Political Science Prof Asks: Is Algebra Necessary? 1010
Capt.Albatross writes "Andrew Hacker, a professor of Political Science at the City University of New York and author of Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What We Can Do About It, attempts to answer this question in the negative in today's New York Times Sunday Review. His primary claim is that mathematics requirements are prematurely and unreasonably limiting the level of education available to otherwise capable students ."
yes (Score:5, Insightful)
substitute in his thesis,
Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white.
and substitute to:
History is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white.
and you have a perfect argument for me and the school system not requiring History.
Even better,
$yourWorstSubject is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white.
and we've eliminated the need for any required subjects.
"I am not good at", or "I don't want to" are not good arguments for not requiring learnin'.
(-e**(i*pi) st post)
Re:yes (Score:5, Insightful)
So by counterexample it's apparent not all mathematics is necessary for everyone... so I think these blanket answers I'm seeing floated around here by people who probably rely on mathematics daily for their jobs is a little short sighted.
Re:yes (Score:5, Insightful)
Mathematics is the language used to describe how the world around you works. At the very least you should understand the concepts of exponential growth and decay (which I think is algebra 2). Most people are going to have credit cards, 401ks, mortgages, car loans, etc. Knowing how these things work is the first step to financial success. I went through differential equations in college and honestly I can't recite off-hand the formulas for those things but I do understand how it works and could look up and calculate loan totals payoffs, monthly payments, etc.
Re:yes (Score:5, Insightful)
Screw that, it doesn't matter what algebra is good for.
My 5th grade math teacher said this, math helps change the way you think. It doesn't seem like much, but you'll need that way of thinking in the future. And she was right.
Advanced math, physics, chemistry, programming, anything that required even a bit of abstract thinking was easier because of those "useless" algebra classes.
Are they perhaps trying to kill institutionalized education? If so, they're definitely on the right path.
Re:yes (Score:4, Interesting)
But as far as advancement in a company is concerned, I found a knowledge of math to be a great impediment, as it causes me to stubbornly stick to things, be a "boy scout", "perfectionist" and other derogatory terms those with "leadership skills" attribute to me.
I am a bit jaded, but it seems to me that the most important skills one can learn is the skill of how to get someone else to do the work.
Re:yes (Score:5, Insightful)
Are they perhaps trying to kill institutionalized education? If so, they're definitely on the right path.
I don't think they want to kill the institutionalized part...
Dumbing down (Score:5, Insightful)
The way I see it the ultimate aim of the author of TFA is to dumb down the future generations
The dumber future generations get the easier they can be manipulated to do the dirty things that the elites themselves do not want to do
Yes, but when does it do so efficiently? (Score:5, Interesting)
Of course math changes the way you think, and often to the good. The real question, left unaddressed in the original article, is when and how do we start teaching math?
There is a body of experimental evidence, mostly from upstate NY in the 20s and 30s (see [PDF] here [republicofmath.com]) that the main problem in early education is that math, with its many abstractions of notation and convention, is brought in far too early. Instead, rigorous verbal and written exercises could cover the necessary conceptual bases for math to be added onto later, while not losing huge amounts of time creating arti-factual stories to get 7-year-olds to learn division, which may then interfere with their later understanding of the actual basis.
Another method that's been suggested, also with a body of experimental evidence (see for an overview [nytimes.com]), takes the opposite tack, and says okay, we can teach everything the first time in a way consistent with later fundamentals, but to do so, we have to recognize that many apparently simple steps are actually 5-7 'micro-steps' and we need to break out and teach these explicitly.
Given that much more rigorous levels of math education don't seem to cause mass dropouts or lack of bachelors attainment in many other countries, I think the emphasis should be on fixing the way we teach math, rather than further devaluing (and yes, the ability to jump through hoops is important for successful employment.. and also, this guy thinks he can do rigorous statistical inference without a rock solid understanding of modern algebra?) high school and college degrees.
Re:Yes, but when does it do so efficiently? (Score:5, Insightful)
>the main problem in early education is that math, with its many abstractions of notation and convention, is brought in far too early
This is a myth from our child development overlords.
My wife, who grew up in Hong Kong, was learning algebra in elementary school. Kids are capable of learning algebra much younger than it's taught here in America. When she immigrated, she literally didn't learn any new math for four years. It's not a mistake we're ranked so poorly in the world math standings.
Re:Yes, but when does it do so efficiently? (Score:5, Insightful)
Re:Yes, but when does it do so efficiently? (Score:4, Insightful)
1869 Harvard entrance exam [nytimes.com]
Take a look at that. Now keep in mind that the best you had at the time would have been a slide rule and paper. You say that we are more educated today than the previous generations, I would argue that the majority of kids these days most likely could not answer any of those questions. Hell, I took Algebra, Calc, Trig, Geometry, 6 years of Latin and speak or are familiar with 11 languages and I can barely answer many of those questions.
You say better educated, and I would disagree. I think more people are educated than previous generations and I think that current generational knowledge extends to more subjects, but definitely not better.
Granted, the rate of improvement has slowed down considerably, during the last few decades. However your great-grandmother's generation was definitely not better educated on average than the current one.
Between the article itself and personal experience with educating kids these days, I can guarantee you her generation would run circles around these kids in math, grammar, vocabulary and probably foreign languages. Hell my 71 year old (at the time) Great -Grandmother was able to help me with my Latin lessons 20 years ago and again, she was raised in the back woods of TN where they really only gave a damn about agricultural knowledge.
Re:yes (Score:5, Insightful)
Re:Political Science Professor (Score:5, Insightful)
No, political science isn't about controlling people any more than zoology is about controlling animal populations.
It's a study. It's no more unified than politics is, because that's what political science is: the study of politics, government, and state.
Also, I'm sure some fringe school somewhere does what you say, but the UK has a standardized uniform grading system that is widely used:
http://en.wikipedia.org/wiki/Academic_grading_in_the_United_Kingdom [wikipedia.org]
I think this guy's idea is dumb too. But your assertions don't seem grounded in reality.
Re:What's the aim of studying politic and governme (Score:5, Insightful)
what's the use of studying the animal kingdom if there isn't any step further - like improving / changing / experimenting on the animals
There are hundreds of thousands of people who spent many years studying biology and zoology to become veterinarians and, you know, help animals who will disagree with you.
