I will never be able to finish this translation if all these articles that need to be addressed keep cropping up. My colleagues in the science departments are in an uproar over the article titled “Is Algebra Necessary?” that appeared in the NY Times.
This is what Dr. Andrew Hacker has to say:
Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.
I always feel very suspicious when political scientists (like Dr. Hacker) opine on whether algebra is necessary, economists want to close down foreign languages, and professors of medicine wonder whether we can dispense with the departments of Classics.
I hope that the resident scientists of this blog weigh in on the value of this article. As a scholar of literature and one of the people Dr. Hacker wants to protect from the horrible burden of mathematical literacy, I can say that I really wish I had received a better education in mathematics than I did. I pride myself on being an independent and resourceful person, yet I’m a total damsel in distress when in comes to managing any aspect of my financial life. I pretty much have to rely on my husband who is a scientist to handle this part of my existence. I’ve always relied on the kindness of strangers fiends and lovers to help me calculate my grades.
But it isn’t even the practical aspect of mathematics that I really miss. I have a strong feeling that I have lost out intellectually by not challenging the mathematical part of my brain. I believe that my mind would be better organized and that I would have found it easier to learn Latin and German if I’d had some mathematical training.
What do you think?
Clarissa's Blog 
I was shocked that an educated person actually tried to argue that we should no longer require Algebra in high schools. It’s almost as if this guy is arguing that we have an even more ignorant population than we already do.
Among other things, Algebra is useful for:
1) Reading a topographical map (Cartesian coordinates)
2) Calculating the point of breakeven for a small business
3) Calculating mortgage payments and the impact of compound interest (Logarithms)
4) Doing taxes
5) Estimating the time it takes to complete a trip or to complete a project
6) Scaling recipes
7) Computer programming
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GOOD points!
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My boyfriend and I were just talking about this last night. The quote makes algebra sound so difficult, but the true, daily applications of algebra don’t go by fancy names that I know of: being able to calculate grades, being able to begin to understand how interest accrues on a loan you’re taking out – I don’t recall ever hearing the words “vectorial angles” or “discontinuous functions” in my algebra classes… And I helped tutor some kids in high school who were in a remedial class for those who struggled with the math, and they were at least being taught basic, useful things like figuring out your gas mileage.
I also think it cuts people off from a lot of professions. For example – people often tell me that they couldn’t do accounting because they’re not a numbers person. However, accounting uses very basic algebra, not anything fancy. I do think that if you get people comfortable at a more difficult level of algebra, then they can confidently do the daily math that they need.
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“I also think it cuts people off from a lot of professions. ”
– Very true.
I have a feeling this will not be a controversial post since I only have very intelligent readers. 🙂
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Very basic arithmetical skill is necessary for accounting, not algebra.
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The people who invented double entry bookkeeping (And this is something like six centuries ago, when literacy was the exception, not the rule) invented the notions of debit and credit so business empires could be staffed by people who don’t necessarily understand the concept of a negative number.
Education as a means to the end of employability is the wrong idea.
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—I’ve always relied on the kindness of strangers fiends and lovers to help me calculate my grades.
Fiends? 🙂 🙂
More seriously, the mathematical concepts mentioned by Hacker are not necessary to calculate the grades. Unless one engages in some complicated curving based on statistical analysis. 🙂 Which I never do. I do not even bother to calculate class averages. And shock the students by proclamations that I do not care to calculate it (and they should find some different motivations too).
And maybe the prestige of the higher education will increase if/when it becomes more elitist again… (Just playing Devil’ advocate here…)
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Math fiends! 🙂 This is another Freudian slip that I will not correct. 🙂
I’m totally for the elitism, of course. 🙂
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Although I’m a physicist, I’m going to play Devil’s Advocate for Hacker, at least for a bit. As far as I know, from my non-systematic observations of high school math curricula, most high school math is aimed at preparing students for the sort of math they’d take in college if they’re preparing to study natural science, engineering, or one of the more stats-oriented social sciences. Or, if it isn’t aimed at that, it’s a dumbed-down version of that. While some amount of mathematical literacy is very important for everyone, training to be a scientist is different from acquiring practical, relevant knowledge. High schools don’t seem to emphasize practical and vocational tracks as much.
The typical high school student who isn’t going into science or engineering might be better-served by a more practical geometry class rather than a proofs-oriented class. They might be better served by a class on Statistics For People Who Read Newspapers than a more formal, abstract statistics class. They might be better served by a class on quantitative reasoning in daily life than a pre-calculus class. They might be served better by a class on basic accounting than a trigonometry class. And so forth.
All that said, some amount of algebra will still be needed to approach these more “Mathematical Skills For Life” classes (or however you want to characterize them). So people will still have to take some sort of algebra class.
The bigger issue, to me, is one of tracking. If at some point early in the high school curriculum we separate students into “potential STEM* majors” and “not potential STEM majors” tracks, that will be a big change for us. I know that some other countries have more tracking in high school, but the US doesn’t have as much formal tracking, at least not these days. We have lots of informal tracking, i.e. disadvantaged kids and kids from weaker schools enjoy fewer opportunities, but we largely resist formal tracking. The opposition comes from multiple directions. There’s a liberal, social justice argument that tracking cuts off opportunity and will have disparate impacts. There’s a more individualist argument that recoils at anybody having their future decided by Authorities when they are young and at the mercy of The System. Let them graduate when they are 18 and then decide their future, many feel.
