American Innumeracy
Education
| November 16, 2006
| Tim
A recent study seems to show nations with students who are impressed with their math skills are also the nations which have poor math skills. A typical example:
... 6 percent of Korean eighth-graders surveyed expressed confidence in their math skills, compared with 39 percent of U.S. eighth-graders. But a respected international math assessment showed Koreans scoring far ahead of their peers in the United States, raising questions about the importance of self-esteem. [1]
Likewise, the Brookings study seems to show that our obsessive emphasis on making math "relevant" doesn't seem to help either.
In Japan, the report found, 14 percent of math teachers surveyed said they aim to connect lessons to students' lives, compared with 66 percent of U.S. math teachers. Yet the U.S. scores in eighth-grade math trail those of the Japanese, raising similar questions about the importance of practical relevance.
Over at the New York Times, they've noticed a need for reform:
For the second time in a generation, education officials are rethinking the teaching of math in American schools...
“When my oldest child, an A-plus stellar student, was in sixth grade, I realized he had no idea, no idea at all, how to do long division,” Ms. Backman said, “so I went to school and talked to the teacher, who said, ‘We don’t teach long division; it stifles their creativity.’ ” [2]
True to fashion, it seems the Times is recommending the very "solutions" which have put us here in the first place. For example, despite the aformention evidence, the experts quoted by the Times appear convinced we're bad at math because we don't spend enough time trying to make math "relevant":
Many parents and teachers remain committed to the goals of reform math, having children understand what they are doing rather than simply memorizing and parroting answers. Traditional math instruction did not work for most students, say reform math proponents like Virginia Warfield, a professor at the University of Washington.
“It produces people who hate math, who can’t connect the math they are doing with anything in their lives,” Dr. Warfield said. [3]
And, sadly, it seems they're also pimping for Everyday Mathematics, an "integrated" mathematics textbook which emphasizes faddish strategies rather than actual mathematical skills -- though you'd never get that impression from their glowing description:
Schools in New York City use a reform math curriculum, Everyday Mathematics, but some parents there, too, would like to see that changed, a step they are advocating through NYC HOLD, a group of parents and teachers that has a Web site with links to information on math battles nationwide.
A spokesman for the New York City Department of Education said that Everyday Mathematics covered both reform and traditional approaches, emphasizing knowledge of basic algorithms along with conceptual understanding. He added that research gathered recently by the federal Department of Education had found the program to be one of the few in the country for which there was evidence of positive effects on student math achievement.
This is so upside-down. When the Times says "reform" -- they mean the new, faddish approaches which are currently failing us. When they say "traditional", they mean the approaches favored by parents who actually wish to see reform.
Books like Everyday Mathematics downplay the maligned "drill and kill" techniques essential for learning passe concepts like multiplication tables -- and attempts, instead, to teach concepts such as statistics, probability, and the use of calculators and computers. To elementary school kids, mind you. [4] To understand why this is such a disaster, read Matthew Clavel's excellent article over at City Journal, which describes his firsthand experiences with this curriculum.
An excerpt:
It wasn’t working. We’d gone through six straight wrong answers, and now the kids were tired of feeling lost. It was only October, and already my fourth-grade public school class in the South Bronx was demoralized. Day after day of going over strange, seemingly disconnected math lessons had squelched my students’ interest in the subject.
Then, quietly, 10-year-old David spoke up. “Mr. Clavel, no one understands this stuff.” He looked up at me with a defeated expression; other children nodded pleadingly. We had clearly reached a crossroads....
... boy, did my kids need a fresh approach. Since kindergarten, most of them had been taught math using this same dreadful curriculum, called Everyday Mathematics — a slightly older version of a program that New York City schools chancellor Joel Klein has now unwisely chosen for most of Gotham’s public elementary schools; the district had phased in Everyday Mathematics grade by grade, and it had just reached fourth grade during my first year of teaching.
The curriculum’s failure was undeniable: not one of my students knew his or her times tables, and few had mastered even the most basic operations; knowledge of multiplication and division was abysmal....
Instead of rote learning and memorization, students move haphazardly from one seemingly unconnected topic to another. In Fuzzy Math lingo, it’s called “spiraling.” On this view, teachers shouldn’t use a single method to get addition across to students; they should try lots of approaches—like adding the left-most digits first. That way, the Fuzzy Math approach says, you have a better chance of getting students to understand the concept of addition. In practice, however, trying to teach a host of different methods if students haven’t sufficiently mastered any specific one—as is all but inevitable, since they haven’t spent much time practicing any specific one—can be very confusing.
Equally mystifying, Everyday Mathematics, like Fuzzy Math programs generally, abruptly introduces concepts like basic algebra that students aren’t officially taught until years later. Imagine you’re a fourth grader and see in your workbook, right next to a relatively easy addition word problem, a forbidding algebra exercise you couldn’t begin to answer because . . . well, you haven’t learned algebra yet. Bewilderment is inevitable.
If you care about the US educational system, you might want to read the whole thing. The New York Times also doesn't tell it's readers about issues like this (written by a NYU math professor):
To see the defects of Everyday Mathematics, one need only examine its treatment of paper-and-pencil subtraction of two multi-digit numbers.
Most adults will have learned to write the smaller number below the larger one, lined up at the right, and write down the result of the subtraction right to left, doing whatever "borrowing" is needed mentally. This is not taught in Everyday Mathematics. Instead, the Everyday Mathematics pupil is exposed to five different subtraction methods, each of them viewed as suitable for the same task. The gymnastics employed to avoid simple methods is truly breathtaking.
