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On July 29 2012 23:38 Deadlyhazard wrote:Show nested quote +On July 29 2012 23:14 omgimonfire15 wrote:
We suck at algebra so we should get rid of it? Good logic. This just sounds like a ploy to make us seem smarter than we actually are. Its not about numbers and equations, its about critical thinking and showing that you are able to do something even when you don't like it. As stated numerous times, in many jobs, actually algebra is useless, but it shows employers that this guy can get through something most people hate, work hard, and think critically. In college, chemistry is mandatory, but the ones who make it through with good grades display their work ethic and set of priorities. + Show Spoiler +1) Nobody is saying it should be removed -- most are saying it should be something that's more optional or taught in a different way so students struggling can understand it or get something useful out of it.
2) Chemistry displaying work ethic and priority making is too black and white of thinking. I failed college algebra three times -- I have a great mathematical learning disability. I can't even do basic math. I miss 7+6 half the time. I had several private tutors and I studied much harder than those that were lazy and smoothly sailed by -- yet I still failed. I was literally making grades below those that were barely trying, yet many were making A's and B's.
I don't think it's that I'm completely stupid -- I simply have a learning disability when it comes to using numbers. So what happens to people like me? It's not because I didn't have priorities set. It's not because I displayed a poor work ethic. It's because of an innate problem with mathematics that I will always have (and have had since I started school as a wee child). For me, it's impossible to have any career related to math because I simply can not understand the type of abstract reasoning it presents. So what use is a mathematics course being mandatory for me? I do fine in almost every single subject. My report cards in college literally read A A B F, and you can guess what I was failing every semester (and having to repeat). I took statistics three times too. It's not that I can't be taught and learn from schooling, it's that I'm absolutely terrible in one department of reasoning -- mathematics. I feel that some courses should be optional for this very reason, so people like me stand a chance at becoming educated without having to suffer through the ordeals of major learning issues like I have. So what am I to do -- not be able to pass regular schooling to get to something more specific (and unrelated) to math just because I can't pass one subject?
Generally if someone who otherwise performs well in school has a single area where they consistently fail or do very poorly compared to their other subjects there is a learning disability present, though possibly undiagnosed. he grades you posted look like you might possibly have dyscalculia, which is basically dyslexia for maths. Someone should have noticed that shortly after it became a big problem, and you very probably should have been given extra help in maths in school and waivers from requirements in college. I'm sorry that no-one did. Did you get through in the end?
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United States24741 Posts
On July 30 2012 00:29 paralleluniverse wrote:Show nested quote +On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:On July 29 2012 23:59 farvacola wrote:On July 29 2012 23:53 paralleluniverse wrote:On July 29 2012 23:51 farvacola wrote:
I'm not exactly sure why the article makes the connection between flawed primary/secondary school math education and a need to remove certain educational requirements; it would make sense, at least to me, to instead focus on better teaching methodologies, as algebra and many of the "hard" areas of study have been taught in relatively the same manner for many, many years now. As posters above are explaining, I certainly think that Algebra ought to be requisite, as it lends itself to so many endeavors in life, and perhaps the key in improving its teaching is a more vocational or everyday focus in application, and a change from the standard drudgery of problem sets and timed tests. I'm thinking on my own honors math education, where in 8th grade we learned the quadratic formula via song and were required to sing it at the door one day in order to get into class. Simple little changes in teaching technique can do wonders for making subjects such as math more palatable. As I see it, there are simply too many inherent problems in putting forth entire populations of people who are unable to the basic algebraic underpinnings of the economy and their own personal finances. Are you saying that's good or bad? I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick.
I would like to see you attempt to teach completing the square to an actual class of average kids... because if you can pull that off well then your plan might work regarding the quadratic formula (I'm not confident), but we have gone away from the topic of singing to teach something.
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In my own opinion, learning math teaches us abstractive thinking.
Being able to manipulate with abstractive ideas and applying them to different situations (which might or might not be abstractive as well) is the only thing, that separates us from the animals. Put it another way - abstractive thinking is the sole tool we use as species to progress.
Hence, teaching math is the only way for us to advance and survive as species.
Could teaching higher provisions of math be targeted better? I am absolutely positive it can.
Do we have to stop teaching math - to myself the answer can be only one - we shouldn't.
---
I have graduated with math and never really had to use in work/real life. I would have made it through in life with simple 5 grade stuff, but the skills I learned I find irreplaceable.