The vast majority of people study history to learn from it, not to make it or rewrite it. The vast majority of people who study psychology don't do so because their plan is to control people and then force them into Cybermen suits. Not everything in life is a conspiracy to rule the world.
Seriously... Slashdot just gets crazier and crazier.
Re:Political Science Professor (Score:5, Funny)
"Does knowing how one is fairing relative to immediate classmates "
While I don't know how either of you are doing in the real world, it's a pretty fair bet that neither of you would fare very well on an English test.
But I bets both of you can al-jabber with the best of them!
Re:Political Science Professor (Score:5, Insightful)
Re:Defective thinking (Score:4, Interesting)
The first 2 statements are true statements about the human condition. The third is a fallacious deduction made by incorrect application of logic. The most you could say logically without additional data is that "if someone dies it may have been from pancreatic cancer."
Another way that thinking can become defective is situations involving the reality of the universe in which an individual rejects valid observational data that contradicts their assumptions about the universe. To give you an example of defective thinking consider individuals whose religious beliefs require them to believe that the universe is no older than a few thousand years old, that the world was created in 7 days, that every word in the bible is both divinely inspired, literal, and infallible. When such individuals are presented with fossils of species that no longer exist, that can be dated by various techniques involving radioactive decay rates to be thousands, or even millions older than the supposed creation of the earth, or when the individuals are presented with an explanation of the General theory of relativity, the gravitational red shift and its implications for how far away some objects truly are in both time and space such as billions of years light years away and billions of years ago, such individuals reject the observational data as obviously incorrect or misunderstood, because the data contradicts their religious beliefs. That ability to hold onto assumptions about the universe in spite of the fact that valid data that contradicts those assumption is what constitutes defective thinking.
Re:yes (Score:5, Insightful)
" Most people are going to have credit cards, 401ks, mortgages, car loans, etc. Knowing how these things work is the first step to financial success."
Not to burst your bubble but this guy teaches future politicians and as you know they have no idea that they have to pay back any loans nor such things as 'interest' and other things.
If you have to promise the moon to people to keep your job, knowing that you can't possibly pay for it is just a hindrance.
Re:yes (Score:5, Insightful)
He is not teaching future politicians ... (Score:5, Interesting)
Not to burst your bubble but this guy teaches future politicians ...
No, he is a political science professor. The law professors teach the future politicians. The political science professors teach the entry level management trainees for various corporations.
I am not kidding. I once sat in on a presentation named "Careers for History and Political Science Majors". The presenter had a BA in History and was the branch manager at a local bank. The first thing he told the audience was that they were not going to work in history or politics. Many corporations want to see a 4 year degree attached to their management trainees, they don't particularly care what the degree is in.
Re:yes (Score:4, Insightful)
Calculus measures the rate of change. IMO, if you don't know how to use calculus, you are unable and unqualified to argue the merits of arguments on Economics, global warming, unemployment, air pollution, groundwater pollution, and thousands of other concerns. Those people who are unable to argue sensibly and knowlageably still have opinions, but those opinions are without merit. Those same people are at the mercy of opinion-makers of questionable integrity.
Perhaps the proper place for Calculus is in high school, and your school is a possible exemplar. However, it most likely that Calculus is taught only to a select few, and the rest of the high school population is graduated ignorant. IMO, Propositional Logic and Rhetoric should also be taught.
Algebra is a prerequisite for Calculus, but not everyone understands Mathematics in the way that Algebra expresses it. Almost all mathematical principles can be described in either Arithimetic, Geometric, or Algebraic terms. Assume that some people count, some people visualize, and others like "recipes". At the very least, graduates should be able to describe mathematical concepts in their preferred method, and to be able to recognize those concepts when described in other thinking styles.
The original article is prima facie evidence that even PhD's are not immune to lousy thinking practices. I would be more impressed with the argument if I thought that Hacker actually understood Mathematics. The reason is that I usually divide people who are into "Political Science" into three major categories:
At one extreme is the "Political Philosopher" who theorizes about the "best" forms of political action.
At the other extreme is the "Political Technician" who concentrates the means of obtaining thier "preferred" political situation.
Sandwiched in the middle is a narrow band of real "Political Scientists" who try to understand the principles behind politics and derive principles that predict the outcomes of various actions. Although these people are hamperred by lack of a "laboratory" in which to conduct experiments and control variables, they have tools such as Logic and Mathematics, particularly Calculus and Statistics, that they can use to evaluate different political actions.
Hacker comes across as a "Technician" and gets a discount on credibility from me.
Calculus and Shakespeare (Score:5, Insightful)
Mathematics is the language used to describe how the world around you works.
I'd go further. It used to be that in the UK everyone going to university had to have a maths O'level which required _simple_ calculus. After all if I had to study Shakespeare before I could do a physics degree shouldn't those studying english study the basic maths developed by Newton to describe the same world that Shakespeare described with his plays?
Re:Calculus and Shakespeare (Score:5, Interesting)
I disagree.
I spent a fair amount of time once with a man who was educated in the fashion you seem to think is appropriate. In his case, he'd started out working on the factory floor at an IBM manufacturing facility in Texas (30 years ago when they still made stuff in the US), and had qualified for and taken a technical math and computer science education culminating in a master's degree. IBM's "school" was accredited and his degree was a real one, but it included only technical subjects; no liberal ed at all. Prior to his IBM education he had barely graduated from high school -- and I'm not sure how he did, frankly.
He was a highly intelligent man, very articulate and perceptive. However, as soon as the discussion left technology his utter lack of education became instantly apparent. He was even ignorant of basic principles of physics -- he knew a fair amount about electronics, but in mechanics he understood less than most high school dropouts I've known. His ability to understand politics was nonexistent because he didn't know any history, or even understand basic civics. And don't even attempt to talk about literature, philosophy, etc.
Now, obviously, a big part of his ignorance was due to his own utter lack of interest in anything outside of computer science. You can't obtain a MSCS without being able to read, and anyone who can read can educate themselves. But the point was that the difference between him and the typical college graduate -- even though he was almost certainly smarter than said typical graduate -- was stark and obvious, and it wasn't in his favor. His lack of general knowledge wasn't just a problem when socializing, either, it often caused him to make dumb decisions that affected the business, and you simply could not put him in front of customers, because unless the discussion was laser-focused, he'd eventually say something that made him look like an idiot.
