I stumbled across an example (shown below) of how marvelous a pattern-recognition engine the human mind is... and came to realize that it shed light on one of the classic tiffs between left and right, the "Phonics vs Whole Language" controversey.
Whole language mavens dominated in teaching schools for decades, pushing the bizarre theory that children never need to sound out or spell out words in order to learn to read. They did have some research to back up a more moderate notion, that a lot of reading consists of scanning and learning whole words by association with a semantic meaning. Sure enough (as the example below demonstrates well.) But this was extrapolated into a lefty idiocy - that teachers should just read stories aloud to kids, who will thereupon automatically WANT to read them, and thereupon voila, read them!
Conservatives were right to consider the more radical version of Whole Language to be utter claptrap -- and ideologically-driven as well. An excuse to extend Story Time through the day with lots of politically correct fables and never any student accountability.
But their alternative, pure Phonics, was another monstrous piece of ideological oversimplification that is now doing just as much harm now that it (and absurd overtesting) has taken over the pendulum swing.
Just take a look at the following (no attribution from my source; anybody out there have it?):
"i cdnuolt blveiee taht I cluod aulaclty
uesdnatnrd waht I was rdgnieg.
The phaonmneal pweor of the hmuan mnid.
Aoccdrnig to a rscheearch at Cmabrigde
Uinervtisy, it deosn't mttaer in waht oredr the
ltteers in a wrod a re, the olny iprmoatnt tihng is
taht the frist and Isat ltteer be in the rghit pclae.
The rset can be a taotl mses and you can
sitll raed it wouthit a porbelm.
Tihs is bcuseae the huamn mnid deos not raed
ervey lteter by istlef, but the wrod as a wlohe. Amzanig huh?
yaeh and I awlyas thought slpeling was ipmorantt"
What fun.
.,, oh, now that CA and Oh voters roundly rejected anti-gerrymandering measures that had no balance, shall we let the pols get away with taking the wrong lesson? or fight for BALANCED redistricting across all party lines?
32 comments:
CITOKATE: You spelt 'rdgnieg' wrong (should be 'rendaig' ;-)
Tying a teaching technique to ideology is also a great way to sell crap.
I doubt that "whole language" theorists every had the interest or chutzpah to do what phonics crusaders have done, creating an industry to push learning materials on stoked-up parents. Cast your opponents as multi-culti secular-humanist leftists and watch the sales soar!
In any case, based on personal experience "whole language" wasn't the first dippy experiment in reading instruction, and I'm sure it won't be the last:
My first and second grade classes (circa 1971?) were the victims / subjects of an experimental ultra-Phonics technique called ITA . . . Initial Teaching Alphabet.
All of the classroom materials -- books, posters, and so on -- were printed in a 44 character phonetic alphabet! There were backward S-es and Z-s, W with weird little loops, backward K-s, and so on.
We were transitioned out in second grade.
I learned to read VERY quickly, didn't need to move my lips and mumble like the other kids, but I'm not sure if ITA deserves credit. It wasn't until I got my hands on "real" books in the elementary school library that I got thoroughly stoked and motivated.
The one lasting effect that ITA had on me was screwed up handwriting. Later teachers thought -- despite reading way beyond my level -- that I was dyslexic because I occasionally flipped Zs and Ss around. They would have been correct under the ITA scheme . . .
Stefan
Stefan:
I, too, had an early encounter with ITA. On my first day of elementary school we were told to copy a couple of ITA sentences from the chalk board onto big sheets of lined paper. My mother had taught me to read years before, so I politely told the teacher she had written gibberish (I'm sure I used another term at the time!) on the board. I was not-so-politely told to copy the sentences as written and shut up (I'm sure the teacher used another term, as well.)
The lesson for me - Teach your kids to read EARLY! If a parent waits until they start school, it's probably too late.
--daniel
I basically taught myself to read, using the tried and true method of asking parents, "What's that word?"
So what kind of learning was that? Did I learn to read English the way the Chinese *have* to learn to read, by connecting the patterns of lines in "prohibited" (oh, yes. 3 years old, pestering parents about the meanings of road signs) with the idea of prohibition?
Nothing like that was done in Whole Language reading, as far as I can remember.