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On July 30 2012 00:35 paralleluniverse wrote:Show nested quote +On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:On July 29 2012 23:59 farvacola wrote:
[quote]
I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived.
Rocket science.
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On July 30 2012 00:22 farvacola wrote:Show nested quote +On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:On July 29 2012 23:59 farvacola wrote:On July 29 2012 23:53 paralleluniverse wrote:On July 29 2012 23:51 farvacola wrote:
I'm not exactly sure why the article makes the connection between flawed primary/secondary school math education and a need to remove certain educational requirements; it would make sense, at least to me, to instead focus on better teaching methodologies, as algebra and many of the "hard" areas of study have been taught in relatively the same manner for many, many years now. As posters above are explaining, I certainly think that Algebra ought to be requisite, as it lends itself to so many endeavors in life, and perhaps the key in improving its teaching is a more vocational or everyday focus in application, and a change from the standard drudgery of problem sets and timed tests. I'm thinking on my own honors math education, where in 8th grade we learned the quadratic formula via song and were required to sing it at the door one day in order to get into class. Simple little changes in teaching technique can do wonders for making subjects such as math more palatable. As I see it, there are simply too many inherent problems in putting forth entire populations of people who are unable to the basic algebraic underpinnings of the economy and their own personal finances. Are you saying that's good or bad? I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. I would also derive the formula. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Memorizing formulas has zero educational value. If you think math is about memorizing formulas, then I would direct you to Lockhart's Lament, which has been linked a few times already: http://www.maa.org/devlin/LockhartsLament.pdf I don't think thats what Micronesia or I are getting at, that memorization is to be frowned upon in the teaching of mathematics is a hotly debated issue among educators, and I wouldn't want to pass judgement either way as there are good justifications behind both sides of the debate (I only know this via a close friend's recent completion of his high school math teaching certification). If it makes you feel any better, we also had a game called "quad crossfire" in which we went head to head against classmates and had to speed solve a difficult problem on the board in front of the class. There was yelling, anger, and even a fight once, but the point is that the unique approach to math education in this scenario greatly improved the learning experience for all involved.
"Memorizing formulae has zero educational value." False.
It works EXACTLY as described above. You look it up enough times, you use it enough times, you remember it.
Please bear in mind that when doing education the most important is always to stick to what appears to work.
I've always thought that Lockhart's Lament is a rather lamentable lament. Sure it would be fun to tailor all mathematical education to the personal needs of a future mathematician. If only every person was to be a mathematician.
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On July 30 2012 00:18 paralleluniverse wrote:Show nested quote +On July 30 2012 00:15 Brutland wrote:
saying that algebra isn't useful to everyday living is almost like saying that oxygen isn't useful for everyday breathing. for instance, i need to go grocery shopping, i need to know how many and at what price my needed items are, then how much money i can spend. thats the heart of algebra (Ax+By...)-Z=0.the problem is most people think of math as this esoteric thing instead of as a way to frame the world and a way to make decisions about concrete ideas. hell, people use calc3 when playing baseball or football (3d analysis and force vector combinations intersecting planes of multiple moving pieces). the problem is that math taught by someone who doesn't understand math is worse than useless. it teaches that math isn't applicable, when in reality, it is how the world works. Nobody uses algebra when doing shopping. No baseball player does calculus. Just because the situation can be analyzed with algebra or calculus doesn't mean anyone does so, or would need to do so.
i guess the real divide comes down to, do you want to be told just what to do? or would you like to be able to decide the best reaction for yourself? if all you want to be in life is someone else's tool, go ahead, don't think about it.
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On July 30 2012 00:38 micronesia wrote:Show nested quote +On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:On July 29 2012 23:59 farvacola wrote:On July 29 2012 23:53 paralleluniverse wrote:
[quote]
Are you saying that's good or bad? I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. I would like to see you attempt to teach completing the square to an actual class of average kids... because if you can pull that off well then your plan might work regarding the quadratic formula (I'm not confident), but we have gone away from the topic of singing to teach something.
It's OK 90% of the thread is still on topic.
Obviously the students should have some proficiency in symbolic manipulation before learning how to solve quadratics. But I fail to see your point. Do you have a better method?
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On July 30 2012 00:35 paralleluniverse wrote:Show nested quote +On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:On July 29 2012 23:59 farvacola wrote:
[quote]
I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived.
