Since John Wilkins has already commented on Paul Hanle’s article on the declining competitiveness of Americans in science, I’ll focus my opinion on a narrower point. I think Hanle is precisely correct when he points out that ID and creationism are shackles that handicap science education in our country.
By teaching intelligent design or other variants of creationism in science classes at public schools — or by undercutting the credibility of evolution — we are greatly diminishing our chances for future scientific breakthroughs and technological innovations, and are endangering our health, safety and economic well-being as individuals and as a nation.
As a college instructor, though, here’s my perspective. The damage is done long before they get to me. The kids who have been indoctrinated in religious mythology are invisible, as far as I’m concerned: they either don’t go to college at all, or they go purely for the job opportunities, and they’re in more vocational programs; or they go to some podunk bible college somewhere; or if they do come to a university (they aren’t stupid, after all, and can qualify), they sure as heck aren’t going to go anywhere near the sciences. I might see one or two students a year who profess belief in some form of creationism, and they either eventually learn otherwise or at least learn to do the science well in exams and essays, or they drop out. We’re a public liberal arts college; survey students in our science degree programs, and you’d think creationism was near non-existent.
That’s the good news. Creationism does not cripple science at the college level and above (which might also explain why you don’t see a lot of university scientists up in arms over it—it doesn’t affect them much.) It’s effects are indirect—those smart students with great potential who get shunted off into Jebusland Bible College are wasting their abilities, and it means that the pool of students is diminished.
(Just a thought: if all the kids who were impregnated with anti-science ideas in America had not had their brains scrambled by fundie mommy and daddy, there would have been more competition for good positions in the universities and grad schools and the professoriate, and I might not have been able to get my current job—I could have become a refrigerator repairman like my father wanted. Think about that, creationists: you are partly to blame for my ability to work my way up the academic ladder.)
Now the bad news. What is the number one problem I see in students admitted to the university? What looming issue is really going to wreck America’s success in the scientific enterprise? That’s easy.
I’m seeing a lot of smart, ambitious kids show up as biology majors who barely understand algebra. We send them off to take remedial coursework to bring them up to speed, but they’re already hurting. In order to complete a biology degree in four years, students have to take general chemistry and biology in their freshman year, and students who don’t have those basic math skills, who are taking basic algebra as freshmen, are going to take a hit in those courses, and their grades will suffer. Their second year compounds the problem, as they have to take cell and molecular biology and organic chemistry while trying to take a pre-calc course.
We do have smart students who are willing to work hard to overcome their handicap, but they pay the price: their first years of college are not happy, their grades aren’t what they should be, and if they’re planning to be doctors someday, the impact on their GPA can annihilate those hopes. I’ve taken to advising some students to hold off on all the chem/biology coursework for a while, resign themselves and their parents to a five-year degree program, and get caught up in their freshman year with nothing but math and general education requirements. If I were to give parents the most important secret for seeing your kids succeed in the sciences at college, it’s to make sure that they have taken at least pre-calculus/trigonometry by their senior year of high school. If they can get calculus under their belts, even better and they’ll have a leg up on everyone, but at least our curriculum is designed for and presumes that freshmen will be taking calculus at our university.
Seriously, if the creationists really want to cut American science off at the root, where they should focus their efforts is in smashing math programs in K-12. Come to think of it, they already know this: why else would a common theme with Intelligent Design proponents also be halting more rigorous programs, like the International Baccalaureate? We saw that in our local Minnetonka school district. The creationist problem goes deeper than just an effort to mangle science: it’s a strategy for crippling our children’s ability to think.
Scott Hatfield says
The situation as you describe it is much the same in my neck of the woods. CSU Fresno is filled with kids who can’t pass the ELM (Entry-Level Mathematics) exam and who are shunted into remedial coursework. The local school district (FUSD) which employs me struggles to prepare students for the CSU system, which is far less picky about which students it takes than, say, Stanford or any UC school. Current statistics suggest that annually 50-55 percent of our graduates who are accepted at a CSU school will require remedial coursework.
Another factor is that the majority of CSU students need to work at least part-time while going to school. So the five or even six-year plans to complete school are very common. In fact, a very common pathway is that students spend 3-4 years at our local community colleges getting an A.A. degree, transfer to CSU Fresno and need an additional 2-3 years to graduate with a bachelor’s.
One of my mentors as both a scientist and a person, Dr. Fred Schreiber, has commented that not only do students come in to the CSU system deficient in math and in writing, but that in his opinion their biggest problem is that they don’t know how to think: how to organize material, how to dissect arguments, how to support their own positions, etc.
I don’t have any simple solutions for these problems, but I believe I can do things to prepare my students for these realities. I can insist, for example, on a certain amount of math skills be demonstrated and rehearsed in my courses. I can require the students to read more than just their textbooks, and more importantly, to write original papers (we use anti-plagiarism software in my course).