After my experience working with him, I decided I wholeheartedly agree with the liberal education philosophy. The worst part about it was that his deep, narrow knowledge and utter lack of knowledge outside of a single field made him believe, quite firmly, that there really wasn't much to know outside of his field. It's often said that that the primary purpose of a BA/BS is to teach the student the breadth of his own ignorance. Well, this guy never learned that.
We don't all need deep knowledge in every area, but an introductory course in each of the major areas of human knowledge really does add significant value. It makes us more rounded, teaches us some much-needed humility and, well, educates us. That education is what differentiates a university degree from a vocational certificate, and the former is more valuable than the latter.
Re:Calculus and Shakespeare (Score:5, Interesting)
Before I explain why, I must note that there are different types of students who respond differently to attempts to make them well-rounded. The first type, I call "robots." Robots essentially drag themselves through a fixed course in life - birth, elementary school, middle school, high school, college, career, marriage, kids, retirement, death. What kind of robot you get depends on the school you attend, but essentially they are all the same person. You get people who are insanely good at some subject (chemistry, biology, etc.) but not so good at everything else. Or so you'd think. What you actually get are people who have no intrinsic motivation, but are good at anything they have to do. That means they'll learn what they need for their career and they'll do well in these sort of general education classes if they have to get a degree. But, there's a problem: they'll never apply that knowledge to anything else. For example, if you have a robot who studies neuroscience and takes a required philosophy class, they won't consider the impact of neuroscience upon moral philosophy. Basically, requiring these students to take these sorts of classes is like programming an industrial welding robot to play a violin. While it might seem like you've done something, all you've really done is make a weird demonstration that doesn't really do much after it quits.
The second type of student here is the party animal. These students just party through college - they're not here for academics really, they're here for the connections. They are here for a variety of reasons - legacy, decent test scores, athletics, etc. As you might expect, they take a "C's get degrees" attitude to required courses. They don't gain anything from such courses but at least they push down to curve for the rest of us. Or you might assume. Actually, they take up valuable resources including TA and professor time, ask basic and banal questions and worst of all annoy the course staff and make them angry at the student body as a whole.
Lastly, there are some students who are truly intellectual. They actually integrate the ideas from the various disciplines together and create better ideas as a result. These students don't actually need much help being well-rounded. They'll read articles and get ideas from other fields on their own because that's part of there personality. They may take non-major related classes out of interest (I'm doing this with physics, chemistry, and maybe biology) for entertainment. The only benefit they may receive from these classes is a little push on the envelope (which they may hit anyway). The disadvantage is that they take required classes, which are bad because forced education is an inherently bad process. Students who don't want to learn are a pain to teach. This annoys professors that take that anger out on the student body. They also force professors to dumb down the course, in turn causing students who are actually engaged to be bored out of their minds. This bordem in turn causes them to become disinterested. Essentially, the entire thing fails for everyone at the same time.
So, to recap, required courses fail for each group of students for different reasons. Robots learn the material and then fail to apply it. Party animals flunk the classes. Intellectual students become disinterested in the basic classes and disconnect
Re:Calculus and Shakespeare (Score:4, Informative)
It's to improve communication skills, not paticularly hard anyway and has the benfit of showing people that there is more to English than correct spelling. A lot of people on this site (eg. every grammar nazi) could benefit from it.
I may have done 100% engineering and science courses back in the 1980s, but I did have a reasonably solid high school English background before it which I am sure helped.
Re:Calculus and Shakespeare (Score:5, Insightful)
If you want to study engineering, that is where you should be able to concentrate.
I did that, 25 years ago. Recently I returned to my alma mater (UWO in Canada, if anyone cares) and 6 of us were invited by the fairly new Dean to discuss what they should be doing to improve the curriculum. While lab methods had changed a lot in 25 years, most of the core curriculum hadn't -- which is probably the right thing. Anyway, when he asked what we didn't get at university, but should have, we came up with two: project management and English.
Project management is an obvious skill for an engineer, and should have always been there. When he was surprised that we mentioned English (specifically a writing course) we all said that a lot of our work since graduation has included writing reports, and learning how to write well early on would have been a great advantage. I have forgotten an awful lot of math in 25 years, and learned a lot of English writing.
By all means learn the math and physics. I think you cannot possibly do anything worthwhile in economics or finance without calculus, and even political scientists must need to know about trends and statistics, both of which are built at least partially on calculus. But to do only, e.g., calculus, leaves one poorly equipped for life.
Re:yes (Score:4, Interesting)
Re:yes (Score:5, Insightful)
Re:yes (Score:5, Insightful)
If problem solving is the goal, then your better served by a Logic/Critical Thinking class then Algebra.
Re:yes (Score:5, Insightful)
Re:yes (Score:5, Insightful)
Re:yes (Score:5, Insightful)
It's been a long time since I took a logic/critical thinking class. Correct me if I'm wrong, but isn't this one of the first things that they teach? Perhaps I misunderstand what you're saying.
I omitted the "not". One need not remember the full probability course... And what I was saying was that most people can't understand what is a correlation. And without understand the nature of the thing, it's nearly impossible to distinguish it from that which is similar to it. This is why most people fall for the correlational arguments. They don't know what a correlation is.
What's wrong with questioning every argument?
This! This is exactly the problem with critical thinking students. They don't know when the argument has been proven. They've been taught to always question, but they have not been taught to understand when a conclusion has been legitimately reached. That would require subject-matter expertise. And that's the part they don't get. And it is why they keep arguing in circles.
Re:yes (Score:5, Interesting)
I would actually say statistics is probably the *most* broadly-applicable branch of mathematics. *Everyone* - scientist, politician, gambler, civic-minded citizen, and commercial watching bumpkin would benefit from a firm grasp of at least the basics of statistics, and of those scientists are typically the only ones who have any clue at all, and even their grasp on it is often shaky, especially in the softer science. And you don't actually need much more than basic algebra to learn it either.