I added some to my post. Point being that as a tool, its application is limitless. Just like your screwdriver. You can use it to erect your shower, create a toy, or to build a car. First you must learn to use it.
For instance, I've used the quadratic formula too many times to count. Not simply to use it, but to solve other problems. It naturally arises in alot of problems. And if not this specific formula, then some other. There's always a tool, like this formula, that has to be applied in any problem in soooo many fields. By not learning maths you'll be limited. Imo math and language are the most important subjects to learn from the get-go. Any other subject you can potentially read upon on your own if you have holes. You can still progress in them. But with math it is very difficult to progress in any direction if you don't have the entire foundation. And language is paramount to everything.
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On July 30 2012 00:39 -_-Quails wrote:Show nested quote +On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:
[quote]
Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. Rocket science.
The x = .5ut + at^2 formula? As if anyone would actually need to calculate the time it takes for a rocket to travel x meters (unless you work at NASA, where you'd probably majored in math or physics anyway).
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Why do I need to learn ancient history? Why do I need to learn foreign languages? Why do I need to learn how to structure a 5 paragraph essay?
Maybe there are a lot of people who finds these to be "more valuable" tools in their daily lives, but in my own life I find algebra more useful.
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On July 30 2012 00:43 Cutlery wrote:Show nested quote +On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:
[quote]
Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. I added some to my post. Point being that as a tool, its application is limitless. Just like your screwdriver. You can use it to erect your shower, create a toy, or to build a car. First you must learn to use it.
You haven't given any specific applications, just written fluff.
For example, an application of the Central Limit Theorem is that it allows us to approximate the standard error of an opinion poll as sqrt(p(1-p)/n).
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On July 30 2012 00:38 micronesia wrote:Show nested quote +On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:On July 30 2012 00:03 paralleluniverse wrote:On July 29 2012 23:59 farvacola wrote:On July 29 2012 23:53 paralleluniverse wrote:
[quote]
Are you saying that's good or bad? I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. I would like to see you attempt to teach completing the square to an actual class of average kids... because if you can pull that off well then your plan might work regarding the quadratic formula (I'm not confident), but we have gone away from the topic of singing to teach something.
I have done that. If you know what you are doing it is not to hard to teach high school students how to derive the quadratic formula.
1. They can already solve z^2 = C , where C is a positive real.
2. ax^2 + bx + c = 0 implies that a(x^2+b/a*x+c/a) = 0.
3. put p = b/a and q = c/a
4. Use (x+y)^2 = x^2 +2xy+y^2 to show that (x+p/2)^2 = x^2+px+p^2/4 (yes they can solve this on their own as an exercise)
5. x^2 + px = (x+p/2)^2-p^2/4 so that x^2+px+q= (x+p/2)^2 - p^2/4 +q = 0 and then (x+p/2)^2 = p^2/4-q
6. show that this is the same as 1. with z=x+p/2 and p^2/4-q=C
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On July 30 2012 00:44 paralleluniverse wrote:Show nested quote +On July 30 2012 00:39 -_-Quails wrote:On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:
[quote]
Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. Rocket science. The x = .5ut + at^2 formula? As if anyone would actually need to calculate the time it takes for a rocket to travel x meters (unless you work at NASA, where you'd probably majored in math or physics anyway).
I'm only quoting this because it's a question that's been directed at you that you've dodged twice - how do you expect a 13-15 year old to make an informed decision about whether they want to learn algebra? Do you think they have the understanding of the consequences of not doing so on their career potential?
Edit - wording
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On July 30 2012 00:45 Mortality wrote:
Why do I need to learn ancient history? Why do I need to learn foreign languages? Why do I need to learn how to structure a 5 paragraph essay?
Maybe there are a lot of people who finds these to be "more valuable" tools in their daily lives, but in my own life I find algebra more useful.
I don't support the mandatory teaching of ancient history or foreign languages, but English is important because people write in English. And it is preferable to the reader that they write in paragraphs.
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On July 30 2012 00:44 paralleluniverse wrote:Show nested quote +On July 30 2012 00:39 -_-Quails wrote:On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:
[quote]
Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. Rocket science. The x = .5ut + at^2 formula? As if anyone would actually need to calculate the time it takes for a rocket to travel x meters (unless you work at NASA, where you'd probably majored in math or physics anyway).
