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United States7483 Posts
On July 30 2012 18:14 Jrocker152 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. 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!
I love you too Jrocker.
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On July 31 2012 00:10 Gogleion wrote:
This makes no sense to get rid of algebra.
How I see it is that our education is decreasing, then we blame something other than the students, and reduce the challenges that they go through. Then the students don't have challenges and don't try in school then they get worse grades, then we reduce the challenges that they go through because it's clearly not their fault, then they don't think school is important so then they don't try and then get worse grades, which then makes us think that the education system is too tough, so then we bring down the challenges, but then the students don't have to apply themselves and then get bored and when they get bored they get bad grades, so then they get dumber and we think it's not their fault so then we reduce the challenges that they go through.
It took millions of years for humans to develop intelligence beyond any other species, but at this rate we are going to lose it faster than we gained it.
In general regression is much more rapid and sudden than progression. So the question is "can we turn this around?" or should we just give up and not teach our children basic math skills? With creationism, increasing disrespect to our teachers, and the rhetoric of anti intellectualism rife in our politics, it's clear that we are in danger of rapid regression.
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On July 30 2012 23:59 paralleluniverse wrote:Show nested quote +On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked.
To be able to read the result u get from the computer u need to know HOW the process works and that u would be able to do that, at least to avoid errors(maybe a error in the input, which gives a huge error on the result, can be tracked really easily if u have an idea of what u expect). Doing regression model btw is just some matrix calculation... the only thing the computer do is just do a massive amount of SIMPLE calculation. Still if u don't know what the computer do u're gonna have huge problems when "shit happens"(and in real life seems to happen a lot)
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Well I was one of those kids that always asked "why do I need this?" I wasn't going to be a scientist or a mathematician. I went through life thinking what a worthless thing to teach unless the person learning it is super smart. Well now I wish I hadn't. I wish I had more direction, more inspiration instead of a teacher telling me "well I guess you don't really need it." I'm 31 and I'm back in school taking math classes (algebra being one of them) and while I'm proud that I'm taking on the challenge and I have no shame in it I do wish I had learned it or paid more attention to it. I'm not completely ignorant to basic math, I do know a lot of it.
I would say it is necessary. People move through life changing their minds and developing at different parts of their life. Planting that seed is crucial. Maybe they wont use it for a while but the neural pathway is there. If they ever decided to use it later on they have a jump start. If there is anything to blame it is our archaic education system that was built during the industrial age, along with uninspiring teachers and parents a like these days. Math awesome.
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Asking how little we can know instead of how much we can know is exactly what is wrong with this country 
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been seeing this article on a few sites; I felt like i had to say something even if it's on page 45.
Any profession where you have to use math you'll benefit from having a knowledge of basic algebra.
So...
Anything business, science, medical, or engineering related. At the very least. So if we take those out of consideration, really what professions are you left with..? If someone wants to give up on school and relegate themselves to a life of custodial services that's their business, I think. Even carpenters ( a skilled carpenter is a valuable asset) need to know basic geometry and its hard to know what a^2 + b^2 = c^2 means if you haven't taken algebra.
The distinction I'll make, is that we only need basic algebra. f(x) = 3x + 2. I haven't solved a polynomial equation since college... Remember gaussian elimination?
The other half of things is... There are some very smart people that don't have the opportunity to go to college, I'd hate to deprive them of the opportunity to learn solid math at an early age because some right-brained artist was just bad at it. Hypothetically say you make math not required and this kid decides not to take it because he's a slacker in highschool. As if nobody makes bad decisions when you're young.
My advice is require algebra up to graphing plot points and geometry. Have a mechanism for opting out... requiring parent/counseler approval, and classes that proceed at a slower pace.
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On July 30 2012 23:06 paralleluniverse wrote:Show nested quote +On July 30 2012 23:03 TrainSamurai wrote:On July 30 2012 22:58 Morfildur wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. "I have to go away from this OP for 10 minutes to get out of the OP room, get rid of the clothes, wash hands, etc., then get to a PC, type in the numbers and then return after following all hygene procedures... oh, now the patient is dead." Some things the PC can do for you, for everything else you have to use your brain. Not to mention that the level of algebra this article is attacking is very basic. If you can't do basic algebra you have much bigger problems to care about than how education is being run. The article mentions parametric equations, which is more advance than the simple calculations that these examples involve, and is on par with first order ODEs, which is about as advance as the medical examples given gets.