More reviews can be found here, via the aforementioned NYC HOLD parents' group.
To be completely honest with you Tim, I feel that mathamatics education has become red herring of the education epidimic. I'm not saying that mathematics isn't an important aspect in the education of children, it is. However, its given far to much attention in my opinion. Its as if falling math and science grades are the herald of a new age of darkness to some people, when they should really be more concerned with other, more important (in my opinion) aspects of education.
My main concern is with the nearly complete lack of any kind of education in logic and rational thinking. Thank God that I had a teacher who understood the importance of this aspect of education and went to great lengths to teach me and all her students about fallacy and the foundations of reasonable debate. Its sad, and in my mind, dangerous, that children have to wait til they are nearly in college to have any hope of getting any kind of real education on HOW to learn. We should be teaching children this stuff the moment they are old enough to learn. Grades aren't falling because kids can't relate what they're being taught to their real lives, they are falling because kids are not taught HOW to learn though any means other than rote memorization.
The other sad fact of the modern education system in this country is the decline in the arts. Music, "art class", ect, are becoming almost extinct in modern America, and I don't think its ALL due to lack of funding. I personally think that its in large part due to HOW these classes are taught. For instance, in music classes I think the focus is too much on HOW to play music and not enough on WHY we play music. Many children, me included, do not have heads for music note or instruments, but we have to sit through 45 minute or hour long classes devoted to trying to stuff those things in anyway. I think I would have gotten more out of actually LISTENING to Motzart that I did out of trying to learn how he created his music. I'm not saying children shouldn't learn how to write music, but its something that should be the focus of higher level music classes, not something they try to teach you 3rd grade.
And my last bone to pick is with the complete and utter lack of any philosophy classes out side of college. I personally think philosophy 101 should be required for every Freshman, with perhaps more advanced classes open as options. Its truly sad that what most children learn about the great ancient philosophers is that they exsisted and how they died, never what they actually thought or wrote. I personally believe that with the right translation and presentation, that 8th graders are mature enough to read, and understand The Repbublic, yet the closest you get to philosophical education is Lord of the Flies or some other fiction novel in English class. Great reads, with great philosophical undertones maybe, but no substitue for a real focus on philosophy.
Speaking as a complete geek whose favourite subject is Maths... (and who, incidentally, believes that Maths is an art...)
...I don't live in America, but I know that the standard of Mathematics teaching in America (and the UK, for that matter) is, well, not good at *all*.
I mean, most people, even up to undergraduate level, still believe that Maths is a dead subject - that there's no more Maths to be discovered.
Whenever I tell someone that I want to be a professional mathematician and research new Maths, they're generally surprised that there actually is more Maths "out there", so to speak.
Children being taught Maths have absolutely no idea what Maths is about, in the end; they identify it merely with arithmetic, or maybe high school algebra.
And it's not apparent to the teaching system that proper Maths can actually be fun without resorting to bizarre teaching methods.
OK, rant over. :-) I just feel strongly about this... :-P
I also agree with Troy about philosophy... some of the systems out there are so ridiculously self-contradictory and impractical that the schoolchildren should at least be give the chance to know that they're logically evil. :-D
First: I'm embarrassed (in a good way) about the ridiculously good quality of the comments posted here. I'd rather have quality than quantity any day -- I'd rather have one or two well-thought-through disagreements than a dozen "dittoheads". Thank you, you two.
First, to Troy, I'm going to have to initially respectfully disagree -- but perhaps you can make your case more strongly and change my mind...
Grades aren't falling because kids can't relate what they're being taught to their real lives, they are falling because kids are not taught HOW to learn though any means other than rote memorization...
Is that so? I've missed it if so. Where is "rote memorization" being emphasized today?
It's certainly not true of math, as far as I can see. The NYC math education program -- to cite one of the largest school systems in the country -- is abysmal, yet it's based on curricula like Everyday Mathematics which do exactly what you perscribe -- downplay "rote memorization" and try to get kids to understand and even deduce the "philosophy" behind mathematics.
I completely disagree: I don't think it's actually very important for kids to understand *why* math works a young age. Once they know how to do 14 x 68, you can easily explain why it works. But it's very difficult to go from a philosophical view to deducing the rules.
(It's a bit like the rules for producing engineering managers: it's much easier to teach management to an engineer than to teach engineering to a manager.)
If I could send a kid out in life missing one of those two aspects, it would definitely be the philosophical aspect. I'd rather they be able to compare a 10% discount on $120 to 25% discount on $140 -- and not know why that works -- than the other way 'round. You must walk before you can run. 6 x 8 is walking. Understanding that, and why, it is being done in base 10 rather than base 13 or 16 is interesting, not nearly as important.
Especially at the elementary school level.
... kids are not taught HOW to learn though any means other than rote memorization.
Call me an iconoclast, but this idea that children have to "learn how to learn" is a bit too much grad school nonsense filtering down to the primary school level. And is destructive.
Again, do you think South Korean kids spend months on faddish meta-educational theories of the sort you describe? They do not, but they kick our kids around the block, educationally.
My generation still verged on pathetic, but we were also still better, by every measure, than what we're producing now. And we did not "learn how to learn" at all. It was all math tables, low-level mechanics (with only minimumal explanation as to what was going on -- the smart ones got it right away, the slower ones wouldn't benefit anyway), phonics, and grammar until the fifth grade.
