Recently, I have come across several otherwise educated people who are innumerate to the point of not being able to calculate simple percentages. I know people who have to use preprinted tables to figure out a tip at a restaurant. I know a Lincoln scholar who is amazingly erudite in history and the liberal arts, yet he had never heard of the concept of limits(this came up when I mentioned Zeno’s paradox in a philosophy discussion.) How is it possible for someone to graduate from university in the US without at least a basic grounding in elementary mathematics? Why are intelligent people comfortable admitting they have never heard of Cantor or Euler, but they would be embarrassed to admit they had never read Shakespeare?
My query would be how many of you are comfortable using math at home and at work; what is the highest level of math in which you are proficient; why are adults so afraid of math; and how do we fix the problem?
An anecdote: I overheard my sister telling her daughter that it was okay to do poorly on a math test because “nobody in the family was good at math.” I took the child aside out of her mother’s earshot and told her that I was good at amth and with hard work she could be, too. I hate to think how many parents are sabotaging their children’s chances of success in math by similarly thoughtless comments.
I use cantor everyday at home, but then I have a ms in math. People are “afraid” of math for the same reason that they are afraid of heights, or public speaking. How to fix the problem? Take them to a high cliff, and drop them off.
John Alan Paulos suggests some solutions in his book “Innumeracy”, which I suspect you’ve read. It comes down to education – which sounds like a long-term approach, but worth it. I like his idea of a logarithmic Richter-type risk scale, or a Russel-Baker-like newspaper column, but nobody’s taken those up yet.
You might also want to read C.P. Snow’s “The Two Cultures”, in which he talks about exactly the prblem you note – people will admit to ignorance of calculus or the laws of thermodynaics who would never dream of admitting ignorance of Shakespeare. I don’t recall if Snow had any solutions, though.
“Tell Zeno I’m willing to meet him halfway.”
“Talking Barbie” doesn’t say “Math class is tough!” anymore.
Math has always been an uphill battle for me. It’s easy to criticize the mathematically illiterate when you have a knack for number crunching yourself. I’m a reasonably intelligent guy in other fields, but my brain just doesn’t seem to retain anything mathematical for very long, no matter how hard I work at it. Too bad, because I need to learn a lot of math for my major. I’m doing fine so far, but I have to push myself to the limit to get good grades in the math courses. My A in calculus is the hardest earned A of my life, and it will remain a badge of honor for the rest of my life.
If you have a natural aversion to the subject, you’re less likely to learn more about it. Maybe it has something to do with that right brain/left brain dominance thing. It seems to me that people who excel at arts, music and humanities tend not to be your mathematicians, engineers and computer scientists.
You’re right though. There’s no good excuse for an otherwise intelligent person to lack basic knowledge of mathematics.
BTW, I’m familiar with Euler, but who is Cantor?
- JB
Nothing in the last 2 million years of evolution has prepared homo sapiens to deal with math, other than simple counting along the lines of, “one, two, many…”
Basic arithmetic has only been around for maybe 5000 years, higher mathematics like algebra for maybe 300 years, stuff like calculus and trignometry for what, 100 years?
You may have to wait another 2 million years before the American public gets “math-ready” en masse.
Part of the problem with math is that most people only need to learn the very basics to get by quite well. Sure, I took calculus years ago, and I remember how to take a first derivative, but that’s about it. Never since have I needed to use it for anything, so the knowledge just leaked away. I do understand the basic concepts of limits, but the rest is fairly superfluous knowledge with regards to the business of living. I have used a little algebra and some geometry (calculations, not those Godawful proofs we spent the whole freaking year doing) but as far as higher math goes, it just isn’t relevant to me personally.
I do not advocate that people shouldn’t learn the math to begin with, but I certainly do understand the attitude of a student that looks at a calculus problem that they know is going to take them an hour to solve when they think “When the hell am I going to ever need this?”
If you’re a banker, a doctor, an engineer, a sales manager, to name a few professions, you will need calculus. Anytime you have math problems that involve change in the value oof variables in rate, speed, or time, you will need calculus.
Algebra was invented by al-Khwarizmi sometime between 800-847 CE, making it about 1200 years old. It is thought that perhaps Diophantus may have independently invented many important algebraic concepts ca. 250 CE.
You can read more about this at The Art of Algebra from al-Khwarizmi to Viète: A Study in the Natural Selection of Ideas
Calculus was invented by Newton and Liebnitz ca. 1665-1673 CE. Although Newton’s work was more general, we owe our modern calculus notation ot Liebnitz.
The introduction to the Mathematics 3010 syllabus claims “It is said of Archimedes: If only the Romans hadn’t sacked Syracuse in 212 BC, he would have invented the Calculus.”
Tangentially, here’s a page listing a variety of interesting paradoxes.
Junebeetle, here’s an article on Georg Cantor.
junebeetle,
Mathematics may not come easily for you, but at least you persevered. I am a college math instructor and I know of many students who switch majors out of fear of the amount of math they have to take. I wish more of my students were like you.
Ptahlis,
Even though I am a math instructor, I do understand the attitude of “when am I ever going to need this?” My point would be why does an engineer or a mathematician need to read Shakespeare? I have seen the reactions to those two questions and they are completely different.
Ptahlis brought up a good point. I suppose it is worthwhile to study a difficult subject just in order to stretch one’s brain. But knowledge that is not used will not be retained indefinitely.
As I understand it, all new information/knowlege is stored in short term memory. If the information is accessed/used frequently, it eventually gets into long term memory and is retained. If it is not used, it fades right out of one’s mind, having never made it into long term memory.