No other field I can think of is as broadly used with as little understanding (how many times have you seen a % today?), which makes it ripe for exploitation. There's a reason for the phrase "there's lies, damned lies, and statistics" - statistics is (mostly) actually pretty simple from a "solve this equation" perspective, the difficulty is that there's a whole lot of counter-intuitive aspects to probability so it can be tricky to answer the question you think you're answering - which makes it ridiculously simple for someone to make a rock-solid sounding statistical argument that's completely spurious.
Re:yes (Score:5, Informative)
I haven't seen a cashier with any math skills in quite a while. In fact, if you really want to screw them up give them the extra penny. I had a chat with a cashier when the customer in front of me did that after she had rung up a payment of $10.00 and was unable to deal with being handed $10.01 (for a purchase of $9.51). She felt very abused about not being able to calculate the right change in her head. As far as I can tell, the cash register is in charge. She felt her job was to do whatever the cash register told her to do.
Re:yes (Score:5, Insightful)
Re:yes (Score:5, Insightful)
Anyone not understanding what an exponential
Anyone not understanding what an exponential is should NOT be making policy decisions at all. Period.
A very sad fact.
Re:yes (Score:5, Insightful)
Re:yes (Score:5, Funny)
Indeed. Unfortunately, power hungry people who are actually not good at real world things jump into politics instead. In other words, we end up with a bunch of retarded ass holes running our nation. What a bunch of fuckers.
So power hungry people need to understand powers!
Re:yes (Score:4, Insightful)
IIRC, math knowledge is one of the most important factors in whether people repay loans. People who can't count (or can't divide by 12, or figure out what interest is, etc) can't manage their personal finance. It's sometimes maddening to hear their explanations. Even if you are good at math, it can be hard to figure out a lot contracts (which are designed to mess with your head), people without math skills who sign contracts are like people who represent themselves in court.
Re:yes (Score:5, Insightful)
How many people use a substantial fraction of their high school education in their working life?
The purpose of a high school education is to enable a person to be able to be able to think and be able to have an intelligent conversation. It is not specialization nor is it designed to train someone how to perform a specific job. Math, arts, science, history, music, language, writing, civics, etc., all play a part. A person with a well rounded education is a person who can make useful judgements as a citizen.
High school doesn't prepare people to be salesmen, barbers, engineers, doctors, receptionists, or mechanics. Each of those fields will have specific training. High school only makes it possible that once you do enter one of those fields that you can do so as an intelligent citizen.
Is this worth it? Some developed societies separate their education systems half-way through high school into a vocational and college prep line because they want to use high school to prepare their citizens for a job. They choose specialization over breadth. It has been argued that this stifles creativity. Math and science scores are nice on paper to show off your education system, but perhaps the true measure is how creative your students are. Everyone is going to specialize after leaving high school, but the well rounded students who might be a step behind on specialization will be two steps ahead with creativity.
Re:yes (Score:4, Informative)
How many people use a substantial fraction of their high school education in their working life?
The purpose of a high school education is to enable a person to be able to be able to think and be able to have an intelligent conversation. It is not specialization nor is it designed to train someone how to perform a specific job. Math, arts, science, history, music, language, writing, civics, etc., all play a part. A person with a well rounded education is a person who can make useful judgements as a citizen.
High school doesn't prepare people to be salesmen, barbers, engineers, doctors, receptionists, or mechanics. Each of those fields will have specific training. High school only makes it possible that once you do enter one of those fields that you can do so as an intelligent citizen.
I use a shitload of science and maths in my daily job, most of it learned in high school. If it weren't for high school, I would not have the prerequisite knowledge necessary to become a network engineer. This may not be true in your country, but High School in Australia does allow one to become specialised, you have four core subjects everyone must take (English, Maths, Science and Social Studies) and in the final two years, Science and Social Studies become optional, you can choose to do history or biology but you aren't forced to.
As for algebra itself. Who uses that in real life eh,
No one needs to figure out how many litres of petrol they'll get for $20. Yep, we never use algebra in real life.
Re:yes (Score:4, Insightful)
Specialization is for insects
Specialization is what makes modern civilization possible. Without division of labor, we'd all be subsistence farmers. Either Heinlein didn't know what he was talking about, or (more likely) the words he put in the mouth of Lazarus Long weren't meant to be taken as gospel truth.
Re:yes (Score:5, Insightful)
Mathematics is a tool, [...]
Math isn't factual or learnable per se - studying math to your brain is what jogging is to your body.
Very very small share of people does the theoretical math. Most people do applied math and most of the time using specialized software.
I have used math last time god knows how many years ago and personally no huge fan of it. Yet, I'm still very grateful and that I had the math. For it taught me the analytical thinking, it taught me how to find the way to dismantle large problems into smaller ones, it taught how to deal with ambiguities and so on.
Math stands apart from the rest of the subjects because it is sole pure abstract one. It is the only subject which was created 100% by humans. Yet, since it relates in no way to the outside world, it is also the most unnatural for our brain to learn.
Instead of all the flames, probably a healthy discussion on how to better teach the math would be more productive?
Re:yes (Score:5, Informative)
Math is a means of describing the world. It is not entirely abstract. It can be balls or calories or dollars.
If I may quote Whitehead:
Suppose we project our imagination backwards through many. thousands of years, and endeavor to realize the simple-mindedness of even the greatest intellects in those early societies. Abstract ideas which to us are immediately obvious must have been, for them, matters only of the. most dim apprehension. For example take the question of number. We think of the number 'five' as applying to appropriate groups of any entities whatsoever - to five fishes, five children, five apples, five days. Thus in considering the relations of the number 'five' to the number 'three: we are thinking of two groups of things, one with five members and the other with three members. But we are entirely abstracting from any consideration of any particular entities, or even of any particular sorts of entities, which go to make up the membership of either of the two groups. We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the m.embers of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it. During a long period, groups of fishes will have been compared to each other in respect to their multiplicity, and groups of days to each other. But the first man who noticed the analogy between a group of seven fishes and a group of seven days made a notable advance in the history of thought.
More directly:
The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. All you assert is, that reason insists on the admission that, if any entities whatever have any relations which satisfy such-and-such purely abstract conditions, then they must have other relations which satisfy other purely abstract conditions.
