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United States7483 Posts
On July 30 2012 17:14 ZapRoffo wrote:Show nested quote +On July 30 2012 17:07 Whitewing wrote:On July 30 2012 16:59 ZapRoffo wrote:On July 30 2012 16:37 Whitewing wrote:On July 30 2012 16:31 ZapRoffo wrote:On July 30 2012 16:17 Whitewing wrote:On July 30 2012 15:30 ZapRoffo wrote:
I've been tutoring middle, high school and lower college math for about 8+ years now, seen tons of students from many different schools, and I've had the same thought as the article to an extent for a little while now. Here's the deal: a good part of algebra (mainly algebra 2), most of geometry, all of pre-calculus/trig and calculus+ math is super-specific and not relevant to the lives of at least 75% of the population's lives. The kids ask me, why do I need to learn this, and I don't have a good answer for them other than to show that you can because people care about it. Geometry (other than an application of logic and just introducing trig functions and right triangles and planes and lines and stuff) is especially useless even as a prerequisite for later math and hard to motivate kids for, yet everyone has to take it.
Ideally, if I were education dictator, here's what my proposition would be. It has one major hairy point I'll point out. For kids who are on track for average to above average non-art university, it's basically the same math system as it is now because that's not really where the problem is. For everyone else though, the non-college bound in particular (which is a lot), most of algebra and on is really pointless and it hangs them up as the article talks about. There are some things in algebra that are basic reasoning skills everyone should learn, like solving for unknowns in simple situations and speed/distance/time problems for example.
But beyond that these students would be so much better served if instead of doing:
most of algebra,
geometry,
algebra 2,
they did:
basic logic
personal finance/very basic economics,
basic statistics and probability instead.
basic mechanical physics
It would be so much easier for them to see how this stuff relates to their lives and for teachers to tie lessons into the kids' experiences than with what they are learning in what high school math is mostly about now. And most of the higher achieving kids end up taking these as more advanced electives at some point and are much more likely to learn things like good finance habits in their home lives.
The hairy issue is you have to place the kids rather early in one of the paths, but I think for the kids who really struggle with things like pre-algebra or algebra it's really a no-brainer that they shouldn't be beating their heads against the wall trying to push through it.
I don't know how you'd teach even very basic economics without introductory calculus, you need to know how derivatives work in order to do anything on the margin, and good luck doing PPF's without it. You can't do any useful statistics or probability without better than basic algebra skills (anyone struggling with algebra 2 will have trouble), and you can't really learn any useful physics without more than algebra 1 level math. I took AP economics in high school that had 0 calculus required, you never learn margins are derivatives in it, you just do all discrete examples, you don't need any complicated math for it, and I mean very basic economics any way (well below , and more focused on household/job finance and practical things. Very basic statistics and probability, the kind that is useful for everyday life (chances of things happening/not happening, expected value, etc.), not the kind that is useful for deciding whether an experiment result is significant (you can go over bell curves in general and some milestones on it, and say you have to fall this far from the center to be pretty sure of yourself, that's the kind of depth I'm talking). Kids who are failing algebra in high school are so far below needing to do what you call "useful statistics"--that stuff is not useful to them. There's a big bias here because this forum is way higher income and educated (or potentially education for the young folk) than the people the article is talking about. Economics based entirely on discrete examples is essentially useless, real life examples generally don't look like that. It's simply not useful. Certain core concepts like the Tragedy of the Commons problem and Opportunity Cost can be useful, but without the proper background, truly understanding these basic things is difficult, and mastering them is impossible. (Good luck properly explaining other important core concepts like dominant strategy and the prisoner's dilemma, and then providing real life examples that actually exist and having them solve it without mathematics). You're going to teach finance (even basic finance) to students struggling with algebra? Really? These are students who have difficulty calculating compound interest. And you don't have to teach econometrics or advanced stats and probability, but I doubt students struggling with algebra are going to get much out of teaching formulas (because you can't do more than that without a stronger background) for basic probability problems. It's useless, and serves no purpose. The issue is one of simple problem solving skills: students who struggle with algebra 1 etc. simply haven't developed them, and they need to. Providing easier classes for them to teach basic skills in these subjects will not help, because of the fundamental lack of problem solving skills. As Neil Degrasse Tyson more or less said in the video, studying math and science wires your brain to solve problems and to reason. Even if the student masters the formulas in the classroom setting, the student is unlikely to be able to utilize the skills in that class in real life due to a lack of problem solving skills. Giving them an easy way out, so that they don't have to learn how to think isn't helping them, and it isn't helping society (since you took economics, you should know what a social good is, and education is one). Taking some different routes and methods to help them learn how to be a problem solver is what would help them, they never developed the skills necessary to think logically, which is the problem. Solve that, and algebra becomes very easy, and the entire issue is moot. You aren't understanding how basic I mean. It's very easy to give examples related to real life that highlight the tragedy of the commons or prisoner's dilemma without going into theory at all, and have it be interactive. If that goes well you can do the simplest math form of a problem. Like finance, just understanding that interest exists and the idea of having money in the bank or invested vs. spending it or holding it as cash, and doing simple interest, that's the sort of thing that would be appropriate and which many of the kids from less strong home situations might not get. On July 30 2012 16:38 dogabutila wrote:
You use algebra working at a gdamn grocery store. I know, I work at one. It's depressing how many times a cashier or even a customer can't do the math right and I end up having to embarrass somebody. Algebra isn't precalc or anything. That's the sort of basic reasoning that I do think is essential in algebra. But then factoring, or finding roots of higher degree polynomials, or simplifying rational and radical expressions, that's the sort of thing that is so removed from life it's just an exercise in weird symbols and rules to them. My argument isn't that teaching those very basic concepts without math at an absurdly simplistic level is impossible, my argument is that it's pointless and useless to do so, because they won't be able to properly apply what little they do learn outside of the classroom. Instead, focus on developing their critical thinking skills and getting them to learn how to solve problems and think logically and in abstract terms as well, then everything else becomes much simpler, and they'll be far more successful. We have different views on how valuable conceptual understanding is. That's one of the main things I learned in economics major. Guess what? Almost all the main economics major courses are useless as far as actually applying anything specific to the world. There are no scenarios you can calculate like a simple monopoly or perfect competition graph, and macro is just nuts how many confounding variables there are, good luck with that, predicting anything with macroeconomic models you learn in school is laughable. It still develops critical thinking skills when you learn about principles. Deciding how many people I can feed on this salary and where I can live: that's practicing a critical thinking skill same as finding polynomial roots. It's just one is more abstract, and some people are never going to, nor need to grasp things in that abstraction.
