Sunday, December 25, 2005
"769. An old brainteaser by Leonty Magnitsky: If a man drinks a barrel of water by himself in 14 days and the same barrel with his wife in 10 days, how many days would it take his wife to drink the barrel by herself?"
First of all, I find this easier to solve when the wording is changed to a barrel of vodka.
Here is my solution:
The sum of the fractional parts (man and wife) of drinking in one day is equal to the fractional part of both drinking in one day:
Let x = days wife takes to consume the whole barrel
1/14 + 1/x = 1/10
Multiply each side by the LCD to clear fractions:
10x + 140 = 14x
4x = 140
x = 35
Sunday, December 18, 2005
Educational ConstructivismThe California science framework has received top marks and can be read here.
Constructivism is not new. It was evident in the first draft
(1992) of the National Science Education Standards, where
it took the form of a claimed postmodern philosophy of science. That, in turn, incorporates one kind of constructivism (“social” constructivism) about knowledge, including scientific knowledge.The adopted philosophy was an application to learning standards of the increasingly popular educational constructivism,whose main tenet is that learning happens only by an individual’s action, his or her making and doing things in the world, not as a result of any conveyance of knowledge (as in teaching).10 A revision of that early draft eliminated the praise of postmodernism but left in place the notion that a learner can do no more than to construct knowledge, which is therefore personal, from things and events in his or her sensed environment. It is supposed to follow from this that scientific knowledge cannot be transferred from one person—a teacher (or from a book)—to another. The learning expectations of standards should therefore focus much more on process, the “doing”of science by the student, and much less on its reputed facts.11
Friday, December 09, 2005
Here, a writer gives thanks to the whole panoply of whole language inventors and promoters:
Thank you Whole Language. Thank you for your many pearls of wisdom. Thank you for Context Clues. Thank you for Prior Knowledge. Thank you for the Initial Consonant. Thank you for Picture Clues. Thank you for Miscues.
But most of all, thank you for my wife. The other day she and I were riding along the highway and saw a sign for a town called Verona, so my wife read "Veronica". It's very simple, you see. First she applied Context Clues (she knew we were looking for a name). Then she applied the Initial Consonant ("V"). Then she applied Prior Knowledge (she already knew of a name "Veronica"). She put these Whole Language strategies together and ... success! At least, as much success as we can expect, I suppose.
Thank you William S. Gray for inventing "Look-Say" and the "Dick and Jane" series of basal readers. Thank you A. Sterl Artley for helping Mr. Gray and for your phonics-bashing diatribes of the 1950s and 1960s. Thanks to the National Education Association for giving Mr. Gray and his friends two years of free promotion in the NEA Journal in 1930 and 1931. Together you all had managed to essentially eradicate phonics from America's public schools by the 1950s and early 60s, when my wife went to school.
But more importantly, thank you for my wife. A while back she was reading a pamphlet about something that was described as "venerable". Now that's a word you don't see every day, so what did she do but cleverly pull out her Whole Language skills? Context Clues, you see, told her that she was looking for an adjective. Next was the Initial Consonant "V". Then out came the Prior Knowledge -- she simply thought of an adjective she already knew that was about the right length and started with "V". And voila ... success again ... she came up with "vulnerable". Perfect! Well, at least as perfect as things get in publik ejukayshun, right?
Thanks Kenneth Goodman for reviving the floundering Look-Say, adding a few New Age twists and renaming it Whole Language back in the early 80s. Just like the Whole Earth Catalog and Whole Grains and everything else that was Whole ... what else could it be but wonderful? Without you, Kenneth, the evils of phonics might have returned, and then where would we have been?
Thank you Dorothy Strickland for "Emerging Literacy" -- the idea that kids are naturally inclined to read if only we will surround them with literature. Thanks to all the other Whole Language textbook authors who cranked out textbook after textbook that either omitted phonics entirely or disparaged phonics openly. Thank you Teachers College, Columbia, for promoting Whole Language to teachers' colleges worldwide. Can you even imagine how effective you were in eradicating phonics instruction throughout the English-speaking world?
Thank you International Reading Association (IRA) and National Council of Teachers of English (NCTE). For decades you appointed people like William S. Gray and Kenneth Goodman to lead your entire organizations in the fight against phonics. Somehow you raised hundreds of thousands or perhaps millions of dollars to pay PR firms to get their opinions so heavily quoted in the press that the public is now completely confused in its ideas about what works and what doesn't work in reading instruction.
