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The thing is, most people do not understand what the Maths that they are taught is used for. Say you want to be an Actuary or Accountant, your doing the maths course and have to do loads of stuff on the heat equation, youll have no idea why and probably think its a waste of time. Then bam! you find out its used to price options on the stock market.
To get to high level maths, you need to be doing low level maths first. If its not mandatory you have to know what you want to do by the age of like 15 which is clearly ridiculous to expect.
"But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar." - Its because they are also potential mathematicians, they might just not know it. What it comes down to is that in todays world, you have to give people more chance of becoming mathematicians than philosophers as they are just far more important.
If all the worlds philosophers disappeared today, nothing really changes. If its the mathematicians, the world crumbles.
So while its clear it should be mandatory, I agree with less memorizing and more understanding. However, school systems should not be forced to set the bar low enough for everyone to pass. As a rule of thumb, if everyone passes, it was too easy
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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.
This is the case for ANY highschool subject. Math is not unique in this.
If you allow it for math, you should allow it for other subjects.
What needs to be the focus is how to make math passable. It needs to be changed to allow more students to pass math. Some limitations based on some choices. Not remove algebra alltogether; but maybe remove something else so you have more time on algebra. Change the curriculum slightly, to make a secondary, but yet general math education possible. Making the entire subject optional is the same as making any other subject entirely optional. Math takes no presedence in this. If anything, math is the second most useful subject you'll learn in school, next to language. Tailoring it slightly to those who realize they have no interest in certain career choices can be a good thing. But algebra is still not what you want to cut out. The implications reach further than the students know, and seemingly further than you realize aswell?
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On July 30 2012 00:54 Deadlyhazard wrote:Show nested quote +On July 30 2012 00:36 -_-Quails wrote: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.
Congrats!
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On July 30 2012 00:55 tenklavir wrote:Show nested quote +On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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.
Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions?
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I still fail to see how anybody can fail high school algebra. I'm not even a math person, but as long as you put in a bit of effort algebra is all pretty simple at that level.
As far as the argument for "Well people do not need to use it, so why teach it?" goes, teaching it at a young age gives options. Chemistry, biology, modern literature, ancient literature, various social sciences; all of those things are only going to be used by some of the people who learn them. But at the age of 14 or 15, the student most likely does not know what they will be doing in five, ten, fifteen, or more years, so we should not say "Ok, Algebra for you, literature for you, and science for you!"
High school is to prepare people not only for further education but also to prepare them with tools which they can use later in their life. Having a high school diploma should mean something, but if we are only going to teach people what they need to know, then it is a fairly worthless certificate. Teaching something like algebra improves problem solving as well as mathematical abilities. A person who can solve algebra problems also can probably solve other logic-based problems better than a person who has not learned algebra, even if there is no actual algebra involved.
On July 29 2012 15:03 Sinensis wrote:
People failing Algebra math have never heard of Wolfram Alpha.
Wolfram Alpha is the greatest thing ever ^^
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On July 30 2012 00:58 paralleluniverse wrote:Show nested quote +On July 30 2012 00:55 tenklavir wrote:On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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. Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions?
It sure is, at least in my state. I needed to take a math class grades 9-12. It was a bit of a strange curriculum admittedly, since it was "integrated math" (not the usual Alegbra I, Geometry, Alegbra II, Trig) path of most schools, but we still had options: discrete math, statistics, AP calculus AB and BC, AP stat, college algebra. You could take stat and college algebra if you wanted an "easier" path, or take the APs if you wanted the harder path.
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On July 30 2012 00:58 paralleluniverse wrote:Show nested quote +On July 30 2012 00:55 tenklavir wrote:On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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. Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions?
I know at my high school you have to have 4 years of math, but you can count Chemistry as one of them. I would assume it varies from school district, but as far as I know math is generally needed even after 10th grade.
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On July 30 2012 00:58 paralleluniverse wrote:Show nested quote +On July 30 2012 00:55 tenklavir wrote:On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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. Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions?
This depends on the state curriculum and the particular school district one is in. At my school, math wasn't hard tied to a grade level, and one had to only complete Algebra 2 by their senior year. Others may require pre-calc or only Algebra 1/Geometry. And as to your second questions, sadly diversity in class structure is a luxury many cash-strapped districts cannot afford.
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On July 30 2012 00:48 one-one-one wrote:Show nested quote +On July 30 2012 00:38 micronesia 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. 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
Oh, very good. I was starting wonder whether I would be able to prove that.
On topic: Yes, I remember being taught that in the first year of high school. As I recall it, it wasn't difficult to understand the proof, but replicating it individually would have been out of the question (and is out of the question for most adult-mathematicians as well I would presume, unless they recall step 3. somehow).