If you study something for a year, or several years – a branch of advanced math, a foreign language – then go for years without making any use of the knowledge, you will forget it. However, should you develop a need for the knowledge, I think that re-learning it would be at least a little bit quicker and easier then starting from scratch.
I thought Indiana Jones was a professor of archeology.
You don’t imagine a professional historian of mathematics would be able to resist this, do you? 
Actually, Feynman, various algebraic concepts have been around since Old-Babylonian times about 4000 years ago; it’s been debated whether some books of Euclid’s Elements are really an attempt to express some Babylonian algebra in terms of Greek geometry. Al-Khwarizmi’s algebra was not his own invention but was based primarily on the Indian algebraic tradition (which was active at least since about 400 CE) with some Diophantine ideas thrown in. Trigonometry, btw, goes back at least to Hipparchus of Rhodes in the second century CE (using only chords of circle arcs) and developed sines and cosines after it passed to the Indians, also in the early centuries CE, so it’s over 1500 years old any way you look at it.
Still, it’s quite true that as DDG says, all of these are just blinks of an eye on the scale of human evolution. But bear in mind that basic literacy is hardly older in human civilization than basic numeracy, and yet as goboy points out, the general public has much higher expectations for command of language than for command of math. It’s just cultural; and it is probably getting worse instead of better, considering the proliferation of mechanical devices for doing our mathematical thinking for us.
Mind you, I completely sympathize with people who just find advanced math terribly difficult—I’m actually not very good at it myself: what I have is the rare combination of low ability and high enjoyment. What I think is disturbing is the high tolerance in our culture for the idea that most people needn’t have any skill or interest in math at all.
Kimstu
Feynman (the user, not the dead physicist) wrote:
Newton’s work was more general? Bullpuckey. He only cared about taking derivatives with respect to time. (Hence, his “fluctions” notation of the dot or dots on top of a function letter – it always meant Nth derivative with respect to time, and never with respect to any other variable.) Leibnitz’s dx, dy, dz, etc. notation speaks volumes about its greater generailty.
Lots of others in this thread have dealt with how long ago various concepts were created, but I wanted to amplify on the implications of that. Speaking in evolutionary terms, nothing’s prepared humanity to record sound visually by arbitrary marks on paper, but no one would PRIDE him or herself on being illiterate, in the way that some are proud of not understanding math.
What’s striking to me is just how old math is, in terms of the age of things people can know and be VERY math-literate. If you have a GOOD high school calculus course, you get up to about the year 1700 or so, and my WAG is that only perhaps 10-15% of the adult American population at most has passed a calculus course.
I was an undergrad mathematics major, and I doubt we spent more than half a semester on things learned in the 20th century–I’m thinking of real analysis stuff like proving that there are more real numbers between 0 and 1 than there are rational numbers–things like that. Granted, I wasn’t taking newer branches like topology, but still . . .
Well, liberal arts majors would argue that the great works of art like Shakespeare, Homer, Ovid and the rest, are illustrative of the human condition, and as such, help us understand the world around us. Also, it helps you get the in-jokes that fly over other people’s heads and wins you big money on Jeopardy.
The advantages literature has over math in winning the hearts of students is that literature (not every work or every author mind you) is often entertaining, usually less demanding, and is more easily accessible. It’s also varied enough to have a little something for everyone. It can inflame passions and offer insight to one’s self and others.
Math-- and I actually enjoyed it in school myself-- doesn’t do much to spur the imagination, arouse one’s indignation, or tug at the heartstrings. It can’t offer you much insight into another place and time or the philosophy of your neighbors. It does have the appeal of being a foundation for a well paying career, and it offers the solidity of right and wrong answers.
The two different reactions come from a certain bias towards the subject matter in that literature is seen as having universal value to all, while math is seen as merely a tool. Just as a carpenter doesn’t need to have an arc welder on his truck, most professions don’t need to have differential equations in their bag of tricks.
True, but most people don’t need to do those things. The one’s that do need to perform those calculations learn how. The others do not. Math as taught in schools is primarily a skill which many see as useless to learn if it will remain unused. I am not making this argument, just illustrating it.
Personally, I am glad that I had calculus even though I can no longer make use of it simply because I have some grasp of the underlying principles. That’s not to say that “I’m never going to use this crap,” didn’t float across my brain a number of times when I was wrestling with difficult problems. Just natural frustration.
When I was doing research on academic motivation, I ran across an interesting phenomenon. Among Americans there is an idea that having to work hard at something indicates ineptitude. If you are smart, things should come easily to you–hence the term “gifted.” However, this attitude was a lot less prevalent among Asian-American students. Their family upbringing taught them that working hard was expected, no matter how “smart” you were.
Guess who does better at math?
As a music major (tuba) I always wondered why I needed to know more than how to count to four. I failed Algebra 2 twice in high school and got a D in geometry yet still scored over 600 on the math SAT. It was my third try in college math before I got a passing grade, an A. I believe that I was intelectually unprepared for the concepts until I finally got it. Some of the terminology can be overwhelming to those of us who are math-phobic. I work in sales that requires reporting that includes elements of statistics, algebra and calculus. But to me, it is just a part of my job, just like writing a letter. If I truly looked at the skill sets used I would become intimidated. However, it has become commonplace to use statistics for forecasting and algebra for underwriting. I truly believe that most people know more than they give themselves credit for. I also have picked up a lot of math from computer programming. Spreadsheets in particular have kept me sharp on some of the basic, daily skills. Application programming uses several math “rules” (if thens, iff, and compilations) that I am not sure where they should be classified. Maybe I am using Algebra, or Trig, or Calculus and don’t even know it. Time to call my high school math teacher and thank him.