But once again thank you for my wife. A while back she was reading about some Congregational Church. And do you know, even with the Context Clues and the Prior Knowledge (about what names churches might have, presumably) and the Initial Consonant, she still managed to come up with "Congressional Church". Even though this was years ago, I remember it like it was yesterday.
Thank you Alfie Kohn and Dennis Baron and Mike Ford and Gerald Coles and Harvey Daniels and Gerald Bracey and Susan Ohanian and Stephen Krashen and Jim Trelease and all the other propagandists who lash out continuously against successful practice in general and phonics in particular. Through your tireless efforts, the public is continually misinformed. Without the public's perpetual state of confusion and misinformation, Whole Language would not have survived a single day. Thank you for keeping Look-Say and Whole Language and Balanced Literacy alive to create yet another generation of people who can read as well as my wife does.
Speaking of my wife, last night she was reading a brochure aloud about a museum with an "eclectic" collection, and what do you suppose she said? You guessed it (and so did she): "electric"! Maybe the absence of the Initial Consonant threw her off.
Thank you Marie Clay for inventing the phenomenally expensive Reading Recovery, a program installed in virtually every public school, it seems, and designed to treat the educational effects of Whole Language by applying yet more Whole Language. Thank you for giving my school district more stuff like this to spend my tax money on. How is it that I am not clever enough to imagine things like this?
Thank you Richard Allington, current (2005) president of the International Reading Association, for your campaign of misinformation against Direct Instruction (a successful phonics-based program). The cleverness of your propaganda puts the Soviets, the Chinese Communists, and all the other tyrants of the 20th century to shame. You know of course that Direct Instruction (DI) participated in a huge study (Project Follow Through) in which all the participants except DI failed, and in which DI succeeded brilliantly. And so you twist this around to say that by virtue of its association in this study with the constructivist-favored instructional styles that failed so miserably, we should all conclude that DI must necessarily also have been a failure. Your logic, so typical of that of the IRA, the NCTE, and the rest of the Constructivist Cabal, is irrefutable.
But once again thank you all for my wife. Hardly a day goes by when she does not demonstrate the success of Look-Say, or Whole Language, or Balanced Literacy or whatever you all call it now. Really, it's so amusing I really can't even quantify it. I never know what she'll read next ... and neither does she! Just imagine all her Miscues!
The sheer unpredictability of listening to her read is astounding ... and unpredictability is the essence of entertainment, right? I mean, she might read "deleterious" as "delicious" or perhaps "injurious" as "injustice" or "parabola" as "parachute" or maybe "quintessence" as "quintuplet", or "signify" as "signature". I could go on and on almost endlessly. The laughs just never stop here. And all thanks to you. All of you.
So thank you, Whole Language. Where would we be without you? The possibilities just boggle the mind.
[Note: This author normally signs his work, but in this case declines because he doesn't want his wife identified in this manner.]
Sunday, December 04, 2005
Wednesday, November 30, 2005
Constructivism is rearing its ugly head again. With this kind of help, students are not going to "own" the algebraic method of solving this problems. They might not even "own" the inefficient guess-and-check method. If you are being taught properly and practice sufficiently to the point of overlearning, then you are more likely to "own" math knowledge than when left groping in the dark.
A farmer sends his daughter and son out into the barnyard to count the number of chickens and pigs. When they return the son says that he counted 200 legs and the daughter says she counted 70 heads. How many pigs and chickens does the farmer have?
A student well versed in algebra might do the following to set up the problem: p = pigs, c = chickens. p + c = 70 (heads) 4p + 2c = 200 (pigs have 4 legs and chickens have 2 legs). These two equations may be used to solve the problem. Students might solve this problem by "guessing and checking," or drawing pictures. Some methods of solving problems might be considered more "efficient." That may be true, but the correct answer can be found using multiple methods. Children think about mathematics in different ways depending on their prior experiences at home and school. By allowing students to think flexibly about numbers, we encourage them to "own" the math forever, instead of "borrowing" until class is over. (Answer: 40 chickens and 30 pigs)
Saturday, November 26, 2005
In what sounds like a three stooges routine, the three "learning specialists" are alarmed by what they see as a trend toward academic achievement:
Perhaps now is a good time to ask this question: What are schools supposed to do for our children? As learning specialists, we see an alarming trend: Our education system increasingly is focusing not on developing children’s aptitude for learning—their ability to absorb new information quickly and solve problems creatively—but on their academic achievements—their mastery of particular subjects and skills as proven by performance on standardized tests.Silly me. I would have thought that academic achievement demonstrates at least an "ability to absorb new information quickly," the purported goal of these specialists.
