As one who reaches conclusions intuitively, I’ve taken a lot of grief from some of you who are more the mathematical-proof types.
So, I appreciated this piece in the WSJ over the weekend, headlined “Great Scientist ≠ Good at Math.” The thrust was that it’s a shame that so many people turn away from a career in the sciences because they aren’t good at math. An excerpt:
Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.
Everyone sometimes daydreams like a scientist. Ramped up and disciplined, fantasies are the fountainhead of all creative thinking. Newton dreamed, Darwin dreamed, you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper, and they take on life as real examples are sought and found.
Yeah, baby! That’s what this INTP is talking about: Intuitive reasoning!
Not that I’m bad at math or lack skills in that regard. I was always in the 99th percentile on standardized tests of mathematical aptitude in school. I’ve just never been overly fond of it.
I lack the patience for the methodology. Here’s what I mean: In geometry class, I’d be asked to prove that triangle A was congruent to triangle B, or some such (I’ve forgotten most of the basic concepts now, which shows what you can accomplish when you really apply your mind to forgetting). I would say, well, it is congruent, and that’s obvious. I didn’t mean that it looked congruent. I meant that I knew all the theorems and such, and in glancing at the triangles, I could tell that all the tests were met. Because I perceived it holistically. Having to go through all the infant-school steps, one at a time, made me want to bang my head against a wall. I hated it. And as I went on, I didn’t like algebra II, or analytical geometry, or calculus, either. I just took all those courses because I thought that’s what you were supposed to do in school. (And yeah, I suppose that proofs have more relevance when you get beyond such simple stuff as congruent triangles, but I didn’t have the patience to pursue it that far.)
I had a calculus professor in college who was very enthusiastic about what the Brits are pleased to call “maths.” He drove me crazy. One day he came in all excited because someone had taken pi out to a million decimal places. I raised my hand and asked, “Why?” He said because it showed the numbers never repeat, even that far out. I asked what possible purpose knowing that could serve. He said it taught us things about the principles governing randomness. I said randomness had no principles governing it, because it was random. I basically was saying anything I could to damp his enthusiasm, because it irritated me. I was unsuccessful; he was a natural enthusiast.
I wasn’t the kind of kid you wanted in your class.
Of course, I would have run into the same problem in science as in math, since there’s all that mind-numbing step-by-step methodology. (The piece in the WSJ later says, “Eureka moments require hard work. And focus.” And not the fun kind of work, either.)
But I was pleased to see the plug for intuition.
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Actually, having praised that piece, I have to take a moment to criticize it. There were internal inconsistencies in it, or at least points that could have used some more development.
For instance, take these two sentences:
The first sentence seems to say something completely different from what the second one says, possibly because of the personal filter I put on it.
The first sentence describes the way I get good ideas. The ones that resonate the most are “in the hallway struggling to explain something to a friend, or eating lunch alone.” To me, that’s very different from “hard work” and “focus.” Especially focus, which is a word used to criticize those of us who leap quickly from topic to topic.
Help me out here. Doesn’t the first sentence sound more like what happens when you set the work aside, and stop focusing on it for a moment, and let your brain run free? That’s what it sounds like to me…
It does seem contradictory.
Frankly, intuition is a fine way to start but without hard facts that intuition is worthless, perhaps worse than worthless. That is how we get into so much trouble as a nation, relying too much on “intuition” and “common sense”. Sometimes the world defies both. Take global warming. Intuitively it would seem that a cold March was evidence contradicting the theory. But it really was just the opposite. The long, cold March weather reflected a weather pattern whereby the northerly air currents persisted for way longer than normal, an effect of global warming resulting in climate change.
The WSJ article is one that the sage of the NPR program Car Talk, Tom Magliozzi, would completely agree with. Tom, who has a degree from MIT and worked many years as an engineer, did a “rant” on the show over a decade ago about the uselessness of most math courses. He ended up the diatribe with the following:
“So here’s my conclusion. The purpose of learning math, which most of us will never use, is only to prepare us for further math courses . . . which we will use even less frequently than never.
The answer I would probably get from math instructors is this: “You may never need it, but it teaches you to think. You mean to tell me that there aren’t enough useful subjects that could be used to teach me to think?”
A link to the entire rant is on the Car Talk website.
Click and Clack!