I have mixed feelings on tracking. However, I think that if we’re going to debate what people “need” to study in high school, we need to be very clear about the fact that we are implicitly debating whether to make certain paths available in their subsequent studies. These decisions have consequences, and however you feel about tracking, we need to be very clear about those consequences.
*STEM=Science, Technology, Engineering, and Math
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“The typical high school student who isn’t going into science or engineering might be better-served by a more practical geometry class rather than a proofs-oriented class. They might be better served by a class on Statistics For People Who Read Newspapers than a more formal, abstract statistics class. They might be better served by a class on quantitative reasoning in daily life than a pre-calculus class. They might be served better by a class on basic accounting than a trigonometry class. ”
– Wouldn’t this end up creating a system where the only people who can go into science programs in college are the ones whose parents paid for tutors who will train them outside of school?
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Thoreau, I really like your analysis. I do think there is a concern around tracking in regards of “authority figures” making so many pre-determined decisions, but I think at the very least schools should actively have a dialogue with high school students and their parents about options. Perhaps a solution where the default is still a “STEM path”, but with the opt out option for those who either are too lazy or consciously realize another set of classes fits them better (this leverage a little consumer/student psychology of making it a conscious choice to choose the “intellectually easier path”.
For the other students I think the basic concepts of algebra should be used in classes that are more focused on dealing with life issues/situations. Maybe something titled “logic and mathematics, skills for succedding in life”. While the title is hokey.. the concept is to have the class geared around calculating basic averages, around the break-even points of small businesses, around comparing options on buying a new car (down payment, interest, high vs. low gas mileage and payback period). By taking this practical approach not only will you prepare students to deal with these situations, you might actually get them to see the VALUE in algebra and similar skillsets/mathematics. In general this practicality driven model of education I feel should be overwhelmingly applied for students from around 7th grade up.
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” the concept is to have the class geared around calculating basic averages, around the break-even points of small businesses, around comparing options on buying a new car (down payment, interest, high vs. low gas mileage and payback period)”
– I wouldn’t mind taking this course right now. 🙂
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I agree with you, Clarissa. Many people don’t know they’re going to be a science major until their senior year of high school, or maybe even when they get to college. While placing students who are completely positive that they’re not going into math or science in more “this is what you’ll need for real life” classes, you can’t just take a freshman in high school and make that decision for them.
In addition, taking a freshman in high school and saying “this kid is doing bad/good in this class, so he/she will/won’t go into science or math,” says absolutely nothing about the student. The tracking that goes on in other countries has its own disadvantages. If a student wants to go into science but does absolutely horrible–for whatever reason–in their freshman algebra class, sure they need to step up. But that one grade means absolutely nothing in the long run if the student really wants to go into science. Imposing stricter guidelines on which students will be invited into which classes only creates a false sense of superiority in students placed in the “real” math classes. It’s like telling a kid in a high school language class that because they did poorly in the first language class they’ve taken that they absolutely will not make it as a language major, or telling a student who does poorly in a freshman English class that they’ll never be an English major.
Students need to learn to make their own decisions and to live up to their goals. Some people take a bit longer to learn that than others. In addition, many high school freshmen don’t take all their classes seriously, and it might take a low grade or two for them to realize that they could do better. It’s a learning experience, not a preparation experience. To be honest, in high school I learned more about what I wanted than what I could do.
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” It’s like telling a kid in a high school language class that because they did poorly in the first language class they’ve taken that they absolutely will not make it as a language major”
– That’s a good point. I sucked in German but when I took Spanish years later, I flourished.
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@Thoreau, I went to elementary school in Spain and secondary school in Denmark. In both places — and they were very different countries then, before the EU — there were 2 types of math: practical and abstract. Depending on your program, you could continue with both or eventually drop out of one or both, but really — it was both you needed.
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I completely agree. Everyone should receive a basic mathamatical education. I am one of those people who don’t have a “head for numbers” but I am very thankful for the math education I received. I took the standard battery for college bound American High School students in my generation : pre Algebra, Algebra, Geometry, Trigonometry, and Pre-Calculus. I had no interest or aptitude for Pre-Calculous so I failed that course. But despite my failure,and despite the fact that I have forgotten much of what I learned, I think that taking math stretched my brain, caused me to grow, and taught me that not everything came easily to me. And some “practical” things stuck with me: how to calcuate area and circumference, how to figure percentages, how to calculate a ratio etc etc. But even beyond practicality, math can provide a nearly aesthetic experience for the right student. My father, for instance, sees math as deeply beautiful if not spiritual. ALL students should be at least exposed to the possibility of discovering the beauty in numbers ……………As a side note, do you know that you can set up an Excel spread sheet to calculate your grades for you? Though I can calculate grades, I still use Excel because it saves me time. It’s wonderful: it can provide class averages, individual averages, weigh grades. And it’s so neat and organized. I love it! 🙂
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I use Excel, too, but I need N. to create the Excel sheet for me. he tried explaining to me how it works but I just get scared.