The authors of the anti-achievement piece do manage to offer "sobering" examples of imperial decline due to memorization and academic achievement. The cause-and-effect scenario painted here does seem a bit fishy to me. I kind of doubt that China went into a tailspin because a few mandarins had the ability memorize Confucian philosophy. Would we as a society suddenly have to live in caves in the unthinkable event that some of our bureaucrats (say, at the board of ed) suddenly had the urge to memorize a few poems by Whitehead and Tennyson?
Snippet from the trio's commentary:
This is a serious concern for our kids and our society. History offers sobering examples of what can happen when standardized achievements are elevated over open-ended abilities.The essence of the anti-academic achievement position as far as I can distill it is a false dichotomy between learning academic subject matter on the one hand and "creativity, innovation, and independent thinking" on the other. Educationists worship at at the altar of ignorance in the name of "creativity" but ignorance is not a prerequisite for "creativity".
During the 18th and 19th centuries, imperial China—once the most technologically advanced civilization in the world—fell into decline as power passed into the hands of a mandarin class of bureaucrats selected for their ability to memorize Confucian philosophy. More recently, Japanese authorities have begun dismantling an education system that long relied on a uniform national curriculum and after-hours classes at juku “cram schools.” The Japanese believe this approach has stifled creativity, innovation, and independent thinking, contributing to the stagnation of the Japanese economy.
We worry that America is heading down a similar path. If promoting our children’s achievements becomes our sole focus, both our children and our society will suffer.
Saturday, November 19, 2005
I would label myself a political liberal and an educational conservative, or perhaps more accurately, an educational pragmatist. Political liberals really ought to oppose progressive educational ideas because they have led to practical failure and greater social inequity. The only practical way to achieve liberalism’s aim of greater social justice is to pursue conservative educational policies.In combating the dominant ed creed, propopents of quality education must have a developed sense of how the language employed by the dominant ed creed is manipulative, charged, disparaging and stacked against them. Some of the phrases that come to mind are "sage on the stage, guide on the side," "chalk and talk," "drill and kill" "teach the whole child," "teach the child, not the subject," "less is more," "up is down," "freedom is slavery" (well, I made up the last two or, rather, stole the last one from Orwell). There is nothing comparable for those who value expository instruction and domain knowledge.
[Fortunately, not all educationist phrases are catchy. There is also some pretty dreary stuff. I culled this from a constructivist site: "This article discusses several active-learning techniques that instructors can use to help students construct knowledge, such as think-pair-share, guided reciprocal peer questioning, jigsaw, and co-op co-op."]
Other words deployed by the dominant ed creed to disparage the notion of imparting knowledge are "lecture", "active" and "passive". "Lecture" has the negative connotation of droning on without regard for the audience's (in this case the pupils') level of understanding and its capacity to follow while the captive audience sits by "passively". No teacher worth anything would teach that way. (Adherents of the dominant ed creed forget that listening attentively to explicit instruction is also being active, but the followers of the creed claim to have a monopoly on "active").
But the disparagement of any explicit instruction by labeling it "lecture" is so strong that explicit instruction is proscribed in many places. That is detrimental to achieving quality education. For example, good math instruction should consist of modeling (interactive modeling if appropriate) followed by guided practice, independent practice and review. In other words, there must be talk as required by the circumstances. And how would one teach history and other subjects without talking?
I coined the impressive, albeit cumbersome, phrase "empathetic, interactive expository instruction" as a counterpoint to the dreaded "lecture". Alas, it can't compete with the catchiness of "talk and chalk" or "drill and kill". (Now I have to put my phrase in rhyme form).
I include "empathetic" in my phrase to stress the importance of discovering and being being sensitive to Vygosky's fabled zone of proximal development (a jazzed-up way of saying that our instruction must be geared to the pupils' ability and level of comprehension).
In his article, E.D. Hirsch takes apart some of the conceits of educationists:
Unfortunately, many of today’s American educators paint traditional education as the arch-enemy of "humane" modern education. Even everyday classroom language unfairly pits the two alternatives against one another. Here are some typical descriptions used by progressives to compare old and new methods:You can read the entire article here.