What you mean subsitutions to introduce a third variable? LOL. Buddy you have much larger problems.
On July 30 2012 23:59 paralleluniverse wrote:Show nested quote +On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked.
Machines have bugs and are also prone to human error from typos, data entry problems whatever. An intuitive will help you recognise when something is not right.
On another note, Statistics without calculus already has a name called common sense.
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On July 29 2012 21:14 Deadlyhazard wrote:
I don't feel algebra is necessary to all students, I think middleschool math (pre-algebra) is fine for most people and I really do feel that you don't need algebra from that point forward. A topic like English, however, most people have to use throughout their entire lives and so I see it fit for something like that to stick (at least in an English speaking country) through high school.
What is taught in US high school english classes?
In Germany all we did after about 9th or 10th grade was talk about famous poets/writers from the past and analyze their stuff. Which was INCREDIBLY useless from my standpoint and really didn't add anything to my knowledge or perception of the german language. It just pissed me off and wasted my time.
If you cut everything from education that is not necessary you don't need more than 3 or 4 years of education. In fact you don't need any education, because no knowledge is necessary. But both society and individuals profit a lot from being educated well. So it shouldn't be cut. Especially not a branch of education which is mandatory for every branch of work that is even mildly related to science, engineering, economics, or numbers in general for that matter.
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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".
If you are teaching them game design, why not let them use torque and teach them torque-script?
Download some assets and give them a challenge to see if they can make a game out of it. The tech lead managed to make a zombie game in less than a day, but you still do a lot of proper coding to do it so you are still learning programming. Its not like they are gonna become programmers anyway so it doesn't matter if they don't know the computer sciency part of it.
Seems much more relevant to me.
Hardly anyone makes games in C# anyway, so it actually is kinda pointless.
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Some followup responses from the NYTimes: http://www.nytimes.com/2012/07/31/opinion/a-national-conversation-about-math.html?_r=1&ref=opinion
Most of the opinions there have already been raised in this thread, although I think the following 2 offer somewhat of a new perspective.
To the Editor:
I not only agree that algebra and advanced math are not necessary in school or life, but they can have a detrimental effect on a person’s self-confidence and future as well.
As a student, I excelled in the humanities and only squeaked by in math as a result of my parents’ being able to afford a tutor. I always thought that there was something wrong with me in that math just didn’t make any sense.
I avoided it in college and am happy to say I have a very successful career in marketing, where only basic math is required. (I avoid doing any metrics analysis myself and happily delegate.)
If I had not had to expend so much effort on a subject for which I had no aptitude, I might have read more and developed even better critical thinking skills, the most important single thing a person can learn. While basic math should be compulsory, advanced math should not be.
MARKE RUBENSTEIN
Stamford, Conn., July 29, 2012
To the Editor:
Andrew Hacker is right: most students will never need to use algebra. Many will struggle to learn it nonetheless. But the answer is not to let students quit as soon as they begin to struggle.
I myself hated mathematics for many years. Through algebra, geometry and trigonometry, I cursed a system that compelled me to take such “useless” courses. Eventually, I was required to take calculus, the most dreaded of all math courses. I prepared for the worst.
It came as a surprise, then, that I quickly found myself enjoying the class. The reason was that I had finally encountered a talented math teacher with a passion for the subject. His passion proved infectious, and now, a year later, I’m looking to study mathematical biology at an Ivy League university.
It’s an outcome I would have never predicted just a few years ago. It could have never happened if I had been allowed to quit when I first struggled with math.
ZACHARY MILLER
Kitty Hawk, N.C., July 29, 2012
The first letter basically supports my comparative advantage argument. The second letter talks about how a great math teacher can make the difference between loving the subject and hating it. I don't think I would have ever studied math at university and love the subject if I hadn't had amazing high school math teachers,
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On July 31 2012 05:22 eusoc wrote:Show nested quote +On July 30 2012 23:59 paralleluniverse wrote:On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked. To be able to read the result u get from the computer u need to know HOW the process works and that u would be able to do that, at least to avoid errors(maybe a error in the input, which gives a huge error on the result, can be tracked really easily if u have an idea of what u expect). Doing regression model btw is just some matrix calculation... the only thing the computer do is just do a massive amount of SIMPLE calculation. Still if u don't know what the computer do u're gonna have huge problems when "shit happens"(and in real life seems to happen a lot)
Just matrix calculations? Have you ever tried to invert a 4x4 matrix without a computer? Not easy. It would probably take 15 minutes, and be highly error-prone. How about a 20x20 matrix? Good luck with that one. 5000x5000? It'll probably take you a lifetime.