Today (if my kids are any example), a *mix* of teaching techniques is used to impress reading and writing skills upon kids. There is reading aloud, but it appears to be geared to getting kids to realize that interesting things are behind all those markings on paper. There is also phonics, but a recognition as well
Who knows? Maybe I live in a sane school district, untroubled by the fads of this or that ideology because, well, enough *parents* take an interest in both learning and administration to watch over the teachers.
(And let's not mince, either. Our teachers are by and large very good at what they do, in the elementary levels. I'm only really worried about 7th through 10th grade instruction in my area.)
But let's not forget to talk about math, because my kids won't get their multiplication facts memorized unless *I TEACH THEM* and force them to commit it all to memory.
(I don't much care that it's a source of childhood pain for most of us. As forced-memorization goes it's been the second most useful thing of my secular life!)
The math program I'm faced with in my area resembles an ideologically based thing. They try teaching "math reasoning" rather than "ciphering" or specific algorithms.
What that ends up meaning is that my kids get presented with nine different ways to do a math problem. And what they end up helpless about is which one to choose for any given problem.
This leaves some kids, like my oldest, helpless in math, because her focus in early elementary ed was on doing precisely what the teacher wanted. But the curriculum specifically directs teachers not to require a child to try each algorithmic approach. It's all just "choose the one *you like*" and "be accurate and precise".
But no shortcuts to accuracy, such as "knowing the answers by heart" are taught any longer.
Meh. My daughter entered the 5th grade without being able to tell me 7x4 in five seconds or less. A scandal, when such a thing along with all its brothers is useful.
So what do we have, then? On the "right", cipherin' algorithms and "do it the teacher's way"? On the "left", something polar opposite but nonetheless just as useless to kids who don't automatically intuit math concepts, the way I and my second daughter did and do?
And, it's not helped in the slightest by the fact that I have yet to find a teacher at the elementary levels who hasn't said, "I don't like math. It's not my strong suit." And they tell this to the children as well!
GAH! My daughters are lucky both their mother and I are willing to help them suss out math concepts.
On the subject of elections: Washington State also rejected the "poison pill" health reform initiatives before them, though largely what was approved in the rural areas (and in my county, which is a fast growing urban rural mix) was soundly defeated in King County, home of Seattle and the aircraft manufacturer's unions.
But the smoking ban in public places was approved. Even for bars and such, which I recall was repealed in CA. Hey, at least we didn't repeal taxes on gasoline...
"shall we let the pols get away with taking the wrong lesson? or fight for BALANCED redistricting across all party lines?"
Let's push for the 5000-member House of Reps. ;)
Seriously, baby steps with this one. Half the problem with initiatives such as the ones in CA and OH is that they aren't perceived as fair to the current ruling party. And they don't appear to solve the problems of fairness, since at least in CA the idea in the Proposition was to hand districting over to unelected people, adding another level of indirection to the districting process.
But if the change were to come upon us over years, rather than all in one complex package, we'd have time to examine the ramifications of a change before introducing another layer of change.
Start simple: Propose a single change to the law requiring legislatures to do something technical, with an unimpeachable argument that this small change makes districting "more fair" while not clearly upsetting the balance of power.
What's more, each State who tries a small thing could try a different small thing. Perhaps one State could try applying a formula relating boundary lengths to surface area, while another tries submitting districting to voter approval, or requiring State Supreme Court review of any proposal. Still a fourth could try another small variant on the current theme.
The ones that work will stick. The ones that don't get declared unconstitutional. By the end of 30 years or so perhaps we have something resembling fairness in districting.
This problem has been with us for 200 years. It's going to take longer than two election cycles to fix.
To Rob:
You might want to be careful not to overstress speed in teaching your kids the times tables. I remember that in third grade I simply could not reliably recall certain facts (7*8, for example). Instead, I would take a nearby fact I knew and add or subtract as needed (7*8=6*8+8). Although this showed that I actually understood what multiplication MEANT, my parents insisted on instant recall. This contributed to a fear of math that I am only now, as a college senior, getting over. Oh, and I still turn 7*4 into 14*2.
to Rob Perkins - I'm a harvard Physics grad student and I can bareley tell you 7x4 from my head in 5 secs. aritmetic is not that important. What I can do is differentiate and integrate in my head. Much more useful in my line of work.
We had lots of memorization in primary school math. I did very poorly. It was not until we hit high school that my ability to do real math became apparent.
Joe
I thought that bit with only having to get the first and last words was just a joke circulating on the Internet.