Traditional vs. Modern
Merely verbal vs. Hands-on
Premature vs. Developmentally appropriate
Fragmented vs. Integrated
Boring vs. Interesting
Lockstep vs. Individualized
Parents presented with such choices for their children’s education would be unlikely to prefer traditional, merely verbal, premature, fragmented, boring, and lockstep instruction to instruction that is modern, hands-on, developmentally appropriate, integrated, interesting, and individualized. But of course this is a loaded and misleading contrast. Let’s look at those simple polarities one at a time.
Sunday, November 13, 2005
From the NYT's Penfield article:
By last spring, these parents had discovered one another and their common exasperation with constructivist math. Jim Munch's father, Bill, a software developer at Kodak, drew up a petition asking the Penfield schools to offer pupils the option of taking traditional math. Nearly 700 residents signed it. Last June, the Board of Education turned down the request.Giving parents a choice between fuzzy and real math is the democratic thing to do and is also a good political strategy. It should satisfy everyone. It's an inoffensive offensive. But I doubt that zealous educationists in a position of power will go along (and don't as the example above shows). Being responsive to reasonable popular wishes is not their thing. I also suspect that many parents are not conversant with the real vs. fuzzy math issues and won't know what to do with choice.
Just yesterday I talked to a parent of a sixth grader I am tutoring in math who had no clue of fuzzy math. (I tutor disadvantaged kids after hours in addition to my regular classes.)
I was helping the kid do homework. Part of the homework required the young girl to cut a sheet of paper into strips to make various fractions. The parent was aghast and thought it was a time-waster. I had to explain the purpose of the exercise. It was all news to her.
The school the kid is in uses the fuzzy math series Connected Math. The homework assignment was quite demanding and way beyond this pupil's abilities. She had neither a conceptual understanding of the task nor the requisite tools (computational skills, procedural knowledge, math facts) to accomplish the task had she had a conceptual understanding of the problem.
This is a key problem with fuzzy math. It is quite pretentious on the one hand, and refuses to teach the necessary skills on the other. The result: the kid was hopelessly drowning and getting straight F's.
Now what was the task? It was a real-world problem.
A class was holding a fundraiser to raise $300.00 in ten days. The progress was shown in the form of thermometers showing progress in two-day increments. The thermometers were all 8 1/2 inches long and showed the money raised so far on the various days in red. The fraction strips were to be used to determine the amount of money raised so far on the various days and then to plot the progress in a coordinate plane. The pupil was to make the strips and mark fractions from 1/2 to 1/12 on the various strips, and then use the strips for measurement.
Making fractions strips of 1/2, 1/4 and 1/8 is of course easy. It's not so easy to come up with 1/3, 1/5, 1/7, 1/9, 1/12. You could do time-consuming trial-and-error folding. Or you could divide 8 1/2 by the denominator of the various fractions if you know how (the child didn't know).
Even if you can get the numbers they don't work well with an inch ruler. You could approximate. Suppose you (meaning the kid) could accomplish all that. Then what?
The goal of the assignment is to come up with dollar amounts derived from the thermometers and then to plot these amounts over time (fundraising progress).
How are you going to derive dollar amounts if all you have is an 8 1/2 in long thermometer (representing $300) and a red bar on the thermometer without any numbers, marks or gradations (the length of the red bar represents the money raised so far)?
You could measure the red bar in inches, form a ratio (the red bar to total thermometer length ratio), calculate the decimal, multiply the decimal by 300.
However, the assignment calls for measuring the red bar with the "fraction ruler". Then you would know what fraction of 8 1/2 the red bar represents. You can then multiply the fraction by 300 to get the dollar amount. All this without instructions in CMP and without computational skills and procedural knowledge.
This is too complicated and frustrating for a math-challenged child who needs to learn at her level and make steady progress.
No wonder the kid is drowning. What a tragedy.
After citing example after example of math cripples, the article has this gem that shows the arrogance of educationists:
LAST spring, when he was only a sophomore, Jim Munch received a plaque honoring him as top scorer on the high school math team here. He went on to earn the highest mark possible, a 5, on an Advanced Placement exam in calculus. His ambition is to become a theoretical mathematician.
So Jim might have seemed the veritable symbol for the new math curriculum installed over the last seven years in this ambitious, educated suburb of Rochester. Since seventh grade, he had been taking the "constructivist" or "inquiry" program, so named because it emphasizes pupils' constructing their own knowledge through a process of reasoning.
Jim, however, placed the credit elsewhere. His parents, an engineer and an educator, covertly tutored him in traditional math. Several teachers, in the privacy of their own classrooms, contravened the official curriculum to teach the problem-solving formulas that constructivist math denigrates as mindless memorization.