On July 31 2012 06:43 TrainSamurai wrote:Show nested quote +On July 30 2012 23:06 paralleluniverse wrote:On July 30 2012 23:03 TrainSamurai wrote:On July 30 2012 22:58 Morfildur wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. "I have to go away from this OP for 10 minutes to get out of the OP room, get rid of the clothes, wash hands, etc., then get to a PC, type in the numbers and then return after following all hygene procedures... oh, now the patient is dead." Some things the PC can do for you, for everything else you have to use your brain. Not to mention that the level of algebra this article is attacking is very basic. If you can't do basic algebra you have much bigger problems to care about than how education is being run. The article mentions parametric equations, which is more advance than the simple calculations that these examples involve, and is on par with first order ODEs, which is about as advance as the medical examples given gets. What you mean subsitutions to introduce a third variable? LOL. Buddy you have much larger problems. Show nested quote +On July 30 2012 23:59 paralleluniverse wrote:On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked. Machines have bugs and are also prone to human error from typos, data entry problems whatever. An intuitive will help you recognise when something is not right. On another note, Statistics without calculus already has a name called common sense.
Developing intuition is very important when working in applied math or working with numbers. But how do you teach intuition. Certainly can't be rigorous and precise like actual math. And computer program rarely have bugs that will affect the user, particularly when it's in production. Does anyone seriously think about possible bugs in MATLAB when it spits out the wrong number? There almost certainly is some bug in some arcane corner of MATLAB, but does anyone even know of any bugs it has? Or is it more likely an error in your code?
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It boggles my mind that the focal point of conversation is whether or not we should remove algebra. Everyone agrees that bad teachers can make a subject horrible while passionate ones can make all the difference.
People should be having a conversation about changing the math curriculum and standardized tests. Yes, spending hours and hours drilling factoring or multiplying polynomials is stupid.
It's ridiculous how everyone memorizes the quadratic formula with some stupid song but probably only 1% of students could prove it (even after doing 20 worksheets about "completing the square").
Nobody sees that the quadratic formula is just the result of a cool trick, not something weird and arbitrary.
Anyways...
It is absolutely pathetic how low we are willing to set the bar. Wtf is this shit?
Also Abstraction is not at all hard to motivate:
If Bob is taller than Alice and Alice is taller than Chris then Bob is taller than Chris
If Michael is taller than Jim and Jim is taller than Tim then Michael is taller than Tim
Ok now let's replace the names with x, y and z. x taller than y and y taller than z implies x is taller than z.
Ok but it's also clear that we could replace "taller" with other relations such as "bigger" or "faster" or "shorter." So why don't we just use ">"
x > y and y > z => x>z
In such a short statement you get complete generality of this simple principle. And then with enough statements and rules for interaction, you can deduce really amazing things. That's the power of mathematics and abstraction.
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Algebra is the tip of the iceberg. The all education system needs a make-over.
I for one loved math classes and it helped me get my BAC with a 4 in Spanish and like 8 in Philosophy because i had like 17 in math 
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On July 31 2012 19:57 paralleluniverse wrote:Show nested quote +On July 31 2012 05:22 eusoc wrote:On July 30 2012 23:59 paralleluniverse wrote:On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked. To be able to read the result u get from the computer u need to know HOW the process works and that u would be able to do that, at least to avoid errors(maybe a error in the input, which gives a huge error on the result, can be tracked really easily if u have an idea of what u expect). Doing regression model btw is just some matrix calculation... the only thing the computer do is just do a massive amount of SIMPLE calculation. Still if u don't know what the computer do u're gonna have huge problems when "shit happens"(and in real life seems to happen a lot) Just matrix calculations? Have you ever tried to invert a 4x4 matrix without a computer? Not easy. It would probably take 15 minutes, and be highly error-prone. How about a 20x20 matrix? Good luck with that one. 5000x5000? It'll probably take you a lifetime. Show nested quote +On July 31 2012 06:43 TrainSamurai wrote:On July 30 2012 23:06 paralleluniverse wrote:On July 30 2012 23:03 TrainSamurai wrote:On July 30 2012 22:58 Morfildur wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. "I have to go away from this OP for 10 minutes to get out of the OP room, get rid of the clothes, wash hands, etc., then get to a PC, type in the numbers and then return after following all hygene procedures... oh, now the patient is dead." Some things the PC can do for you, for everything else you have to use your brain. Not to mention that the level of algebra this article is attacking is very basic. If you can't do basic algebra you have much bigger problems to care about than how education is being run. The article mentions parametric equations, which is more advance than the simple calculations that these examples involve, and is on par with first order ODEs, which is about as advance as the medical examples given gets. What you mean subsitutions to introduce a third variable? LOL. Buddy you have much larger problems. On July 30 2012 23:59 paralleluniverse wrote:On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked. Machines have bugs and are also prone to human error from typos, data entry problems whatever. An intuitive will help you recognise when something is not right. On another note, Statistics without calculus already has a name called common sense. Developing intuition is very important when working in applied math or working with numbers. But how do you teach intuition. Certainly can't be rigorous and precise like actual math. And computer program rarely have bugs that will affect the user, particularly when it's in production. Does anyone seriously think about possible bugs in MATLAB when it spits out the wrong number? There almost certainly is some bug in some arcane corner of MATLAB, but does anyone even know of any bugs it has? Or is it more likely an error in your code?