I too have an economics degree, and I think you missed the point. The purpose of all those graphs and models wasn't to show you how real life works at all, they were to explain relationships between different variables and events (such as the relationship between supply and demand, or the relationship between the supply of the labor market and wages). You used mathematics to learn principles and concepts, principles and concepts which aren't really possible to properly learn without the math. Sure, someone can tell you "price ceilings cause dead weight loss!" and can even color in the triangle on the graph for you to make you see it, but without actually knowing and understanding where all those lines on the graph come from, you learn absolutely nothing.
The point I made before that you somehow missed is that with your plan, you aren't teaching any principles, because they don't have the background to learn principles. You are teaching watered down, fluffed up formulas with a description that will go right over their heads, that they won't be able to apply when faced with a situation in life that calls for it due to a lack of basic, fundamental understanding and critical thinking skills.
Thus, useless.
Cutting out fundamentally important mathematical learning simply because it might not be directly applicable in their lives is not helpful, it merely compounds the problem in the first place, by denying them even more opportunity to develop critical thinking skills and writing them off as students. I have a friend who struggled in high school, the school guidance counselor even told him to forget about college. His mother hired me to tutor him as a classmate after school for a year, and I showed him how to think about things completely differently. He just got accepted into business school at the University of Chicago, one of the (if not THE) top ranked business schools in the world, and sent me the nicest thank you letter I've ever received in my life. I shudder to think of what would have happened to him if he'd been dropped out of algebra 2 and told to take the remedial no-math-because-you-won't-need-it classes instead of sticking with it and getting extra help to see things from a different perspective.
So no, the solution isn't that these students should be written off and given easier courses in what they will need for their skilless career at McDonald's flipping burgers, it's teaching the students who are struggling in a different manner and getting the parents more involved.
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People should learn a wide variety of things while in lower/upper school. to help them to find where they want to be, and give them some understanding of what's out there.
You could look at any subject and call it useless in x/y/z.
If tonnes of students can't learn it, that's an attitude problem. If anything, the rest of school should be made harder so they learn to put effort in right from the start. It's much harder to catch up once you fall behind.
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United States5544 Posts
On July 30 2012 17:19 Whitewing wrote:Show nested quote +On July 30 2012 17:14 ZapRoffo wrote:On July 30 2012 17:07 Whitewing wrote:On July 30 2012 16:59 ZapRoffo wrote:On July 30 2012 16:37 Whitewing wrote:On July 30 2012 16:31 ZapRoffo wrote:On July 30 2012 16:17 Whitewing wrote:On July 30 2012 15:30 ZapRoffo wrote:
I've been tutoring middle, high school and lower college math for about 8+ years now, seen tons of students from many different schools, and I've had the same thought as the article to an extent for a little while now. Here's the deal: a good part of algebra (mainly algebra 2), most of geometry, all of pre-calculus/trig and calculus+ math is super-specific and not relevant to the lives of at least 75% of the population's lives. The kids ask me, why do I need to learn this, and I don't have a good answer for them other than to show that you can because people care about it. Geometry (other than an application of logic and just introducing trig functions and right triangles and planes and lines and stuff) is especially useless even as a prerequisite for later math and hard to motivate kids for, yet everyone has to take it.
Ideally, if I were education dictator, here's what my proposition would be. It has one major hairy point I'll point out. For kids who are on track for average to above average non-art university, it's basically the same math system as it is now because that's not really where the problem is. For everyone else though, the non-college bound in particular (which is a lot), most of algebra and on is really pointless and it hangs them up as the article talks about. There are some things in algebra that are basic reasoning skills everyone should learn, like solving for unknowns in simple situations and speed/distance/time problems for example.
But beyond that these students would be so much better served if instead of doing:
most of algebra,
geometry,
algebra 2,
they did:
basic logic
personal finance/very basic economics,
basic statistics and probability instead.
basic mechanical physics
It would be so much easier for them to see how this stuff relates to their lives and for teachers to tie lessons into the kids' experiences than with what they are learning in what high school math is mostly about now. And most of the higher achieving kids end up taking these as more advanced electives at some point and are much more likely to learn things like good finance habits in their home lives.
The hairy issue is you have to place the kids rather early in one of the paths, but I think for the kids who really struggle with things like pre-algebra or algebra it's really a no-brainer that they shouldn't be beating their heads against the wall trying to push through it.