Somewhat farther afield, did you ever see “Peggy Sue Got Married,” in which a middle-aged woman finds herself transported back in time to high school? She gets to say to her algebra teacher, “Well, Mr Snelgrove, I happen to know that in the future I will not have the slightest use for algebra, and I speak from experience.“
Have you noticed anyone calling into Car Talk has no business opening the hood of a vehicle? Nearly all are ultra-liberal New Englanders who’s only mechanical ability is to make vehicle related noises and typically can’t tell if it’s coming from the front of the vehicle or the rear. Nearly as bad as the people on This Old House who build $600,000 additions onto their houses and think they’re helping by putting on a blue dress shirt and usually getting in the way.
Nope, haven’t noticed that…
That’s because you’re just like the ones that call in. To you it’s normal.
Brad, there is a significant difference between being an INTP and being ADD or simply intellectually lazy. My husband and most all of his theoretical computer science colleagues are INTPs, and while they may intuit potential theorems, they do a lot of hard work proving them, or not, deductively.
The component of the MBPI that says one prefers to gather information intuitively is the N. I am also an N, but I find that checking my intuitions leads to better results.
You’re describing three very different things:
1. Being INTP
2. Being ADD
3. Being intellectually lazy.
… And I didn’t mean to say they were the same thing.
I have been the first two things, but not the third. It’s not enough to leap to the conclusions. You have to persuade other people that you’ve reached a legitimate conclusion. I’ve done fairly well at that over the years. It takes a lot of hard work.
Hmm. Not so sure I’d agree with that. You can have all the intuition in the world but that means zero to others. It’s about facts. Take you big coup with John Edwards. You had him pegged correctly but your arguments were extremely weak because they were based on your own personal observations and nothing else. And no one was convinced. Once the poopy hit the fan the facts lined up with your intuition and you came across as a hero. As for your fawning over John McCain, not so much. Your intution failed you miserably on that.
To expand on this thought. Whatever you might have felt about John McCain his credibility was called in to question, perhaps destroyed alltogether with his choice for a running mate. Anyone who based their opinion of McCain on intuitive “feel” alone could always find some reasoning, no matter how strained, to still believe McCain was a good choice for president. But a person who relies on facts and information quickly found themselves in an untenable situation that left him with only 2 choices. If Obama was not too unreasonable philosophically then support him. If he was just too unreasonable on the issues then a good choice would have been to simply not vote at all. But a vote for McCain was not an option to the deductive thinker.
Bud, this is completely untrue:
You had him pegged correctly but your arguments were extremely weak because they were based on your own personal observations and nothing else. And no one was convinced.
Basically, the column caused a sensation, and divided people very sharply, and probably evenly, between people who said “You’ve nailed it! You’ve described something I had struggled to put into words…), and people who reflexively dismissed what I was saying.
Nothing that happened subsequently “proved” what I was saying. It wasn’t directly related to what I was saying. Subsequent disclosures showed him to be a phony, but a different kind from what I was describing.
And on the McCain-Palin thing: You have that backwards. The Palin choice caused you and others to leap to an intuitive conclusion about McCain that dismissed every good thing you’d ever known about him. Or, perhaps, gave you an excuse to dismiss all the good.
For me, that was just one fact laid alongside many, many others. And it lacked sufficient weight to counterbalance all the reasons to support him.
If you read this column, published just before the election, you’ll see how I was basing my judgments on actual things being said and done in the campaign, not on some “feeling.”
That’s another misconception. Intuitive reasoning is as fact-based as the deductive kind. It’s just not step-by-step, like deduction. You take in information, and you keep taking it in, and suddenly you see the whole pattern. This is seldom from a single instance (such as the Palin nomination), but more of what a larger body of evidence indicates.
I read the column Brad and it seemed all intuitive, hence worthless to ME. The Palin choice may have only been one of many, many, many facts but it was decisive in a crushing, fact-based way that collectively the others just were not. I can’t imagine any fact-based decision process that could be so completely dismissive of that HUGE event.
How was the column intuitive? It was argument on the basis of point after point, fact after fact, far more like a mathematical proof. Here are the last few grafs…
Kathryn,
And then there are those INTJ’s; total trouble…
Naw, they actually write the papers and send them off!
But…deductive logic is dependent on inductive logic (e.g. repetitive observation/testing) for it’s basic building tools. Otherwise it is very susceptible to GIGO.
Deduction is dependent on induction. And…
I don’t know what this means, but I am INFP and I loved doing proofs in Geometry. Algebra was tedious and Calculus became too abstract and was confusing, but I loved Geometry. Vector calculus was alright because it was like 4 dimensional Geometry which made it not abstract – it had shapes I could relate to. But I really did like doing Proofs, in Mr. Melonas’ class in 10th grade.