Finally, by emphasizing over and over again the nature of science and the key concepts needed to apply that understanding to evolution I hope to give them some of the intellectual tool kit that will allow them to formulate and evaluate arguments, to take ‘baby steps’ toward learning to think. For example, I don’t just teach some ‘cookbook’ version of scientific method. I teach my students about falsifiability, about tautologies and other errors in reasoning, etc.
I’m not always the most popular instructor on campus, but if student surveys are any judge, many of them think that they were better prepared by being exposed to some of the above strategies than if they had been given a pass on them. I would be interested in hearing what anyone else who actually teaches would have to say would be helpful or desirable in improving high school science instruction.
You really can only play one note, can’t you?
What Minnetonka did is stupid re: the IB program. Granted. But to generalize this as a trend in ID movements is lazy and irresponsible, but when has that ever stopped you?
Finally, suggesting that IDists are contributing to poor science prep seems far less likely than the following two factors:
-Excess emphasis on literacy preparation. This issue is further exacerbated by the “teaching to the tests” phenomenom encouraged by NCLB. Sciece gets the short end of the stick
-Science (and math) takes WORK. Why would kids be interested in WORK when they have video/computer games to play?
But then, why should you focus on the likely causes when you can start beating your favorite stalking horse?
Yeah, video games. That’s the ticket.
Plus Judas Priest records.
Get with the times PZ.
I agree entirely about maths, however in the UK it is even worse. It is quite easy to go through an undergraduate degree (in Geology in my case) avoiding maths entirely – indeed lecturers often make a point of saying “don’t worry, there won’t be too much maths involved.”
Despite appreciating the significance of maths in the physical sciences, I wasn’t overly bothered by its absence for the simple reason that I’m not very good at it. Of course, inevitably, this has come back to bite me and I now spend more time in my PhD than I should be doing, training myself up to the appropriate level.
PZ Myers says
NCLB is a Republican program, pushed by the same people who peddle intelligent design. NCLB, ID, they’re all symptoms of the same narrow, uninformed mindset.
What, exactly, should we do about those darned video games, anyway?
Kevin W. Parker says
I’m shocked that students can get into college with so little math background. I was a geek, admittedly, but I had FIVE years of high school math going into college: two years of algebra, geometry, trig/logarithms/other stuff I’ve mercifully forgotten, and differential and integral calculus. And I was far from the only one.
PZ Myers says
Basic math is something we should take for granted. I have handed students a simple recipe for 1 liter of a salt solution, for instance, told them to make up 100 mL of the stuff (or worse, 200 mL), and seen them look stricken. Then I have to show them how to figure out the reduction.
That’s something to worry about.
Further to my point about maths in the UK vs. US, I did the third year of my degree at UC Santa Cruz. I took a couple of classes, in which the maths hit me like a tonne of bricks. I had done comparable courses in the UK and they were a world apart.
I think this emphasis on maths and problem solving is a definate advantage of the system in the US. However, there are some areas where we in the UK are ahead of the game, particularly where essay writing and critical thinking are concerned.
Over here, undergrads are encouraged to read the primary literature early in their first years and if they are not using by the second year then its a serious problem. At this point, lengthy discussions and disections of a particular topic are required, using journals and not textbooks. From my experience in the US, this same level of engagement with a subject did not take place.
I was lucky as an undergraduate because I got the best of both systems. However, in general a better balance needs to be struck IMO.
PZ Myers says
When I was in high school, lo these many years ago, we had a college track that explicitly laid out requirements above and beyond the minimal graduation requirements that would get you into college well prepared. I took math courses every year of high school, and foreign language, and various other essential classes that I know helped me get through college.
I don’t know if high schools now are as good about doing that. My kids all got shuttled off to take courses at the university in our PSEO program as soon as they could, to get away from the timewasting in the high schools.
Steve LaBonne says
That was already true back when I was teaching over a decade ago, at a private college that theoretically is considerably more selective than UMM. I’d say it’s something to panicabout. Even now, just think what our scientific and, even more, engineering workforces would look like without their large foreign-born contingents. How will we survive economically in the long run, now that our stupid immigration policies threaten to dry up the flow?
Steve LaBonne says
P.S. NCLB was co-sponsored by Ted Kennedy. One must distinguish between the conception (somewhat reasonable and at least on the right track) with the implementation (beyond dismal). The mistake was imagining that anything good could come out of the Boy Emperor’s court, which could turn apple pie into a deadly poison and motherhood into a social pathology.
Wow. I’d express incredulity at kids getting to college without understanding algebra, except I’ve just been tutoring a friend of mine in basic physics. She’s a bright young woman, but she simply cannot do trigonometry for the life of her. She’s picking it up well enough now, but she somehow just never learned it in high school.
It makes me grateful I went to a very good (and mostly secular, for that matter) private school growing up.
I think the math issue is relative. I’m at UW Madison right now, and I believe for a B.A. you only need two years of high school math and one elementary college math course, a B.S. requires 3+ years of high school math and at least 2 intermediate college math courses, while anything engineering, medical, or science based needs considerably more.