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I live in excel… free lessons if you can give me cliff notes on cultural/literature issues if I have a date that is into that sort of thing…. 😉
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“if you can give me cliff notes on cultural/literature issues if I have a date that is into that sort of thing….”
– Any time. 🙂
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You might find a post from Mathbabe’s blog an interesting counter point to this post. She is a professional mathematician.
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I actually find it rather ominous that a political scientist, of all people, would be arguing in favour of greater mathematical illiteracy. Leaving aside this tiresome notion that things are only worth learning if they’re “useful,” the average North American is subject to a mathematically-based tax code (which they generally have to take on faith), enacting by governments whose elections constitute a non-trivial applications of statistics. Their access to food, shelter, clothing, medicine and entertainment is governed by how well they can balance numbers (namely, they’re salaries) each month; they owe cumulative trillions of dollars in debt, which compound exponentially. In short, every aspect if their life is governed by mathematics, even if they themselves are not the ones performing it. Does the author really think that paring back public knowledge of mathematics (in essence, limiting knowledge of the interior mechanisms of civilization to a privileged class of numerate mandarins) is a good idea? Does he not see how this could be (and already has been) abused by those with power?
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This is very insightful. I have a feeling a day will come when we will hear that not everybody needs to learn to read because there are books on tapes and television.
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Kids are already having problems with knowing how to write by hand because they are so used to using keyboards.
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@Venerable, he must have thought about this and decided ignorance benefited “the country.” I am a professor of literature and it falls to me to explain to students the difference between simple and compound interest. Their not knowing benefits the banks, of course. This is of course within the mundane and tiresome realm of “usefulness,” but still.
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And I had to explain why paycheck loans are daylight robbery. 😦
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My computer science degree featured a math minor, so I got a lot further in math than most people do. And I’m pretty bad at finances.
Finances aren’t complicated because they use heavy math. They’re just a huge mess of little simple details that never ever stop coming and it exercises your executive function a hell of a lot more than it exercises your mathematical function.
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Reminds me of this cartoon (not about finances, but a joke about advanced vs. simple math):
http://www.phdcomics.com/comics.php?f=1356
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What is this executive function that I just discovered I don’t have?
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Prioritizing and decision making, and yes you have it. It is an invention of the self help movement I think.
I disagree with the idea that people lack an “executive function.” I think there is a whole lot of misinformation out there that is marketed as objective information, and that people get legitimately confused.
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” I think there is a whole lot of misinformation out there that is marketed as objective information, and that people get legitimately confused.”
– Oh yes. There are powerful interests that feed off people’s ignorance. See how well the pharmaceutical industry is doing as a result. 😦
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Nope it’s real, and real researchers are studying it. People with autism tend to have problems with executive function. People with ADHD by definition have problems with executive function.
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“Nope it’s real, and real researchers are studying it. People with autism tend to have problems with executive function. People with ADHD by definition have problems with executive function.”
– But what is it, though? 🙂 🙂 I honestly never heard of it before.
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Here’s a link to the wikipiedia article on “executive dysfunction”, which has a link to an article on “executive system” (executive function) and lots of goodness that should get you started:
http://en.wikipedia.org/wiki/Executive_dysfunction
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Sadly, the discussion of this article among my male colleagues has degenerated into making fun of some stupid hoax video where some women pretend to say stupid things about math. And then we wonder why women don’t go into STEM fields. These are male scientists whose defense of their field is reduced to making dumb blonde jokes. I’m kind of disgusted right now. The level of discourse on the subject on my blog is much higher.
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And anyway if someone leaves something really offensive on your blog you can delete it! Sometimes I wish I had the power to do that in real life. The heck with flying or being able to see through solid walls: I’d like to have the superpower of making people who tell sexist jokes be mute for a week, or something.
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After I was doing humanities courses for a long time, I began having dreams where I was supposed to turn up for a maths course and pass an exam, but I never made it on time. Even today, the dreams seem more real to me than the fact that I made my best score in maths when I did the university entrance exam.
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God, I also keep having these dreams where I have to go back to high school and pass the math exam or all my diplomas will be taken away from me.
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Oh, I just get the sense I had a free pass, but really I ought to go back and try to get some more mental roughage in my diet.
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“God, I also keep having these dreams where I have to go back to high school and pass the math exam or all my diplomas will be taken away from me.” Oh my God! I have that EXACT dream multiple times!!! It’s AWFUL!!!
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““God, I also keep having these dreams where I have to go back to high school and pass the math exam or all my diplomas will be taken away from me.” Oh my God! I have that EXACT dream multiple times!!! It’s AWFUL!!!”
– Well, at least we know we are not alone! 🙂 The strange thing is I have a similar dream about history but I always loved history and did really well.
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You’d better take the GED exam just to be on the safe side.
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Anyway, yeah, like someone else said, “vectorial angles” and “discontinuous functions” are not things that are brought up in basic high school math (and yes, I took that twice, both in high school and as a remedial course in college when I did poorly in the entry exam in that subject. I rarely made better than a low B in math in high school; in college I did much better, and made it all the way to Calculus 1 before my brain went “no more”). This guy is basically pushing a load of bullshit to get noticed. He should be ignored.
