an easy switch to me.
The biggest problem I see for that is the English teacher's reluctance to do anything new. There's a reason we only read 'classics' and the classics haven't really changed since the 1970s. (Maybe only the teachers I had, but the English teachers were the worst educated, least openminded, most annoying teachers I ever had, except for one, and she was a fullfledged, man hating FemiNazi.)
Re: Trigonometry and Logic
Even in college logic is often taught by the philosophy department, which generally fits in more with English and history classes. And arguing against teaching logic in English classes on the gounds that they do not already include it in the curriculum is rather stupid in a forum that is already about reforming curriculae.
Re: Trigonometry and Logic
In my university, there are at least 2 places which teaches logic. One is philosophy, the other is discrete math. The logic taught in discrete math is more formal, but that's not too surprising given that it's intended for math and CS majors.nash1429 wrote:Even in college logic is often taught by the philosophy department, which generally fits in more with English and history classes.
Re: Trigonometry and Logic
It seems that we generally agree on two things:
a) The current high school math education system SUCKS (perhaps some don't feel quite as strongly, but at the very least it can be improved).
b) Logic is valuable and should be taught in high school.
I just don't see why adding logic necessitates the removal of trigonometry (the system at the schools I went to stopped being quite so bad when I got to this point, and many people don't make it to this point, for that matter). There are a number of things in the usual high school curriculum that could be removed or done faster, some of which could have value if taught right (PE, art, health) and some of which have approximately epsilon value (Career Ed, I'm looking at you; seriously, "Jewelry Making" is not going to help me get a job).
a) The current high school math education system SUCKS (perhaps some don't feel quite as strongly, but at the very least it can be improved).
b) Logic is valuable and should be taught in high school.
I just don't see why adding logic necessitates the removal of trigonometry (the system at the schools I went to stopped being quite so bad when I got to this point, and many people don't make it to this point, for that matter). There are a number of things in the usual high school curriculum that could be removed or done faster, some of which could have value if taught right (PE, art, health) and some of which have approximately epsilon value (Career Ed, I'm looking at you; seriously, "Jewelry Making" is not going to help me get a job).
Re: Trigonometry and Logic
nash1429 wrote:a) The current high school math education system SUCKS (perhaps some don't feel quite as strongly, but at the very least it can be improved).
I wouldn't say that. They could do a better job of impressing on students what math is actually used for, but going through the basics is actually a pretty solid strategy in terms of preparing them for STEM careers.
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
J.W. Morris
Re: Trigonometry and Logic
Although problems decreased as classes became more advanced or higher track, it always seemed to me that there was an emphasis on calculation through memorization (some of which I admit is vital) as opposed to creative problem solving. When I was in high school I thought it was interesting that the "regular track" classes and below were the ones that skipped deriving and proving equations and went straight to using them to solve a series of problems that were practically identical. I am of the opinion that people who aren't as good at math need the proofs even more than the "gifted" because it would impart true understanding.
 cjmcjmcjmcjm
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Re: Trigonometry and Logic
Solt wrote:cjmcjmcjmcjm wrote:Because none of my English classes actually taught me any. I learned what I know about analyzing academic arguments through writing history papers. My English classes were about writing based on the literature we read. Those really wasted my time
You might have missed the point of those literary essays.
That's quite likely
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Re: Trigonometry and Logic
Apologies for the Necrobump, but I feel I have something to add.
The way my school does it, is that for Advanced Freshman math students, (Geometry/Algebra2) Logic is the first unit covered (formal logic, mind you), complete with proofs, as a means to prep us for the beast that is proofs for geometryrelated theorems (We're only allowed to use a theorem after we've proven it). Trig is taken as a unit sometime during sophomore year. I personally really like it that way. What do you think of it?
The way my school does it, is that for Advanced Freshman math students, (Geometry/Algebra2) Logic is the first unit covered (formal logic, mind you), complete with proofs, as a means to prep us for the beast that is proofs for geometryrelated theorems (We're only allowed to use a theorem after we've proven it). Trig is taken as a unit sometime during sophomore year. I personally really like it that way. What do you think of it?

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Re: Trigonometry and Logic
Apologies if I skimmed the preceding 38 posts too quickly and missed this being suggested, but what's wrong with teaching both? The school I went to had both a year for Trigonometry and a required course on the side in formal (but not symbolic) Logic, and I ended up enjoying Logic so much that it's my favorite class from H. S..
Re: Trigonometry and Logic
Brother Maynard wrote:Apologies if I skimmed the preceding 38 posts too quickly and missed this being suggested, but what's wrong with teaching both? The school I went to had both a year for Trigonometry and a required course on the side in formal (but not symbolic) Logic, and I ended up enjoying Logic so much that it's my favorite class from H. S..
Theres only so many hours in the day, and I get the feeling that most would rather be spending less, not more, time in classes. Plus theres the required additional hours teachers/profs would need to spend, and they'd need to be paid, and that money would need to come from somewhere, and similar issues.
I don't really feel logic courses are going to make someone any more 'logical' in their day to day life, or at least not any more than English courses make students more likely to 'think deep' about the stuff they read. Idiots and/or illogical people forced to take such a course are for the most part going to remain that way, even if they might know the names of their fallacies, or how to represent them in a more concrete fashion. These people are most often the ones who hate using "school stuff" at any point outside of their classroom, including things like logic.
Theres plenty of political barriers as mentioned anyway, where people are expected to learn certain things by a certain point, and if they don't, even if they learned something else instead, their education is considered incomplete. I believe theres a great deal more known about how people learn and the relative importance of various subjects now then a couple hundred years ago, and so if the system could be restarted from scratch, then many things would likely be different (I know theres even some arguments that abolish grading!). However, parents have expectations of what should be taught based on what they learned, universities have various entry requirements that are based on existed curicculums, employers may look to grades, and so on, so change is a slow process in terms of education.
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