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.
The way I see it, algebra isn't just needed for its technical value. I learned it in middle and high school, and it taught me discipline and honed my problem-solving skills. For example, I'm likely not going to use the knowledge I "gleaned" from my 10th grade English course books, but they did help me learn to think critically about whatever I'm reading. (...I think X-D)
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.
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..
I'm probably biased on this one since I love algebra and always have, but I think it is necessary for proper development of a child, at least at a high school level, which is pretty easy.
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.
90% of the shit I learn in high school I'll never use in the real world; that doesn't mean I should only go through 10% of school. High school is about learning how to balance your schedule more than actual subjects -- a lesson you will use every day of your life.
On July 30 2012 13:41 sluggaslamoo wrote: Logic is not maths. I'm terrible at maths and I understand programming a lot better than most people. While lambda calculus falls under maths, it is nothing like "maths", its pure logic. You do not need to be good at maths to be able to understand lambda calculus, and what becomes of it currying with functional programming. Same goes for algorithmic programming, and learning data structures, sorting algorithms, etc.
I've seen heaps of programmers who were pretty bad at highschool mathematics who became geniuses when they started learning sorting algorithms and lambda calculus.
Hmm, seems like you have an extremely narrow definition of math? Discrete math is still math. Yes, it isn't really taught in high schools, but that doesn't change the fact that all algorithms require both verification of correctness and time/space complexity analysis... which are both math.
Also,
Wikipedia wrote: Lambda calculus (also written as λ-calculus or called "the lambda calculus") is a formal system in mathematical logic for expressing computation by way of variable binding and substitution.
There's a good reason schools like MIT cross-list algorithms and logic in the math department.
I agree, know they fall under the same umbrella, but you are missing the point of my argument.
Hmm, well then, what's your argument?
On July 30 2012 12:15 sluggaslamoo wrote: The algebra needed for comp sci can be learned in just a week,
This is false; you need to know about things like exponential functions and polynomials and logarithms and their relative growth rates.
and you won't see it as "algebra" you will see as something far more interesting as that.
Algebra is a tool, much like arithmetic, which is necessary for understanding computer science. You don't study high-school algebra just to "do algebra" later. Indeed,
With comp sci you are also not really learning maths, you are learning about logic and patterns.
Algebra is among the first steps in gaining the mathematical (or more generally, intellectual) maturity to think abstractly---and abstract thought is essential in any sort of technical subject. There's "logic" and "patterns" to be learned in algebra as well.
The rest like lambda calculus and big O notation is stuff that you will never learn in school anyway. That's the problem.
Yes, most high schools don't teach it (which suggests that high schools ought to offer more math classes, though that's sort of unrelated to whether algebra should be mandatory or not.) But to learn lambda calculus or big-O notation requires algebraic abstraction.
Once you see the relevance the basic stuff that took you years to learn in school will take just a few days to learn. That's why there is no point.
Very true for anyone in a technical field, though perhaps not so much for those who are not so inclined. American schools spend far too much time on rote memorization of arithmetic and the like, while Eastern European/Asian schools introduce interesting problems (i.e. not just regurgitating formulae) early on.
On your friends who were "bad at math" yet brilliant programmers/computer scientists: high school geometry (a sad excuse for the word "geometry"), trigonometry (more memorization), and calculus (yet more memorization, though often at this level there may be glimpses of actual mathematics) are, indeed, not so relevant to discrete math and problem solving. But the solution here isn't to get rid of them or make them electives; it's to improve the teaching of these subjects so that it does actually teach problem solving.
Exponential functions and polynomials can be learned in just a few days, I don't see why it would take any longer than that. I learned polynomial functions when I was 12 years old in just a few days, and I learned how to do it by balancing experience point calculations in excel for a game I was making.
My point is that learning things before it has relevance is pointless. There is only point to learning something when there is relevance. It doesn't matter how good you are at teaching, if you can't see e.g algebra, having any benefit to your future career its gonna take months instead of days to learn, and your ability to recall it will diminish significantly within the next few weeks. That time could have been much more efficiently spent learning material relevant to your future career.
If I'm gonna become a panel beater when I grow up, it doesn't matter how good the teacher is, I'm not gonna give a shit about maths. It makes no sense to put future panel beaters with future maths professors in the same class. There's nothing wrong with education, if this panel beater ends up leaving school without knowledge of algebra, because regardless of whether algebra is taught or not, this person is going to leave school without knowledge of algebra. The only difference is that in one case, he can leave college more adequately equipped for his career, or he leaves college with low self esteem thinking he's really dumb when he's not.
Communication and organisational psychology is hardly taught in schools, yet even as a programmer, I believe it is the single most important thing that needs to be taught. Even for professors and academics, communication is a problem, garnering support for global warming is frustrating for a lot of scientists, but they don't understand its because their ability to share their information to the rest of the world is lacking.