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Just to clarify: he should be ignored by the people whose influence he’s seeking to further his own career; but his troublemaking and twisting of reality should be pointed out every time he tries it.
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I’ve noticed it, too. The only math class I’ve been in which mentioned vectors was an optional class. Discontinuous functions weren’t even mentioned until the following year, and only my calculus classes really went into detail. The most I’ve done with vectors in college has been for physics classes.
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Oh, vectors totally slaughtered me back in sixth grade.
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I only barely tolerate vectors. They seem to exist solely to frustrate me. Only using them constantly prevents me from hating them entirely.
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Vectors in sixth grade is actually very impressive by American standards. I didn’t get vectors in coursework until 12th grade.
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Now everybody is off making fun of Miss USA contestants in this video: http://www.youtube.com/watch?v=RRdAe3UAIVs&feature=related
Apparently, it does not occur to our geniuses that women who want to win the contest have to say whatever he audience wants to hear. No, it’s so much easier to ridicule the “dumb females.” Especially when they dare to look pretty. Pretending that a beautiful woman is an idiot allows to see them as less threatening.
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How could they do that? Do they have any idea how brilliant some of the contestants are, regardless of what they say during the actual competition?
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Don’t read the comments to any Youtube video. They will make you pray for the Earth-destroying comet.
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“Don’t read the comments to any Youtube video. They will make you pray for the Earth-destroying comet.”
– Yes, I’m finding that out. 😦
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As others have pointed out, algebra is useful in daily life. Also, math trains your brain and makes you smarter, it really does. I figured out how to write English papers because of math. And it is aesthetically beautiful.
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Pretending that a beautiful woman is an idiot allows to see them as less threatening.
This is precisely why I like the movie “Legally Blonde.” Any story which has a beautiful female protagonist who is also brilliantly intelligent thrills me greatly.
I also think that proof-based geometry is a wonderful way to teach careful reasoning, which leads people not to be susceptible to sloppy reasoning and sales pitches. The distinction between, say “true” and “valid” is not obvious to many people.
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This point was kind of baked into my earlier response to Thoreau, but what do you think about having “logic & basic analysis” classes. Granted I say this as a consultant whose sole justification for a high salary is my ability to do analysis on a wide array of topics, but I feel creativity to analyze any situation is so massively helpful in personal situations and is an extremely valuable asset to get a great job.
I also think students would actually be interested in learning when all of sudden they can see how it is interesting to think about how seemingly complex things/systems/business etc. work by just applying basic logic.
Brain teasers are fun, practical, and thru them you can persuade students to WANT to learn.. and inspire them to talk about the exciting things that STEM fields and skills can offer. What I would give to be 15 and know how renewable energy will change the world, or to want to be a computer science programmer or realizing how engineering could be an amazing skillset etc.
Instead.. I always got the top grades in science… was a mini-math prodigy (not trying to be an arrogant ass.. jsut trying to make the larger point), took Calc 2 senior year.. got a 5 on the AP test.. did well in math competitions, and NEVER used it a day after high school because the practicality of it had been shown to be NADA at that point in my life.
What i would give to be 15 .. i would leverage my mind so differently. Of course in my mid-20’s i could still chane.. but it would be a massive disruption to my life.
Anways, my long winded point is over, but any opinions on the practicaliy and/or desirablity of such a “logic, anysis” class and approach to teaching math and science.?
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Yes. People who don’t like math (or foreign languages) are those who have not found out that it is about logic and analysis. They think these subjects are about rote learning and oppression by the right answer but no – they are about managing abstraction and signs.
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And a lot of reasoning in the humanities requires those skills. For instance, working out how the system of patriarchy is structured requires a logical, almost spacial form of reasoning. You have to figure out what sorts of acts, events or attitudes are included within its system and which are excluded. Secondly, there is an algebraic aspect, whereby if something is added to one side it is excluded from the other side. I had a lot of fun exploring the patriarchal proposition, “men are intellect, but not emotion.” If this were so, where does emotion in human affairs come from? Patriarchy excludes emotion and makes reasoning without emotion into its definition of the active principle. At the same time, we can observe that males, like any creature, are emotional. So where does the emotion come from and where does it disappear to? Also, an entirely different question: Where does PATRIARCHY say the emotion comes from and disappears to — and what MUST it be bound to say if it is true to its own internal logic about active and passive principles?
All of my analysis has yielded some very interesting results.
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Z, it is nice to see validation that someone completely gets what I am saying 🙂 and you may have said it in quite a fewer number of words too 😉
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Z, 100% agreed. Many people never understand this. When I started high school, I was extremely bad at geometry. It took me about a year to figure out that I could apply logic to it and then it became easy.
I always found it interesting how some people are clearly good at abstract thinking and can make complex logical arguments in real life, but as soon as it comes to maths, the logic seems to evaporate. I suspect this just has one reason: Fear.
People, especially women, are often extremely afraid of mathematics, as if it would hold something powerful and dangerous for them. I find this interesting.