And Joshua, even though I got A’s in calculus, I could never keep all those relationships from trig straight either…
I was educated in the British system too long ago to imagine; the problem, as I recall, was not that the training wasn’t any good, but that it just came to an abrupt end unless you happened to be doing math “A” levels (exams at the end of senior year, usually in only three subjects). My math GREs were embarrassing, mainly because I hadn’t done any of this stuff for eight years or so, and I was completely unfamiliar with the fine old American tradition of cramming for a stupid multiple choice test. I suspect the problem with math is that the habit of dividing students into “good at math,” and “can’t do math” dies awfully hard — for some reason, in a country where almost everyone thinks they can become a world-class fiction writer with a writing course or two, there is still a crisis of confidence surrounding doing sometimes pretty elementary math. Not that we’ve got writing figured out either, expository writing that is…. The students we see are hopelessly unprepared to use writing as a way of thinking.
David Utidjian says
Yes, I see that a lot when helping students with simple physics.
How much force does a 1kg mass exert on your hand on earth? And their eyes glaze over and reach for their calculator.
I find it interesting that foreign students almost never display such innumeracy… even from countries we call “Third World”. Sadly it seems to be the norm for our home grown US students to not be able to do simple arithmetic in their heads… let alone more complicated stuff.
Aaaah, the joys of multiple choice ‘tests’, surely the most pointless things in the history of anything, anywhere. For one of my second year exams in the UK, I had an hour in which to write a critical evaluation of theories concerning the role of predation in structuring ecological communities. In roughly equivalent classes in the US, I was doing multiple choice exams.
If I had one recommendation to make for the US education system, it would be increase the intellectual rigour of your classes by removing multiple choice and short answer style tests. Replace them with examinations that actually require some understanding of a topic. Keep the problem sheets and emphasis on problem solving though.
ID proponent mom says
I agree with hoody. My three kids all took rigorous college prep classwork in high school (public). The youngest got her IB diploma. Try not to cast ID proponents as being against education please, it is simply untrue.
Rick @ shrimp and grits says
What is the number one problem I see in students admitted to the university? What looming issue is really going to wreck America’s success in the scientific enterprise? That’s easy. Math.
And that’s from students that have met the entry requirements to a university. For the rest, math’s an even greater problem.
Steve LaBonne says
ID proponents may not be “against education” in general but they are most certainly against good science education, since they want to promote religion-inspired claptrap as an “alternative” to real science. If the shoe fits…
Reed A. Cartwright says
As a mathematical biologist I couldn’t agree more. I’ve seen a lot of students that go into biology because they think it math-free. Biologists compound the problem by rarely making students do math in biology class. For a lot of biologists being educated today, the first time they encounter calculus in a biology class is grad school.
Re: multiple choice tests
They’re no better or worse than anything else really (except for the obvious fact that they don’t give you any practice writing).
It just takes work to make good questions/answers. The problem is a reliance on the test banks that come with most textbooks, which are almost uniformly dreadful.
Steve LaBonne says
Oh cripes, don’t I know it. I taught genetics. In the lab writeups we would make them do some very simple statistical tests. That always guaranteed some wailing and gnashing of teeth from the “I thought this was supposed to be biology not math” crowd.
My other pet peeve was the kids who would use calculators for simple Mendelian genetics problems and give answers in decimals rather than the obvious fractions. WTF??
I have seen this problem first hand as a tutor at local colleges in Texas. The “teaching to the test” and emphasis on the exams has produced a generation of students that think math is guessing. Witness this verbatum note a student wrote to he instructor (my friend) at the end of an algebra exam:
“Just to let you know, I don’t know many people who can perform well on a test like this in algebra. Multiple choice tests are much better, because you can check your answer and if your like me, your brain works backwards. Given the solution I can plug it into the question. I know I don’t come to class often and more than likely thats why I failed this test. However, I have been in many classes before and this is the first time I have ever had no idea on a test.”
This is typical. As a tutor in a math lab, I was told by one student that I didn’t really help anyone, all I did was “ask a lot of questions”. This attitude is more influenced by video games than I think is generally known. For what is a video game? It is a completely artificial and arbitrary world where the way you win is to find the “tricks”. This is precisely how these kids look at math, not as a truth to be learned, but as some artificial exercise to get through as fast as possible by finding the “tricks”. They don’t want to actually learn how it works, and literally look at you like you are crazy if you try to explain it to them. They simply wait for you to stop talking and retort with “so when I see this I do that right?”
NCLB was a great idea, but the implementation has been far worse than doing nothing.
Hm. Anecdote time! My step-father, who was very much a science nerd in his youth–big chemistry geek–got into college without knowing the order of operations. I believe he managed a ‘B’ in calculus through a lot of struggle. He only found out about the order of operations when he got a good calculator and found it wasn’t giving the “correct” answers.