Showing the proof, which always happened with whatever was on the menu, wasn't too much of a hassle and it certainly expanded our understanding of how mathematics worked in general. The actual learning process would begin with memorization and repetition.
A little bit of thread summary:
I think we are in agreement that (1) mathematics needs better and more teaching rather than policy-makers lifting their hands up in surrender. Also, we are essentially in agreement that (2) the original author ought to make his case against mathematics more specific, seeing as how (3) the principle of comparative advantage does not hold. Lastly (4) the original authors complaint that mathematics leads to too many dropouts cannot be remedied by dropping mathematics as a subject, as this may in the long run have dire ramifications on American excellence in hard sciences.
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On July 30 2012 00:57 Squigly wrote:
The thing is, most people do not understand what the Maths that they are taught is used for. Say you want to be an Actuary or Accountant, your doing the maths course and have to do loads of stuff on the heat equation, youll have no idea why and probably think its a waste of time. Then bam! you find out its used to price options on the stock market.
To get to high level maths, you need to be doing low level maths first. If its not mandatory you have to know what you want to do by the age of like 15 which is clearly ridiculous to expect.
"But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar." - Its because they are also potential mathematicians, they might just not know it. What it comes down to is that in todays world, you have to give people more chance of becoming mathematicians than philosophers as they are just far more important.
If all the worlds philosophers disappeared today, nothing really changes. If its the mathematicians, the world crumbles.
So while its clear it should be mandatory, I agree with less memorizing and more understanding. However, school systems should not be forced to set the bar low enough for everyone to pass. As a rule of thumb, if everyone passes, it was too easy
The Black-Scholes equation is one of the most beautiful pieces of mathematics. When people talk about mathematical beauty, that's the first thing that comes to my mind.
It's derived by combining price neutral pricing, measure theory, probability theory, stochastic differential equations, Ito calculus, partial differential equations, and can be solved by transforming it into the heat equation (as you've said) and using Fourier series.
It combines so many areas of analysis in such a mathematically elegant and beautiful way.
Unfortunately, it's absolutely bullshit and partly caused the global financial crisis.
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Most people could find a use for algebra almost every day. I guess you don't need it if you are a floutist - but it sure as hell helps to know - especially if you ever plan on investing money or like building something. I'm not entirely sure whats so difficult about it in the first place?
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On July 30 2012 01:05 paralleluniverse wrote:Show nested quote +On July 30 2012 00:57 Squigly wrote:
The thing is, most people do not understand what the Maths that they are taught is used for. Say you want to be an Actuary or Accountant, your doing the maths course and have to do loads of stuff on the heat equation, youll have no idea why and probably think its a waste of time. Then bam! you find out its used to price options on the stock market.
To get to high level maths, you need to be doing low level maths first. If its not mandatory you have to know what you want to do by the age of like 15 which is clearly ridiculous to expect.
"But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar." - Its because they are also potential mathematicians, they might just not know it. What it comes down to is that in todays world, you have to give people more chance of becoming mathematicians than philosophers as they are just far more important.
If all the worlds philosophers disappeared today, nothing really changes. If its the mathematicians, the world crumbles.
So while its clear it should be mandatory, I agree with less memorizing and more understanding. However, school systems should not be forced to set the bar low enough for everyone to pass. As a rule of thumb, if everyone passes, it was too easy The Black-Scholes equation is one of the most beautiful pieces of mathematics. When people talk about mathematical beauty, that's the first thing that comes to my mind. It combines price neutral pricing, measure theory, stochastic differential equations, partial differential equations, and can be solved by transforming it into the heat equation (as you've said) and using Fourier series. It combines so many areas of analysis in such a mathematically elegant and beautiful way. Unfortunately, it absolutely bullshit and partly caused the global financial crisis.
Whether or not it did cause the massive issues (not going to debate, not the time or place), it still shows how you need maths in a job which is crucial to the economy. People can only get there if you put them on the right path to start with.
Sure they may decide to go do an Arts degree instead, but the important thing is that you never took the option away.