From Science And The Modern World Lowell Lectures, 1925
Re:yes (Score:5, Insightful)
No, the point of educating people is not so that, one day, they will go "aha!" and use their knowledge of geometric series or the battle of Gettysburg to found a company and make a million dollars, but to ensure that the constituents of the very influential body politic (in a democratic society) are capable of interacting effectively with their world. While you will never be asked to solve for X in your daily life, you will likely be asked to apply similar concepts, and you will definitely be asked to use your knowledge of, for example, plotting of functions, to understand things like graphs which are presented to the public by the media in ways which are either unintuitive or outright deceptive.
The same arguments in the TFA could easily have been applied, in an earlier time, to literacy: there are historically plenty of people who lived long, happy lives who never knew how to read. However, it is essential in today's society, because our commitment to a literate society has gone hand in hand with out commitment to an advanced society capable of effective and efficient engagement and contribution to the experience and knowledge of our collective self. Mathematical literacy, of an increasingly advanced degree, is a similar requisite in the modern society, where the sheer amount of information available grows larger and more formidable every day. In such a time, it is the duty of us as a community to ensure all persons are capable of effectively interacting with and utilizing this information. To do less, simply because the individuals prove recalcitrant, or might find ways to ignore our information rich society, is to condemn ourselves to mean regions of social existence, consciousness, and ultimately human experience.
Re:yes (Score:5, Insightful)
I was a Data room tech, field engineer, service tech, systems administrator, and second level support tech (not in that order) for over thirty years, and while I had taken (and done well at) algebra, calculus and geometry/trigonometry etc I don't remember ever actually using it on the job
I work as a programmer. I took and did well in Spanish, geography, history, chemistry, physics, biology, sexual education, art, wood shop and gym classes in high school, but I don't remember ever using them on the job.
The idea that education should be reduced to voc-tech work is bizarre.
Re:yes (Score:5, Funny)
Sex ed helped with one of my engineering jobs. In fact, we got special training during a 1 week course. I still have the certificate. We even had dirty pictures on the wall. Friends from other divisions would freak when they visited my cubicle. I was lucky. My job dealt with OB/GYN and breast cancer (lots of drawings of boobs on my cubicle walls).
Another division dealt with enlarged prostates! No body liked visiting their cubicles. Pictures of wangs and needles. Shudder!
Oh, and I used algebra too.
Re:yes (Score:5, Interesting)
If you understood things that might have exponential basis, or you made projections of some value based on the increase/decrease evidence in the past --- even if you didn't do anything on paper but just did fuzzy concepts in your head to get the gist of it --- then you did use it. Chances are that you did use, at least, algebra, and didn't notice.
Here's an example of me using C Programming education in my current work, stem cell biology: In C programming you can take something complex, like a database, or some complex string of things, and you can OBJECTIFY it. And in this you simplify future treatment of that complex thing by calling it some name -- it is objectified. From that education the powerful method of objectification is made clear in my head. So now in cell biology, to speed up my thinking and make complex concepts simple, I objectify them. So, for example, I take a well designed and intricate process that takes several pages to describe, and I call it something like "XA-2", or whatever I want. At that point my conscious understanding of XA-2 has become baked into the brain, and to consider that process in even bigger concepts, I can logically apply XA-2 in my follow up experiments without trying to conceive each step every moment of the way.
There are lots of hidden benefits to education. And there are lots of ways to learn.
I find all the time I spent dancing in packed clubs to be extremely helpful in maneuvering through big crowds or dense traffic. I became experienced in carrying expensive liquids through heavily packed crowds that have unpredictable pulses in various directions --- in time I learned where to look and how to defocus my eyes to see the periphery and predict the movement of people to see when openings happen and closings (squished) may happen.... you get good at it and you push right through crowds that most people go really slow through.
I find lots of learning from video gaming -- predictions and efficiencies, etc. This is why experienced gamers do well on new games whereas new gamers usually take longer to pick up on new games -- experience in analytical perspective in gaming contexts.
If you can recognize how you've improved in some skillset -- even skillsets that are seemingly recreational -- you can translate/articulate those skills to other facets of life.
Re:yes (Score:5, Insightful)
Perhaps should someone clue in this "political science" professor.
In the rest of the industrialized world Algebra is considered an elementary schools subject. The idea that it is too cumbersome to bother average students with simply boggles the mind.
Formalized education should challenge the students in some way. Otherwise, there is no point in bothering at all.
It needs to be diverse enough to push everyone outside of their comfort zone if only by a small amount.
Re:yes (Score:4, Funny)
Absolutely! I cannot agree more. How many of us would not have even bothered learning something if we weren't "made to do it"? As a child, my parents forced me to do things I thought I'd hate only to find out I really, really liked some of of those things. Pushing that comfort zone is crucial to developing an educated and open mind about a great many things.
But, leave it a to politician to see a problem (in this case, our students failing mathematics miserably), and to propose a solution that states "well, we don't need that anyways." Call me crazy, but that seems a bit retarded even for a politician. Wait, no it doesn't...
Re:yes (Score:5, Informative)
Not really. Arithmetic is about the operations you do with numbers (addition, multiplication, etc.). Algebra (or rather, elementary algebra) is basically solving equations. The examples the GP gave are usually solved by using very simple elementary algebra and arithmetic: build an equation representing the problem, solve it by isolating the variable (algebra), and then calculate the numeric answer (arithmetic).
Re:yes (Score:5, Informative)
10bands * x = $5, solve for x [wikipedia.org].
Re:yes (Score:5, Interesting)
Also this New York Times article seems to be intentionally misleading.
He keeps on mentioning algebra repeatedly, and says that his question applies more broadly to "geometry through calculus", not just algebra. But then most of his examples are calculus-level or pre-calculus level.
And then, he takes a quick jab at University Legacy admission programs and Athletes admission programs, which have much lower Math admission standards, (which I completely agree with), but then he completely forgets to mention Affirmative Action which basically does the same thing and the special Summer/Spring/Transfer admission University programs which also admit students with much lower Math SAT scores (as a way to avoid including those scores in their main official published advertised statistics).
Re:yes (Score:5, Informative)
If I have $50, and I have to buy lunch every work day for two weeks, how much can I spend on average?