Daniel Martin says
How does this get addressed? Can it even be addressed beyond a certain stage, or is there something fundamental to childhood development that dictates that specific math concepts must be learned by specific ages, as there appears to be with language? Do we have objective measures that mathematics isn’t being learned in US schools, and do we have those measures on a state-by-state basis? (I’m extremely wary of the “kids these days” syndrome of being ignorant of the failings of one’s own generation and hyper-aware of the failings of the current generation; I’m also aware that there are huge state-to-state differences in math and science)
I’ve seen this effect – entering college without adequate mathematics – in my youngest sister, and I honestly don’t know what went wrong. I went off to college and she was doing fine in kindergarten; when I next took a close look it was almost a decade later, and she was struggling through alg2/trig. making very basic algebra errors that I just couldn’t understand. I’ve since watched her do the “fail algebra while taking calculus” routine. My other sister and I went through the same school system as she did, yet with apparently very different outcomes. This leads me to speculate that the result (learning algebra) is determined by factors that the school doesn’t influence – either because these are factors that the school cannot influence (genetics; home environment) or because they are factors the school doesn’t know about (i.e. maybe exposure to a certain teaching method could fix things, but we don’t know it).
What’s the current accepted best practice on getting kids to understand algebra and do it without blinking?
As a molecular biologist, I’ve forgotten most of the math I ever learned. It wasn’t until recently when I had to statistically analyse a lot of data that I had to re-acquaint myself with math.
Fortunately in Canada we required at least two grade 12 maths (usually differential/integrative calculus and advanced geomety and discrete math) and at least two grade 12 sciences to gain acceptance into a university scince program. My first year undergrad mandatory requirements for biology included a full year of physics, chemistry, biology, calculus and statistics. All of which had grade 12 prerequisites.
Nevertheless, our system has a lot of choice at the high school level and so one sees many high school ‘graduates’ who are innumerate. Indeed numeracy has been the push over the last five ears in our high school system to combat this. My spouse is a teacher and she’s been involved in improving numeracy for her school board. The problem starts even earlier however. We’re finding kids coming in from gade school who can’t add/subtract fractions, and these kids are doomed from the start to underachieve in math and eventually drop out of math as soon as they can.
Daniel Martin says
Do you have evidence for this? I ask because I’ve seen it happen even with no evidence of an interest in video games. Now, I’ll heartily agree that most “educational” games suck in this respect, in that they encourage the strategy of “get the right answer by clicking randomly”. However, I don’t think that video game experience or a game-influenced mindset is sufficient to explain a broad population trend.
(Again, with the caveat that we may not be seeing such a trend at all: it may be that the same portion of the population gets algebra as did 20 or 30 or 50 years ago, but that we’re pushing a larger portion of the population into four-year colleges. I don’t have the numbers to say either way.)
One of my mother’s pet theories for this decline in practical math ability is the rise of prepared food and subsequent decline in the number of people looking at recipes and adjusting them for a different number of portions.
As a current undergrad (biology and pre-med), I have to agree that this is rampant — just last week, a fellow senior (4th-year to the non-U.S. folks) had to have a professor explain how to make up a dilution from a stock solution. I’ve also had to explain the concept of serial dilutions to another senior.
I’ve noticed in my own case that I’m far too reliant on my TI-89. Since I’m good at algebra, and the calculator lets me use variables, I can get away with not knowing basic calc, even though I’ve taken four calc courses! And I’ve taken five math courses at the high-school level and two at the college, all at swanky private schools. I also know I’m not the only one with this problem. Though I don’t really see any need to incorporate calculus into the biology classes themselves, since most of the basic concepts are not tied to an understanding of it (and both biology and pre-med at my school require two classes of calculus anyway).
Is there another solution at the college level besides requiring more math courses? A calculator-less math course? I went through an MCAT class this summer (which doesn’t allow calculators), and breaking my calculator habit was very useful.
Steve LaBonne says
If I were dictator I would ban calculators until grad school. They long ago killed off any concept of significant figures, as well as competence in basic arithmetic. The habit of punching buttons to obtain an answer they never actually had to think about has a very bad effect on students.
I’m not necessarily convinced this is a math problem for your stricken students. One of the things a freshman in a new course is up against is his confidence in his common sense, and it may well express itself here. You are counting on him making the obvious (to you) deduction that 100ml of sodium solution is created in exactly the same fashion as a litre with a linear reduction in the proportions of the reagents. I am sure you can think of cases where such a recipe is not linearly applicable, and he has no particular reason to believe that this one is.
One of the biggest problems facing any teacher is discovering what’s obvious to someone without the teacher’s depth of knowledge.
I know that the problem with writing is that students just don’t do enough of it (my 10th grader has written one, *one* essay in her English or History classes to date… they’re all doing powerpoints, and seminars and god knows what…) I really can’t speak to what works or doesn’t work in math, but could there be something comparable going on? Are students just not spending enough time practising certain skills?
Steve LaBonne says
If that’s not obvious to anybody who’s had high school chemistry, something is VERY wrong with the way they’ve been taught. And sadly, it often isn’t obvious to kids who have had COLLEGE intro chemistry. And that’s just plain scary.