In the ideal case, the math education helps people to trust their own mind and their own logical thinking and thus makes people more independent thinkers. Is that what people who are afraid of maths are really afraid of? Is that the reason girls are told that they do not have the head for it? I wonder. Trusting your own brain is scary in a way. It makes you feel a little alone.
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“I always found it interesting how some people are clearly good at abstract thinking and can make complex logical arguments in real life, but as soon as it comes to maths, the logic seems to evaporate. I suspect this just has one reason: Fear.”
– Exactly.
“People, especially women, are often extremely afraid of mathematics, as if it would hold something powerful and dangerous for them. I find this interesting.”
– Again, I agree completely. My father didn’t want me to like math, so I didn’t.
“In the ideal case, the math education helps people to trust their own mind and their own logical thinking and thus makes people more independent thinkers. Is that what people who are afraid of maths are really afraid of? Is that the reason girls are told that they do not have the head for it? ”
– Not in my case, but I think you are on to something very important for most people here.
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But, when did this alleged female math phobia start? I do not remember it existing when I was in school, yet now people talk about it all the time.
I am starting to wonder whether it isn’t parallel to the discussion about how men and women were completely different and often, mutually incomprehensible, which seemed to get big in the 90s.
According to that dogma men were reasonable, “visual”, non conversational, and preferred sex without commitment … women were irrational, tactile, chatty, and had to have commitment (which is “love”) to have sex. Men wanted to solve problems, whereas women wanted to “feel listened to,” it was alleged.
After a few years of this discussion, it was announced that women feared math. Maybe it is true but I just randomly wonder, is it part of this backlash?
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//My father didn’t want me to like math, so I didn’t.
Did he like math himself?
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“Did he like math himself?”
– Hated it! Failed trig 8 times and geometry 7 times in a row in college. 🙂 Which obviously happened before I was even born.
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Z, female maths (and even more physics) phobia was a pretty common thing in my high school, but it was in the 90s, so maybe it fits with your timeline. I also don’t know where this comes from. Maybe it has to do with a general backlash and people getting more conservative and sexist again?
Clarissa, the thinking ‘my mother/father/older sister sucked at maths too’ is a really very common theme amongst the math-phobics I know. It is a wonderful example of self-fulfilling prophecy. Sometimes it nearly seems to be a source of family pride to be bad at maths. 🙂
I suspect from your love for consistency and logic you would have the ability to be very good at maths. It is very likely ‘just’ a childhood trauma. Whenever you experience something mathematical, your childhood fear comes back and logical thinking goes out the window. I am sure you could get over this with some good and empathic tutoring, if you wanted. Maybe it would be an experience. 🙂
Btw, wasn’t your mother a maths teacher? Or do I misremember this?
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” Sometimes it nearly seems to be a source of family pride to be bad at maths.”
– That’s my case, to a T.
“I suspect from your love for consistency and logic you would have the ability to be very good at maths. ”
– Thank you. 🙂 You see, I was always told that math is completely illogical. And what do you know at 7 or 8 years of age?
“Btw, wasn’t your mother a maths teacher”
– Yes, she was. So you can imagine what a tangled web of family conflicts was involved here. Sometimes, math is just math. But not in my case. 🙂
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headdesk
Among students I have tutored in math, both female and male, about 50% of cases of a seemingly math-resistant mind are people who have an emotional objection to a domain in which the answers are non-negotiable. I think this is especially true at the intersection of innumeracy and personal finance. When “we can’t afford it” is an objective, non-negotiable reality, pain can result. Often this can be constructively addressed once it’s out in the open. The other 50% of cases I haven’t figured out, but I don’t intend to give up.
Perhaps it would be wise to plan for the possibility that there may be some people who will never learn math. In that case, instead of a more pragmatic math course, maybe it would be more pragmatic to develop a portfolio of skills either to deal with the consequences of innumeracy, or to solve some of the same problems by non-mathematical means.
There may be a tendency for weaknesses in one area to be compensated (out of adaptive necessity) by strengths in others. I suspect my strength in mathematics may be a compensation for my weakness at negotiation. I can’t bargain my way out of a paper bag, so why wouldn’t I gravitate to a domain in which the power of bargaining is effectively neutralized? I can manage money practically to the point of living on air, and thank Dog for that, because going out into the wheeler-dealer market economy and getting my hands on some is the most intimidating thing in the world for me.
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@n8chz:
Really? That’s fascinating. I have definitely seen the “math-resistant mind”, but hadn’t ever formed any ideas about why some people’s minds resist math.
(I have, however, seen a lot of the opposite condition, humanities resistance, that was obviously caused by psychological discomfort with ambiguity. Some people who like math, and are good at it, find they can’t deal with a field where there is no right answer, and no right way to arrive at an answer.)
I also tend just to accept things — my mom says, “We can’t afford that,” I say, “oh, okay” and get on with my life — and not negotiate, but I had never thought that my being good at math stemmed from this. I had always felt some connection between my faculty at math and my faculty at art, as both seemed to me to be like special, extra-focused ways of seeing what was around me.