X = $50 / (2 weeks * 5 days)
X = $50 / 10
X = $5
This is a hard question for people who don't know algebra. Those who DO know algebra do most of the math in their head because it's so ingrained.
The fact that you don't realize you're using algebra every day should be taken as how vital it is to teach it.
Re:yes (Score:5, Informative)
The word Algebra comes from "The Compendious Book on Calculation by Completion and Balancing" written in ~820AD by a mathematician called Muhammad ibn MÅsÄ al-KhwÄrizmÄ (algorithm). The word "al-jabr" was an arabic word standing I beleive for the idea of adding/subtratcing the same amount from both sides of the "equation" (I stand to be corrected)
The entire book is a giant collection of arithmetical word problems.
The term "algebra" came to be understood not as a single technique, but as a general term for the entire framework of techniques used to solve these arithmetical word problems. The problems could be understood and the solutions confirmed using arithmetic, but to actually find a solution, in a systematic way, required the application of the techniques that al-KhwÄrizmÄ espoused in his solutions.
Algebra is how we solve problems systematically, not the problem itself. If you solved the problem, even a basic one, you used some kind of algebra. Even if it was now now an unconscious operation, at some stage you were taught the technique explicitly, or learned it in class through solving problems.
Re:yes (Score:4, Insightful)
No you don't. A basic understanding of our shared history is important for the proper functioning of a democratic society. An understanding of math beyond what is needed to balance a checkbook (or national budget) is not. 90% of us never use algebra, even once, after leaving school. It is basically pointless for non-techies.
It's a very good analogy, actually. You're right that a basic understanding of our shared history is important, but the vast majority of people rarely if ever use more than what they'd learned of history by the end of middle school.
I'd argue that that doesn't make it worthless to teach more in high school--although only maybe 5% will benefit directly from taking more advanced history classes, you don't know which 5% it is and you're handicapping your culture slightly by not providing that knowledge. It's exactly the same argument that I'd make about algebra, except more people are likely to use algebra at some point.
And in both cases I'd argue that even if you don't directly pull some history facts out now and again or have to figure out how much each of those 10 cars cost pre-tex, you still benefit indirectly by taking those classes--for one thing, it's a lot easier to forget the final levels of coursework than it is the stuff that you used again in later years of school. So if you want people to know, say, algebra I and 7th grade history for the rest of their life, then a very good way to help do that is to make sure they take algebra II and 8th grade history--not only did they just learn the former out of the book, but they practiced it as part of something else for another year.
Comment removed (Score:4, Informative)
Mathematics is a tool (Score:5, Insightful)
NO.
It's the unintuitive ways in which it's taught (which in turn causes the societal alienation of the subject) that is the problem, not the fact that it's a requirement.
Mathematics is nothing less than the upmost tool of rationality. Lose it, and all progress decays.
remember Heinlein's assessment? (Score:5, Insightful)
Re:remember Heinlein's assessment? (Score:5, Funny)
"At best". Nobody was talking about you.
Re:Mathematics is a tool (Score:5, Informative)
NO.
It's the unintuitive ways in which it's taught (which in turn causes the societal alienation of the subject) that is the problem, not the fact that it's a requirement.
Mathematics is nothing less than the upmost tool of rationality. Lose it, and all progress decays.
Yeah. Somebody should point Prof. Hacker to this essay [nytimes.com], in which the writer states that
Perhaps if he were to read that, he'd change his mind. :-)
(Shorter me: "You did RTFA, right? If not, please do so before ascribing to Prof. Hacker opinions he does not hold.")
Re:Mathematics is a tool (Score:5, Interesting)
Exactly THIS. The way higher levels of math are currently taught and in particular the lack of true relation to practical problem solving is a huge issue.
I have seen a few professors and textbooks which remedy this great problem. Probably at the top of the list is Morris Kline. His Mathematics for Non-mathematicians (or Liberal Arts Majors) textbook, its language, and approach are a perfect template for better broad discourse on mathematics to non-STEM majors. Even his Calculus text better relates the importance of concept and understanding far better than the current popular books by Thomas, Tan, and Stewart (though the latter two books are both mere knockoffs of Thomas' book, made popular to obsolete Thomas' skus). Consider that I am a STEM major, in Physics, and all of my courses within the department manage to relate skills and knowledge in vastly more useful manners and with little abstract ambiguity.
Calculus and Chemistry seem to be the most popular courses Universities use as "weeding" courses. The observed problem every time is teaching in overly abstract terms and with little relation to useful problem solving approaches in the subject matter. Anytime a professor offers an outside of class time "problem solving" session shortly prior to a test, they are letting you know they failed to teach all of the problem solving skills and especially never related practical knowledge. While I can appreciate the dedication it demonstrates on the part of the professor, they should be doing their jobs and putting it in the classroom to begin with.
A Mathematician's Lament (Score:5, Interesting)
It's the unintuitive ways in which it's taught ... that is the problem
Lockhart put this quite elegantly in his A Mathematician's Lament [maa.org]. Treating math as a rote subject (as it is now) is the moral equivalent teaching art as paint by numbers.
Re:Mathematics is a tool (Score:5, Interesting)
You are right, I made a mistake, my bad. I never took an English course. I never needed to, an online dictionary and some persistence taught me enough English to communicate on the level required. I've never been to an English-speaking country so far.
How many languages do you speak fluently?
Re: (Score:3)
GodGell (897123) made a pretty convincing display of how mathematics has to be taught (classes mostly suck, books mostly suck, online mostly sucks, turns out there is no royal road to geometry even after centuries...) but we don't really "need" language classes because immersion works well enough for everyone but the grammar fascists. Therefore I think "we" need algebra class a lot more than "we" need english lit.
Re:Mathematics is a tool (Score:4, Informative)
That's A Convenient Theory (Score:5, Insightful)
Re: (Score:3)
It's more likely that the engineer will one day make the political scientist obsolete than the other way around, but until that day comes, we have to suffer with them.
Re:That's A Convenient Theory (Score:5, Insightful)
Political Science is an oxymoron, and insult to the term science. It should be Political Skullduggery, or something to match the true ilk of it, being an observation of the human nature at its finest and worst at the same time.