IMHO your attitude, which is widespread, is a very big part of the problem. I know you’re just trying to be understanding, but if at each level instructors keep excusing the lack of learning that clearly occurred at the previous level, how will the situation ever improve?
Steve LaBonne says
(That was a reply to BMurray.)
I agree — but in that case it’s not the math problem PZ claims, it’s a chemistry problem, which is my (tangential) point. The idea that teachers need to be congnizant of what their students actually know doesn’t strike me as problematic — I’m not saying they need to re-teach K-12 in college. I’m saying this is a problem any teacher always confronts and it’s easy to be blindsided by it and at the same time dismiss it as bad prior teaching. It may be, but it also may be the case that the teacher has made assumptions that aren’t true.
In any case, you do have to confront the problem of students being confident deploying knowledge they have. They may well strongly suspect the correct solution (har!) but prefer a baffled expression as it leads to an explanation which is certain. Teaching is to some extent a social science — you can’t just declare the necessary inputs and then grind them through the teaching black box and expect results.
Why treat it (the salt solution thing) as some sort of esoteric chemistry problem when it’s the kind of everyday math you often need when buying and cooking food, for example?
Rick @ shrimp and grits says
I’m not necessarily convinced this is a math problem for your stricken students. One of the things a freshman in a new course is up against is his confidence in his common sense, and it may well express itself here.
Here’s something to try – provided you’re actually teaching students. Give the students a pre-test, testing the mathematical concepts needed to solve the kinds of problems your students will face but without using any scary “scientific” terms or language.
I teach introductory and general chemistry, where students will occasionally be asked to calculate percentages. So I ask something on a pre-test like: “Rena and Claude split six pieces of candy. Rena has two pieces of candy, and Claude has four. What percentage of the candy does Rena have?”
Now, what percentage of students do you think will miss that question?
Steve Watson says
I’m old enough to have used a slide-rule through most of high school (in fact, I used my father’s slip-stick that he had used 40 years earlier). Universities only just started allowing calculators at about the same time I entered.
Now fast forward 15 years to my time as a (belated) grad student: my Networks prof was taking up the mid-term and chiding the class for a generally poor showing (I had aced it). One comment he made was that some of the answers submitted were off by orders of magnitude — giga-packets/sec throughput over a link specified to be 100kbps, things like that. “The trouble with many of you” he scolded, “is that you believe whatever number your calculator tells you, without stopping to look at it! You should at least ask yourself if the order of magnitude looks sane. Back when we had to use slide-rules, you had to keep track of the exponent yourself, so you didn’t get this kind of error….by the way, how many of you know how to use a slide-rule?” In a class of ~40, half-a-dozen hands went up, mine among them.
Did I mention that I had aced that mid-term? ;-) (And yes, part of it was the habit of sanity-checking the magnitude, as well as giving only as much precision as the original numbers allow).
Pieter B says
I still have a couple of slipsticks around, collectors’ items one day, perhaps. K&E, Dietzgen . . . they were works of art, almost.
I can’t claim to do much beyond algebra these days without a bit of cramming, but I can still do mental arithmetic fairly handily.
Some years — make that decades — ago I was in a bookstore at closing time, and noted that my books totaled an even $20, so I calculated the tax and wrote out my check. The young woman at the till punched in all the prices, then the amount of tax from the card next to the register — announcing each like it was a surprise — and then the total. I handed her the check. She looked at it, blanched, dropped it on the counter, stepped back and shrieked “How did you do that?!”
I scored in the 99th percentile in the math part of the GRE and work in a technical field in which I use math all the time, which I think have to note to in order to say the following.
I think everyone here is spooked at the wrong problem, a problem for which you have only ancedotal evidence. What generation has not complained about the failings of the ones that come after? When has there ever been a science or math teacher who has said, “Gee, I’m really happy with the skills my new students bring to my class”?
If there is any notable, verifiable stat it’s that a large proportion of math teachers didn’t even major in math. Why is that? Because they can get jobs with better pay, working conditions, and higher status elsewhere. Fix that problem and you’ll see an uptick in math skills. It is also true that a far greater percentage of highschool students go on to college than ever before. Doesn’t it make sense that there would be a dilution in the number of them with good math ability?
But that’s already buying into PZ’s hypothesis that it is a lack of math skills which is responsible for, as he puts it: the “looming issue is really going to wreck America’s success in the scientific enterprise.” What evidence is there for this impending wreck? Last I knew scientific enterprise was doing well all over the world including right here in the USA.
Five years ago when I was hiring a technical team in Silicon Valley I could not find qualified, homegrown American candidates for what were very high paying jobs with good benefits and easily hired a number of talented immigrants — people who were the cream of the crop in their own countries. Given that China and India both have a billion-plus people and a much lower standard of living than the USA I don’t find it at all surprising that many those with special skills in the countries look for jobs here.