"My whole experience in math the last few years has been a struggle against the program," Jim said recently. "Whatever I've achieved, I've achieved in spite of it. Kids do not do better learning math themselves. There's a reason we go to school, which is that there's someone smarter than us with something to teach us."
By last spring, these parents had discovered one another and their common exasperation with constructivist math. Jim Munch's father, Bill, a software developer at Kodak, drew up a petition asking the Penfield schools to offer pupils the option of taking traditional math. Nearly 700 residents signed it. Last June, the Board of Education turned down the request.The superintendent haughtily dismisses parent concerns. Many of the parents have extensive math backgrounds:
Susan Gray, the superintendent, attributed the criticism of the math program to "helicopter parents" who are accustomed to being deeply involved in all aspects of their children's lives. "Because the pedagogy has changed, the parents who knew the old ways didn't know how to help their children," she said. "They didn't have the knowledge and skills to support their children at home. There's a security in memorization of math facts, and that security is gone now."
YET many of the dissident parents have extensive math backgrounds and thus the ability to criticize the curriculum. It is also true that most of them tolerated the constructivist program for its first several years, until bitter experience drove them into rebellion.
"Mathematics achievement in America is far below what we would like it to be. Recent "reform" efforts only aggravate the problem. As a result, our children have less and less exposure to rigorous, content-rich mathematics. The advocates of the new, fuzzy math have practiced their rhetoric well. They speak of higher-order thinking, conceptual understanding and solving problems, but they neglect the systematic mastery of the fundamental building blocks necessary for success in any of these areas. Their focus is on things like calculators, blocks, guesswork, and group activities and they shun things like algorithms and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement."
One way out of this disastrous state of affairs is to create national standards. This is, of course, fraught with danger as past experiences show, e.g. the experience with the Gary B. Nash history "standards". Such a project would attract the usual suspects. But I think the risk has to be taken. The advocates of sound, rigorous standards must organize and mobilize and be in a position to counter the inevitable attempt to dilute the standards and to institute educational lunacy.
It is therefore gratifying to read that Diane Ravitch is calling precisely for such standards. [Diane Ravitch's article was first published in the NYT but the article will soon disappear into the paid archives.]
The release last month of test results by the National Assessment of Educational Progress, which is part of the Department of Education, vividly demonstrated why varying state standards and tests are inadequate. Almost all states report that, based on their own tests, incredibly large proportions of their students meet high standards. Yet the scores on the federal test (which was given to a representative sample of fourth and eighth graders) were far lower. Basically, the states have embraced low standards and grade inflation.
Friday, November 11, 2005
So why don’t I like it? Why do I belittle it as kitsch? Kitsch, after all, usually refers to something of tawdry design or appearance created to appeal to nondiscriminating tastes—for example, those portraits of Elvis or bullfighters painted in neon colours on black velvet. But the Woolfolk text can hardly be accused of tawdry design or appearance. Indeed, measured against its competitors, it is presumably the crème de la crème.
Miseducative kitsch. In name-calling the Woolfolk text “kitsch,” I have in mind a less obvious, but perhaps more definitive, meaning of the term suggested by writer and critic Robert Fulford. In a recent CBC radio interview, Fulford dismissed so-called “victim-based art” as kitsch, but not necessarily because of any cheap or garish aesthetic qualities. Rather, Fulford argued, this “art” is kitsch because it seeks, by design, to compel the viewer to experience certain predetermined responses to it—in this case, sorrow, sympathy, compassion, and, perhaps, guilt. Fulford went on to liken victim-based art to the kitschy Saturday Evening Post cover art of Norman Rockwell, the artist whose slice-of-Americanlife paintings are typically unambiguously and irresistibly “cute” and, hence, admit of no other viewer response. For Fulford, what makes both victim-based and Norman Rockwell’s “art” quintessentially kitsch is that both contrive to over-determine and, consequently, to limit the viewer’s range of intellectual and emotional response. Neither allows for any interpretive or responsive ambiguity; both attempt to coerce thought and feeling.
Sunday, November 06, 2005
The teacher appreciates multiple perspectives and conveys to learners how knowledge is developed from the vantage point of the knower.What is it with these "multiple perspectives?" It seems to me that at the bottom of this excitement is this postmodern notion that evidence, scholarship, objectivity and truth are illusory. There are only perpectives -- influenced, no doubt, by some "power" considerations.
The teacher appreciates and values human diversity, shows respect for students’ varied talents and perspectives, and is committed to the pursuit of “individually configured excellence.”