This guy is an idiot (Score:5, Insightful)
Re:This guy is an idiot (Score:5, Funny)
Re: (Score:3)
And if nothing else, you learn that some things are hard and the people who work to master them are worthy of respect. Except this guy seems to have missed all of those lessons. Maybe he somehow dodged out of required math?
Re: (Score:3)
Critical thinking, logic, and problem s
Re:This guy is an idiot (Score:5, Insightful)
No exaggeration at all, this is completely true! The author himself states that he's not in favor of ruling out quantitative reasoning, which he considers important. The fact that the thinks algebra isn't an important component of this skill only shows how ignorant he is of mathematics (why he's given his soapbox in light of this is only more concerning, but I digress).
Algebra builds an understanding of abstract and unknown concepts. You can train students to do quantitative reasoning problems like machines, but algebra is much more abstract, but then you can throw them a curveball and they'll be totally hopeless. You end up with situations where students can solve problems like 'how much should 3 apples cost if one costs 1$' and then they won't be able to solve things like 'if you have 5$, how many apples can you buy?' We have freaking tip calculators on our phones because we're too lazy to learn that all you have to do is slide the decimal over, round to a convenient number and double it. Is that really so hard?
No, the problem isn't the subject - it's the students. Get over the fact that you have to learn things that you don't like. I feel like all the time I spent on my humanities subjects in secondary school and college were thoroughly wasted as well, but I put up with it because I had to. I fell off the honor roll when I was 12 because I got straight A's and a B in Art. Art for Christ's sake! Pardon me if I suck at using a pair of scissors! I guess that's what should hold me back from being recognized in my math and science achievements, right?
I'm not gonna stand here and suggest that I never complained about it, but at the same time, I went into that class every day fighting for my life because I knew that was the one thing standing in the way of my being recognized as a good scholar. So ultimately I didn't reach my goal, but at least I can say that I tried as hard as i could. I don't make excuses. The problem is that nowadays we have a problem telling kids to suck it up and deal with it. Math is a requirement - deal with it. I'm not gonna get a damn thing out of reading Dante's Inferno, or buillshitting about character development and relationships in Dickens, but do it because I must. Kids (and their parents) seem to not accept that as a reason nowadays.
Maybe alongside with learning algebra (or whatever subject trips you up), we should learn to accept that not eveything's gonna be easy in life and that we shouldn't make excuses and just blame ourselves instead.
And before I forget, obligatory xkcd: http://xkcd.com/1050/ [xkcd.com]
And also before I forget, not only should algebra be mandatory, but statistics should as well.
Unnecessary roughness on statistics (Score:3, Interesting)
The article's author should be penalized for pointing out the unemployment rates for hard sciences graduates with no comparison to the corresponding rates for liberal arts majors.
Re:Unnecessary roughness on statistics (Score:5, Funny)
An engineer asks - how is that?
A physicist asks - why is that?
A polisci major asks - would you like fries with that?
Re:Unnecessary roughness on statistics (Score:5, Funny)
Give the guy a break. He can't do algebra. That means he can't do statistics.
If you want to understand the world... (Score:5, Insightful)
If you want to understand the world, you need math. If your education doesn't include that, what sort of education is it?
Re: (Score:3)
Re:If you want to understand the world... (Score:4, Insightful)
I certainly prefer my banker to know algebra, and so should the lawyer and notary. Social studies (history plus geography) was ALSO required when I was in school. And if you haven't noticed, studying and actually solving a lot of those "social realities" that have such a big impact in everyday life depends on statistics, which is... math.
Re:If you want to understand the world... (Score:4, Insightful)
And how exactly do you define the world? The world is vast, and we can probably define and describe less than 1% of all we know with mathematical formulas. What about poets, artists, authors... do they not understand the world? I can't tell you the last time I read an equation that elicited more emotion than Whitman or Frost. So maybe it's apt to say those who do not understand love or nature or poetry or biology do not understand the world.
The real question is: (Score:5, Insightful)
... is High School necessary?
Re:The real question is: (Score:4, Funny)
Emo prof asks: Is anything necessary?
Re:The real question is: (Score:4, Funny)
... is High School necessary?
The high school reunion industrial complex, as one of the few remaining vibrant industries in America, so its been declared "too big to fail" so we can't get rid of H.S.
Interestingly the reunion industrial complex is failing due to facebook... Why do you need a retro-cover-band and a rented hall to find out whats new, when every one who cares about such things, already knows from facebook.
My learning almost completely stopped in H.S.... its curriculum moves too slow. Made a very painful impact when I suddenly had to start learning again at university. Whoa, I haven't studied since middle school, WTF? You mean I have to read the book now?
Don't really get the American system (Score:4, Interesting)
Re:Don't really get the American system (Score:4, Insightful)
I agree to a point. General education is useful to provide a well rounded education. Sometime in the teen years you can start allowing children to specialize, which is something adults do anyways. Heck, even our brains do it, unless I am wrong about my limited understanding of neuroscience.
The value in math is not what you can do with it. Highest math courses I passed were Calculus and I never went on to anything else in college. To this day I don't use very high level math, the standard deviation equation being a notable exception. I just don't need an absolute ton of math to be programming and administrating the systems that I do. I know there is a *huge* amount of math involved in the platforms that I am using, but I'm working at a much higher level of abstraction and can just use a math class or plugin where required.
The true value of math is learning critical thinking skills and logic. While only a very small percentage of students will ever use it daily, 100% could be benefiting from the critical thinking skills and logic.
Regardless of specialization, those skills need to be taught. Could there be a better way than pure math? Perhaps.
Flamebait Headline (Score:4, Insightful)
The professor in the article is asking something completely different and reasonable: since everyone is different, and everyone has a set of proficiencies and aptitudes, why do we try to teach everything a set of knowledge someone somewhere has somehow determined to be paramount? What if everyone's talent was fostered at a young age instead of forcing them to neglect their proficiencies and learn skills which perhaps they will never use? Would we end up with a society where everyone was an expert at something, rather than a society where everyone has a little knowledge everywhere but no real spectacular skill?
I don't know the answer to any of these questions, but really, I think they're worth considering. I for one was fostered at a young age because my parents identified that I was good at science and math, and I benefited tremendously. I could only imagine if that kind of fostering was afforded to every child, we might be better off.