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BTW Clarissa, you know if you have some spare time, you can self-teach yourself math. Get some books; for practicing problems, try the Schaum’s series.
I think people need a good well-rounded level of education to be an intelligent citizen, which includes at least up to basic algebra training, along with appreciation of mathematics, literature, and so forth. The idea that people need only learn “practical” knowledge will result in a nation of idiots when it comes to knowing who to vote for and what policies to support, and also simpletons culturally. An educated citizenry is one of the most important checks on a power-hungry government. This isn’t to say that “practical” knowledge isn’t important. If you like literature or art, but don’t think you’ll be able to really make a career out of those, then you will need some set of other skills to be able to produce something for society, as nothing is free.
Henry Ford it is said once said that he didn’t need much in the way of education because he could pay experts for knowledge on anything he needed. And well yes, if you need to know how to set up a computer network in a building, design a turbine for a jet engine, build a bridge, etc…you call in the experts. But EVERYONE should have knowledge of history, math up to algebra I’d say, literature, how government works, and such. Also critical-thinking skills.
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I agree with much of what you are saying but your last point about critical thinking skills is so important.
If you have critical thinking skills and the ABILITY TO LEARN (which is maybe the most important skill of all… which can definitely be taught) then the rest will/would flow naturally. Sadly, these two skills are not taught, at least from a designed curriculum and focus of learning standpoint.
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“And well yes, if you need to know how to set up a computer network in a building, design a turbine for a jet engine, build a bridge, etc…you call in the experts. But EVERYONE should have knowledge of history, math up to algebra I’d say, literature, how government works, and such. Also critical-thinking skills.”
– I agree completely. Wow, Kyle and I agree, something must be in the air. 🙂 🙂
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There’s something to this, but I think that, even if you don’t, and can’t, have the same depth of knowledge as an expert in whatever field it is — let’s say computers — it helps to have enough of a grounding in the basics of that field to know bullshit when you see it. (Pardon my French.)
An example: I have a bachelor’s degree in biochemistry, and my mom has a bachelor’s in nursing, which means that she has a nodding acquaintance with human physiology, and a very tentative grasp of some aspects of biochemistry. We both frequently laugh at ads in our local newspaper for obviously bogus medications that are supposed to slow down aging, cure chronic pain conditions, make fat people skinny, etc. These ads have copy that can best be described as “biotechnobabble”: string a lot of long, fancy words having to do with cell biology together and hope the reader doesn’t notice that what you’re describing is either incoherent or impossible. (One of my favorite ads involves a pill that’s supposed to reverse “brain aging” by purging the blood vessels of accumulated sugary buildup, using antioxidants. If you’re a biology person, you’re probably either laughing or going “WTF???”, while if you’re not, you’re probably not reacting in any particular way.)
Someone who did not have the background that we have might not notice that the pill being hawked could not possibly do what it’s touted as doing, and thus might waste their money on those things.
You might say this is where critical thinking comes in, along with a general wariness of advertising, and I’d agree with you, but sometimes emotional states can bias you away from those things. Like, if you had a serious illness, you’d probably be a lot more vulnerable to medical hucksterism, and find it easier to set a generalized skepticism aside. But if you actually know something about medicine, or physiology, you’d have a better idea of how slender the thread really was, and what risks you ran trying a certain alternative treatment.
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It’s horrifying how these vile ads explore people’s fears about their health and sell them a bunch of lies.
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Math doesn’t always click early. Nor does confidence in your ability to do math come early. If we make calculus to be a big scary monster to be avoided at all costs except for those people we view as being intellectually superior how many potential innovators will we lose?
Call it Elitism but I’d rather have more technological innovators then theologians or artists.
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In fact, calculus is such a beautiful topic that Everyone ought to understand the rudiments of it. Probably not everyone needs to be able to calculate complicated integrals, but understanding what the derivative and integral are, and what can be done with them, are so central to much of modern thought that not knowing something about them is sad indeed, similar to not knowing how to eat with a fork and knife. The calculus of polynomial, logarithm, and exponential functions would be enough, with the hope that many people would be eager thereafter to learn a bit of the calculus of trigonometric functions.
I suspect that artists are more important to a culture than technological innovators, in the grand scheme of things, although I include mathematicians in the artist category.
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Yes David. I totally agree with you.
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Well I agree with you that there definitely is an art in science. However I can’t help but feel that technology has had a far greater impact on my life then art ever has. We are surrounded and so utterly depend on science and technological inventions of our predecessors.
Think how agriculture, the internet, computers, the internal combustion engine and space travel have affected our lives. Now think of what may be the next great step we take and how it will affect people’s everyday lives and by extension our culture.
I agree with you completely on the math part though.
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There is probably more calculus in the spoon than in the knife or the fork. There is a relative minimum at the bottom, and a boundary curve that is almost but not quite horizontal. It is these features that make a spoon a spoon. Perhaps something to meditate about next time I eat soup with a spoon.
I don’t know whether mathematics is an art, but it definitely is not a science. Its methods are not empirical.
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Reblogged this on OyiaBrown.
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I think people should have extensive and comprehensive math education no matter if they will have use for it or not. The reason why is this: Have you ever tried to learn, understand and be able to apply one specific, advanced mathematical topic after not having any kind of math education for a year or two? If the answer is no, then be happy, because doing so is a major PITA.