Kat:
That is terrible. Kudos to you for helping those poor kids out.
I do sometimes feel that I learned everything I did in spite of school, not because of it. And the most important and interesting things I learned, they didn't cover in school, even though they really should have, since it was clearly in-scope.
I'm still a bit fuzzy on how phonics is the right-wing analogue to whole-word. I read Why Johnny Can't Read last year or thereabouts, and I didn't see any sort of political agenda--and as for it being a plot to sell supplies, the book includes a full curriculum as an appendix. (It's about twenty pages.)
So far as I can tell, there's a right way to teach kids to read, and a wrong way. Not right or wrong as a sort of platonic ideal, but right in the sense that it works, as opposed to wrong, in the sense that it doesn't work.
Funny, I can read whole sentences of scrambled words, but not individual scrambled words. Makes me think of scrabble. Any anogram tips anyone?
@jane shevtsov -- I think at least a partially memorized multiplication table is essential so that time is not wasted computing a basic number relationship.
It's the underpinning of number theory, after all, to understand and recognize patterns arising from that.
But I guess my point got lost in my rant. Each new math curriculum introduced focuses on one thing or another, to the apparent detriment some other thing, based on this or that ideology.
This wouldn't be so bad, (since there's no avoiding some measure of that sort of thing) except it's being done in an environment where virtually no teacher has a love of the subject. They rote through a curriculum which asks kids to approach math from any of nine non-rote techniques.
The end result was a 10 year old who was still multiplying by counting on her fingers, or drawing pictures, because that was the easiest of the nine approaches for her in the second grade, and no teacher bothered to require her to try the other seven.
That's the frustrating bit.
@joe -- Abstract higher maths might be more useful for a physicist by far, (and I can do simple differentiating and integrating in my head as well, to at least a third degree polynomial. Don't ask me to try big-I notation problems or any taylor series, tho, I can't remember those) but for leaving a tip or estimating sales tax, you gotta know your times tables, and how to easily double, halve, and do powers of ten.
I don't mind calculators and such for even single digit multiplication, but I value today the requirements by my parents to just know certain math relationships. They were right to insist, and I'm better off today because I have the skill.
When I asked my daughter what half of thirteen was, the other day, she couldn't do it! I asked her "What's seven percent of 100?" She couldn't do that either.
(She can do it *now*, because we sat down together and reviewed some techniques. But I had to be the one to do it; she didn't get those techniques at school.)
There's stuff missing, and I think it's enthusiasm for the topic from teachers.
@rob:
... for leaving a tip or estimating sales tax, you gotta know your times tables, and how to easily double, halve, and do powers of ten.
This is just a silly digression, but my mother always taught me that it's usually easier to divide by 7 (1/7 == .142) and add a bit.
But on the general theory of requiring memorization, I am 100% ambivalent. On the one hand, I had to memorize my times tables up to 10*10, and am reasonably happy for it, but I also remember coming up with dozens of shortcuts for various math operations, and being told I couldn't use them because they didn't fit the template the teacher gave us for solving the problem. I also remember a friend of mine telling me that her teachers told her it was impossible to subtract 5 from 3, even after she explained that it had to be, and even pointed out on the number line (this was New Math) where -2 ought to be.
What we really need, I agree, is teachers who love the subject, who can teach simple, easily-understood techniques, but can also follow and understand when their students come up with other approaches to a problem. I suspect that may be part of the motivation behind the methodology of teaching multiple approaches to a specific problem.
I am heavily involved in my daughter's elementary school leadership, and am working with the numeracy team. Here is my take on it:
-Many elementary teachers do not like math, most are trained in literacy. We have made it a strategic objective of the school to improve our math scores, one of two things that are "most important" for everyone to work on.
-The requirements from the state and district are insane; they are contradictory, overlapping, documented in multiple places, and are not integrated across grade levels. The first assignment the team gave to the teachers was to distill a list of what the kids were supposed to learn from these documents. This means that each teacher in the state has to do this, or if they don't they risk missing something. You can imagine what this means for consistency between teachers. The district curriculum does not meet their own requirements!