What defines my income is not my programming skill, it is my ability to carry myself, talk to other people, do good presentations, not say stupid things, etc. My skills as a programmer comes secondary to that. Communication is taught very little if at all in schools, yet if you look at all the successful people in the world, their primary asset is communication.
Look at Steve Jobs, he's a great presenter/communicator, Microsoft's success was initiated by Bill Gates ability to receive help from other people at his university and even convincing IBM to use the worst product on the market. Mark Zuckerberg, Facebook, pretty self explanatory there. Creator of Minecraft, wrote terrible code. There are plenty of genius code monkeys, taxi drivers, who can't land a job because they don't know how to talk to people.
What you are saying here is that you believe your experience of learning to understand some polynomial functions by yourself at 12 over a few days is representative of the general ease with which students learn to manipulate all simple algebraic functions. You are mistaken. Also, if you gained an understanding of polynomials in general from playing around in excel you are deluding yourself by claiming to be bad at maths. Even if you only taught yourself how to solve or manipulate one or two types, doing it by yourself shows significant mathematical aptitude.
The majority of children take weeks of instruction to learn to manipulate each new function type well enough that they can integrate it into their existing knowledge. Even then they will only succeed if they adequately grasp certain key concepts - many of them explictily shared between CS and algebra - of abstraction.
I believe quite strongly that core academic subjects, especially languages and the hard sciences, should be set according to ability. Every class should cover at least the basics of the curriculum, but the more advanced classes should cover it more quickly and potentially include additional enrichment activities or be telescoped so students can finish the entire curriculum more rapidly or complete a curriculum which extends upon the core. It is pointless to have high-ability students sitting bored in a class where most students take a few days to puzzle out each core concept even though they seem self-evident to the high-ability student. But there needs to be a baseline of skill, and basic algebra should be included to allow students a reasonable minimum of mobility later in their education and careers.
Interpersonal skills should be built as well as technical ones not in replacement of. We need bright technical minds who know how to communicate, not people for whom communication is its own purpose.
Some of the core concepts are detailed in papers attempting to work out early indicators of success or failure amongst first -year CS students. I was a peer-tutor for maths in one HS, and have done a few bits and pieces since. The outliers in maths stand out more than in most subjects because there is little context needed so apt students can race ahead and some other students can get blocked at one topic (in history, knowledge of one empire is not necessary to learn about another). So you can have 16 year olds that understand the quadratic formula as well as they understand telekinesis, and 9 year olds who can get a handle on the generalised idea of orthogonality (orthogonality not restricted to spacial dimensions) in a couple of hours.
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.
High school economics requires next to no maths. I went through IGCSE/IB economics and most of that is teaching theory without the rigorous proofs and underpinnings. The maths and formalisations of generalisations can wait until university or later.
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.
High school economics requires next to no maths. I went through IGCSE/IB economics and most of that is teaching theory without the rigorous proofs and underpinnings. The maths and formalisations of generalisations can wait until university or later.
Economics without math, beyond the concepts of opportunity cost and discussion of the tragedy of the commons is pretty useless. There's no point to teaching the subject at a high school level, (which is my point entirely), because there is very little to be gained by it without a stronger background. It's like teaching astrophysics in high school or circuit analysis. You might learn just a little bit of the most basic concepts, but you can't actually apply any of it for the most part. Without actually understanding the reasons why things function the way they do (which requires a fundamental understanding of a rate of change for economics, along with reasonable algebra for interpreting even basic graphs), you might as well be memorizing formulas and only solving problems that fit the format you expect.
Principles matter in any subject (especially math based subjects like economics), and you can't learn principles without the proper foundations and understanding how a result is derived.
It's like how schools teach FOIL (they shouldn't, it's really stupid of them) rather than the distributive property of multiplication when they introduce students to binomials.
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.
Oh and that's how I started in economics (a no calculus/little math other than graph interpretation), guess what? I loved it and got my degree in economics after that. Same thing with physics, started that in a no calculus, no advanced math high school course with lots of labs and discovery, loved it, same for the E&M course, I end up taking Physics C AP exam after starting like that.
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 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.
Just because you won't use it doesn't mean you should not learn it. There are some very basic things in life that everyone should know, and I think Algebra is one of them. It's not even that hard. Maybe it's because of where I was born, but elementary school kids can start learning Algebra, and people are arguing that it's too difficult for people that are trying to pass High School? Then they shouldn't pass. They don't meet the minimum requirements. Algebra is not necessary, but if people actually spent more time thinking about it, then they'll find it more often than they think.
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. Or this is your salary, how many people can it feed, how much does it cost to live in different places/situations, this is how to calculate taxes using a simple tax code, these are the sort of ways you can be exempt different kinds of taxes, etc..
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.
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.
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.
EPT