Children don't need to spend (nor do they have the mental capacity) innumermal months learning meta-educational theories, or theories of information processing. Dogs can learn without knowing why they do it. So can children. They are naturally inquisitive, and naturally learn by imitation and sythensis.
True, you can also focus on tips like improving study habits, focus, ease fears, etc. But that's not so much learning how to learn as eliminating distractions and barriers.
The other sad fact of the modern education system in this country is the decline in the arts. Music, "art class", ect, are becoming almost extinct in modern America...
Please provide evidence for this assertion. Everything I can see shows funding for these areas has generally increased overall (except for a few cuts in the Clinton years) -- and definitely so compared to the 1950s and 1960s. (Example, and here, for a longer view -- see also my rant here.)
I personally think that its in large part due to HOW these classes are taught. For instance, in music classes I think the focus is too much on HOW to play music and not enough on WHY we play music.
Again, I completely disagree. For example, studies show that kids who learn to play music at a young age do better at match -- indicating a positive influence on brain development.
I don't know of any studies which show a similar effect on kids who learn why we play/like music -- in part, I suspect, because nobody knows -- even neurobiologists -- precisely why we like music so much. So I'm not at all sure what you're on about here, since it's impossible to teach something to small children which isn't even know by post-doctoral researchers.
And my last bone to pick is with the complete and utter lack of any philosophy classes out side of college. I personally think philosophy 101 should be required for every Freshman...
Again, I respectfully disagree: I'm grateful they currently don't foist "philosophy" classes on 8th graders. They'd probably end up indoctrinating them into Peter Singer's idiocy. And who are the "great" philosophers? Do they include Plato but not Aquinas or Augustine? That's the impression I'm getting from the names I usually see selected. Sounds lopsided. Plato was an eltist with horrifying values. It never even occurred to Aristotle to test his theories: people just blindly accepted his pronouncements for ages until the Medieval Christian universities started to point out he was often completely out on a limb.
Logic? Now that's another matter: I'm 100% in favor of that. But again, you can't really do this stuff if you can't even do the basic maths skills, since the way it is learned it the same: modus ponens, modus tolens, etc, are all similar transformations to what must be mastered in arithmetic, algebra, or calculus.
Don't get me wrong, I'm incredibly in favor of philosophy. But an 8th grader has no critical thinking skills with which to accept or reject idiocy -- and won't unless they are first taught formal reasoning. Which requires some basic, mechanical, mathematic skills.
Which American children generally lack.
So at that level, I think we need to focus on uncontroverisal facts -- which they're not getting -- before we go off into discourses about more fanciful and abstract areas. If there is no notion of "right" and "wrong" inculcated about 6 * 8 = 48 (in base 10), they will be utterly unable to consider applying the idea to more intangible, abstract areas.
I believe in creativity. But creativity is impossible unless you first master the tools you must use, and the rules you must eventually question.
And, in response to the "Complete Geek", who bring a British persepctive (thank you!):
And it's not apparent to the teaching system that proper Maths can actually be fun without resorting to bizarre teaching methods...
If so, that's sad, since I think the whole reason the "bizarre" teaching methods are fun is because the children generally aren't learning math. It's a bit like saying we can make learning math fun by watching Gilligan's Island: Sure, that will be fun, but how much learning is involved?
As I read through my paper, I thought about the experiences I’ve had with the Everyday Mathematics Program. There were a few questions that I could not erase from my mind. Why do students enter middle school still not knowing basic multiplication facts? Are they getting enough practice? That’s when I decided to explore the Everyday Mathematics Games Curriculum to see how many of the games actually have the students practice multiplication skills....
Following this spiral of games shows me that the program has very good intentions when it comes to having the students practice multiplication skills throughout a student’s elementary learning experience, but I’m not convinced that the games are very effective at having the students confidently know their multiplication. I feel that games ultimately put the students in the mind frame of “I want to win the game,” instead of “I need to learn this concept.”
Overall, I think the idea of having students practice skills through games is a good idea. However, I feel that the Everyday Mathematics program depends too much on the games as a way for students to practice skills. The games just simply do not work for all students. [Tawnya Ford, teacher]
I think once the basic skill is learned, it could easily be turned into a fun game. Good teachers make learning fun, in my experience, without necessarily resorting to educational fads. I remember I had a little electronic game which helped me practice my multiplication. But it wasn't doing anything more than drilling me on the basics, which I had already learned to do, at least slowly, with some pain.
Closing: These comments show how deeply indoctrinated our society has become, regarding these assumptions. Plentiful, clear evidence sits right in front of us that these sort of approaches simply don't work, and here are my friends, fairly conservative thinkers, spouting the very same failed ideas which are crippling children and denying them a happier life.
This convinces me I need to write a general defense of why basic logic, math, and reading skill are important, and why you cannot even move a student reliably into the more philosophical areas without mastery of these foundations.
Regardless, I'm still deeply grateful for these comments: they raise areas and views which are critical for people to discuss and understand. Thank you.
Thanks so much for your wonderfully detailed reply! :-) To be honest, I actually agree with you...
I think once the basic skill is learned, it could easily be turned into a fun game.
I completely agree! Actually, I don't necessarily mean fun as in a game; I believe that once you have mastered Maths to a certain degree, researching problems and finding patterns can be incredibly addictive and fun. :-)
Not that you'll necessarily need to use them in real life. :-)
For the record, I haven't been in conventional school since Grade 3, so my memory is somewhat foggy. :-)
There is one thing that I don't understand, though.
Shouldn't the students be able to understand what you're learning?