I would think that working out the steps to a proof would be similar to the satisfaction one gets from getting something written effectively to make a point. It is to me, anyway.
I totally agree with Scout; I found Geometry to be the exception to my general disinterest with math (which is pretty funny as most of my career has centered on financial analysis). But I don’t think I approach numbers the same way as most people. I perceive trends and spot inconsistencies, but then can’t always explain why these caught my eye. Geometry was sort of a closed system, and it was fun nailing the proofs – like target shooting. Satisfyingly complete.
I too liked Geometry best. But all math had a certain appeal to me because it was a lot like solving puzzles. Not that I was great at math but it was fun. Unlike English literature which was really dreary and completly useless to me.
Oh my God!!! bud and I have something in common.
And here, Bud and I are opposites. I was glad I could solve those “puzzles,” and felt bad for the people who struggled with them. But I didn’t think of it as fun. Oh, maybe I did in arithmetic in elementary school, as the basic relationships between numbers were revealed to me. But not so much later; it just felt like drudgery. Actually, I think the drudgery started with having to do a page of multiplication and/or division with three- and four-digit numbers for homework. That was just tedious, pointless make-work, it felt like to me. After I’d done one or two, I had the point and wanted to move on.
Math never lit up my brain the way literature, and history, and political science did.
So it was that after that one calculus class as a freshman, I never took another math course in college — I tested out (or something; I forget how it worked now). I did the same with the foreign language requirement, being (back then) fluent in Spanish. One test and bingo, there were two years of language classes I didn’t have to take.
I used all the extra room in my schedule for history and political science electives, and an occasional upper-division English class on American or British lit. I took so many history classes that I realized to my surprise when I was about a semester from graduating that I only needed two more for a second major (in addition to journalism, which frankly is not very interesting as an academic subject, not compared to history). So I took those two additional history courses, which turned out to be two of my favorites (U.S. Social and Intellectual History, before and after 1865).
But it made my college education sort of lopsided, I guess.
I can think of a hundred different subjects that would have been more useful to me in my life and career than the math classes I took in high school and college. I can look at a square and know it is a square. Proving that the sum of the angles is equal to 360 degrees is about as meaningful as doing a Sudoko puzzle.
Advanced math should be for people who are either good at it or interested in it. Everyone else should spend that same instructional time on topics like reading comprehension, writing effectively, communication, personal finance, civics. I’d suggest that a course in Excel is much more relevant than Algebra.
And here’s a case in which Doug and I are in (almost) complete agreement. I think there are some things useful about the simplest algebra (solving for a single variable can come in handy in life), and plane geometry — say, when you’re trying to do repairs on your house.
Then of course there are those extreme cases in which an emergency comes up in your life in which you need math. Like when the prisoners in “The Great Escape” used trigonometry to figure out the distance of the trees for their tunnel, and came up 50 feet short because they did their sums wrong. But you know, that’s not a good example. It’s not like that’s something they would have incidentally learned in high school. Those men were aviators, and at least some of them should have been well grounded in navigation, which requires trig (especially in those pre-computer days). They really had no excuse to screw up.
Actually, I may be showing my ignorance — is solving for x or y in a single-variable equation actually algebra? I don’t know.
But that’s something I use all the time, on the very simplest level. Like sizing pictures on my blog. I have a picture that’s 768 px by 1,024 px, and I want to reduce it to a width of 450 px, and need to know what height to enter into the WordPress form. So, in my head, I run a very simple equation and use the calculator for the multiplication and division.
Professor Fenner says that is algebra.
Middle school algebra at best…
Easy, I don’t think you have the academic credentials to argue with the likes of a PhD…. isn’t that “Piled high and Deep).
Here’s a place where Brad and I have a bit of common ground. I enjoy history, civics and politicial science but don’t see much point in taking classes on those things. Can’t you pretty much learn the order of presidential succession on your own? Or what state the battle of Gettysburg took place in? I only took a couple of history class but I doubt many people know more about WW II than I do. And it’s useful knowledge too. The more you know about the horrors and uselessness of war the more clear it is that it should be avoided. Not sure why that’s so hard for many of our presidents to understand.
As for Doug’s point about Excel, that is a useful skill to know, but it’s in the same category as algebra. Once you master the basics the in-depth stuff is probably only useful to someone with a serious need for it.
But seriously is there anything in this world more utterly boring, useless and offputting than a Shakespeare play? Gadzooks that was the very worst time I spent in school.