Also any person designing firework shows or pyrotechnics. And you only asked for a non-contrived example, not a day-to-day one.
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On July 30 2012 00:44 paralleluniverse wrote:Show nested quote +On July 30 2012 00:39 -_-Quails wrote:On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:On July 30 2012 00:06 micronesia wrote:
[quote]
Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. Rocket science. The x = .5ut + at^2 formula? As if anyone would actually need to calculate the time it takes for a rocket to travel x meters (unless you work at NASA, where you'd probably majored in math or physics anyway).
Name a single thing in highschool that is applicable to everyone, not related to language. You can say this about everything. About every tool. Not everyone will use them. And that specific formula has a wide group of applications: In it's current form it only speaks of position. But where the formula was derived from, you will see that as a tool, its applications are endless. This is simply the version of it that is cited in physics books.
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On July 30 2012 00:48 tenklavir wrote:Show nested quote +On July 30 2012 00:44 paralleluniverse wrote:On July 30 2012 00:39 -_-Quails wrote:On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:On July 30 2012 00:10 paralleluniverse wrote:
[quote]
I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved. I would also derive the formula. You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Back to my first question of the current post. Memorizing formulas has zero educational value. Almost completely agree with you. I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't. Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. Rocket science. The x = .5ut + at^2 formula? As if anyone would actually need to calculate the time it takes for a rocket to travel x meters (unless you work at NASA, where you'd probably majored in math or physics anyway). I'm only quoting this because it's a question that's been directed at you that you've dodged twice - how do you expect a 13-15 year old to make an informed decision about whether they want to learn algebra? Do you think they have the understanding of the consequences of not doing on their career potential? Edit - wording
Before electives, they can be given a pep talk on careers. If they want to keep the option open then they should continue with math, otherwise drop it.
I do admit there is a risk of bad decisions if it's done too early.
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What the fuck man...
If math requirements get dumbed down, I want English, Science, and History also dumbed down...
I just read 90% of the article, and stopped in disgust at the ideas given. "If math isn't integral in the job, just lower it"... well in Computer Science (at least of what I've experienced), not many other courses BESIDES math are necessary... so does that mean we should only require math for CS students?
+ Show Spoiler [more rage] +COME ON PEOPLE... GET WITH IT.... IF MATH IS USELESS, SO IS HISTORY, SCIENCE, ENGLISH, AND WHATEVERTHEFUCKELSE...
DEBATE ME... I CAN TAKE IT!
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On July 30 2012 00:36 -_-Quails wrote:Show nested quote +On July 29 2012 23:38 Deadlyhazard wrote:On July 29 2012 23:14 omgimonfire15 wrote:
We suck at algebra so we should get rid of it? Good logic. This just sounds like a ploy to make us seem smarter than we actually are. Its not about numbers and equations, its about critical thinking and showing that you are able to do something even when you don't like it. As stated numerous times, in many jobs, actually algebra is useless, but it shows employers that this guy can get through something most people hate, work hard, and think critically. In college, chemistry is mandatory, but the ones who make it through with good grades display their work ethic and set of priorities. + Show Spoiler +1) Nobody is saying it should be removed -- most are saying it should be something that's more optional or taught in a different way so students struggling can understand it or get something useful out of it.
2) Chemistry displaying work ethic and priority making is too black and white of thinking. I failed college algebra three times -- I have a great mathematical learning disability. I can't even do basic math. I miss 7+6 half the time. I had several private tutors and I studied much harder than those that were lazy and smoothly sailed by -- yet I still failed. I was literally making grades below those that were barely trying, yet many were making A's and B's.
I don't think it's that I'm completely stupid -- I simply have a learning disability when it comes to using numbers. So what happens to people like me? It's not because I didn't have priorities set. It's not because I displayed a poor work ethic. It's because of an innate problem with mathematics that I will always have (and have had since I started school as a wee child). For me, it's impossible to have any career related to math because I simply can not understand the type of abstract reasoning it presents. So what use is a mathematics course being mandatory for me? I do fine in almost every single subject. My report cards in college literally read A A B F, and you can guess what I was failing every semester (and having to repeat). I took statistics three times too. It's not that I can't be taught and learn from schooling, it's that I'm absolutely terrible in one department of reasoning -- mathematics. I feel that some courses should be optional for this very reason, so people like me stand a chance at becoming educated without having to suffer through the ordeals of major learning issues like I have. So what am I to do -- not be able to pass regular schooling to get to something more specific (and unrelated) to math just because I can't pass one subject? Generally if someone who otherwise performs well in school has a single area where they consistently fail or do very poorly compared to their other subjects there is a learning disability present, though possibly undiagnosed. he grades you posted look like you might possibly have dyscalculia, which is basically dyslexia for maths. Someone should have noticed that shortly after it became a big problem, and you very probably should have been given extra help in maths in school and waivers from requirements in college. I'm sorry that no-one did. Did you get through in the end?