Now that other countries are providing more opportunties for their more gifted citizens, more of them are choosing to stay home which means we can not continue to drain the brains from the rest of the world. What’s wrong with that? You are not going make people natively more capable by pressing them into training for fields for which they do not have the talent or interest. And the USA has no inalienable right to be the world center of high tech and scientific work and more than we have the right to suck the oil out of the rest of the world to fuel our SUV’s and absurd lifestyles.
Pierce R. Butler says
(Sticking my neck out as a non-parent & non-teacher) –
How ’bout modernizing the school curriculum to require a year or more of basic computer programming? Few 21st-century students would claim to find this irrelevant, there are beginners’ languages which could make the process relatively painless, and simple exercises such as re-creating “Pong” and the like would hold the interest of many non-nerds while involving all sorts of mathematical & logical concepts. Even for those who don’t follow a scientific career, this kind of background knowledge is likely to come in handy at multiple points.
Rick @ shrimp and grits says
How ’bout modernizing the school curriculum to require a year or more of basic computer programming?
Schools used to do this sort of thing in the eighties, when you actually had to do a little “programming” in order to use a home computer such as a Vic-20 or C=64. These days, programming seems to have been replaced by tutorials on Word, Excel, and Powerpoint.
I just graduated with a degree in mathematics. When it comes up while I’m talking to someone, the conversation almost always turns to mathematics education.
The problem? A lack of repetition.
I don’t have to think about how to take a derivative or solve a system of linear equations. It’s not because I have some special math ability that other people lack. I’ve met some truly gifted mathematicians, and I can tell you that I’m not one of them. The reason that I can do those things is because I’ve done them over and over and over again. Kids need to do pages of arithmetic and algebra problems. They need to keep doing them until they can get them all right.
Arithmetic and basic algebra are mechanical operations. There’s a set of rules that can be applied the same way to any problem that will give the correct answer.
It’s the same way you learn to hit a baseball. It might take a long time, and it’s not a lot fun, but anyone can do it, and anyone who wants to succeed in the sciences needs to. The biological sciences are only going to get more quantitative as time goes on, and physics and chemistry are already quite math-intensive.
The Christensen Gang of Four says
Wht ld f crp. Hr n Kns, crtnsm s nt tght, D s nt tght…nd nvr wll b… bt thnks t th prpgndzrs vr t Knss Ctzns fr Scnc vryn thnks D hs tkn vr.
Th flr f th scntsts s thr wn. Wht thy hv bn cmmntctng t th pblc s thr cntmpt fr th pblc, nt scnc.
Thnks fr nthng, PZ!
Peter Barber (a.k.a. Square-Root Pete) says
I’ve just woken up to the near-certainty that most of my contemporaries at a grammar school in the UK never studied calculus. I’d always assumed that since everyone has to do a GCSE in maths, they would have at least have been shown some examples of simple differentiation.
I always enjoyed mathematics, but for me, it really took off when I started learning calculus. As you learn how its rules are derived, it dawns on you that calculus renders the world explicable in a fundamental way. It can be inspirational if taught properly. Sadly many of my schoolfriends missed out on this and so are left with the impression that maths is dull, and in any case unnecessary – surely that’s what stats packages are for?
PS. I mostly agree with Steve LaBonne on calculators. If they were banned in school, new undergrads would be sufficiently numerate to be trusted with them. There was a ban until sixth-form at my school, and my mental arithmetic is much better as a result. Long division, anyone? ]:-)>
Xerxes… thanks, that answered my question. It’s funny how repetition is emphasized in music, or sports, but dismissed as “boring” and therefore unacceptable in other educational domains. I’m amused that the determined pursuit of excellence in school sports involves demands (for repetitive practice, full-stretch effort, punctuality) that are otherwise rare in the curriculum. I’m not arguing that the sports model needs to be imported into the classroom (the opposite in fact…well, except for the repetition bit, but that could come from the arts too…), but I’m just struck by the contrast.
Just to add more information to the fire… I’m currently teaching math at a small private university (Jesuit, of all things). Because I’m an adjunct, I get to teach high school algebra to college students. What’s remarkable to me is that, in a university with a total enrollment of around 6800, there are nearly 300 students enrolled in algebra sections this quarter alone.
I will grant that (a) more students take math in the fall, and (b) I have some students who probably belong in a class one step up, but any estimate of the total number of students eventually taking this course leads to a troubling number.
I had an undergraduate student working as a dishwasher in our lab. They also are supposed to make basic solutions.
Well, we told him we needed 5 gallons of 70% ethanol, and to just make it up from 95% ethanol and water. I told him the simple equation to figure out how much of each ingredient was needed, basically conc1 x vol1 = conc2 x vol2. I came back about 20 minutes later and he had gone onto google, printed up a recipe for making solution from 95% ethanol and was just following it!
It just about made my head explode. This was a kid, affluent, sophomore in college, not otherwise dumb, who was so afraid of doing simple algebra he ran to google.
So, I’ll agree with you PZ, especially about at least needing math to trigonometry/basic calc and that we’re failing to do it.