-As far as phonics et al, I think the research is clear on this. Phonics, natural reading, whole language, fiction, and non-fiction all have to be blended together. No kid learns the same way. This gets to the math bit as well. By providing various algorithms, the teachers can get the most kids a way to do it, but they need to help the kids choose a way to get there. This is exactly analagous to how I do a problem. Since I understand numbers, I can approach it from a variety of ways. As long as the teacher clear that a way needs to be chosen, I think it will be OK. At our school, they have to show their reasoning as part of the problem answer. Just seeing that there are many ways of approaching a problem is valuable in learning how numbers work.
-Any child will benefit from parental teaching moments. When you are spending quality time with your kids, there is so much they can learn.
To Rob:
I agree that knowing at least a good fraction of the multiplication table is valuable. You can't use landmarks if you don't know any. It's the insistence on speed that I have a problem with.
To Joe:
I can relate, except that I had trouble with 7th grade algebra and struggled for a long time afterwards. I always passed my math classes but never did well. After finishing my calculus requirement in college, I thought I'd never see the stuff again, except in physics class. (I'm an Ecology, Behavior and Evolution major.)
Soon afterwards, I took ecology. The professor emphasized the equations for things like population growth and predator-prey systems. To my surprise, I did very well and even found myself explaining the material to other students.
The following year, I enrolled in a mathematical ecology class taught by the same prof -- partly, I think, because I knew he was good at explaining these things. The class was 90% derivations. The homework was tough, but with a lot of time in office hours (where, typically, a group of students would go over homework together, with the prof's guidance) I did reasonably well. Then came the midterm.
That exam was a disaster. After it was returned, I went to the prof's office and said I was thinking of dropping the course. I simply didn't see another choice -- this was the seventh week of a ten-week quarter.
To my surprise, my professor immediately told me that dropping the class would be a mistake. He said I had good intuition for the problems and we spent at least half an hour going over everything I had gotten right. My mistakes were usually computational, not conceptual.
After that, I got a fellow student to tutor me. It turned out that only five or six different things from algebra, plus a tendency to go too fast and make careless errors, were repeatedly tripping me up. On the final, I more than doubled my midterm score and actually scored a bit above the class average. Oh, and the other student and I ended up starting a math and biology discussion group that has been running for two quarters.
Looking back, I recognize a pattern. I had trouble with the multiplication table, long division and trigonometry. However, I did well with fourth-grade fractions, ninth-grade imaginary numbers and even the concept of a limit. I was also practically the only person in most of my classes to do better on word problems than on straight computational ones. The professor in my last calc course even raised my grade because he thought my questions and comments meant I understood more than my test scores would indicate. But, somehow, I had gotten caught up in an "I'm bad at math" mentality, never realizing that my style of thinking could be valuable.
I cannot be the only person in this situation. What could be done to prevent it from happening to others?
Not sure of the origin of this but snopes has more info
http://www.snopes.com/language/
apocryph/cambridge.asp
The text uses a number of cheats not just changes in letter order to make it easy to read. Letter shapes and the context is retained, so its a half truth.
On the topic of threats to the human race I notice the epoch times is reporting that H5N1 bird flu has been found in pigs in Xiangtan County, Hunan Province ouch.
Anyone who wants to know how well or poorly school is doing different things, how well the educational cirriculum works, etc, simply must read this annual report. I don't trust gvmt statistics very much, but I trust my own anecdotal experiences far less when considering educational policy and I have been a teacher and have tutored for years.
http://nces.ed.gov/nationsreportcard/
I hate to mention this, but there's actually data on this. In the 'year of the brain' the Clinton administration funded a review of reading modalities. The bottom line is the data is pretty good, for most kids the structured phonics stuff works best for learning to read:
Scientific American did a good review:
http://bestyoucanbe.blogspot.com/2005/01/teaching-reading-scientific-american.html
Since I'm a true commie socialist liberal traitor I was disappointed that the neolithic right wingers were mostly right, but they were.
Drifting away from data, I suspect somewhere about 1/2 of boys will do pretty well with any method, about 1/4 do much better with structured phonics, maybe 1/8 do better with whole language and 1/8 do very poorly with anything.
As for girls -- they probably would learn to read by glancing at passing street signs :-). (Only a mild exaggeration there ...)
Random idea... if it's difficult to find elementary-grade teachers who like math, how about recruiting older kids who are at the top of their math class, and quite possibly bored out of their skulls? Give them extra credits or special privileges or something for helping tutor the younger kids.
This was sparked by the anecdote about the friend who deduced the existence of minus two from looking at the number line, which made me think of other occasions when "math-challenged" friends of mine have told me things that teachers told them which were just... not right...