I don't know how you'd teach even very basic economics without introductory calculus, you need to know how derivatives work in order to do anything on the margin, and good luck doing PPF's without it. You can't do any useful statistics or probability without better than basic algebra skills (anyone struggling with algebra 2 will have trouble), and you can't really learn any useful physics without more than algebra 1 level math. I took AP economics in high school that had 0 calculus required, you never learn margins are derivatives in it, you just do all discrete examples, you don't need any complicated math for it, and I mean very basic economics any way (well below , and more focused on household/job finance and practical things. Very basic statistics and probability, the kind that is useful for everyday life (chances of things happening/not happening, expected value, etc.), not the kind that is useful for deciding whether an experiment result is significant (you can go over bell curves in general and some milestones on it, and say you have to fall this far from the center to be pretty sure of yourself, that's the kind of depth I'm talking). Kids who are failing algebra in high school are so far below needing to do what you call "useful statistics"--that stuff is not useful to them. There's a big bias here because this forum is way higher income and educated (or potentially education for the young folk) than the people the article is talking about. Economics based entirely on discrete examples is essentially useless, real life examples generally don't look like that. It's simply not useful. Certain core concepts like the Tragedy of the Commons problem and Opportunity Cost can be useful, but without the proper background, truly understanding these basic things is difficult, and mastering them is impossible. (Good luck properly explaining other important core concepts like dominant strategy and the prisoner's dilemma, and then providing real life examples that actually exist and having them solve it without mathematics). You're going to teach finance (even basic finance) to students struggling with algebra? Really? These are students who have difficulty calculating compound interest. And you don't have to teach econometrics or advanced stats and probability, but I doubt students struggling with algebra are going to get much out of teaching formulas (because you can't do more than that without a stronger background) for basic probability problems. It's useless, and serves no purpose. The issue is one of simple problem solving skills: students who struggle with algebra 1 etc. simply haven't developed them, and they need to. Providing easier classes for them to teach basic skills in these subjects will not help, because of the fundamental lack of problem solving skills. As Neil Degrasse Tyson more or less said in the video, studying math and science wires your brain to solve problems and to reason. Even if the student masters the formulas in the classroom setting, the student is unlikely to be able to utilize the skills in that class in real life due to a lack of problem solving skills. Giving them an easy way out, so that they don't have to learn how to think isn't helping them, and it isn't helping society (since you took economics, you should know what a social good is, and education is one). Taking some different routes and methods to help them learn how to be a problem solver is what would help them, they never developed the skills necessary to think logically, which is the problem. Solve that, and algebra becomes very easy, and the entire issue is moot. You aren't understanding how basic I mean. It's very easy to give examples related to real life that highlight the tragedy of the commons or prisoner's dilemma without going into theory at all, and have it be interactive. If that goes well you can do the simplest math form of a problem. Like finance, just understanding that interest exists and the idea of having money in the bank or invested vs. spending it or holding it as cash, and doing simple interest, that's the sort of thing that would be appropriate and which many of the kids from less strong home situations might not get. On July 30 2012 16:38 dogabutila wrote:
You use algebra working at a gdamn grocery store. I know, I work at one. It's depressing how many times a cashier or even a customer can't do the math right and I end up having to embarrass somebody. Algebra isn't precalc or anything. That's the sort of basic reasoning that I do think is essential in algebra. But then factoring, or finding roots of higher degree polynomials, or simplifying rational and radical expressions, that's the sort of thing that is so removed from life it's just an exercise in weird symbols and rules to them. My argument isn't that teaching those very basic concepts without math at an absurdly simplistic level is impossible, my argument is that it's pointless and useless to do so, because they won't be able to properly apply what little they do learn outside of the classroom. Instead, focus on developing their critical thinking skills and getting them to learn how to solve problems and think logically and in abstract terms as well, then everything else becomes much simpler, and they'll be far more successful. We have different views on how valuable conceptual understanding is. That's one of the main things I learned in economics major. Guess what? Almost all the main economics major courses are useless as far as actually applying anything specific to the world. There are no scenarios you can calculate like a simple monopoly or perfect competition graph, and macro is just nuts how many confounding variables there are, good luck with that, predicting anything with macroeconomic models you learn in school is laughable. It still develops critical thinking skills when you learn about principles. Deciding how many people I can feed on this salary and where I can live: that's practicing a critical thinking skill same as finding polynomial roots. It's just one is more abstract, and some people are never going to, nor need to grasp things in that abstraction. I too have an economics degree, and I think you missed the point. The purpose of all those graphs and models wasn't to show you how real life works at all, they were to explain relationships between different variables and events (such as the relationship between supply and demand, or the relationship between the supply of the labor market and wages). You used mathematics to learn principles and concepts, principles and concepts which aren't really possible to properly learn without the math. Sure, someone can tell you "price ceilings cause dead weight loss!" and can even color in the triangle on the graph for you to make you see it, but without actually knowing and understanding where all those lines on the graph come from, you learn absolutely nothing. The point I made before that you somehow missed is that with your plan, you aren't teaching any principles, because they don't have the background to learn principles. You are teaching watered down, fluffed up formulas with a description that will go right over their heads, that they won't be able to apply when faced with a situation in life that calls for it due to a lack of basic, fundamental understanding and critical thinking skills. Thus, useless. Cutting out fundamentally important mathematical learning simply because it might not be directly applicable in their lives is not helpful, it merely compounds the problem in the first place, by denying them even more opportunity to develop critical thinking skills and writing them off as students. I have a friend who struggled in high school, the school guidance counselor even told him to forget about college. His mother hired me to tutor him as a classmate after school for a year, and I showed him how to think about things completely differently. He just got accepted into business school at the University of Chicago, one of the (if not THE) top ranked business schools in the world, and sent me the nicest thank you letter I've ever received in my life. I shudder to think of what would have happened to him if he'd been dropped out of algebra 2 and told to take the remedial no-math-because-you-won't-need-it classes instead of sticking with it and getting extra help to see things from a different perspective. So no, the solution isn't that these students should be written off and given easier courses in what they will need for their skilless career at McDonald's flipping burgers, it's teaching the students who are struggling in a different manner and getting the parents more involved.