I can see you coming away from WWII mindful of the “horrors” of war. But the “uselessness?” You should have gotten the opposite of that — that some wars, however horrible, just have to be fought…
No war ever HAS to be fought. Let’s go through the list:
Revolution – Was being a part of the British Empire really so bad?
War of 1812 – Seriously? My choice for stupidest war ever fought by the USA. The major grievances of the Americans were already resolved. This was mostly about invading Canada
Mexican War – This was nothing but a land grab. Imperialism at it’s worst.
Civil War – The South ended up losing slavery anyway. The North lost hundreds of thousands of young soldiers. Both should have simply allowed slavery to end on it’s own accord. Probably would have occurred by about 1900.
Spanish American War – The Spanish didn’t blow up the Maine.
WW I – Over 100,000 Americans died defending British Imperialism.
WW II – Really just an extension of WW I. Had we stayed out of WW I there would have been no WW II.
Korea – Still unresolved. Had we allowed them to settle this on their own we’d be much better off today.
Vietnam – Again, really? We needed to fight this? Seriously? Another war that an American president lied us into. Too bad the lessons didn’t stick.
Panama and Granada – I guess every president has to have a war to call their own.
First Iraq War – It was all about oil.
Afghanistan – Perhaps necessary to get Bin-Laden but this should have ended many years ago.
Second Iraq – Still about oil plus settling of old scores by Bush. Perhaps the worst choice for a war ever, maybe worse than Vietnam. This should teach us once and for all NEVER to trust what a president says about the threat posed by a small, third world country.
The best classes to take are those taught by the best teachers. The subject matters less than the the person.
As Doug said, it is all about critical reasoning, persuasive communication, and historical understanding. I would add that motivation to embrace challenges and experience with rising above experienced failure are also cornerstones of a solid education. We value these traights on the athletic field, but not nearly enough in the classroom. That’s not helpful when life comes a roaring…
Study after study supports Mark on this. The most important variable in a classroom is the teacher.
I was a lousy student, but a great learner. I have never been in a class or training session where I didn’t come away with some new-found knowledge or skill I have found useful or enjoyable. Whether Shakespeare, history, science, math, or whatever, there’s always something new to discover. I hated homework, because, as Brad said, it seemed pointless. My grades weren’t so good, and grades of themselves were never a motivator. There’s a push now in education to design work for students that has authenticity, not just something for the teacher to score. Authenticity engages students, and engagement produces learning.
Requiring students to successfully pass courses like calculus serves a purpose beyond the learning of formula or computation of parabolas (was that calc?). Often we don’t know what we like, or what we might be good at until we’ve tried it. Middle and high school students need the widest variety of experiences we can offer them, just so they know what their possibilities and potentialities are.
Full disclosure: I’ve been teaching 23 years. I’m biased.
Norm,
Thanks for striving to be a good teacher! It’s a hugely important role and responsibility.
I hardly ever go back to school reunions; but the ones most missing when I do are the teachers – it would be great to say thank you from the perspective of life’s distance.
Yeah. I want to thank Mrs. Bourguet and apologize to Mr. Hall. And shock both of them.
Norm
How many math classes does it take to determine what a students likes or is good at? Algebra I, Algebra II, Geometry, Trigonometry, Pre-Calc, Calc I, Calc II, Statistics?? Those are the eight classes I took from high school on. In hindsight, I could have stopped after Algebra I without impacting my career. There are so many other topics I wish I had spent the same amount of time studying…
I can’t prescribe, but I agree that not all students need all those courses. My first degree was BA Humanities. I certainly didn’t need Calc for that. But I learned it (poorly and temporarily), and I’m glad I did. I later had to take a Stats class. Pretty much useless in advancing my career except as a degree requirement, but it was eye-opening. As far as needs, algebra and geometry were probably enough.
Would I have preferred other classes that were more appropriate to my goals? Absolutely. But I don’t regret the classes I took or missed, and I don’t let the fact that I am no longer formally enrolled in a program stop me from continuing to learn. The things I missed in school, I seek out on my own. I’ve learned more history on my own than I ever did in school, and I’ve learned more about politics on Brad’s blog than I ever was taught in school.
I’m learning to brew beer. I wish I had a stronger foundation in chemistry so I could better understand what I’m learning now. I should take back what I said earlier about never having a course I didn’t learn anything in–I failed Chemistry in high school. Twice. [Later taught 6th grade Science for 8 years…the irony!]