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On July 29 2012 16:53 paralleluniverse wrote:Show nested quote +On July 29 2012 16:49 sOda~ wrote:On July 29 2012 16:41 paralleluniverse wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:On July 29 2012 16:00 TheRabidDeer wrote:
[quote]
position = .5(acceleration)(time)^2 + (initial velocity)(time) + (initial position)
Solve that without pemdas. Show me how that is arbitrary. Without it, we wouldnt have gone to space or done any number of other things. It is vital. Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation. If the convention was to do addition then multiplication, we could have just written, position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position) and still have gone to the moon. There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication. Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Then the convention I stated, putting x=1 gives 4, under the usual convention it's 3, but that's because 2 different concepts are written. The concept that my example expresses is 2(x+1), so (2x)+1 would be an incorrect translation of the concept -- a misreading. Why are you arguing about notation? Because some people think they are sooooo smart because they memorized that the usual convention is to do multiplication before addition, and that our educational system has failed because most people have failed to remember this arbitrary convention. It reflects the sad state of education that people are obsessively fixated on written notation to prove that people are stupid, instead of the understanding of actual mathematical concepts.
From reading your posts, it makes it seem like your knowledge of mathematics is far more vast then mine. While I am willing to admit this, I do believe my general graps of mathematical concepts is pretty fair.
With this being said, BEDMAS (PEMDAS) is a method of interpreting the basic language of mathematics. Although I've never been told or explained this by any teacher, the reason is because these are the levels of interactions with regards to mathematics. I've come to understand this as a basic rule:
Addition and subtraction are mathematical parrallels - the same numerical process.
Multiplication and Division are mathetmatical parrallels - the same numerical process.
Exponents /Square Roots are mathetmatical parrallels...
Brackets are a mathematical language restriction - they indicate that the problem requires you to deal with them first. They indicate importance, and without brackets in more complicated equations it would be too difficult to interpret the language and it would be too ambigious to the solver. They are a necessicity for communication of math, but not a necessicity of math in and of itself.
All of the above are related to addition/subtraction at a very basic, expanded level.
Multiplication is multiple additions. 4x5 for example, is saying you have added 4 a total of 5 times.
Division is multiple subtractions. 20/5 for examples says you have equally subtracted from 20 a total 5 times.
Exponents is multiple sets of multiplication. This is interesting in that it relates to sequencing, but implies addition as well. For example 4^3 expanded in terms of multiplication is 4x4x4 or rather (4)x(4x4). Broken down further using multiplication/addition logic (4)x(16), or the long hang process 4+4+4... You get the picture. (Brackets used to demonstrate the concept I am conveying) Basic math concepts always break down to the basic functions of addition, and it's reverse process, subtraction.
This is why BEDMAS must be used. Essentially you are breaking down the equation into its most basic forms as I did above to break it down into the common language of addition/subtraction. BEDMAS is not just an interpretation of math at a basic level, it is a simplified way of mainstreaming the interaction of math in and of itself.
That being said, I can understand why algebra is being considered to be removed from school. I never struggled with math in school, and haven't had to use anything outside of basic algebra for med calcs in University either. High school is meant to provide you with general knowledge in many different areas so when the time comes to specialize (if you want to) you have the basic skills to do it. In this manner, I believe basic algebra is necessary. I think the failures of the education system indicate that the cirriculum may need to be changed, but it also indicates that there is a failure somewhere along the line that needs to be solved.
IF ONLY THERE WERE SOME SORT OF MATHEMATICAL WAY TO ANALYZE WHERE THIS FAILURE IS COMING FROM...
[edit] Not having auto-correct sucks.
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On July 30 2012 00:58 paralleluniverse wrote:Show nested quote +On July 30 2012 00:55 tenklavir wrote:On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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. Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions?
Sorry to press the issue, but since I answered your question, can you answer mine?
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. Added, sometimes even earlier. I started algebra in 7th grade. I didn't enjoy it then, but I'm an electrical engineer now. You cannot put that kind of decision onto children.
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On July 29 2012 15:16 paralleluniverse wrote:Show nested quote +On July 29 2012 15:14 Slithe wrote:
The solution to people failing algebra is not to remove algebra, but to improve our education so that people stop failing it. I am positive that avery large majority of failing students would do just fine if they were given the right environment and tools to learn the subject.
On the matter of whether algebra is necessary or not: It's such a basic subject that is required for such a large number of jobs. It is a much safer option to teach algebra to everyone, since so many careers require it. It would be a terrible gamble for someone at the age of 15 to assume that they won't need algebra in the future. Really?
I have coworkers that think 3 oz (3 ounces) is 0.18 lbs, when it's actually 0.1875, meaning we should be rounding to 0.19 when making...deli sandwiches. When I have to fight my manager over this, part of me dies inside, especially given we've had the discussion numerous times. Even though I sort of have my manager on board, at least enough not to fight me about it, there's no way we're getting the signs posted that say 3 oz = .18 lbs changed, it would cause utter havoc for the rest of our coworkers, and they'd be mad at the person who caused this change.