I mean, knowing how to multiply three times three is all very well, but if you don't understand why you're doing it, it's about as helpful as taking an intensive course in advanced Klingon. (Although some people might say that that is quite helpful.)
I'm sorry if I'm not expressing myself clearly; I am a complete geek, after all. ;-)
Thanks again so much! :-)
-TCG
Personally, my music classes were all complete disasters, despite attempts to learn the recorder and coronet. Either I have no musical ability, or else I've never desired to develop it. In the same way that early math focuses on arithmatic tables, early music should focus more on recognizing and reproducing pitch rather than learning a particular instrument. But I was never once tested on pitch recognition. They did teach scales, but we recited them as a group and I didn't have much of a clue why we were learning them. Instead, I was taught to play a recorder, which just required me to cover certain holes in response to certain dots on a page, and not learn any real skills at all. That perfect pitch is so much more common in people who learn a tonal language before the age of five indicates that this training would likely have a more directly positive effect on a person's development. I assume that it's this skill that leads to the benefits of musical education mentioned above. But perhaps I'm missing somthing. link
While I agree that junior high kids don't need mathematical theory, I personally feel that I would have benefitted from more historical context once in High School. The applications of, say, calculus or geometry required more explaining and contextualization than simple arithmatic. It was interesting, recently, reading some code which used a sine function to produce simulated 3D in a program. Because while I'd learned trig I'd never been taught to apply it in the way the program did. Some people become more motivated to learn when they can apply their knowledge to a useful task.
Again, do you think South Korean kids spend months on faddish meta-educational theories of the sort you describe? They do not, but they kick our kids around the block, educationally
America is a big place.
On a mathematics test for 13-year-olds, for example, U.S. students on the whole ranked 14th. Students in Taiwan and Korea ranked first and second, respectively, with average scores more than 20 points higher than those of U.S. students. But students in Iowa and North Dakota did just as well as the Korean students, and those in Minnesota scored only one point lower. And the scores of students in other states--including Maine, Nebraska, New Hampshire, and Wisconsin--were in the upper half of the international ranking. (The District of Columbia, on the other hand, would have come in dead last on an international comparison, 12 points behind Jordan, and Mississippi would have tied for last.)link
Is that so? I've missed it if so. Where is "rote memorization" being emphasized today? This isn't exactly "today" (I'm 28) but my school taught arithmatic by rote. And for somthing as simple and obvious as arithmatic, I think it worked very well for me. But only because arithmatic is simple and its application is obvious.
Children don't need to spend (nor do they have the mental capacity) innumermal months learning meta-educational theories
I wish they'd at least teach more of these theories to teachers. I had a few teachers that insisted we copy information down from the book and turn in the copied pages because that's how they learned. I got absolutely nothing from those activities. And I would literally zone out for a half hour while listening to the teacher talk in Math class. But given a good book, I could sit down and learn the material on my own, if I could force myself to pay attention long enough. The material wasn't difficult. Just painfully boring. Some kids have problems that aren't nessicarily related to 'intelligence.' Lack of motivation and unusual learning styles are two of them. What would you do with those kinethetic learners who aren't picking up on the verbal lectures? You can help them get the information in another way, or you can label them as 'stupid' and blame them for their inability to adapt. Either flies, but which is better for the student?
TCG:
I completely agree! Actually, I don't necessarily mean fun as in a game; I believe that once you have mastered Maths to a certain degree, researching problems and finding patterns can be incredibly addictive and fun.
I don't know about the UK, but one of the sad facts about the US system is that -- I get the strong impression -- the best people -- the kind who could make such learning fun -- tend to be drive away from teaching, and encouraged to do other things these days.
Shouldn't the students be able to understand what you're learning?
Of course! BUT the problem I see with stuff like "New Math" and Everyday Mathematics that that "understanding" is emphasized AT THE COST of the mechanics. Again, both are important, but if I had to just choose one, I'd say focus first on the mechanics, and the understanding will fall in place at some point, maybe even later.
Instead, students "spiral" from one concept to the next, never staying long enough on anything (apparently) to get really good at it. Particularly the most boring stuff -- multiplication tables -- which took slow kids like me years to finally get down. (I'm not kidding.)
Ryan:
Personally, my music classes were all complete disasters...
Mine mostly also. I learned much more from private lessons.
Good point on the comparative differences between different regions of the country! Sounds like the world should be learning from Iowa and North Dakota, two places which tend NOT to, I would imagine, subscribe to more "progressive" educational trends.
But hey, perhaps I'm wrong about that!
This isn't exactly "today" (I'm 28) but my school taught arithmatic by rote...
I'm a decade older, and the same was true for me. Don't get me wrong, I *hated* it, but in the long run, I realized it was better. By counter-example, they let me get away with a "longhand" form of long division, which I did for over a year, which put me behind the other kids. It was a false kindness in the end...
I wish they'd at least teach more of these theories to teachers...
I expect the teachers learn quite a bit of "theory". I think that's the whole problem.
I had a few teachers that insisted we copy information down from the book and turn in the copied pages because that's how they learned. I got absolutely nothing from those activities. And I would literally zone out for a half hour while listening to the teacher talk in Math class....
Ryan, you and I were bright kids. It's unfair to structure the entire learning experience around our needs, or what might have worked with us.
Now I'm not here to defend just copying things down (but perhaps it works in some cases, I don't know) but the fact you were bored indicates you were being insufficiently stimulated, intellectually. That's why they should have multiple tracks for kids, though that's called "elitist" today.