Say you are training to become an electronics engineer. That means sooner or later you will encounter funny things like the fourier transformation. You will not understand how to handle these transformations without knowing how to integrate. And you won’t understand integration without knowing how to differentiate. And for proper differentiation, you need tons of other stuff, like addition theorems for sine functions and the like.
It means just to add one more topic to your math education you will have to refresh a good portion of what you already learned a while ago! And that is really a pain, because you are essentially relearning stuff you already know.
It is much easier to just learn as much as possible while you are already at it and in the materia than to try and go back later.
Also, while I am at it, I want everybody to know that math really, really sucks -.-
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“Also, while I am at it, I want everybody to know that math really, really sucks -.-”
Simply false. Mathematics is endless fun, far moreso than sports or computer games. Unless by “sucks” you mean that it sucks up all the time you allow it to.
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” Mathematics is endless fun, far moreso than sports or computer games. Unless by “sucks” you mean that it sucks up all the time you allow it to.”
– I spent my entire life thinking that mathematics sucks and that it’s nothing but torture. But now I have come to realize that this was probably because I was told this so many times before I even started studying it that my mathematical experiences were poisoned by that idea.
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”the concept is to have the class geared around calculating basic averages, around the break-even points of small businesses, around comparing options on buying a new car (down payment, interest, high vs. low gas mileage and payback period)”
I think all these can be taught (or are already taught) BEFORE high school. Easily.
In Israel education is compulsary till 9th grade (including), while high school is grades 10-12. I suppose in US it’s the same? That’s why a school math program must concentrate on those practical skills before high school, and it can be built this way, if it isn’t already.
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In general, that style of practicality driven teaching IS NOT the norm in the US. I went to a public school, but one that was generally considered to be in the top 5%-10% of public schools.. and our education was much more boring and rote memorization with token practical examples. In all honesty, I think one reason is that most teachers have little practical “real job/world experience” outside teaching. I don’t mean this as a criticism. Really. Most go to school at 18, learn teaching pedagogy for 4 years.. then start to teach. I would think if someone worked as a scientist in industyr, or as a businessman, or marketer or any job where “theory” is not emphasized and critical thinking skills are needed, teachers would teach differntly.
Again, not implying teachers don’t ahve critical thinking skills, but rather they don’t have enough perspective on “how the jobs/business world” MOST people will one day be entering works. This theory def. held true with my professors in college, I wonder of additional thoughts on this perspective for teachers in k-12! I think I may be on to something here 🙂 I normally have thought about a situation from most angles.. but this practicality one I have really not heard many people talk about and it makes a lot of sense!
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In Israel there is a mandated, government-approved math curriculum. Ministry of education constantly creates new math programs (my mother, a math teacher, thinks it’s since they’ve to justify their salary). A teacher gets a state curriculum, a shool gets a choice between several schoolbooks. That’s it. Imo, that, and not teachers experience or lack of it outside schools, explains the way math is taught, whether in Israel or in US.
Having state standards is a must. And they can easily be improved to be more practical.
//they don’t have enough perspective on “how the jobs/business world”
Most people have to take loans to buy a flat/ education/ etc., manage their salaries, choose which car to buy, but teachers do that too! So, I guess, when you talk of “jobs/business world”, you talk of highly paid fields, like hi-tech, accounting, etc. Many (most?) people don’t work in them.
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@Matt, that’s part of the conservative trend … school board and Federal government decisions (cf. NCLB, now Race to the Top) to make things more rote and so on. They actually seem to think *this* is more practical … if you don’t just memorize answers, you are being too theoretical and too creative and it is a “frill” and so on.
I now have students who come from high school with the belief that “true learning” is mechanical memorization of facts. They are not able to actually use these facts nor do they believe they should. This change is very noticeable, and dates from the beginning of NCLB.
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Z is absolutely right. Students expect to be given the right answers that they can memorize and reproduce. They don’t even realize that any other procedure is possible.
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I’m suspicious when pseudo-intellectual elite opines on what I should learn. I love algebra, so I learn algebra, and I love even more algebra now!
David Gendron (B. Sc. Mathematics, M. Sc, Statistics)
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Also, why this fucktard didn’t say anything about the creationism fraud and the religious brainwashing at school?
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“Also, why this fucktard didn’t say anything about the creationism fraud and the religious brainwashing at school?”
– I wouldn’t be surprised if he supported it. 😦
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I have a soft spot for statisticians, as we all know. 🙂
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You know, if some day, you have unattended problem, I’ll be there 😉
Nah, just kidding, no false rumors! 😉
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Fair enough for this fucktard, I don’t think that abstract mathematics and algebras are for everyone, but it’s so great for those embracing these topics!
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“Z is absolutely right. Students expect to be given the right answers that they can memorize and reproduce. They don’t even realize that any other procedure is possible.”
And that’s a topic where mathematics is really interesting, because in mathematics, memorizing is not very important.