People are irrationally afraid of math, we need attitudes towards math to change. This article's evidence of people getting worse at algebra over time indicates, imo, people are getting lazier and more indolent over time. I believe this is mostly the fault of students/culture telling them math is their enemy.
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On July 29 2012 16:59 ]343[ wrote:Anyway, more on topic: this (admittedly over-referenced) article by Lockhart has much to say on this issue. The problem isn't that algebra is unnecessary, but that the way it (and everything up to intro undergraduate math) is taught in the US turns people off.
This article is really good and gives a picture of how Math is taught in the US.
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On July 30 2012 01:02 The Final Boss wrote:Show nested quote +On July 30 2012 00:58 paralleluniverse wrote:On July 30 2012 00:55 tenklavir wrote:On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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. Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions? I know at my high school you have to have 4 years of math, but you can count Chemistry as one of them. I would assume it varies from school district, but as far as I know math is generally needed even after 10th grade.
Yeah, a lot of high schools just require x "years" of math, and a lot of them have other things that can count as a math credit. In my high school there was the remedial levels -> Math A -> Math AB -> Math B/pre-cal -> calculus. I only had to take math A and AB, because I took all of the programming classes my school offered and those transferred over. But really, they have such a horrible labeling system lol.
Not that I disliked math, but I much preferred my senior year to be me playing ping pong in the senior cafeteria for more than half of the day, so I overloaded my previous years in a similar manner for other classes.
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On July 30 2012 01:01 tenklavir wrote:Show nested quote +On July 30 2012 00:58 paralleluniverse wrote:On July 30 2012 00:55 tenklavir wrote:On July 30 2012 00:50 paralleluniverse wrote: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:
[quote]
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. Is math still compulsory in the US after grade 10? And are there different levels of math? Like easier and harder versions? It sure is, at least in my state. I needed to take a math class grades 9-12. It was a bit of a strange curriculum admittedly, since it was "integrated math" (not the usual Alegbra I, Geometry, Alegbra II, Trig) path of most schools, but we still had options: discrete math, statistics, AP calculus AB and BC, AP stat, college algebra. You could take stat and college algebra if you wanted an "easier" path, or take the APs if you wanted the harder path.
Sounds quite convoluted. In Australia (NSW at least), there's just math, it's not separated into algebra and geometry because both subjects are math. There's 3 levels: noob, easy, and normal (not these words precisely). And in year 11 and 12, math is optional. There's again 3 levels in year 11, but a 4th level in year 12 which is the hardest level.
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On July 30 2012 01:08 Satire wrote:Show nested quote +On July 29 2012 16:53 paralleluniverse wrote:On July 29 2012 16:49 sOda~ wrote:On July 29 2012 16:41 paralleluniverse wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:On July 29 2012 16:22 TheRabidDeer wrote:On July 29 2012 16:18 paralleluniverse wrote:On July 29 2012 16:13 dudeman001 wrote:On July 29 2012 16:08 paralleluniverse wrote:
[quote]
Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation.
If the convention was to do addition then multiplication, we could have just written,
position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position)
and still have gone to the moon.
There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth.
Everything in mathematics that is true would still be true in exactly the same way if we arbitrarily chose to do addition before multiplication.
Obviously it's efficient to have conventions because it saves writing, and basically everyone understands to do brackets first. And really that's all anyone needs to know. I'm confused about your argument. Mathematics is a system developed by humans with underlying foundations. The system works because operations have specific orders. Under the system, they are in fact true. If they were in fact arbitrary, the mathematical system would numerically come out to different results and therefore be a different system. It would still be math I guess, but you couldn't classify it as "true" under current mathematics. No, it won't come out to a different answer. The only thing that would change is the notation you use to write down the concept. There's a difference between axioms and notation. The integral of sin(x) should still be -cos(x) regardless of what order of operation convention you use. You'll just have to write the brackets in a different way. Alright, lets throw PEMDAS out the window. You are somebody new to math that does not know PEMDAS, how do you construct an equation using brackets if you dont know the order in which it is supposed to be solved? What order you solve an equation in is irrelevant. Consider 2x+1 = 0, under the convention that addition happens before multiplication. So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? Everyone agrees that we do brackets first, so this isn't a problem. But suppose not, and that someone insists that (9+3)^2 = 9^2 + 3^2, then the difference between this and (9+3)*(9+3) is purely convention. You're expressing different concepts. The concept of 9+3, then take the result and square it, is the same. It's like how different languages express the same concepts