Let's look at the larger picture (Score:5, Interesting)
There is so much missing from high school and post high school education. I'm from Quebec so the system is a bit different, you go to CEGEP between high school and university here. Anyways, nobody learns about how the society works here. We need young people to learn about the Civil Code, how contracts work, how renting works, how buying real estate works. Nothing in depth, but at least a functional knowledge so you don't walk into bad situations.
Am I making sense? We are focusing on things that are easy to teach like piles of math. Things that are complex and can create aware citizens seems to interest the system less.
Oblig xkcd (Score:5, Funny)
Re:Oblig xkcd (Score:4, Insightful)
Re:Oblig xkcd (Score:5, Interesting)
Some have argued that the so called soft sciences actually have to deal with far more complex systems than humans can handle. If you compare this to engineering where you can frequently synthesize systems, some soft social science looks much harder.
Yup. (Score:5, Insightful)
Most students do not really understand mathematics anyway, they simply memorize equations and techniques. Why should students who can't manage that be barred from the higher levels in other courses?
Of course it is necessary... (Score:5, Informative)
Algebra is a subset of mathematics, and forms the basis for statistics. Statistical analysis is required in just about every science field as well as arts. Social studies and biology require analysis of population dynamics; geology and geography require understanding of hydrodynamic equations. Psychology requires statistical analysis in many different ways. There's even a mathematical package called SPSS - Statistical Package for the Social Sciences. Even history will require the use of probabilty analysis to determine the most likely chain of events.
Is there a /. department of Ironic Headlines now? (Score:3)
Political Science Prof Asks: Is Algebra Necessary?
That's Political Science.
Everyone wants Excel skills. (Score:5, Insightful)
If you've been in any large business you realize that it operates primarily on Excel spreadsheets being repeatedly e-mailed back and forth. While many of the folks creating these spreadsheets don't even realize it, each of the cells are little algebraic equations. People often ask "what from math class do you use every day", well algebra is an easy one, people write business formulas in Excel.
Short answer: yes. (Score:5, Insightful)
Longer answer:
The fact that anyone felt the need to ask this question says to me that we're doing education wrong in the USA. Very wrong. Fundamentally wrong. Yes, algebra is necessary, possibly more necessary than any other branch of math, because there are so many other fundamentally useful concepts wrapped up in it -- formal logic, proof, and a whole bunch of other basic building blocks of epistemology, not just mathematics -- that IMHO it's crucial to teaching students to think and reason answers and not just churn them out by rote memorization the way they do with arithmetic .. the way we're currently teaching it.
But why are we approaching the subject as though it's something "hard" that we have to "work" to learn and then question whether the effort is necessary? The only reason we have that view of it is that by the time our kids hit algebra, they've had all the curiosity and fascination for new knowledge hammered out of them, by normalizing their curriculum to death assembly-line style. Arithmetic by addition and multiplication tables and memorization is boring, mind-numbingly so, and any kid who gets through that gauntlet and is still interested in algebra didn't learn his/her math in the classroom, they learned it by exploring and playing around with it and getting a feel for number theory and how arithmetic operators work .. you know, real math, the kind that gets the imagination flowing.
And if you haven't had curiosity crushed out of you by memorization drills, algebra is fascinating. If you're teaching it right and letting the math itself do the teaching, you'd be hard pressed to stop kids from learning it. Case in point: In my 6th grade math class, a "substitute" (who I'm fairly sure was actually an education researcher experimenting with math teaching methods, but "substitute" was what they called him) came into the class, which was starting on basic algebra, and taught us what turned out to be differentiation by the power rule. I ended up using that one method in every math class I had from then on -- much to the consternation of my teachers who weren't quite sure how to deal with me doing differential calculus on high school algebra tests -- but I also ended up exploring how polynomials went through simpler and simpler derivatives until they ended up as a constant, and then zero, and gained a whole new appreciation for how they worked, and later on, integration and the fundamental theorem of calculus just sort of fell into place. The power rule is still one of my old friends when it comes to math. But I have that "substitute" to thank for most of the algebra I learned on my own because I couldn't get enough of it -- that one little seed sparked a whole adventure that continued to teach me mathematics for decades afterward.
Granted, I'm a hardcore nerd in a lot of ways, but I'm not entirely sure that's an aspect of who I am and not just an artifact of a society raised on the "math is hard" meme. It's hard, yes, but it's irresistible to a curious mind, and we're all born curious .. it's how we bootstrap every bit of knowledge we gain firsthand about the world. If we stop killing it in the schools, give it a few generations and our PolySci professors wouldn't even think to ask this question..
I'm an English professor (Score:5, Insightful)
This guy, Hacker, is a troll. (Score:5, Insightful)
He has gotten a few minutes of glory by killing a sacred cow. In this case The-Math-Is-Vital to-Higher-Education cow. The cow is sacred because it is a good and right cow. An all-the-way-down cow. It is so easy to make a name for yourself by taking contrary positions -- especially if they are outrageous. This specious argument was born to be reported on Cable News. Or *"cough* on Slashdot. Of course these pay-as-you-go degree mills would like to have more customers. So let's just change these ridiculous standards. This guy has an agenda.
Here is my next book? "The Reading Railroad. Speak Don't Write." The summary: With the advent of text to speech and audio recording reading and writing is an unneeded barrier to many otherwise smart people getting PH.Ds. As long as they can get a student loan they can get a doctorate.
"Here. Let me help you with that wordy loan application."
The brain is a mathematical engine. When you catch a fly ball you are solving a differential equation. Intuitively. When you gauge the speed of an oncoming car to cross the street that is Algebra. Hell, even dogs can do it. Sometimes. Mathematics when taught elegantly is interesting. It is a critical structure for the first of the two main components of Education: 1) The Discipline of the Mind (The ability to think) The other being 2) The Furniture of The Mind (Knowledge). Learning a second language, doing mathematics, reading music, writing computer code are all mental disciplines that require a disciplined mind. Knowledge without mental discipline is furniture without a room.
There's a shirt for that (Score:4, Funny)
"Dear Algebra,
Stop asking us to find your X.
She's not coming back"
Re:A more fitting question... (Score:5, Funny)
Is political science necessary?
YES! If political science majors studied things like engineering or computer science instead, then who would sell me coffee?