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A better read on how we need to change the attitudes surrounding mathematics can be found in A Mathematicians Lament by Paul Lockhart (you can read the essay on-line here – http://www.maa.org/devlin/LockhartsLament.pdf) He does a good job of lamenting the current attitude in schools and by students and how to make it better.
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There are a couple of thoughts I had in response to this article that I don’t think have been already said.
Firstly, not everyone has a right to a college degree. If many students end up turning away from higher education because they can’t pass – not even do well, but pass – an algebra course, then maybe these students would be better served getting apprenticeships or going to a technical school. I understand our system now kind of dictates and encourages everyone regardless of their goals to go to college, but that’s just silly, and should be changed rather than changing the standards so that it is easier to get a college degree.
Secondly, other countries have much, much higher standards for high school math *and* higher graduation rates. Erego, requiring high schoolers to take math courses isn’t the sole reason why american students drop out in such high rates.
To remedy this, I think the whole way math is taught should be overhauled. I consider myself a very, very bright student and I’ve always been eager to learn anything. But somewhere in middle school, I became discouraged with math for an unknown reason I had been pondering for years.
But, my interest in computers has reintroduced me to math, and my affinity for math has slowly grown over my undergraduate career. The college professors are much better at emphasizing the “wow, look what we just did/proved with numbers, isn’t that cool!” aspect of math than my high school teachers were. In high school it was just “here is a technique, learn how to do it – you will be tested on it.” But in College the professors really make it clear that numbers behave in shocking and intriguing ways, and math is studying those behaviors. So, if math were taught more like that in high school and middle school, and even elementary school, I feel students would be as enthusiastic about it as about biology, english, and history.
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Wow, this is such an incredible discussion, thanks, Clarissa. I also apologize, because I just read the whole comments thread and have been taking down things I wanted to say. As a scientist and “mathematically minded person” the whole things pissed me off quite a bit. grrr. Anyway, my thoughts: (Apologies for the length)
Math is taught as a “hard thing” – its mental… I’ve tutored many people at all ages (especially girls) who are failing math, and its not that they don’t get it, or they’re stupid – its that they *think* they don’t get it and are stupid because math “isn’t for girls”, or “isn’t for them” – they’ve got a mental block that has been built up. And when they get a concept, they won’t even accept that they understand it. It’s really sad. But I’ve had many students I’ve worked with decide that they actually like and are good at math, so I really think its an institutional thing. This kind of mentality, that you shouldn’t even bother teaching math, is just another way of saying “you aren’t smart enough to make it’. Yes, I agree that practical applications of math education are necessary. But if people don’t have to take algebra because they’re bad at math, then by that logic, I shouldn’t have had to take a foreign language or literature classes, because I’m bad at writing and speaking. And Pen touched on this – its like saying “if you fail your first language class, you’ll never make it in a language.” Well, guess what? I was the only student my high school French teacher EVER told to “go buy a copy of the book in English, so you can compare them, and read them both” because I was failing so badly. And now? I speak nearly fluent French. (According to French people – and they have high standards! I think my French is not quite there yet, but still… same principle)
Also, as a scientist, I see a lot of issues with scientists communicating things to the rest of the world – and a lot of the “skeptics” out there have no grasp of the basic mathematics that go into scientific conclusions… this is a major problem, because then they say that the scientists are full of s**t, or that their conclusions make no sense. Because they can’t understand the idea of a trendline, or an exponential function versus logarithmic function. Or ya know, basic logic. And again, it was touched on by some commenters already, but the thing that math teaches most is logic. And the thing that is lacking perhaps the most in the US? Yep, you guessed it… LOGIC. Sure, you don’t have to remember how to decompase a polynomal, or solve a quadratic equation, but the logical thought process is something that one would hope stays with you forever. Less math = less logical people = things like concluding that male politicians should have the sole right to decide what a woman many states away does with her body and when. And really, that’s just utterly terrifying.
That being said, I feel like the US in particular, does a terrible job preparing kids for “adulthood” now – I wish I’d had a class on “how to pay your taxes”, “how to get and deal with a car loan or house mortgage”, and other such things. I am a mathematically-minded person (I prime-factorize the time (eg: 19:45 = 5*389) when I’m bored, and was definitely a math-genius as a kid), but even so, those things make me very confused. Or better “how to manage credit cards and balance your checking account”. Too many people in the US don’t have a *clue* how these numbers work, and just keep piling on debt. And they just ignore it instead of working to try and understand.
Anyway, In defense of Math… it’s super important to have a basic understanding of how the world works. Without it, we are simply automotons. Even if math is hard, or literature, or history, or languages are hard, they should be learned. Or at least attempted. Perhaps not exactly as we do it now, but still, the idea that math is so unnecessary just confuses me beyond belief. *sigh*
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“Anyway, In defense of Math… it’s super important to have a basic understanding of how the world works. Without it, we are simply automotons. Even if math is hard, or literature, or history, or languages are hard, they should be learned. Or at least attempted. Perhaps not exactly as we do it now, but still, the idea that math is so unnecessary just confuses me beyond belief.”
– This, I believe, is the perfect conclusion to an important discussion. I find it quite frightening that all these voices about not teaching this or that or not teaching anything at all because education is useless are becoming so loud.
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