That is fine for individual cases and where parents are involved enough and have means enough to get private tutoring. But the article is talking about vast swaths of kids probably mostly from low income situations and poorer public schools, many bad family situations, etc.. I feel like it's how to get a little bit more for them (cause I really don't think it's nothing) even if it's not the ideal curriculum, rather than the nothing of struggling and just never really getting something like algebra.
And hey, if one of the things you do in basic finance class is learn about how education is an investment and makes you more money in the future, if any of that sticks, maybe some % of them are more likely to think tutoring is a good idea when their kids struggle in school (or even ask their own parents for it). I'm thinking of them as life skills like this that help their situations, or help them in bringing up next generations.
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United States7483 Posts
On July 30 2012 17:38 ZapRoffo wrote:Show nested quote +On July 30 2012 17:19 Whitewing wrote:On July 30 2012 17:14 ZapRoffo wrote:On July 30 2012 17:07 Whitewing wrote:On July 30 2012 16:59 ZapRoffo wrote:On July 30 2012 16:37 Whitewing wrote:On July 30 2012 16:31 ZapRoffo wrote:On July 30 2012 16:17 Whitewing wrote:On July 30 2012 15:30 ZapRoffo wrote:
I've been tutoring middle, high school and lower college math for about 8+ years now, seen tons of students from many different schools, and I've had the same thought as the article to an extent for a little while now. Here's the deal: a good part of algebra (mainly algebra 2), most of geometry, all of pre-calculus/trig and calculus+ math is super-specific and not relevant to the lives of at least 75% of the population's lives. The kids ask me, why do I need to learn this, and I don't have a good answer for them other than to show that you can because people care about it. Geometry (other than an application of logic and just introducing trig functions and right triangles and planes and lines and stuff) is especially useless even as a prerequisite for later math and hard to motivate kids for, yet everyone has to take it.
Ideally, if I were education dictator, here's what my proposition would be. It has one major hairy point I'll point out. For kids who are on track for average to above average non-art university, it's basically the same math system as it is now because that's not really where the problem is. For everyone else though, the non-college bound in particular (which is a lot), most of algebra and on is really pointless and it hangs them up as the article talks about. There are some things in algebra that are basic reasoning skills everyone should learn, like solving for unknowns in simple situations and speed/distance/time problems for example.
But beyond that these students would be so much better served if instead of doing:
most of algebra,
geometry,
algebra 2,
they did:
basic logic
personal finance/very basic economics,
basic statistics and probability instead.
basic mechanical physics
It would be so much easier for them to see how this stuff relates to their lives and for teachers to tie lessons into the kids' experiences than with what they are learning in what high school math is mostly about now. And most of the higher achieving kids end up taking these as more advanced electives at some point and are much more likely to learn things like good finance habits in their home lives.
The hairy issue is you have to place the kids rather early in one of the paths, but I think for the kids who really struggle with things like pre-algebra or algebra it's really a no-brainer that they shouldn't be beating their heads against the wall trying to push through it.
I don't know how you'd teach even very basic economics without introductory calculus, you need to know how derivatives work in order to do anything on the margin, and good luck doing PPF's without it. You can't do any useful statistics or probability without better than basic algebra skills (anyone struggling with algebra 2 will have trouble), and you can't really learn any useful physics without more than algebra 1 level math. I took AP economics in high school that had 0 calculus required, you never learn margins are derivatives in it, you just do all discrete examples, you don't need any complicated math for it, and I mean very basic economics any way (well below , and more focused on household/job finance and practical things. Very basic statistics and probability, the kind that is useful for everyday life (chances of things happening/not happening, expected value, etc.), not the kind that is useful for deciding whether an experiment result is significant (you can go over bell curves in general and some milestones on it, and say you have to fall this far from the center to be pretty sure of yourself, that's the kind of depth I'm talking). Kids who are failing algebra in high school are so far below needing to do what you call "useful statistics"--that stuff is not useful to them. There's a big bias here because this forum is way higher income and educated (or potentially education for the young folk) than the people the article is talking about. Economics based entirely on discrete examples is essentially useless, real life examples generally don't look like that. It's simply not useful. Certain core concepts like the Tragedy of the Commons problem and Opportunity Cost can be useful, but without the proper background, truly understanding these basic things is difficult, and mastering them is impossible. (Good luck properly explaining other important core concepts like dominant strategy and the prisoner's dilemma, and then providing real life examples that actually exist and having them solve it without mathematics). You're going to teach finance (even basic finance) to students struggling with algebra? Really? These are students who have difficulty calculating compound interest. And you don't have to teach econometrics or advanced stats and probability, but I doubt students struggling with algebra are going to get much out of teaching formulas (because you can't do more than that without a stronger background) for basic probability problems. It's useless, and serves no purpose. The issue is one of simple problem solving skills: students who struggle with algebra 1 etc. simply haven't developed them, and they need to. Providing easier classes for them to teach basic skills in these subjects will not help, because of the fundamental lack of problem solving skills. As Neil Degrasse Tyson more or less said in the video, studying math and science wires your brain to solve problems and to reason. Even if the student masters the formulas in the classroom setting, the student is unlikely to be able to utilize the skills in that class in real life due to a lack of problem solving skills. Giving them an easy way out, so that they don't have to learn how to think isn't helping them, and it isn't helping society (since you took economics, you should know what a social good is, and education is one). Taking some different routes and methods to help them learn how to be a problem solver is what would help them, they never developed the skills necessary to think logically, which is the problem. Solve that, and algebra becomes very easy, and the entire issue is moot. You aren't understanding how basic I mean. It's very easy to give examples related to real life that highlight the tragedy of the commons or prisoner's dilemma without going into theory at all, and have it be interactive. If that goes well you can do the simplest math form of a problem. Like finance, just understanding that interest exists and the idea of having money in the bank or invested vs. spending it or holding it as cash, and doing simple interest, that's the sort of thing that would be appropriate and which many of the kids from less strong home situations might not get. On July 30 2012 16:38 dogabutila wrote:
You use algebra working at a gdamn grocery store. I know, I work at one. It's depressing how many times a cashier or even a customer can't do the math right and I end up having to embarrass somebody. Algebra isn't precalc or anything. That's the sort of basic reasoning that I do think is essential in algebra. But then factoring, or finding roots of higher degree polynomials, or simplifying rational and radical expressions, that's the sort of thing that is so removed from life it's just an exercise in weird symbols and rules to them. My argument isn't that teaching those very basic concepts without math at an absurdly simplistic level is impossible, my argument is that it's pointless and useless to do so, because they won't be able to properly apply what little they do learn outside of the classroom. Instead, focus on developing their critical thinking skills and getting them to learn how to solve problems and think logically and in abstract terms as well, then everything else becomes much simpler, and they'll be far more successful. We have different views on how valuable conceptual understanding is. That's one of the main things I learned in economics major. Guess what? Almost all the main economics major courses are useless as far as actually applying anything specific to the world. There are no scenarios you can calculate like a simple monopoly or perfect competition graph, and macro is just nuts how many confounding variables there are, good luck with that, predicting anything with macroeconomic models you learn in school is laughable. It still develops critical thinking skills when you learn about principles. Deciding how many people I can feed on this salary and where I can live: that's practicing a critical thinking skill same as finding polynomial roots. It's just one is more abstract, and some people are never going to, nor need to grasp things in that abstraction. I too have an economics degree, and I think you missed the point. The purpose of all those graphs and models wasn't to show you how real life works at all, they were to explain relationships between different variables and events (such as the relationship between supply and demand, or the relationship between the supply of the labor market and wages). You used mathematics to learn principles and concepts, principles and concepts which aren't really possible to properly learn without the math. Sure, someone can tell you "price ceilings cause dead weight loss!" and can even color in the triangle on the graph for you to make you see it, but without actually knowing and understanding where all those lines on the graph come from, you learn absolutely nothing. The point I made before that you somehow missed is that with your plan, you aren't teaching any principles, because they don't have the background to learn principles. You are teaching watered down, fluffed up formulas with a description that will go right over their heads, that they won't be able to apply when faced with a situation in life that calls for it due to a lack of basic, fundamental understanding and critical thinking skills. Thus, useless. Cutting out fundamentally important mathematical learning simply because it might not be directly applicable in their lives is not helpful, it merely compounds the problem in the first place, by denying them even more opportunity to develop critical thinking skills and writing them off as students. I have a friend who struggled in high school, the school guidance counselor even told him to forget about college. His mother hired me to tutor him as a classmate after school for a year, and I showed him how to think about things completely differently. He just got accepted into business school at the University of Chicago, one of the (if not THE) top ranked business schools in the world, and sent me the nicest thank you letter I've ever received in my life. I shudder to think of what would have happened to him if he'd been dropped out of algebra 2 and told to take the remedial no-math-because-you-won't-need-it classes instead of sticking with it and getting extra help to see things from a different perspective. So no, the solution isn't that these students should be written off and given easier courses in what they will need for their skilless career at McDonald's flipping burgers, it's teaching the students who are struggling in a different manner and getting the parents more involved. That is fine for individual cases and where parents are involved enough and have means enough to get private tutoring. But the article is talking about vast swaths of kids probably mostly from low income situations and poorer public schools, many bad family situations, etc.. I feel like it's how to get a little bit more for them (cause I really don't think it's nothing) even if it's not the ideal curriculum, rather than the nothing of struggling and just never really getting something like algebra.
That's why I specifically said to examine teaching methodology for struggling students. You are attempting to treat a symptom of the problem with a solution that makes the problem itself worse. I'm suggesting to solve the problem itself. I never said it would be easy or simple, but few things truly worth doing are.
Telling students "you won't be successful, so here are some useful skills you'll need for your lousy career that requires no actual training" is beyond demoralizing: if they haven't already given up entirely, they most likely will at this point.
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seriously?! such a dumb article... sorry.
It sounds like the author wants to just hand diplomas to everyone, without actually achieving anything.
come on... you need to weed out stupid people, before university.
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Here is what I gather from the article. "The American education system is a slowly sinking ship, those who try to polish the brass are fools. If destruction is inevitable I want to be its agent rather than its victim, let us remove all the brass".
Man alive, it makes no sense to me. Must be useless. I give up trying to understand. I guess I won't read any further.
<sarcasm off>
Simply because it is a barrier to some, algebra should be taught better in American schools. American schools need an overhaul and culture needs it too as our culture has anti-wisdom elements in it everywhere. Unfortunately those who want to overhaul it are often stopped by those who want to sell the very steel- and for scrap, if you get my drift.
I know I'm being really opinionated. I'm sorry. They're deep set opinions so don't let them sway you or argue against them. This is just my two random as a cow on a cotton house roof cents. Cause it's 2AM and I can't sleep for pain.