“I have handed students a simple recipe for 1 liter of a salt solution, for instance, told them to make up 100 mL of the stuff (or worse, 200 mL), and seen them look stricken.”
I teach Medical Physiology to first-year medical students at an Ivy League university. When they come in, some of these students cannot figure out the total mass of NaCl in the human body if we tell them the total intracellular and extracellular fluid volumes, the molarity of NaCl in the intracellular and extracellular fluids, and give them a periodic table.
I was shocked by this when I started. Now I am just resigned to it. The first week of physiology, we do a remdial class on dimensional analysis.
Rick @ shrimp and grits says
Xerxes… thanks, that answered my question. It’s funny how repetition is emphasized in music, or sports, but dismissed as “boring” and therefore unacceptable in other educational domains.
Don’t forget video games. It’s almost impossible to get good at a game without lots of repetitive practice. DDR, anyone?
I think, though, if homework were more like the link below, kids would have more incentive to get it right. :)
Alon Levy says
The continuous slashing of research funds, the proliferation of adjunct professors, the drastic reduction in the percentage of American articles in top journals…
And I don’t have to think about how to take a derivative or solve a system of linear equations because I learned to understand the concepts behind them. If you’ll look at my transcripts, you’ll see that the repetitive, computational classes that tried teaching me math by making me do a million exercises were the ones I got B’s on, and the more advanced ones, which taught me math by explaining concepts, were the ones I got A’s on.
I’d say the problem starts frighteningly early — long before the high school curriculum. My mother’s on the front lines of this problem (both creationism and math) as a rural Southern middle school math and science teacher.
I teach Koreans English. Our five and six-year-old kindergartners can already add and subtract two-digit numbers, some with ease. I have a sixth grade student who, in the process of telling me how much his Yu-Gi-Oh cards cost, multiplied a three-digit number by a two-digit number with absolutely no hesitation. In fact, we looked at his math book and they’re adding and subtracting in base 2 — something that I never saw outside of MathCounts.
Three-quarters of my mother’s sixth-graders don’t know their multiplication tables. My Korean third-graders play a game in which they go in a circle to a chanted rhythm snapping off two numbers at the person on their right, who is required to provide the product on cue with the chant.
And I absolutely agree that calculator use should be eliminated in elementary school and drastically decreased in middle school, especially until Algebra 1. I find them similar to spellcheck — people brag about not being able to spell or do math, because they can always use the cheats, as if that’s something to be proud of.
It’s surprising to see so much emphasis on repetition as a way to learn math. The problem, I think, is getting kids to want to do math. Yes, repetition is used with great results in sports and music. Haven’t you, for example, ever had a kid sign up for music lessons but only bother to practice the day before the lesson? There needs to be some positive feedback in the activity. You get better at sports you get to play more, you master an instrument, you get to play more. You learn math well, you get … what? Only some kids experience the pleasure of mathematical problem solving, the rest are doing it to pass the class.
I would put my money on finding ways to make the study of math relevant and meaningful to students before asking them to repeatedly practice a skill from which they get no satisfaction.
I’m not convinced about the argument that the prevalence of calculators is the root cause of the problem here. I would tend to suggest that the way the classes are taught have more of an effect.
I finished high school in 2000, so calculators were universal, and graphics calculators almost so by the end, however, everyone at my school knew how to manage mental arithmetic (not that they liked it, but they knew), sanity checks on exponents were expected, and knowing how many figures to include in the answer wasn’t a problem.
Why? Because the mathematics teachers felt that it was important that we should be taught these sorts of things, so they did. If you make people do it (and test them on it), they learn. You don’t have to force people back to the slide rule to teach them to truncate the information the calculator gives them, or to think about how sane the exponent is. It doesn’t take trig tables to give people a basic understanding of what range the cosine or sine should fall in given an angle.
Admittedly, it was a small private school only covering the last four years, so there was more attention to detail, and a generally intelligent student body due to the school being able to select the students admitted allowed more time for topics not strictly demanded by the syllabus, but clearly it can be done.
Scott Hatfield says
Let me add a few more tidbits from my neck of the woods. Many commenters here are focusing on the inability of collegiate types to prepare serial dilutions and the like.
I would ask those commenters to ask themselves the following questions:
1) Do I know the state math standards in my neck of the woods?
2) If so, do those standards actually *require* math teachers to *do* dimensional analysis or (for that matter) use the metric system in solving problems?
I already know the answers to the second question in *my* neck of the wood: no, and no. Is it any wonder we have a problem?….SH
The student described by ‘quitter’, the student who went to google to petition the authority for a magic formula, is paradigmatic.
‘quitter’ mentions “afraid of doing simple algebra”. But notice that student ran to google. Unless ‘quitter’ has hooves and horns, that requires explanation, too.
And ‘MarkP’, way up, describes a student, who knows how to get the required answer, who knows how to select the answer which authority really wants, provided only that authority will tell him what is the right answer. The student describes his own strategy quite accurately.