With all the data we are able to collect about people now, we should be able to build a more customized and individualized educational program for every student. Such a program would spend less time trying to correct a student’s weaknesses, and instead work to develop his strengths. And if math is not his forte, invest that time elsewhere. If Netflix can guess what kind of documentaries I might like, surely we can design algorithms that would guide a student’s lessons in a similar manner.
What if we used that data instead to figure out how to use the student’s strengths to improve his weaknesses – i.e. what approach would work best for that student. I think we still need to expose students even if it is not their strength.
I have found that it is a lot easier to get data than it is to analyze it appropriately and use it effectively. So even though, yes, we have a great deal of data, there still is a lot of work to do. It is a worthy ideal but I feel we have a long way to go to get to a place where systemically we know how to use data effectively to the end of individualizing education plans. To get things individualized to this degree, you’d either need more manpower or better training in this sort of differentiated teaching and data analysis or both. Computer analysis and teaching has a place but only goes so far in my opinion. Real gains happen as a result of the teacher-student relationship which I think is something that’s been said here a few times already in this thread.
But isn’t one of the problems we have with keeping kids in school that they fail courses they probably shouldn’t be taking in the first place? I can see where a lot of dropouts would say “Why am I doing this?” and instead of trying to force them to retain enough knowledge of geometry to get a C or D, why not just say “hey, it’s not for you… but maybe you’d rather learn about communication skills or just learn to read better?” Which approach would keep kids engaged in learning versus engaged in trying to meet a mandated curriculum with little value?
I think parabolas might have been trigonometry. They have asymptotes. I always liked that word. I also liked drawing them on graph paper. Symmetry is satisfying.
I always liked synecdoche.
Ipsilateral is also good.
Parabolas are Algebra I. I believe they are described by quadratic equations.
Learning advanced math develops useful higher skills, even if you never have to compute the height of a tree using only a protractor.
Kathryn, I agree with you. Sometimes the key to gaining insight into other subjects comes in the form of learning how to solve a complex math problem. I know algebra and other forms of math boring when I was in school but later in life it finally dawned on me that the process of learning and solving a math problem was applicable to my work in IT or as the “long in the tooth” generation of computer geeks called it, data processing. My work as a systems analyst and the ability to work my way through the intricate details of the input required to develop a successful management information tool were greatly assisted by the boring days in math classes. Logic IMHO is a gift some have but it can be developed by way of a math class with a good teacher.
@Bart
Here’s a case where I disagree with you, Bart. I think my skills as a computer programmer were developed because I was doing computer programming from the time I was 14. I went to a vocational high school where we spent half of our school year focused only on programming from the second half of freshman year on. One week in the computer lab, then one week in academic courses. We had 1000 hours of training by the time we were seniors and then were allowed to go out to work every other week (shared a job with another student) instead of going to the computer shop after October of our senior year.
The math in high school was just a requirement to get diploma and qualify to go on to college (which only 5 out of 300+ seniors did).
When your avocation is also your vocation, it’s a perfect mix. That’s why the vocational schools in Massachusetts are so successful at creating productive people with useful skills. It’s too bad South Carolina is trapped in the ideas of the 60’s that vocational schools are for the bad kids. Every student in Massachusetts has a right to attend a vocational school. I stopped in at mine a couple weeks ago – their new focus across all the vocational classes is biotech. Even the plumbing students learn about it because there are niche jobs (higher pay) for people with that specialized knowledge.
I wish we’d require a rudimentary level of programming for all of the kids, starting by grade 5 or 6. My son (he’s 12) decided he wanted to learn to program over Spring break, and so I did some research and was amazed at how many great tools there are for kids to do this, and yet they haven’t used any of them in his schooling so far.
I set up Scratch and Alice for him, and he’s off and running — the tools are so good (and fun) he requires very little help from me. The transition from these tools to Java will be pretty painless I think. And after playing with these myself, I realized that kids could probably start with something like Scratch when they’re 8 or 9.
And when he went back to school after Spring break and told his friends he was learning to program, they thought that was so cool — so I think kids that age are really primed for it. And it provides real insight into how the world they live in (video games, apps, etc) works as well as some logic and thinking skills, even if they never choose to code for a living.
The great thing about programming is that you can solve the problems you want to solve versus trying to do X^2 – 5x + 7 = 43.
I wrote programs in high school to play tic-tac-toe, determine which football teams would win, simulate auto traffic patterns, and determine
which baseball player would produce the most runs if you had an entire team comprised of that one player.