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On July 30 2012 17:19 Whitewing wrote:Show nested quote +On July 30 2012 17:14 ZapRoffo wrote:On July 30 2012 17:07 Whitewing wrote:On July 30 2012 16:59 ZapRoffo wrote:On July 30 2012 16:37 Whitewing wrote:On July 30 2012 16:31 ZapRoffo wrote:On July 30 2012 16:17 Whitewing wrote:On July 30 2012 15:30 ZapRoffo wrote:
I've been tutoring middle, high school and lower college math for about 8+ years now, seen tons of students from many different schools, and I've had the same thought as the article to an extent for a little while now. Here's the deal: a good part of algebra (mainly algebra 2), most of geometry, all of pre-calculus/trig and calculus+ math is super-specific and not relevant to the lives of at least 75% of the population's lives. The kids ask me, why do I need to learn this, and I don't have a good answer for them other than to show that you can because people care about it. Geometry (other than an application of logic and just introducing trig functions and right triangles and planes and lines and stuff) is especially useless even as a prerequisite for later math and hard to motivate kids for, yet everyone has to take it.
Ideally, if I were education dictator, here's what my proposition would be. It has one major hairy point I'll point out. For kids who are on track for average to above average non-art university, it's basically the same math system as it is now because that's not really where the problem is. For everyone else though, the non-college bound in particular (which is a lot), most of algebra and on is really pointless and it hangs them up as the article talks about. There are some things in algebra that are basic reasoning skills everyone should learn, like solving for unknowns in simple situations and speed/distance/time problems for example.
But beyond that these students would be so much better served if instead of doing:
most of algebra,
geometry,
algebra 2,
they did:
basic logic
personal finance/very basic economics,
basic statistics and probability instead.
basic mechanical physics
It would be so much easier for them to see how this stuff relates to their lives and for teachers to tie lessons into the kids' experiences than with what they are learning in what high school math is mostly about now. And most of the higher achieving kids end up taking these as more advanced electives at some point and are much more likely to learn things like good finance habits in their home lives.
The hairy issue is you have to place the kids rather early in one of the paths, but I think for the kids who really struggle with things like pre-algebra or algebra it's really a no-brainer that they shouldn't be beating their heads against the wall trying to push through it.
I don't know how you'd teach even very basic economics without introductory calculus, you need to know how derivatives work in order to do anything on the margin, and good luck doing PPF's without it. You can't do any useful statistics or probability without better than basic algebra skills (anyone struggling with algebra 2 will have trouble), and you can't really learn any useful physics without more than algebra 1 level math. I took AP economics in high school that had 0 calculus required, you never learn margins are derivatives in it, you just do all discrete examples, you don't need any complicated math for it, and I mean very basic economics any way (well below , and more focused on household/job finance and practical things. Very basic statistics and probability, the kind that is useful for everyday life (chances of things happening/not happening, expected value, etc.), not the kind that is useful for deciding whether an experiment result is significant (you can go over bell curves in general and some milestones on it, and say you have to fall this far from the center to be pretty sure of yourself, that's the kind of depth I'm talking). Kids who are failing algebra in high school are so far below needing to do what you call "useful statistics"--that stuff is not useful to them. There's a big bias here because this forum is way higher income and educated (or potentially education for the young folk) than the people the article is talking about. Economics based entirely on discrete examples is essentially useless, real life examples generally don't look like that. It's simply not useful. Certain core concepts like the Tragedy of the Commons problem and Opportunity Cost can be useful, but without the proper background, truly understanding these basic things is difficult, and mastering them is impossible. (Good luck properly explaining other important core concepts like dominant strategy and the prisoner's dilemma, and then providing real life examples that actually exist and having them solve it without mathematics). You're going to teach finance (even basic finance) to students struggling with algebra? Really? These are students who have difficulty calculating compound interest. And you don't have to teach econometrics or advanced stats and probability, but I doubt students struggling with algebra are going to get much out of teaching formulas (because you can't do more than that without a stronger background) for basic probability problems. It's useless, and serves no purpose. The issue is one of simple problem solving skills: students who struggle with algebra 1 etc. simply haven't developed them, and they need to. Providing easier classes for them to teach basic skills in these subjects will not help, because of the fundamental lack of problem solving skills. As Neil Degrasse Tyson more or less said in the video, studying math and science wires your brain to solve problems and to reason. Even if the student masters the formulas in the classroom setting, the student is unlikely to be able to utilize the skills in that class in real life due to a lack of problem solving skills. Giving them an easy way out, so that they don't have to learn how to think isn't helping them, and it isn't helping society (since you took economics, you should know what a social good is, and education is one). Taking some different routes and methods to help them learn how to be a problem solver is what would help them, they never developed the skills necessary to think logically, which is the problem. Solve that, and algebra becomes very easy, and the entire issue is moot. You aren't understanding how basic I mean. It's very easy to give examples related to real life that highlight the tragedy of the commons or prisoner's dilemma without going into theory at all, and have it be interactive. If that goes well you can do the simplest math form of a problem. Like finance, just understanding that interest exists and the idea of having money in the bank or invested vs. spending it or holding it as cash, and doing simple interest, that's the sort of thing that would be appropriate and which many of the kids from less strong home situations might not get. On July 30 2012 16:38 dogabutila wrote:
You use algebra working at a gdamn grocery store. I know, I work at one. It's depressing how many times a cashier or even a customer can't do the math right and I end up having to embarrass somebody. Algebra isn't precalc or anything. That's the sort of basic reasoning that I do think is essential in algebra. But then factoring, or finding roots of higher degree polynomials, or simplifying rational and radical expressions, that's the sort of thing that is so removed from life it's just an exercise in weird symbols and rules to them. My argument isn't that teaching those very basic concepts without math at an absurdly simplistic level is impossible, my argument is that it's pointless and useless to do so, because they won't be able to properly apply what little they do learn outside of the classroom. Instead, focus on developing their critical thinking skills and getting them to learn how to solve problems and think logically and in abstract terms as well, then everything else becomes much simpler, and they'll be far more successful. We have different views on how valuable conceptual understanding is. That's one of the main things I learned in economics major. Guess what? Almost all the main economics major courses are useless as far as actually applying anything specific to the world. There are no scenarios you can calculate like a simple monopoly or perfect competition graph, and macro is just nuts how many confounding variables there are, good luck with that, predicting anything with macroeconomic models you learn in school is laughable. It still develops critical thinking skills when you learn about principles. Deciding how many people I can feed on this salary and where I can live: that's practicing a critical thinking skill same as finding polynomial roots. It's just one is more abstract, and some people are never going to, nor need to grasp things in that abstraction. I too have an economics degree, and I think you missed the point. The purpose of all those graphs and models wasn't to show you how real life works at all, they were to explain relationships between different variables and events (such as the relationship between supply and demand, or the relationship between the supply of the labor market and wages). You used mathematics to learn principles and concepts, principles and concepts which aren't really possible to properly learn without the math. Sure, someone can tell you "price ceilings cause dead weight loss!" and can even color in the triangle on the graph for you to make you see it, but without actually knowing and understanding where all those lines on the graph come from, you learn absolutely nothing. The point I made before that you somehow missed is that with your plan, you aren't teaching any principles, because they don't have the background to learn principles. You are teaching watered down, fluffed up formulas with a description that will go right over their heads, that they won't be able to apply when faced with a situation in life that calls for it due to a lack of basic, fundamental understanding and critical thinking skills. Thus, useless. Cutting out fundamentally important mathematical learning simply because it might not be directly applicable in their lives is not helpful, it merely compounds the problem in the first place, by denying them even more opportunity to develop critical thinking skills and writing them off as students. I have a friend who struggled in high school, the school guidance counselor even told him to forget about college. His mother hired me to tutor him as a classmate after school for a year, and I showed him how to think about things completely differently. He just got accepted into business school at the University of Chicago, one of the (if not THE) top ranked business schools in the world, and sent me the nicest thank you letter I've ever received in my life. I shudder to think of what would have happened to him if he'd been dropped out of algebra 2 and told to take the remedial no-math-because-you-won't-need-it classes instead of sticking with it and getting extra help to see things from a different perspective. So no, the solution isn't that these students should be written off and given easier courses in what they will need for their skilless career at McDonald's flipping burgers, it's teaching the students who are struggling in a different manner and getting the parents more involved.
Ahhh... Whitewing, can I say thanks for being a breath of fresh air to me in the wee hours of the morning? This is beautiful, beautiful!
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I think it is worthwhile to discuss a different approach in terms of math and school.
I was fairly good in math at school and by that decided to graduate in university as something invovled with maths, which ended up being business information systems.
When i compare university algebra to schools algebra I would always choose the first. Not only because it is more complete, but also because it is way more understandable.
In school they always left so many blank spaces because they feel they are too hard to teach or too much. But with those blank spaces I, for me, didn't really get what algebra was about in school.
edit: and what a lot of people here forget is that maths need a high level of abstraction-niveau. This isn't something a human being poses as a giving thing. It could be viewed as talent. And since im teaching some pupils in math (home lesson) who are not necessarly dumb, i know that it can be friggin hard to try to explain someone algebra.
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On July 30 2012 15:36 ZapRoffo wrote:Show nested quote +On July 30 2012 15:31 Swede wrote:
It would be interesting to compare the maths curriculum of different countries as well as pass/fail rates. The article is interesting, but it's hard to know whether the low pass rate is a systemic failure or simply because algebra is too hard. A statistical comparison between countries would probably shed some light on that. It's about income inequality, at least here in the US. Poor kids with bad home lives living in bad neighborhoods and go to bad poor schools do way worse on everything, and it seems like the US system fails because the US has super high income inequality compared to the first world. You have to look at social factors like this that are at the core. Like our ridiculous incarceration rate messing up home lives, etc..
You might be right that income inequality contributes to the problem, but it's all just pointless speculation without some statistics in there. Hence my other post. It would be more more beneficial to investigate failing and succeeding systems from around the world and note the differences than make potentially misguided claims that algebra is unnecessary.
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At first I thought this article was talking about Calculus. But then I reread it and saw "algebra".
I'll give that there are certain areas where merit does stem somewhat from natural talent. I could probably be good at art and sketching, but compared to someone who had talent as an artist I'd probably take twice as long to become half as good.
Algebra, is not one of these subjects. It has nothing to do with creativity or preferences. Algebra, when you break it down, is application of logic. And if you're struggling with algebra, or indeed any form of high-school maths, then you are simply not trying hard enough, because if you can wake up in the morning and put your socks on the right feet then you have the brain power necessary to understand algebra.
Most people have the ability to do algebra. They simply don't try, or they don't want to. That's not the same as not understanding it, and I think the article glosses over this fact somewhat.
As for whether it is truly necessary in real life. Well, that's another story.
I mean Calculus I can understand. But algebra? If we're going to come this far, then where does it stop? Are we going to question whether we need to learn multiplication in 5 years?
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Mathematics execises the logical parts/functions of the brain. Therefore it is necessary and not just for calculating stuff.
My 5 cents..
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Basic education should be as broad as possible because a 12-16 year old kid DOES NOT KNOW what he/she wants to become later on (we would all be pilots/firefighters/superhero/othercoolstuff then...). So if the kid skips learning algebra at age 12 and later discovers, let's say, when he approaches 16-17, that he/she wants to become an engineer? What then? The kid is majorly fucked.