Yeah, I passed college algebra and statistics after many failures. I dropped out of high school solely because I had to retake physics and I couldn't possibly do it. I was never diagnosed with discalculia, but I've been making D grades (considered passing in elementary/middle) so it was never brought up as an issue. It's later in life that it's really presenting a struggle to me.
I'm done with math classes forever though, seeing as how I finally managed to make a C in them for college. It was the biggest relief I've felt in my life on the day I received a passing grade for college statistics. I had taken over 8 courses for 3 math classes in college (I had to repeat intermediate algebra, which is basically pre-algebra in high school). It was really a big struggle for me.
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On July 30 2012 00:50 paralleluniverse wrote:Show nested quote +On July 30 2012 00:48 tenklavir wrote:On July 30 2012 00:44 paralleluniverse wrote:On July 30 2012 00:39 -_-Quails wrote:On July 30 2012 00:35 paralleluniverse wrote:On July 30 2012 00:32 Cutlery wrote:On July 30 2012 00:29 paralleluniverse wrote:On July 30 2012 00:22 micronesia wrote:On July 30 2012 00:19 paralleluniverse wrote:On July 30 2012 00:18 micronesia wrote:
[quote]
How? Assuming factoring and the like is already covered, and you are going on to problems that require the quadratic formula to be solved.
[quote]You've lost the majority of students at this point, lol. I like the idea in certain applications, but not all. Remember that we are talking about public school education in the USA in this thread.
[quote]Back to my first question of the current post.
[quote]Almost completely agree with you.
[quote]
I've read it, and you are assuming that teachers actually have 100% control over what happens in their classes, which they usually don't.
Completing the square. Okay so if I understand correctly, you would cover completing the square prior to the quadratic formula (different from most programs I'm aware of) because it makes it easier to learn rather than just be given the quadratic formula. Can you explain how students will get from completing the square to the quadratic formula? We also have a similar problem with completing the square. How would you teach it without simply giving them a list of steps (the algorithm)? In theory you can use derivation, but as I said earlier this doesn't work for every student. A good plan would go like this: 1) How should we solve (x+1)^2 + 4 = 0? 2) Now that we've established that 1) is really easy to solve how do we solve x^2 + 9x - 1 = 0 3) The problem reduces to writing 2) in a form like 1). 4) We work out how to do that, and hence solve 2). 5) We apply this to solve ax^2 + bx + c = 0, hence arriving at the quadratic equation. At no point would I impress upon my students all the wonderful applications of the quadratic equation, because there seriously are none. I would present this as a neat math trick. There are none? Math is a tool, tools have applications. Trust me. But you don't need to present it in any other way than simply a tool. I can think of many applications of math. But I cannot think of any applications of the quadratic equation that isn't contrived. Rocket science. The x = .5ut + at^2 formula? As if anyone would actually need to calculate the time it takes for a rocket to travel x meters (unless you work at NASA, where you'd probably majored in math or physics anyway). I'm only quoting this because it's a question that's been directed at you that you've dodged twice - how do you expect a 13-15 year old to make an informed decision about whether they want to learn algebra? Do you think they have the understanding of the consequences of not doing on their career potential? Edit - wording Before electives, they can be given a pep talk on careers. If they want to keep the option open then they should continue with math, otherwise drop it. I do admit there is a risk of bad decisions if it's done too early.
You're still putting an incredibly difficult decision with life-long implications on an adolescent mind, and hoping that a "pep talk" will help them choose what's best for them. How many times do people change their major in college, and now we're asking what we consider to be children, to choose what their path will be?
Imo currently, the decision is made at the right time - when they're adults. You have been given all the tools you need to go to college and figure out what you want to do with the rest of your life, and if you change your mind, you aren't completely screwed because of a decision you made when you were 14.
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EPT