@ Doug,
No problem with your response and disagreement with me. Makes for a good debate point. However, based on your educational background and the fact that you were programming at the age of 14, you were given the advantage of learning from practical experience whereas I was not. My skills as a programmer and system analyst were enhanced by on the job training and attending IBM educational classes. I was able to learn at a quicker pace than many of my co-workers and classmates because of the process of solving equations and formulas I studied and learned in math classes. Several of my classmates struggled with learning how to write a program because of a lack of rudimentary skills in algebra and other higher math disciplines.
While you had the good fortune to attend what apparently was a very good vocational school, during my educational process, we did not have the same opportunities. And as you pointed out, most of the vocational schools in the South were not geared to development of computer skills but how to lay brick and block, carpentry, and other manual skills that were usually taught to problem or students who had difficulties in a regular classroom setting.
So, in essence, I agree with your comments but at the same time, I still believe in what I have experienced first person as well.
Mark makes a good point. The world really does need folks with all kinds of different knowledge. It really doesn’t all have to do with making a living. Sometimes just knowing about something in a deep and comprehensive way is valuable even if you never earn a dime from it.
It’s the APPLICATION of knowledge that is important. Being able to learn anything is just a function of intelligence combined with the desire to learn it. I learned calculus back in 1980-1983. I have never applied it since. My desire to learn it was driven solely by wanting to maintain a high GPA and meet the requirements for my degree. When the need for the GPA disappeared, so did my desire to retain the calculus knowledge.
And here’s the problem so many students encounter: GPA and grades are not motivators for more kids than you might realize, and so the desire to learn calculus (or whatever) doesn’t exist. In every group of students I’ve taught, there were always a few who were brilliant, but had no need for grades. None.
Al Todd was a student in my 7th grade ELA class back in the early 90s. He may be the most intelligent (meaning his ability to understand, learn and reason) person I have ever met, present company included. He was reading Dianetics in my class when I taught 7th grade. I asked him about why he was reading it, assuming a parent or an elder sibling had it as required reading. No. He was reading it simply because he found it interesting. I ache for how his life might have unfolded differently if we had been able to meet his educational needs, and been able to offer him a motivation greater than You’ll get an F if you don’t do this work. Boring, pointless work.
I took math all the way through 4 semesters of Calculus. And then I changed my major anyway. But I don’t regret any of it. Though Calculus was the most challenging and frustrating thing I ever did as a student. Maybe I’m weird but I feel like I do use my math on a regular basis. Even though I got lost in the details, I remember enough about the general principles of Calculus to notice potential applications of it in daily life – even though I can’t personally do it. I’m sure Doug will say, give me a specific example of such a time. So I will try – I think it is usually when I notice some sort of pattern (which is the influence of the Intuition thing) and I’ll think a scientist or a mathematician could probably graph this and write an equation for this curve using calculus and then use it to predict what will happen next, or I’ll be listening to some science show or report on the radio and know they figured something out using calculus, even if they don’t explain that in the story. I think it happens when analyzing data from my students, or when listening to news stories on the radio or science shows on tv mostly. Even though I can’t do it, I like understanding the world that way. But I do use algebra and geometry in my regular everyday life a lot. Just yesterday in Lowes, I calculated what length of zip tie I needed to buy to be able to go around a 3/4 inch PVC pipe.
But Doug isn’t knowledge simply for the sake of knowledge a good thing regardless of how much you use it later in life? Perhaps I was a bit too dismissive of Shakespeare. While I would never, ever take a class devoted to Shakespeare I can see where others may see value in it and perhaps grudgingly it would have been better had I not been so miserable in high school English class but rather embraced the experience in a positve way. Measuring the value of education is complicated but it seems to me that to equate it entirely to earnings potential misses the point. Having folks who know math, philosophy, biology, physics, statistics, art, music and yes, English literature is a valuable asset to a well rounded society. Knowing Excel, personal finance and computer skills are certainly useful but that should not be the ultimate measure of a well-rounded, educated society.
Bud, I was wondering how you were going to square up your dismissal of Shakespeare with your support for knowledge for the sake of knowledge.
I did enjoy Chaucer, Donne and Beowulf far more than Shakespeare, but I would read any of his lesser plays before I ever look at Milton again.
How do I square my dismissal of Shakespeare with support for knowledge for the sake of knowledge? Easy. I flip-flopped. After thinking about I decided that in spite of my own personal distaste of Shakespeare as a 16 year old it really was something I should have been more appreciative of at the time.
Fair enough!