"Whole language" and "integrated math" are both mistakes which pattered teaching after observations about bright kids. I know kids who could derive theories for themselves, once given the basics. And yes, once a person learns to read well, they simply recognize whole word shapes, rather than sounding out things phonetically.
But these two systems put the cart before the horse, and treat all kids as little Euclids. They sit them in a circle and give them some implements and hope they'll "deduce" the laws of mathematics -- which it took us thousands of years to work out -- for themselves, in a 45-minute class. They tell kids to memorize word-shapes, and leave them without the necessary phonetic skills that even talented (English) readers must occasionally fall back on.
I believe the basic motivation behind these mistakes was a religious-like unwillingness to accept that there were limits to our ability to engineer society. More later, God willing.
What would you do with those kinethetic learners who aren't picking up on the verbal lectures?
The kids? The kids aren't the problem: it's the teachers who have swallowed half-baked theories like that one.
The whole "multiple intelligences" thing is a crock, Ryan. Yes, there are different skills. Yes, kids can better in one area than another, or vise-versa. But the dirty little secret you're not being told is that the different "intelligences" aren't independent variables; they cluster around a region, in the middle of which lurks "g". It's also arugable whether they've even "intelligences" at all.
So yes, one girl can be happy with verbal learning, and another girl will get it better if she has to read it. I've seen this firsthand. But, except perhaps in odd cases (autism, or specific impairments) you don't find kids who range from idiot to savant between two "intelligences" (which are usually better termed "skills").
Further, the idea of teaching math using "kinetics" is laughable. What next? Trying to get kids with sensitive noses to learn to "smell" the equations? Puhlease. People will swallow anything these days.
And indeed, they have:
Is working with twigs and leaves supposed to help my child learn to spell? Yes, according to Thomas Armstrong, author of Multiple Intelligences in the Classroom, especially if your child is high in “naturalist” intelligence... [1]
More here [PDF] and here.
Gardner questioned the construct validity of g... In this reply, we explain that the construct validity of g is well established, pointing out (a) that g is expressed in a wide variety of tasks (not all of which are “school-like” tasks), (b) that g predicts many important criterion variables (not only academic achievement), and (c) that g has a well-established biological basis. With regard to the measures used in our study, we point out that the verbal content of those tasks is unlikely to contribute to individual differences in task performance, and that the logical content of those tasks is consistent with Gardner's description of his intelligence domains. [2]
When I was in middle school, they put us in a huge building which was designed to have no walls at all, with hundreds of kids in the same room. It worked so badly that just a few years later, by the time I got there, they'd erected ersatz walls using movable blackboards. The ceiling still extended far above and carried sound like crazy.
This was called "open concept" and it was another educational fad, just like MI, which (a) had almost zero or specious research backing it up, (b) came out of the educational schools, (c) a child could (and I did) see it was a mind-blowingly stupid and idea, (d) was widely accepted and implemented anyway, and thus (e) screwed up tens of thousands of schools and children.
Sorry that I don't "ooh" and "aah" appropriately at the religious claptrap we're supposed to blindly accept these days. I've done that, then I did my research, and now I'm just bone-tired of the incessant lies which hurt so many and deprive them of the lives they might have lived.
The whole "multiple intelligences" thing is a crock, Ryan.
Perhaps, or no. I'm a little familiar with general vs. multiple intelligences. But I was referring to learning styles only.
That's why they should have multiple tracks for kids, though that's called "elitist" today.
I agree wholeheartedly. And our school did. They were typically the best classes, and taught by some of the best teachers.
My only concern is that anyone should be able to take the class if they really want to.
As long as you keep things open that way, I've never understood the labeling of accelerated tracks as 'elitist'.
The huge workload should keep out those students who aren't really interested.
It's unfair to structure the entire learning experience around our needs, or what might have worked with us.
I agree it's unfair to have a few students needs dictate how an entire class is taught. On the other hand, I worked with a company called Aventa recently.
They did e-learning for public schools. Aventa's take was that if you have two students in one school that wanted to learn, say, Japanese they they could.
You just needed to match them up with a classroom full of other kids from other schools. You use message boards, voice chat, recordings, online texts etc.
Some distance learning programs are horribly designed, but some are at least functional.
So I agree that in the past it might have been unfair to structure classes around the needs of a few students. However if it's possible to
teach two kids in a school Japanese, it should at least theoretically be possible to design classes to meet certain other
educational niche desires as well. Whether you acutually want to do this is a different question. I'm just saying that the capacity is there.
The whole "multiple intelligences" thing is a crock, Ryan.
Or were you referring to my introductory paragraph, and claims that I had no musical ability?
Ryan: What would you do with those kinethetic learners who aren't picking up on the verbal lectures?
Tim: The whole "multiple intelligences" thing is a crock, Ryan.
Ryan: Perhaps, or no. I'm a little familiar with general vs. multiple intelligences. But I was referring to learning styles only.... Or were you referring to my introductory paragraph, and claims that I had no musical ability?
No, I was referring your statement about "kinethetic learners". "Learning styles" is typically just another way of stating belief in "multiple intelligences", the underlying theory. The whole idea of a "kinesthetic learner" arose because Gardner postulated that there was a separate "kinesthetic intelligence" by which they would learn.
It's amazing how often people absorb and repeat theories like these without, apparently, even being aware of it.
As long as you keep things open that way, I've never understood the labeling of accelerated tracks as 'elitist'.