This is dangerous drivel. What would stand in the way to conferring to creationism and to Holocaust denial the status of just another, equally valid, "multiple perspective?"
It would be much more appropriate to talk about "multiple ignorances."
UPDATE: See Chris Correa for a thoughtful examination of dispositions.
Sunday, October 30, 2005
Abstract: Reading instruction is one of the very few areas where it is not the case that “more research is needed.” Educational policy makers already have the theory and the evidence supporting it to guide the implementation of effective reading programs from K-12. In fact, they have had the theory and the evidence for decades. The central problem they face in providing effective reading instruction and a sound reading curriculum stems not from an absence of a research base but from willful indifference to what the research has consistently shown and to a theory that has been repeatedly confirmed. Using Jeanne Chall’s The Academic Achievement Challenge as a point of departure, I suggest why our education schools, through their influence on teachers, administrators, textbook publishers, and state and national assessments of students and teachers, have come to be the major obstacle to closing the “gap” in student achievement.
One of the sharpest education writers in the edusphere has done just that and now has convinced herself that posting such samples is unethical and will take down her post.
Here is a tiny snippet from these samples from 11th graders:
"in [title]. will has to deal with alot of racism bieng that she is a nigga during slavery. she sees her father get killed and then have to go home and find out that her mother is tooken buy the british. then will y goes to her aunt besty house and captian ivers try to put her back into slavery."My view is that any lingering ethical concerns are far outweighed by the public service rendered by exposing this appalling state of affairs.
Read the rest of the samples before they disappear into electronic heaven.
Saturday, October 29, 2005
Thursday, October 27, 2005
But all is not well. The good folks at the Fordham Foundation have assembled a
crack team to take a closer look at what the NAEP drafters are up to. The signs are not encouraging. Apparently, the discovering drafters are smitten by the fashionable but absurd educationist creed according to which barely literate pupils can "discover" the vast knowledge contributed by giants of science and accumulated over thousands of years on their own. Ignis fatuus is their guiding light.
Let's not allow the reinvent-the-wheel crowd to follow the will-o'-the-wisp unhindered.
Our basic position is that every child in America should receive a rich and rigorous science education in the primary and secondary grades, one that provides a broad understanding of key scientific concepts and ways of thinking. We reject the trendy notion that children, unaided, can “discover” key scientific concepts. Most of science must be taught if it is to be learned.
In these ways we demur from the “consensus” represented by several professional organizations that have offered national guidelines for science education (the National Science Education Standards of the National Research Council and Benchmarks for Science Literacy of the American Association for the Advancement of Science [AAAS]). Unfortunately, the NAEP Science Assessment Steering Committee encouraged the Framework’s authors to rely upon those very documents as their guide stars. This was a mistake. Just as the National Council for the Teaching of Mathematics (NCTM) is a partisan in the “math wars,” so, too, do these organizations represent one pole of the debate over science education and instruction. To follow their guidance is to “take one side” in an important debate rather than to strive for balance.
Wednesday, October 26, 2005
Sunday, October 23, 2005
Something must have gone awfully wrong with these students' math instruction in high school and probably even earlier in elementary school. I am on the case investigating.
I teach math to eighth graders and know that teaching math successfully need not be rocket science. Most of my students can now convert fractions to decimals and percents (and vice-versa) in their sleep. They can also solve the three different types of percent word problems (unkown rate, whole and part) in their sleep.
The following is an aspect of how I teach percentages after teaching the concept that a percentage is an equivalent fraction with a denominator of one hundred.
I have my students create a table with three columns. Each column is labeled fraction, decimal, percent. This visualizes the operations and helps reduce confusion. They can go from left to right to start with fractions and end up with percents, or from right to left to start with percents and end up with fractions.
Converting percents to fractions generally poses no problems when the percent is a whole number, e.g. 47% --> .47 --> 47/100. A special problem arises when the percent is a fraction like 5-1/4 %. This is where the students need to realize that an additional step is required. Many students want to enter 5.25 in the decimal column. The task of the teacher is to focus on this problem and to show that the students must first convert to 5.25%, then to the decimal .0525 and on to the fraction.
A good way to drive home this point is to contrast the conversion of 5-1/4 (without %) and 5-1/4% to decimals and writing 5-1/4% and 5.25% in the percent column. Only now can 5.25% leave the percent column and move to the decimal column to become .0525. Bingo!