I wrote originally “went to google to petition the god”. I think that is more accurate.
Alon Levy –
I don’t know about you, but the only way I can learn math is by doing lots of problems. I’m not saying that understanding the concepts isn’t important–understanding why you’re doing a particular sequence of steps is important–but the way to become proficient at something is to practice it. You get better at computing derivatives by computing lots of derivatives. It even applies to advanced math classes. The way you get better at writing proofs is by writing lots of proofs. I’m not saying kids need to sit around adding up columns of numbers all day; they can do a variety of problems. They just need to do a lot of them.
Teaching in a small high school has advantages. Since I am the only science teacher the students see from 10th grade on, I get to design the curriculum. Racing through the chemistry book to be sure of covering everything, out! Spending an inordinate amount of time with dimensional analysis and significant figures, in! Wasted hours with students following cookie cutter recipe labs, out! A few well chosen lab experiments with indepth discussion and analysis (over several different class periods), in! Math problems as extra credit out! Math problems as instructional aides about how the universe really works, in! My one true goal with my chemistry students, they will be the students in intro chemistry at college that the rest of the class turns to for help when the scary math stuff arrives!
Steve LaBonne says
I agree with that. The role of the calculator was simply to make it possible for teachers and students to neglect these things. But it doesn’t have to be that way and I certainly didn’t mean to suggest that teachers should throw up their hands and use calculators as an excuse.
Keith Douglas says
Alecto: On my final exam in my second course in calculus it was emphasized that a calculator wouldn’t help you, and one problem read explicitly something like “do not use a calculator to find an approximation to sqrt(42.1)”.
Pierce R. Butler: My high school tried that – both with Logowriter in early grades and Pascal in grade 10. I understand now they have phased out the latter requirement. I do remember when I took it a lot of students found it very difficult. I (being one of the better students) had to just resist the urge to help all the time, because otherwise I never would have done my own work.
PhysioProf: Thus illustrating (anecdotally) that medical students are often the best crammers. I’m sure they aced the test in chem 101 where that was a single 5 point problem, but forgot it the next morning when it was time to cram for calculus or that “evil physics course they are being forced to take because nobody seems to understand that medicine doesn’t need physics”. (The fake quote is almost what I remember hearing from medical school hopefuls.)
One thing to realize through this is that there are different learning styles. The difficulty is accomodating them.
First the anecdote: I think there’s an awful lot of bad math teaching out there. The approach always taken in my high-school math classes was that the teachers would do a few examples on the board and somehow expect you to get what they were doing. Nobody bothered to explain the “set of rules that can be applied the same way to any problem that will give the correct answer,” at least not in any way that ever made sense to me. I can remember having immense amounts of difficulty with trying to do algebra, something I’m still struggling with 15 years later, because everyone would say, “Just do the same thing to both sides,” and I’d say, “Okay, just do what same thing to both sides?!” Even learning how to unpack a logical proof didn’t help me much there, because at least with propositional calculus, you know that if it looks like this, you do that, and it all works out in the end. As far as I can tell, there’s no pattern like that for algebra. The other problem is that my teachers would never really tell you what you could do with the various things you were learning — they were basically presented as an empty intellectual exercise. Frankly, if I can’t see a purpose to it, I’m a lot more likely to perceive any sequence of actions as arbitrary. Even telling me, “You can use this equation to plot arcs on a graph,” would have been good enough for me. I quit taking math after Grade XI (General level), which you could do in those days, and I’m still feeling it.
If you think I’m bad (and I plead dyscalculia, as well), you should have seen my former students at a community college in Canada. Not only were they basically incapable of doing even basic math that I found fairly uncomplicated, but they even had trouble with vaguely mathematical concepts that I got, generally through the back door, with little difficulty. Risk perception, nil. A lot of my students were basically computer illiterate because they simply didn’t understand computers at all. I was trying to explain to them how to make a logical argument, and how logical fallacies worked, and I had one student who understood — once I made the parallel with computer programming, which he had done.
I think in their case, you could hypothetically blame the last Premier of Ontario (he’s a good target, anyhow) for basically breaking the educational system by radically changing (reactionarily changing?) the curriculum. I don’t have that excuse. NCLB isn’t a factor in this case.
Pointless repetition is not what I’m advocating; it’s just that, as Xerxes says, you don’t get used to doing a particular calculation or operation unless you do it a lot. There are all kinds of ways to ‘package’ practice so that it doesn’t just become a rote chore. But practice is still what needs to be done. Let me use the writing analogy again; you can ask students to write essays about anything you (or they) want, but unless they write essay after essay after essay, they’ll suck at writing term papers when they get to college.
This is a hugely significant point which is sorely overlooked. In an ideal world, we would have class sizes of 5-10 in order to be able to accommodate distinct learning styles; however, no one is currently willing to put forward the resources for that. On the other hand, increasing educational funding enough to decrease class sizes from, say, 30 to 20 would probably go a long way toward improving the situation.