...not to mention the time when my (then-2nd-grade) daughter came to visit, with "I hate math!" on her lips, after which we spent 2-3 hours playing with numbers on a sheet of paper at her insistence. I seem to recall her saying "they didn't tell me that!" a lot.
(Favorite technique for figuring a 15% tip: take 10%, which is just all the numbers shifted one place to the right, and then halve that number, and finally add the two results together. The *main* problem with tips, though, for me anyway, is that I apparently can't do math and be social at the same time -- so this only works when I'm eating by myself. "Go figure", as they say. <rimshot>)
aulaclty
uesdnatnrd threw me for a loop. I thought I was reading "audacity usedtarnnd".
Teachers know what succeeds for the most part. Students whose physical health and security are satisfied (aka Maslow's Hierarchy of Needs foundation). Small class sizes that allow for differentiation among children at a similar level. Small classes consistently outperform large ones. We need more teachers, not super-teachers. Try to imagine the difference between managing a group of 6 children while allowing 12 to work unsupervised for fifteen minutes, and that of managing a group of 10, while allowing 20 children to work unsupervised for fifteen minutes. No you can't send them out to recess. The potential amount of individual instruction in that fifteen minute block goes from 2.5 minutes per student to 1.5 mps.
My wife teaches elementary grades in an urban school district. She has no fondness of whole language alone and prefers phonics predominating in blended approaches . I would say she is more pragmatic than ideological, because she was RIF'ed from several systems before acquiring tenure, and had to work with the material provided.
The current buzzword in literacy programs is Scientifically Based Reading Research (SBRR). She coordinates a set of schools in a larger funded study of a particular publisher's curriculum and they are seeing good results. Although testing is extensive, the curriculum provides supplemental materials for the children on each side of the theoretical bell curve. So testing actually promotes corrected behavior on the part of the teacher, when the teacher has a class size that allows for differentiation in the first place.
We can actually thank "No Child Left Behind" for promoting this, even if they don't fund appropriately.
My daughter was caught in the whole language trap. Her spelling is less than excellent. She is slow and thorough as a reader but does not often read for leisure.
What really struck me about my daughter's curriculum was that little time was spent learning words as composed of root, prefix, and suffix. I think this methodical instruction was a critical part of extending my vocabulary.
Four years later, my twin boys evaded the whole language approach, are also slow and thorough readers (I am not saying this is a good thing) and enjoy leisure reading.
My college friends and I were all flipping nerds. We figured out the tip with our calculators . . . .
No calculator?
* On Long Island, the sales tax was 7.5%. You doubled the tax to find the tip.
* Not on Long Island? You leave one buck of tip for every $6.66 of bill. Or $1.50 for $10. That's enough data points to extrapolate.
* Woozle's technique. Like him, I find it harder to do the math when I'm with a crowd.
* * *
Whole language versus Phonics? I really don't know.
I do know this: If more parents read to their kids, and let the kids see them reading themselves, and had books around the house, they'd be a lot more willing to try themselves.
Same with math. If parents could show their young kids why they shopped at store A rather than B, and make them aware of higher and lower prices, and cents-off coupons, and percentage-off sales, they'd be giving them a big leg up.
Stefan
OK. If you insist on talking about math shortcuts,(a whole different intelligence than language) around Ohio the sales taxes run from about 7% to 8.5%. So take your sales tax, double it and fudge the difference.
I picked up a few math tricks over the years to speed along mental calculations. One is "Russian division". I don't know the provenance, but it is simply the fact that you don't need to use the precise divisor to get the correct result. 300 / 12 can be dealt with as (300 / 3) / 4, = 100/4 = 25. Another I put under the heading of "Russian Math" is simply estimating and refining. 29 * 12 = (30 * 12) - (1 * 12) = 360 - 12 = 348. You may find that no better than 290 + 58 but in social conversations I find the ball park answer is often good enough.
Anyone know the provenance of 'Russian Division'. I think I read the peasants used it because the weren't taught a formal paper and pencil approach.
@Stefan
Does this mean someone that can do the math in his head is a 'Geek'? I never had a good differentiator before.
Some of that reasoning suffers from the chicken and the egg paradox in poor neighborhoods. Parents shop at store A because it is the only one in walking distance and the only one that provides them credit. The parents themselves may be unable to do the math or reading you suggest or be out of the home in the afternoons and evenings.