Here's a leftist criticism of the practice:
Terman and other educational psychologists successively convinced many school districts to use high-stakes and culturally-biased tests to place "slow" students into special classes, rigid academic tracks, or entirely separate schools. The racist and class assumptions behind these recommendations were justified as scientifically sound because the "tests told the truth." IQ tests soon became the favorite eugenic tool for identifying "superior and inferior" students and then charting their educational destiny.
And:
Critics argued that tracking, especially in practice, created greater learning opportunities for high-performing students at the expense of their lower-performing peers....
[In 1985, Jeannie] Oakes characterized tracking as an elitist practice that perpetuated the status quo by giving students from privileged families greater access to elite colleges and high-income careers. “Tracking is not in the best interests of most students,” Oakes concluded....
While many teachers favored detracking, a large number of parents, politicians, and other teachers resisted.
I don't personally feel tracking is elitist either. I'm just pointing out this is a prevailing view.
The huge workload should keep out those students who aren't really interested.
If an accelerated track has a "huge workload" something has gone terribly wrong.
Tim: It's unfair to structure the entire learning experience around our needs, or what might have worked with us.
Ryan: I agree it's unfair to have a few students needs dictate how an entire class is taught.
I wasn't referring to how a particular class was taught. I contended that the educational fads I referred to -- which shape massive parts of the educational infrastructure, not just a class here and there -- were structured around observations based on bright kids.
See above.
"Learning styles" is typically just another way of stating belief in "multiple intelligences"
I do believe there's some truth to multiple intelligences as well, to a point.
My own personal experience with the matter is that different people remember things differently. My mother, who is an artist, remembers things as pictures. When she wants to think of how a word is spelled, she sees it written out. I tend to have an auditory linear sequential memory. When I want to think of how a word is spelled, I hear it. I can remember longer sequences of information compared to most people. But I have a terrible time with precise images in 2d and 3d space. I can still do art, I just need to redraw things more frequently than some, and I'm less consistant. My sense of direction is horrible. If I want to get from point "A" to point "B" I often have to connect paths that I've already traveled. I'm getting better at thinking spatially as I get older, but I'm still behind most people. Back in school, I had a terrible bit of trouble remembering chemical structures that weren't essentially just straight chain alkanes with one group or another branching off.
Intelligence in one area can often be used to compensate for weakness in another, of course. So I didn't want to argue with the fact that all intelligences tended to correlate (which I agree that they do.) This doesn't mean that there aren't also some differences in how different people's memory works.
Tim: It's unfair to structure the entire learning experience around our needs, or what might have worked with us.
Ryan: I agree it's unfair to have a few students needs dictate how an entire class is taught.
Tim: I wasn't referring to how a particular class was taught. I contended that the educational fads I referred to -- which shape massive parts of the educational infrastructure, not just a class here and there -- were structured around observations based on bright kids.
I see now that you're also assuming bright kids would be in accelerated tracks devoted to them and other kids would have tracks devoted to their learning needs. I wasn't considering the two at the same time.
If an accelerated track has a "huge workload" something has gone terribly wrong.
Perhaps, but my AP history class was incredibly demanding and also a very good course. How are you suggesting that enrollment in accelerated tracks be determined? Is there any case where a student should be outright barred from attending an accelerated track? The 250 level chem courses in college were harder than the 230 level courses. In that case, students seemed to self-select. Were you hoping for a different criterion?
Tim: "Learning styles" is typically just another way of stating belief in "multiple intelligences"
Ryan: I do believe there's some truth to multiple intelligences as well, to a point.
I agree, "to a point." I stated an example. But that "point" is rather smaller than the educational community believes, and doesn't include the belief that "kinethetic [sic] learners who aren't picking up on the verbal lectures" need to be making number-shapes with their body to learn math. Most likely, reading will help, but only a bit, since "intelligences" (abilities, really) are clustered.
How are you suggesting that enrollment in accelerated tracks be determined?
Aptitude and interest.
Is there any case where a student should be outright barred from attending an accelerated track?
When that student's presence clearly disrupts the learning experience for others who are doing better, or when there are limited resources.
Technically, I wasn't supposed to be allowed to take the computer class in the 8th grade, since admission was based on math (not verbal/structural, which is probably more relevant) abilities. But I begged in, and got to use the computer during a free hour.
I blew the other sections of the classes away (I had a bit more time on the computer, which was part of it, but I'm also good) but I didn't impose a burden on the others.
Were you hoping for a different criterion [for higher-learning track]?
I don't think a student's aptitude should be related to workload. Smart children need the same balance between "task" and "fun" as slower children -- there's nothing about intelligence that determines less need for recess or family time.
Conversely, smart children should be able to cover more in the same time. So perhaps they should even have a lighter workload.
Long time lurker, first time poster ;)
Unfortunately, I wish I didn't have to post on this one. My daughter has been subjected to this horrid curriculum for the past two years. Last year, she had a wonderful math teacher that apparently made up for it, so we didn't notice how bad it was.
But this year, my daughter's gone from loving math and doing extremely well in it, to tears and frustration every week. This stuff simply is not explained to the kids. They don't know how to solve these problems. We, as parents don't get to see the textbook, since they can't take them home. All we see are homework pages with poorly written and often outright incorrect instructions with barely an example problem to be seen. They throw problems in at the end that I *know* the kids would have no way of solving properly, and my poor child is simply at a loss. I thought it was her for a while, but no, it's just that bad.
We'll talk to the teachers and the principal, but I sincerely doubt we'll get very far. So it looks like now we get to be part-time math teachers. Guess I'll have to dust off my times tables and long division skillz. :)
Thanks for digging this info up and posting it. It was a real help to us as a family. We're not crazy - it's just awful.