That's why it's necessary. That...and it's easy. We are not talking about high-level calculus and solving partial differential equations etc. ;-)
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Is Algebra truely nessercary? not really.
But many things aren't actually needed in real world situations 90% of people will frequent, History for example knowing the battle of hastings was 1066 won't help me when it comes to cleaning windows or having a paper round but I'm glad I know it.
Same for Algebra being able to rearrange formulas and so on won't help me sweeping floors and so on, but I'm glad I know it, knowing Algebra also makes the transition into higher maths much easier in the event that I want to swap my career prospects
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yeah I mean... I can vouch for optional learning in Algebra only if I can attain optional learning of Literature.
Do I quote shake-a-spear?
Do I care if some essay was written cleverly to "prove" a point supposedly another writer wrote?
No.
So... to make it even, make high level literature beyond grammar and 3 paragraph essay optional. Then I can take algebra as optional.
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I think that Algebra is definitely something which should be learnt in school.
It's not that hard if you have a teacher who will teach the structure and is patient with people constantly asking questions. It's also applicable for having sound logical arguments too. Structurally, Logic is very VERY similar to algebra. It's a lot of balancing to make sure your argument is structurally sound. If it's not, then your being a fucking tool. Making sure your arguments balance out in English or any other area of discourse is essential in maintaining a good grasp of what your saying.
In university, I had an introduction to logic, which was basically Algebra, and I got my highest mark (shame it didnt count).
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On July 30 2012 20:30 OptimusYale wrote:
I think that Algebra is definitely something which should be learnt in school.
It's not that hard if you have a teacher who will teach the structure and is patient with people constantly asking questions. It's also applicable for having sound logical arguments too. Structurally, Logic is very VERY similar to algebra. It's a lot of balancing to make sure your argument is structurally sound. If it's not, then your being a fucking tool. Making sure your arguments balance out in English or any other area of discourse is essential in maintaining a good grasp of what your saying.
In university, I had an introduction to logic, which was basically Algebra, and I got my highest mark (shame it didnt count).
I tutored at a middle school for over 4 years and I can tell you the kids that had a hard time with Algebra (basically all of them) weren't struggling because of their teacher's flaws-- it was because they didn't give a shit, and who can blame them?
To make America's education work you're going to need to find a way to force kids to open wide and accept the shit being shoveled down their throats for 12 years of their life-- and I just don't think that's going to work.
Kids nowadays think for themselves. They all have phones and access to the internet. Parents aren't as strict as they used to be-- hell they go to jail if they leave a bruise on their child's ass.
I graduated high school with a 1.3 gpa. My quarterly grades were: D, F, C, F for every class, every quarter. I just found it pointless to learn useless things that I could learn on google in 10 seconds if I wanted to.
I mean I understand why an education system is in place. It's like throwing shit at a wall and hoping some sticks. The some shit that sticks to the wall are the students that go on to be engineers, scientists, programmers, and etc.
Do I find it unfair that everyone else has to suffer just so some people can go on to be on their knees for the rest of the world? You bet.
I also tutored in GED classes for sometime, and I can't even count the amount of nice people with normal jobs, making good money, that didn't even know their times tables. Hell, most of them stopped showing up. I guess they figured it was pretty pointless too.
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Well from my experience if you're not learning algebra in high school...well there's not much else maths to do. All the basic maths was covered for us in primary school, and even then early refreshed in year 7. Algebra is not that difficult a concept, it's just some of the applications of algebra and memorising formulas and steps for working out that people struggle with.
Anyway, I'm behind the concept that every student is an individual and some just haven't got the discipline for mathematics. I like the above note that kid's "didn't give a shit" for maths. As a teacher at a private college I always try make the boring stuff relate to necessary elements, but it's definitely still a struggle to get some of my game designers to care about programming in C#. Others just take right to it. Such a difficult balance in just the few people I teach, I can't imagine the complexity of designing a curriculum for thousands of kids with such a pressure to ensure that they are measured to be intelligent along such strict guidelines and then trying to make kids relate to it.
A lot of our programmers learned calculus at some stage, but ask them how they can use it to make a game or program and they'd shrug at you. Specific example, but students don't come out of school with job titles like "generic worker a".
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School isn't about learning actual content. It's about learning how to learn, how to think critically, and how to overcome intellectual challenges. It's a terrible idea to remove those challenges just because some people do, in fact, find them challenging.
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On July 30 2012 21:13 bittman wrote:
Well from my experience if you're not learning algebra in high school...well there's not much else maths to do. All the basic maths was covered for us in primary school, and even then early refreshed in year 7. Algebra is not that difficult a concept, it's just some of the applications of algebra and memorising formulas and steps for working out that people struggle with.
Anyway, I'm behind the concept that every student is an individual and some just haven't got the discipline for mathematics. I like the above note that kid's "didn't give a shit" for maths. As a teacher at a private college I always try make the boring stuff relate to necessary elements, but it's definitely still a struggle to get some of my game designers to care about programming in C#. Others just take right to it. Such a difficult balance in just the few people I teach, I can't imagine the complexity of designing a curriculum for thousands of kids with such a pressure to ensure that they are measured to be intelligent along such strict guidelines and then trying to make kids relate to it.
A lot of our programmers learned calculus at some stage, but ask them how they can use it to make a game or program and they'd shrug at you. Specific example, but students don't come out of school with job titles like "generic worker a".
C# is a horrible language.
I guess they don't think about game physics.
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Lol at some of the posts here and there.
If you truly want kids to be 'smarter' these days. Take away all of those Jersey Shore, American Idol, LMFAO, Justin Bieber, and most importantly Cellular Mobiles. They are detrimental to the intellectual mind of the adolescent.
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EPT