"The parents themselves may be unable to do the math or reading you suggest or be out of the home in the afternoons and evenings."
Yes indeed. There are also a lot of parents who can barely read.
This is why programs like Headstart are utterly vital.
There's a large fraction of parents who can read and do math. Maybe they need something like the Teachers' Edition of Sesame Street. Or early learning classes.
Stefan
When I leave a tip, I usually just make it 20% to make the math a little easier. Unless the service was awful, then it's less.
"if it's difficult to find elementary-grade teachers who like math, how about recruiting older kids who are at the top of their math class, and quite possibly bored out of their skulls?"
Because (and this is based on my experiences leading teenagers) while they might be very good at math, it doesn't stand to reason that they'd be consistently good at teaching. Both are important.
I don't doubt that phonics instruction "works best", but the problem is that we've got the English language, rather than something like koine Greek or ancient Hebrew. Personally I think a mix of whole reading and phonics works alright for beginning, but eventually we all have to get to the point where we read word by word, and not phonic sound by phonic sound.
@Jane -- The insistence on speed isn't primary, but when someone needs a full minute to count out six times seven (which I get by doing six times eight and subtracting six, natch, since 6x8 rhymes with its answer), that's a problem. I tossed out "five seconds" because that's about how long it takes me to do the ones I haven't memorized.
1. Re: redistricting in Ohio.
Want to know why I didn't vote for it? Because there was no accountability in the plan. A judge appoints two, those two pick two others and voila! They can spend as much money as they like, regardless of the state budget.
Until I read about the lack of control on funding, I was there: it was the only state issue of the four "reform" issues on the ballot I would have considered.
I have not yet confirmed the truth of this, but the local rumor was that should this measure pass, Cinci and Toledo - at opposite ends of the state - would be in the same congressional district. That's gerrymandering at its finest.
My father is mystified why these four issues didn't pass. After all, we have a governor who pled no contest to a crime. We need to clean up Ohio - but clearly these initiatives were not the way to go. I am bemused by the explanations why they crashed and burned: too long, bad advertising, lying and misleading ads from the opposition, etc. Hey, folks, give me a break. We voted against it because they would make bad law. End of story.
2. Re: math/reading.
I'm a homeschooler so I've had plenty of experience teaching both. Phonics is the way to go, hands down. One does not have to put a great deal of money into it: I purchased a book "How to Teach Your Child To Read in 100 Easy Lessons" for less than $25.00 and taught 3 of my 4 children from it. Nothing is perfect, of course, or right for every child, thus the one who needed a different presentation but still got the phonics and is now reading Daniel Pinkwater to her youngest sister.
I learned math in the '60's under the guise of New Math. I memorized my times tables, but I cannot do long division. I can figure fractions and do geometry, but someday, somehow, I will make pay whomever it was who started mixing letters in with numbers. Thank the good Lord for good math programs that have lots of practice and scripts for me to follow. My oldest just started high school and is acing his Algebra 1 class. He's doing much better than I ever did in Math. I attribute it to demanding memorization of math facts and repetitive homework that doesn't just focus on the day's lesson. That's Saxon Math I'm recommending, if anyone cares to know.
As for tipping: I was a waitress. 20% is moving the decimal place over 1 column to the left and doubling. Dead simple.
Buckeye Girl
@Kat
"I looked at it, and was mostly confused. As far as I can tell, there's been a decent upward climb in the skill levels of 9 and 13 year-olds in both math and reading since 1973... and essentially no change in the skill levels of 17-year olds. So the younger kids can read and do math better, but they're still graduating with the same skill level as their 1973 counterparts? That doesn't make sense."
A matter of lies, damn lies, and statistics. :) You neglected to think about the graduation rate. The ones who dropped out went untested. Presumably there has been a steady increase in graduation rates. Does the website tell you?
The tests themselves may top out at 10th grade and if you have more superior readers than previously, you may not recognize them. But how much better can you get at a mechanical art like reading and how well will a test measure it?
Even taking into account a better graduation rate, I still think high school curricula are less rigorous than they should be, for the sake of our kids.
This is not to say that everything we were doing in the early 20th as re high school was approvable.