in different words. But English is not "more correct" than French. Then the convention I stated, putting x=1 gives 4, under the usual convention it's 3, but that's because 2 different concepts are written. The concept that my example expresses is 2(x+1), so (2x)+1 would be an incorrect translation of the concept -- a misreading. Why are you arguing about notation? Because some people think they are sooooo smart because they memorized that the usual convention is to do multiplication before addition, and that our educational system has failed because most people have failed to remember this arbitrary convention. It reflects the sad state of education that people are obsessively fixated on written notation to prove that people are stupid, instead of the understanding of actual mathematical concepts. From reading your posts, it makes it seem like your knowledge of mathematics is far more vast then mine. While I am willing to admit this, I do believe my general graps of mathematical concepts is pretty fair. With this being said, BEDMAS (PEMDAS) is a method of interpreting the basic language of mathematics. Although I've never been told or explained this by any teacher, the reason is because these are the levels of interactions with regards to mathematics. I've come to understand this as a basic rule: Addition and subtraction are mathematical parrallels - the same numerical process. Multiplication and Division are mathetmatical parrallels - the same numerical process. Exponents /Square Roots are mathetmatical parrallels... Brackets are a mathematical language restriction - they indicate that the problem requires you to deal with them first. They indicate importance, and without brackets in more complicated equations it would be too difficult to interpret the language and it would be too ambigious to the solver. They are a necessicity for communication of math, but not a necessicity of math in and of itself. All of the above are related to addition/subtraction at a very basic, expanded level. Multiplication is multiple additions. 4x5 for example, is saying you have added 4 a total of 5 times. Division is multiple subtractions. 20/5 for examples says you have equally subtracted from 20 a total 5 times. Exponents is multiple sets of multiplication. This is interesting in that it relates to sequencing, but implies addition as well. For example 4^3 expanded in terms of multiplication is 4x4x4 or rather (4)x(4x4). Broken down further using multiplication/addition logic (4)x(16), or the long hang process 4+4+4... You get the picture. (Brackets used to demonstrate the concept I am conveying) Basic math concepts always break down to the basic functions of addition, and it's reverse process, subtraction. This is why BEDMAS must be used. Essentially you are breaking down the equation into its most basic forms as I did above to break it down into the common language of addition/subtraction. BEDMAS is not just an interpretation of math at a basic level, it is a simplified way of mainstreaming the interaction of math in and of itself. That being said, I can understand why algebra is being considered to be removed from school. I never struggled with math in school, and haven't had to use anything outside of basic algebra for med calcs in University either. High school is meant to provide you with general knowledge in many different areas so when the time comes to specialize (if you want to) you have the basic skills to do it. In this manner, I believe basic algebra is necessary. I think the failures of the education system indicate that the cirriculum may need to be changed, but it also indicates that there is a failure somewhere along the line that needs to be solved. IF ONLY THERE WERE SOME SORT OF MATHEMATICAL WAY TO ANALYZE WHERE THIS FAILURE IS COMING FROM... [edit] Not having auto-correct sucks.
I don't want to go over this again. So let this me a final summary on the issue.
The order:
1. exponentiation.
2. multiplication/division
3. addition/subtraction
is an arbitrary convention that people have agreed to.
There is no reason that it can't instead be:
1. addition/subtraction
2. exponentiation.
3. multiplication/division.
You're argument that it has to be the first way because multiplication is repeated addition is irrelevant. Multiplication can still be repeated addition (for integers) even if the convention was changed. E.g. If we interpret 2+3*3 to mean that (2+3)*3 because addition is first, then multiplication is still repeated addition because the expression is equal to (2+3)+(2+3)+(2+3). And this is a different concept to 2+(3*3), which is why they aren't equal. But once you've agreed on a convention and translated everything to using your invented order of operation convention, everything in math that is currently true is still true. BIDMAS is not a theorem. It's a convention.
The idea that multiplication is repeated addition is something that is taught in primary school, but it's not generally true, how is pi*e, the sum of pi, repeated e times?
If you want to give a rigorous definition of pi*e, it should not be the sum of pi, repeated e times. It should be: let {x_n} be a sequence that converges to pi, and {y_n} be a sequence that converges to e, we know these sequences exist because the real field is a complete metric space, then {x_n*y_n} is a Cauchy sequence because {x_n} and {y_n} are, so it's limit also exists in the real field, call this limit pi*e.
Yes this is a lot more complicated and highly technical, that's why it's not taught outside of university level calculus. It's also less intuitive, unless you know a lot of math. But thinking of multiplication as repeated addition is not a good way to think about higher mathematics.
This is also a good post: http://www.teamliquid.net/forum/viewmessage.php?topic_id=356624¤tpage=8#152
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EPT