"Tracey",
Welcome!
Some post on such matters because their interest is academic -- not for me. I have friends who, like your family (you have my sympathies) have been affected by this. I post out of white-hot hatred that this is being done to so many nice little people. And what is being done to my country's ability to compete in the world.
(I don't hate the teachers or educators -- many of whom are just doing the best job they can -- but my loathing for harmful philosophies is hard to understate.)
Part of what's so insidious about these strategies are the way children can seem to be doing fine for years, and parents don't realize the damage before it's almost too late. (I'm not saying this is the problem in every case, or yours... It seems to have been a factor in the Mathew Clavel article above.)
I have a friend, call her "Jesse", who has a high IQ, and whose also-smart daughter was doing just fine in her elementary school studies. Then, around the fifth or sixth grade, they noticed something was wrong: she suddenly started having all this trouble reading -- and having trouble with her other schoolwork.
Jesse eventually discovered her daughter had been taught to read using "whole language" techniques, where instead of learning phonics, children are taught to memorize the "look" of whole words, as though English were Chinese. Then -- what makes this truly insidious -- the rest of the curriculum had been carefully attuned to use only those words which had already been introduced in reading texts. So, for years, it seemed Jesse's daughter was able to read everything needed for her other classes.
Then, about the fifth or sixth grade, this tuning stopped, and Jesse's daughter, for the first time, had to negotiate completely unfamilliar words, words she hadn't previously memorized. And, since she knew no phonics, she had NO way to understand them or sound them out.
And thus her grades suddenly plumetted, and a smart, kind little girl, who previously seemed to be doing "just fine" (or even excelling) was suddenly utterly demoralized and failing!
I told this story to another friend of mine, who is single ("Jesse" has three daughters), and her response was mocking: "Well, if I had children, I would try to be involved in their education!" Yeah, maybe, if you had the time for it, and didn't have two other daughters and a job. And Jesse was involved in her daughter's education.
But she doesn't understand: Parents, good parents, honestly believe the schools are doing a good job with their children. In study after study, when they ask people: "How is the American educational system?" They say: "Terrible." Then when they ask them: "How is your school?" They generally say: "Good" or "Very good!" It doesn't add up. And we see the same thing with kids, where they are impressed with their own skills, but yet, on objective tests, compared to other nations, they're not doing that well. (And yes, Kudos to North Dakota. And all 3,041 children there.)
And Jesse would spend time with her daughter: She'd read school books with her, help her with her homework. But again, Jesse's daughter seemed to be doing fine on the pre-memorized words -- better than the other kids, in fact, because she was smart.
At this point some parents buy "Hooked on Phonics", or enroll their kids at Kumon or Sylvan, supplement their kids' education themselves using techniques they had been taught thirty years ago. In Jesse's case, she lobbied her school to try to get -- for her other younger daughters who were coming up in lower grades -- a phonics-based education in place.
The school, like many others, switched to something which was a bit like Everyday Mathematics, in that it blended a little bit of a traditional approach with mostly "reformist" (e.g. faddish) content, and then marketed itself as "traditional" (phonics-based, in this case).
For example, here's a reference to a similarly deceptively-named curriculum being used in NYC, called "Month by Month Phonics"...
Month by Month [Phonics, is,] in reality, a “whole language” program with but a tiny sprinkling of phonics... [it] would now be supplemented in every classroom by yet another phonics program, this one developed by a Dallas company named Voyager Expanded Learning. According to Deputy Chancellor Diana Lam, the more heavily scripted program would be used for “students who are finding it more difficult to learn to read,” while the presumably more advanced readers in the same classroom would make do with Month by Month. [1]
(Amazing! They name it "Month by Month Phonics", and it's basicly a "whole language" approach.)
So, in the end, Jesse felt she had no choice but to take her kids out of the public system and home-school them herself.
Many parents don't go this far, but work hard to supplement their children's "education" with an actual education they help provide, themselves. They pay big bucks enroll their kids in Sylvan or Mathnasium, they work hard with them at night to learn phonics, they teach their kids actual science when it seems to be missing from the "science" courses. They supplement their kids' civics and history studies with actual civics and history. Etc, etc.
(In my case, I was blessed to receive one year of absolutely elite private-school education. Which made a huge difference.)
But eventually, some ask: "If I have to all this, then what, precisely, are my kids going to school for?" Since we pay about $8-10K per yer per kid -- a taxpayer pays about $100,000 for each child to receive a public education -- that's an entirely reasonable question.
Tim, thanks for responding.
My comment about rote memorization was meant as a comment on education in general and not specificly mathematics. I feel that, at least in my education, subjects I was taught were almost always related to simple rote memorization. I realize that education must START with such techniques, but the problem is MY education(and I'm talking about just a few years ago here, I'm only 22) NEVER moved beyond such subjects excepting a a lady who holds a very special place in my heart, my Senior year Honors English class.
Perhaps I'm odd compared to most children, but I'm 100% positive that I was ready to be introduced to some extent in 8th grade that aren't really even broached in modern day highschools. It could be that I'm different than most, but as a child I LOVED to learn, not just memorize, and my public school education did not provide that to almost any extent even during the latter years of highschool.
""If I could send a kid out in life missing one of those two aspects, it would definitely be the philosophical aspect. I'd rather they be able to compare a 10% discount on $120 to 25% discount on $140 -- and not know why that works -- than the other way 'round. You must walk before you can run. 6 x 8 is walking. Understanding that, and why, it is being done in base 10 rather than base 13 or 16 is interesting, not nearly as important.