I have a couple of interesting experiences in connection with No Child Left Behind and with state mandated testing in general. One is that universally, teachers and principals at the elementary level are beginning to hate it. They probably crossed the threshold years before I did, precisely because it makes planning the school year much more rigid.
And, it *is* getting way too far out of hand, when there is a Washington Assessment of Student Learning *every year* from the second grade through the seventh, when the original proposals called for testing only in the fourth, seventh, and tenth grades.
However, the standardized tests in Washington State, at least, are not at all like the standardized tests, such as older SAT, CogAT, and ITBS tests we remember from our youth.
(Those tests are still around, natch, and used in the most ironic places around here, such as identification of gifted children. What?! Identify a gifted child with the ITBS?! Oh yes! Right here where I live!)
Instead of bubble sheets and syllogisms, the WASL tests are all pretty much essay questions. In addition to a few multi-choice answers, students must explain their math answers, for example.
There's an example keyed to the seventh grade, here: http://www.k12.wa.us/assessment/WASL/testquestion/2004/WASL2004RIDMathGr07.pdf
Think about the scope of such a test; it's impossible to computer-grade half of it!
Useful tax tip for those in Los Angeles area. 25% covers tax and tip. This is nice to know if you're out with a group. Everyone orders what they want, individually figures out what they owe, and the total generally comes out right.
On math, I've long believed that a major cause of math anxiety is that people don't understand that *simple* and *easy* are very different things. People think that they should be, and then when they finally figure out a math problem that was hard for them they say, "That was so simple. I must have been an idiot not to get it!"
Quick exercise. Write down 100 numbers and try to add them by hand correctly the first time. I bet you can't do it. Second part, see if you can recognize a friend's voice. I bet it is trivial for you.
Clearly adding 100 numbers is not an easy task. And recognizing someone's voice is. But adding 100 numbers is a very simple task, while recognizing someone's voice is an extremely complex one. Why is that?
The reason is that we are wired to do certain kinds of complex pattern recognition tasks easily. We are not wired to handle incrementally building simple things on top of each other.
The moral is that math is both simple and hard. In my experience, people who are good at math aren't so much geniuses as they are people who have their expectations set right. For instance a professional mathematician might read a technical math paper at about one page a day. The mathematician doesn't get frustrated at that glacial pace because the mathematician expects it to take that much work! And the mathematician doesn't get upset at having trouble on a simple point, because again the expectations are set right.
"i cdnuolt blveiee taht I cluod aulaclty
uesdnatnrd waht I was rdgnieg....
Could that have been written by or for a dyslexic?
My daughter's five and we've started teaching her multiplication. For now, when I ask her "how much is three fours", she still counts up from four on her fingers but at least she's getting the gist of it down. I don't know if she'll ever memorize multiplication tables (I haven't, much) but if she knows how to get the answer, she'll do ok.
For those who want to try it, here's a simple python script to 'dispell' your lexical phobias:
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from random import randint
def scramble (a, b):
"A comparison routine which returns a random result!"
return randint (-100, 100)
def dispell (text):
"Scrambles the middle of each word in text, and returns the result."
newText = ""
wordList = text.split()
for word in wordList:
#Scramble the middle. First and last letters remain unchanged.
if len(word) > 3:
middle = list (word[1 : len(word)-1])
middle.sort (scramble)
word = word[0] + "".join(middle) + word[-1]
# Now put it back together
newText += word + " "
return newText
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Hey, David! Have you seen this?
http://www.mrc-cbu.cam.ac.uk/~mattd/Cmabrigde/newscientist_letter.html
Seems the work on comprehension of scrambled words was done back in '76.
I wonder where people got the idea that "whole language" was a leftwing project? Oh, yeah, from the rightwingers selling phonics. Geez, you ought to know better than to believe anything those people tell you. I do recall when whole language was the rage in the mid-'60s, my little brother failed first grade because he didn't learn to read. My mother taught him to read in about three or four weeks over the summer using phonics...but he still had to repeat the grade.
A lot of interesting stuff about math from your correspondents. I never really learned the multiplication tables, just a few key items like all the squares, 5x, 6x and 9x, and extrapolated everything else from there. However, I did learn set theory and non-decimal bases in 3rd grade...they called it New Math and the parents hated it because they couldn't help their children with their homework. ("1 + 1 is NOT 10!!! I don't care what your teacher said!") In 4th grade we pretended the whole year never happened. Boy was I surprised to encounter that stuff again in college!
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