Its not always bugs in MATLAB(sftware computers have testing teams) but any algorithm that you write(does not have to be matlab, btw this needs maths) will be prone to human error. Whether you're an engineer or whatever someone down the line needs to make sure the numbers should be what they expect. Thats where algebraic way of thinking comes in handy for people who need the numbers but have a computer to do everything. Any engineer who can't do calculushas a higher risk of allowing a mistake to waltz right past him. It doesn't even need to be something complicated.
For example if he integrated exp( x) from whatever bounds and gets a negative number then obviously the coding is wrong. If he did know calculus he would know this is garbage and go back find the mistake and save us all a shit ton of time and money. This was a very simplified example but in more complicated case an algebraic way of thinking will help, eg 2 negative numbers multiplied together should be positive, if I divide these two symbols the answer should be less than one w/e.
I think we can all agree that one who knows calc would be less likely to give a nonsense answer. The point is even if a computer can do everything people still need to know how results are derived. This is the best way to gain an understanding of what they should be expecting from machines.
It might not even be the algorithim but the data cleaning thats producing problems. Just because you can use a computer does not mean mathematics is useless.
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On July 31 2012 23:09 TrainSamurai wrote:Show nested quote +On July 31 2012 19:57 paralleluniverse wrote:On July 31 2012 05:22 eusoc wrote:On July 30 2012 23:59 paralleluniverse wrote:On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked. To be able to read the result u get from the computer u need to know HOW the process works and that u would be able to do that, at least to avoid errors(maybe a error in the input, which gives a huge error on the result, can be tracked really easily if u have an idea of what u expect). Doing regression model btw is just some matrix calculation... the only thing the computer do is just do a massive amount of SIMPLE calculation. Still if u don't know what the computer do u're gonna have huge problems when "shit happens"(and in real life seems to happen a lot) Just matrix calculations? Have you ever tried to invert a 4x4 matrix without a computer? Not easy. It would probably take 15 minutes, and be highly error-prone. How about a 20x20 matrix? Good luck with that one. 5000x5000? It'll probably take you a lifetime. On July 31 2012 06:43 TrainSamurai wrote:On July 30 2012 23:06 paralleluniverse wrote:On July 30 2012 23:03 TrainSamurai wrote:On July 30 2012 22:58 Morfildur wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. "I have to go away from this OP for 10 minutes to get out of the OP room, get rid of the clothes, wash hands, etc., then get to a PC, type in the numbers and then return after following all hygene procedures... oh, now the patient is dead." Some things the PC can do for you, for everything else you have to use your brain. Not to mention that the level of algebra this article is attacking is very basic. If you can't do basic algebra you have much bigger problems to care about than how education is being run. The article mentions parametric equations, which is more advance than the simple calculations that these examples involve, and is on par with first order ODEs, which is about as advance as the medical examples given gets. What you mean subsitutions to introduce a third variable? LOL. Buddy you have much larger problems. On July 30 2012 23:59 paralleluniverse wrote:On July 30 2012 23:54 Judicator wrote:On July 30 2012 22:53 paralleluniverse wrote:On July 30 2012 22:45 TheFlash wrote:So what exactly do you use math for?
