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 ."
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.
Don't really get the American system (Score:4, Interesting)
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?
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.
Re:Mathematics is a tool (Score:3, Interesting)
Depending on what you call mathematics, I'd argue that formal logic is closer to the essence of rationality.
You are correct, but what tool do you use to teach people logical thinking (and only logical thinking - you could argue that programming computers is the 'purest' form of applied logic, but most people don't have the mindset or sufficient interest for that), if not - mathematics?
Consider how mathematics came to be: as far back as thousands of years ago, the drive of the most intelligent thinkers of society to understand the world, and to create a system of documenting (and thus passing on to later generations) identified and verified connections within it, is what led to the invention of what we now call "mathematics". It rose directly from the desire to put rational thoughts and ideas into a systematic, and thus advancable, way of thinking.
This in turn has lead to the exponentially increasing complexity that we see today - slowly, layer by layer, raising the level of effort and intelligence required to acquire a "reasonable" level of understanding. Compounded by a way of education that does not adequately address the diversity of capability within human populations, the prevalence of the idea that mathematics is unneccessary and too far removed from reality was bound to inevitably become widespread enough to matter.
And hence: this article.
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, 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: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: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.
Re:remember Heinlein's assessment? (Score:3, Interesting)
A man should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyse a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialisation is for insects.
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, 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.
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 (Score:4, Interesting)
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: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: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: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