We’ve pretty much stopped teaching trigonometry cause the kids aren’t shooting cannons so much any more.
This is a great thread!
I took Organic Chemistry in college, as an Art History major, and was the only one in the class who was not pre-med. The course was way over my head. Halfway through, the professor called me into his office; I had just failed the midterm. He nicely explained to me no one but pre-meds took the course (I knew it was the deciding class on who the college would back for medical school), and he said that he saw that I was a declared Art History major. He suggested that dropping the course looked like the best option. I told him I knew I was being dumb, but I wanted to finish the course, regardless. He helped me a lot the second half. And I worked hard trying to keep afloat. I earned a C+ on the final – and received a D+ for the course. While I thought it would sink my grad school prospects, the reality is that the lesson of the struggle to swim against insurmountable odds is something that gives me the confidence to try stuff. I have seen failure, and while it really sucks, it doesn’t scare me. School shouldn’t be all about correcting shortcomings (strengths are the first focus), but we all need to be well rounded and battle scared to make it in the world.
But you wouldn’t go back and take three more Organic Chemistry classes, would you? (or maybe you are a masochist 🙂 ) It’s pretty easy to tell by the time you’ve taken Geometry whether you need or want to take a half dozen more math classes.
Doug, that’s interesting that you programmed a computer to play tic-tac-toe. Let’s use another example, chess. It’s now possible to program computers to beat the best chess players in the world. Does that make them better chess players? Of course not. The skills needed to be a great chess player are vastly different from the skills needed to program the computer to play chess. Is one skill more valuable than another? isn’t that subjective? Sure the programmer is likely to have more earnings potential but that doesn’t fully answer the question of which skill is more important. You can probably also program a computer to diagnose diseases, design bridges or evaluate traffic crashes. But would you want to do away with doctors, civil engineers or statisticians? Of course not. I would suggest that a wide array of skills and knowledge is what makes a nation great. Limiting the skill set to what creates stuff is just one category. That is probably what brought down communism, a much too narrow focus on concrete skills at the expense of the abstract.
I haven’t suggested limiting the skill sets in any way. I have suggested that people should learn what they want to learn and are good at. Learning is learning. Learning something that you don’t use is a waste of time.
@ Doug,
It is obvious that you approach learning in a pragmatic manner and if it is not something practical and useful, as you say, it is a waste of time – that is – for Doug. For others, myself included, sometimes learning something new is the adventure of expanding who we are as a person. That may sound trite to you but when I learn or understand the basics or principles governing a new topic, it is satisfying on a personal level.
Apparently Mark enjoys the classics in literature and seems to be well versed in them. When we were reading Chaucer in high school, I found a recording of Canterbury Tales spoken in old English:
Whan that aprill with his shoures soote
The droghte of march hath perced to the roote,
And bathed every veyne in swich licour
Of which vertu engendred is the flour;
Whan zephirus eek with his sweete breeth
Inspired hath in every holt and heeth
Tendre croppes, and the yonge sonne
Hath in the ram his halve cours yronne,
And smale foweles maken melodye,
That slepen al the nyght with open ye
(so priketh hem nature in hir corages);
Thanne longen folk to goon on pilgrimages,
And palmeres for to seken straunge strondes,
To ferne halwes, kowthe in sondry londes;
And specially from every shires ende
Of engelond to caunterbury they wende,
The hooly blisful martir for to seke,
That hem hath holpen whan that they were seeke.
Needless to say, the language was totally foreign to all of us but it gave some insight into the times of Chaucer. No one uses it today except when someone tries to revive Tales in a theater but it was something to enjoy for the time, never to be used again. Can you imagine Mark speaking to a client using Chaucer’s English?
Point – learning something new doesn’t necessarily have to equate to a pratical application – it can be for the pleasure of the experience.
Holy cow! I had to memorize that verse in high school. And as I was reading it I began to recite it it old English – as if it were just last week. Had not thought about it since college, but there it was in my brain.
I guess I did learn it, whatever that’s worth. Thanks, Bart!
Truthfully, I had a headache for a week after memorizing and reciting the same thing. I had forgotten the entire thing except for a few words but once reading it again, the headache returned! 🙂
Wow, me too. Took me back to 11th grade. I can picture my desk and how it was facing in the room when I hear those words. Most of it was still there in my brain.