Especially at the elementary school level.""
I think this is where the misunderstanding might be coming into play. I'm not suggesting we start teaching Aristotle in 3rd grade, early education is rooted in rote memorization, things like fractions, percentages, dates, names, and places. However, as to you're point above about percentages, ect. I'm not sure about you, but I had a firm grasp on that part of mathematics for about three years before they stopped teaching it. THAT is my problem, it takes forever and a day for curriculim to catch up to most kids IMHO. Maybe I'm wrong, or put to much faith in children as a whole, but I believe we could stand to have the system move a bit faster so that subjects like those mentioned in my original post can be broached before you send them packing for college.
"My generation still verged on pathetic, but we were also still better, by every measure, than what we're producing now. And we did not "learn how to learn" at all. It was all math tables, low-level mechanics (with only minimumal explanation as to what was going on -- the smart ones got it right away, the slower ones wouldn't benefit anyway), phonics, and grammar until the fifth grade.
Children don't need to spend (nor do they have the mental capacity) innumermal months learning meta-educational theories, or theories of information processing. Dogs can learn without knowing why they do it. So can children. They are naturally inquisitive, and naturally learn by imitation and sythensis.
True, you can also focus on tips like improving study habits, focus, ease fears, etc. But that's not so much learning how to learn as eliminating distractions and barriers."
It seems to me here that you are overly complicating what I said. You don't have to teach some kind of complext theory of learning in order to teach children the basics of critical reasoning and logical thinking. I personally believe that there is a basic level of these things that COULD be taught to children in, say, the 5th or sixth grade, things that ARE not taught, at all now.
I think I can shorten this all up by qouting from http://www.classical-homeschooling.org/introduction.html, a site which promotes ans seeks to educate parents about the same basic system I would support and hopefully use to educate my own children.
"The core of Classical Education is the trivium, which simply put is a teaching model that seeks to tailor the curriculum subject matter to a child’s cognitive development. The trivium emphasizes concrete thinking and memorization of the facts of the subjects in grade school; analytical thinking and understanding of the subjects in middle school; and abstract thinking and articulation of the subjects in high school. Subjects unique to Classical Education which help accomplish the goals of the trivium are Grammar, the science of language usage; Logic, the science of right thinking; and Rhetoric, the science of verbal and written expression."
As you can see, its basicly talking about what I've tried to get across, that there is a place for rote memorization in education, especially early on in a child's development, but children hit an age where they are more than capable of handling some aspects of analytical thinking, which the modern educational system, think the last 100 to 150 years, has slowly but surely denied more and more to children mature enough to handle it.
Again, try not to over complicate what I'm saying. When I say teach philosophy in highschool I don't mean Existentialism, Postmodernism or anything like that, I mean Plato's Republic. Is the Law of Non-Contradiction, the very foundation of rational thought, beyond the abilities of a middle school or junior high student to understand or be taught?
Perhaps our disagreement was one of simple misunderstanding or perhaps we just have two very different views on the educational proccess. Either way, its been a stimulating article and talkback, as always, thanks again Tim and keep 'em coming.
The comment rules will apply. Please post only once.
« Roseanne Barr: A Prophet for Our Times |
Front Page |
Page Two
| In the News: Sins of the Flesh »
|
To be completely honest with you Tim, I feel that mathamatics education has become red herring of the education epidimic. I'm not saying that mathematics isn't an important aspect in the education of children, it is. However, its given far to much attention in my opinion. Its as if falling math and science grades are the herald of a new age of darkness to some people, when they should really be more concerned with other, more important (in my opinion) aspects of education.
My main concern is with the nearly complete lack of any kind of education in logic and rational thinking. Thank God that I had a teacher who understood the importance of this aspect of education and went to great lengths to teach me and all her students about fallacy and the foundations of reasonable debate. Its sad, and in my mind, dangerous, that children have to wait til they are nearly in college to have any hope of getting any kind of real education on HOW to learn. We should be teaching children this stuff the moment they are old enough to learn. Grades aren't falling because kids can't relate what they're being taught to their real lives, they are falling because kids are not taught HOW to learn though any means other than rote memorization.
The other sad fact of the modern education system in this country is the decline in the arts. Music, "art class", ect, are becoming almost extinct in modern America, and I don't think its ALL due to lack of funding. I personally think that its in large part due to HOW these classes are taught. For instance, in music classes I think the focus is too much on HOW to play music and not enough on WHY we play music. Many children, me included, do not have heads for music note or instruments, but we have to sit through 45 minute or hour long classes devoted to trying to stuff those things in anyway. I think I would have gotten more out of actually LISTENING to Motzart that I did out of trying to learn how he created his music. I'm not saying children shouldn't learn how to write music, but its something that should be the focus of higher level music classes, not something they try to teach you 3rd grade.
And my last bone to pick is with the complete and utter lack of any philosophy classes out side of college. I personally think philosophy 101 should be required for every Freshman, with perhaps more advanced classes open as options. Its truly sad that what most children learn about the great ancient philosophers is that they exsisted and how they died, never what they actually thought or wrote. I personally believe that with the right translation and presentation, that 8th graders are mature enough to read, and understand The Repbublic, yet the closest you get to philosophical education is Lord of the Flies or some other fiction novel in English class. Great reads, with great philosophical undertones maybe, but no substitue for a real focus on philosophy.
Posted by: Troy on November 16, 2006 02:30 AM