I also have my students solve percent problems as proportions and equations. I drill them in identifying the rate (percent), part and whole in any percent problem. For equations I have them use the rb=a formula. r=rate (percent), b=base (whole) and a=amount (part). This is also a nice algebra exercise since they need to solve for a, b or r as the case may be.
I once again have them make a table with three columns and several rows. The columns are labeled r, b and a.
Then I have them look at various percent problems and ask them to identify what's known and unknown. If the percent is unknown, a question mark goes into the box of the r-column and what's known (whole and part) goes into the respective boxes of the b-column and a-column.
If a (the part) or b (the whole) is unknown, the procedure is repeated accordingly. This works amazingly well and the visualization once again helps to minimize confusion.
An added advantage is that the students learn how to solve for the various variables and how to manipulate the rb=a formula, e.g. r=a/b, b=a/r.
It is amazing, though, how many of these 8th graders find this manipulation of variables difficult. Adults might consider this manipulation child's play. But it really represents a huge jump to this age group to go from the concreteness of numbers to the abstractness of variables (letters).
This concludes the lesson on how to teach percents for understanding. Instructivist will give other lessons on how to teach math successfully to middle graders as he sees fit.
Sunday, October 16, 2005
Good teaching is far more than directly observable and measurable behavior. Good teachers possess traits and qualities that either cannot be quantified or are hard to quantify. I would even go so far as to claim that trying to quantity these traits and qualities is a case of scientism, which I idiosyncratically define as an attempt to quantify qualities that are ill-suited for quantification.
How, for example, do you go about quantifying an inspiring, radiating personality? How do you quantify a sense of humor, wit, a capability for empathy, a developed sensitivity to the zone of proximal development? How do you quantify imagination, creativity and a capacity to teach for understanding? How do you distinguish numerically between genuine and phony sentiment and what numbers would you assign to a story-telling capability?
I think education would be much better served if we approached the question of what makes a good teacher from a humanistic-philosophical perspective. But then, of course, we would first have to have a notion of desirable educational goals because "good" does not exist in a vacuum.
Saturday, October 08, 2005
Trying to pin down constructivism -- to see if it can be defined in a meaningful way and whether there is any sense that can be separated from nonsense -- is like searching for the unicorn.
At this point of my search, the best I can do is conclude that constructivists display a case of arrested development. Constructivists are stuck in the Piagetian sensorimotor or, at best, pre-operational stage. This infantilism that manifests itself in constructivists goes a long way in explaining educationist hostility to knowledge and educationist anti-intellectualism. But this infantilism is golden compared to the denial of objective reality by radical constructivist gurus like von Glaserfeld.
Let me elaborate a bit.
Constructivists cite Piaget and Vygotsky as their progenitors. Piaget did groundbreaking work on how toddlers develop intellectually and came up with different stages (really a continuum divided into stages to get a better handle on this development). For example, a toddler might recognize at some point that an object that is moved behind another object and disappears from sight does not cease to exist (permanence). Or a toddler might discover on his own that an object falls when released or that bumping into a wall is not a good idea or that a flame is hot.
The constructivists' fallacy is to carry this notion of discovery and individual experience to absurd lengths and apply it to later years -- to adolescence and even adulthood. Learning then becomes solely a matter of discovery and individual experience from which one constructs one's own knowledge and meaning. But you cannot "construct" broader knowledge ex nihilo and keep reinventing the wheel endlessly. You need external input. You need to benefit from the knowledge accumulated over thousands of years. This is where constructivism breaks down. Constructivism presents itself as a theory of learning based solely on experience. But personal experience is limited. Broader learning also needs to tap into an existing body of knowledge that constructivists disparage.
This otherwise imcomprehensible educationist hostility to knowledge and especially imparting knowledge becomes clearer when one considers the views of leading radical constructivist gurus like von Glaserfeld who seem to come straight out of the loony bin:
Von Glaserfeld is one of the leading apostles of radical constructivism. Radical constructivism rejects the traditional philosophical position of realism and adopts a relativist position. The traditional view of realism sees knowledge as a representation of an absolute reality - a world "out there" prior to having been experienced. The radical constructivists sees knowledge as "something that is personally constructed by individuals, in an active way, as they try to give meaning to socially accepted and shared notions." As von Glaserfeld himself says "knowledge is the result of an individual subject's constructive activity, not a commodity that somehow resides outside the knower and can be conveyed or distilled by diligent perception or linguistic communication"
This explains why educationists don't believe in an external body of academic knowledge that should be communicated to students. It explains why teachers are not allowed to teach, i.e. give explicit instruction.