-trach tube size calculations -acceptable blood loss calculations during surgery or procedures -Calculate FIO2 when air is being used rather than N2O. -deterimining how long an E oxygen tank will last any given air flow rate (there are a lot of calculations that are important when discussing patient breathing) -quick, on the fly drug dosing for patients (much is weight-based) Are you serious? This sort of stuff isn't done on a computer like every other profession? It almost seems archaic. You go away to solve a math problem during surgery? Also, nothing here seems to involve math beyond grade 12. Mostly just arithmetic and simple formulas, possibly a first order ODE, but nothing more sophisticated than that. More like computers and machines stop working, what do you do now? Oh shit I didn't take algebra in grade school and now my patient is dying; let's hope the other people in the OR knows whats going on. Since when does a machine just stop working? The reason why calculations are done on a computer is because it would take days to do by hand. Not everything is as simple as substituting a number in an equation. Computers use algorithms. Try fitting a linear regression model with 20 data points and 2 response variables by hand. It would probably take an hour. Try it for 1000 data points and 20 response variables, it would probably take a week. Try solving a partial differential equation numerically, for example with finite difference methods, by hand. It would probably take a month. Try a MCMC simulation without a computer. It's virtually impossible. If the computer breaks down, the solution isn't to do it by hand -- it's fix the computer or you're fucked. Machines have bugs and are also prone to human error from typos, data entry problems whatever. An intuitive will help you recognise when something is not right. On another note, Statistics without calculus already has a name called common sense. Developing intuition is very important when working in applied math or working with numbers. But how do you teach intuition. Certainly can't be rigorous and precise like actual math. And computer program rarely have bugs that will affect the user, particularly when it's in production. Does anyone seriously think about possible bugs in MATLAB when it spits out the wrong number? There almost certainly is some bug in some arcane corner of MATLAB, but does anyone even know of any bugs it has? Or is it more likely an error in your code? Its not always bugs in MATLAB(sftware computers have testing teams) but any algorithm that you write(does not have to be matlab, btw this needs maths) will be prone to human error. Whether you're an engineer or whatever someone down the line needs to make sure the numbers should be what they expect. Thats where algebraic way of thinking comes in handy for people who need the numbers but have a computer to do everything. Any engineer who can't do calculushas a higher risk of allowing a mistake to waltz right past him. It doesn't even need to be something complicated. For example if he integrated exp( x) from whatever bounds and gets a negative number then obviously the coding is wrong. If he did know calculus he would know this is garbage and go back find the mistake and save us all a shit ton of time and money. This was a very simplified example but in more complicated case an algebraic way of thinking will help, eg 2 negative numbers multiplied together should be positive, if I divide these two symbols the answer should be less than one w/e. I think we can all agree that one who knows calc would be less likely to give a nonsense answer. The point is even if a computer can do everything people still need to know how results are derived. This is the best way to gain an understanding of what they should be expecting from machines. It might not even be the algorithim but the data cleaning thats producing problems. Just because you can use a computer does not mean mathematics is useless.
Where did I argue that you can be an engineer or a computer scientist without knowing math or algebra? In fact, I've been arguing that math or algebra is useless UNLESS you're a engineer, computer scientist, mathematician etc.
I'm just ridiculing the idea that calculations done on a computer can be done without a computer. You can have a look at the answer and use your intuition to guess whether the output is nonsense, but intuition is hard to teach, it comes with experience.
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On July 31 2012 20:30 Nizaris wrote:Algebra is the tip of the iceberg. The all education system needs a make-over. I for one loved math classes and it helped me get my BAC with a 4 in Spanish and like 8 in Philosophy because i had like 17 in math
I find it especially funny how America always worries about unemployment, while at the same time STEM workers are at a shortage, and somehow lowering (the already low) educational standards are a consideration.
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United States987 Posts
On July 31 2012 06:43 TrainSamurai wrote:
On another note, Statistics without calculus already has a name called common sense.
You sir have never taken statistics. Or looked at someone who hasn't.
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Really, mr universe? Anecdotal letter from someone who does not need a degree of any kind to do their job?
Come on, man. You're better than this.
You are arguing against education in general, not algebra.
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On August 01 2012 01:26 DoubleReed wrote:
Really, mr universe? Anecdotal letters from people who do not need degrees of any kind to do their job?
Come on, man. You're better than this.
If you're talking about the letters to the editor at the NYTimes, then that's not needed for me to make the argument of comparative advantage. It just adds a real world example to support the argument I made earlier based on economics. Or are you talking about the Washington Post article?
I'm not arguing against education, I'm just noting that not everyone needs to know math beyond a very basic level.
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EPT