But Doug how will you know what you won’t use. How do you know that your life wouldn’t be more enriched if you had had other experiences even though you may, at the time, have thought them frivolous or unnecessary. Seems like you are closing yourself off to a lot of possibilities by refusing to be open to anything that doesn’t seem relevant in the moment. That is a very specific limited view. It does not take into account that our judgement and perspective can change over time and what was not relevant can become relevant – or likewise – that our environment can change such that even if our judgement was correct at the time (it was irrelevant), the world may change such that it becomes relevant. Or even that we may simply make the wrong judgement in the moment not having enough information about the subject, since we haven’t in fact studied it yet. It may be that it is far more relevant than we realize. But following your prescription we would simply miss out on these opportunities.
Maybe I’m not making myself clear – I’m not against learning something new. I am opposed to continuing to spend time being forced to learn something that you either do not care for or do not have an aptitude for. I go back to the eight high level math classes I took. I probably got A’s in 5 or 6 of those classes so I could do the work but didn’t enjoy it. And I haven’t used those skills since.
In my vocational school, we spent six weeks in a variety of trades during our freshman year – two that we were allowed to choose based on our interests and four that were assigned randomly. I had computers and electronics by choice and welding, carpentry, commercial art, and graphic arts. I learned something in each experience. I also learned that I did not want to be a carpenter or welder. But those six weeks were useful. Contrast that to the MONTHS spent across several years on math curriculum. There is a point where the time spent on a topic reaches a point of being a waste of time. It’s my belief that that happens sometime around algebra I/geometry. And if you try to tell me that calculating the length of a tie wrap based on a diameter of a circle requires years of math, I’d say we’re teaching it incorrectly.
Yes, I’m pragmatic. It has worked for me to be pragmatic. If something else works for you, great.
Would any of you be interested in spending six months learning how to throw a curveball or understand how to draw up basketball plays to defeat a full court press? I doubt it – because it wouldn’t interest you. You might feign interest for an hour.. then you’d say “well, I think I’ve learned enough about that for now”… that’s how I feel about math.
As a statistician I have long ago forgotten the intricacies of the theory behind the various tests used to evaluate data. But I remember that the complicated mathematics that went into those tests were important in developing the methodologies needed to establish the necessary equations. Today I program a computer to perform the calculations. But because at one time I was exposed to the complex math it gives me a greater appreciation for the end result knowing that what I do is not just pulled out of thin air.
@bud
Yes, you use the math and the methodologies behind it in your job. Do you also use sines, cosines, tangents in your job? Do you ever do anything that looks like X^1/2 + 3y^2 – 16?
Do you also use sines, cosines, tangents in your job?
-Doug
Not in my current job. But when I dabbled in computer animation there were occassions when trigonometry skills were useful. Admittedly only on a limited basis.
But the analytical skills you developed are doubtless useful, no?
@Kathryn
If you are asking me that question, the answer is “No’. I don’t recall any analytical skills being developed in my math classes.
Whatever skills I have are innate and were developed through learning to program… and most of that was self-taught through practice.
How can you know what skills are innate, and what are acquired in passing?
That’s another innate skill I have… the ability to tell which skills are innate or not. 🙂
But, seriously, I was scoring well on aptitude tests by the time I was in 4th grade, particularly in those that would suggest I would do well in fields like computer programming. I knew by 8th grade what I wanted to do for a career and I did it. I know it’s bragging but I was a better programmer in 10th grade than my instructors were.
Doug’s the iNtuitive type…
Is it really such a bad thing to admit that many hours spent in our educational system yield little value to people in the long run?
I’m reading a book now called “Naked Statistics”.
http://www.amazon.com/Naked-Statistics-Stripping-Dread-Data/dp/0393071952/ref=sr_1_1?ie=UTF8&qid=1365629621&sr=8-1&keywords=naked+statistics
It pretty much covers everything a typical adult would need to know about statistics in a way that anyone with a basic understanding of math can grasp, A review from the New York Times describes it well: ““While a great measure of the book’s appeal comes from Mr. Wheelan’s fluent style—a natural comedian, he is truly the Dave Barry of the coin toss set—the rest comes from his multiple real world examples illustrating exactly why even the most reluctant mathophobe is well advised to achieve a personal understanding of the statistical underpinnings of life.” (New York Times )”
Now, it’s my guess that you could teach from this book to high school freshman over the course of one month of classes and pretty much cover everything most of them will need on the topic.
Let those math nerds dive into the minutiae and let everyone else learn how to balance a checkbook, figure out how mortgages work, learn how to invest, etc. Apply math every day with a purpose.
I would think statistics are useful in practically any profession. Then again I’m biased. And I can say that with 99% confidence.