On the other hand, how constructivists can claim Vygotsky as one of their own still remains a mystery to me. His notions of the zone of proximal development and scaffolding are sensible and don't rule out explicit instruction (despised by constructivists). His emphasis on socio-cultural factors doesn't fit in with "constructing one's own knowledge" either.
I wish someone could explain all these mysteries to me.
UPDATE #1: In the meantime, reader Rob has helpfully directed me to a scholarly article called Does No One Read Vygotsky’s Words? Commentary on Glassman that exposes attempts to Deweyize Vygotsky through omissions, distortions and inventions.
From the abstract:
In the May 2001 issue of Educational Researcher, Michael Glassman proposed several commonalities in the thinking of John Dewey and Lev Vygotsky. However, in addition to general problems in the article (misstatements about scholars’ writings and a reliance on unsupported inferences), the discussion misconstrues major concepts and topics addressed by Vygotsky’s theory of cognitive development—psychological tools, the role of the cross-cultural study, the zone of proximal development, and the nature of conceptual thinking. In addition, Glassman attempted to force Vygotsky’s goals into a Deweyan framework. The result is a misportrayal of Vygotsky’s work.UPDATE #2: I dug out my ed psych text (Anita Woolfolk) we used in grad school to see what it says about Piaget and constructivism. From it I learn that knowledge is "constructed by transforming, organizing, and reorganizing previous knowledge. Knowledge is not a mirror of the external world, even though experience influences thinking and thinking influences knowledge. Exploration and discovery are more important than teaching." The quote is Woolfolk speaking and giving a summary of Piaget's purported views under the heading "Assumptions about Learning and Knowledge."
Woolfolk goes on to helpfully explain how knowledge is constructed citing Moshman (1982). Knowledge construction is directed by internal processes like Piaget's organization, assimilation and accommodation. This means that new knowledge is "abstracted from old knowledge." It turns out that "[k]nowledge is not a mirror of reality, but rather an abstraction that grows and develops with cognitivie activity. Knowledge is not true or false; it just grows more internally consistent and organized with development."
Talk about being self-referential. Where is the external input?
I don't know what to make of this. I can understand that we might have to readjust our thinking when we learn new things that might conflict with or supplement our previous knowledge. But apparently there is no input of new knowledge from an external source. Saying that knowledge is constructed by transforming, organizing, and reorganizing previous knowledge is purely self-referential. Previous knowledge is simply remixed and stirred the way you might mix the ingredients of a cake. Nothing new is added. How relevant is all this to teaching reading and writing skills, math, science, history, geography, literature or languages?
Neither relevant nor helpful. It's all nonsense -- nonsense on stilts that has managed to become the dominant creed of the ed establishment. Constructivism is to education what creationism is to science. Both lack an empirical basis and rely on some unfathomable, ineffable, magical, supernatural thing said to "construct" something out of nothing.
How refreshing, then, to have someone like Prof. Plum rip the mask off this pretentious drivel:
What is Constructivism?What does progressive/constructivist education actually look like in practice. Here we have a smartly written account from someone who is experiencing it first hand:
Constructivism is big word that makes education perfessers think they are intelligent.
Constructivism is an invention that makes education perfessers think they know something that everyone else doesn't.
Constructivism is a set of statements about learning that are quite simpleminded and generally false.
"Knowledge can't be transmitted from one person to another. 'Learners' have to construct knowledge." [This very statement shows that constructivists don't believe what they say. Isn't the statement an effort to transmit knowledge?]
"Therefore, teachers should not teach directly by telling or showing (e.g., how to solve math problems). Instead, they should guide students as STUDENTS figure out concepts (what granite is) and strategies (how to sound out words, how to solve math problems)." [Constructing knowledge means NOTHING more than comparing and contrasting, identifying sameness and difference, making inductions and deductions. This is all OLD news. There is NO reason why teachers can't teach in a direct and focused fashion. In fact, students "construct knowledge" (figure things out) better--faster and with fewer errors--when they ARE taught directly, rather than expected to "discover" knowledge--which makes no sense, anyway. If knowledge is constructed, what IS there to discover?]
"How each person constructs knowledge is unique. Therefore, teachers should not arrange instruction in sequences. Instead, students should select learning tasks. Don't worry. They will select what they are ready for." [Unique in the DETAILS but not in the general logical operations by which human beings learn. If each person is unique, I guess physicians should not take their blood pressure.]
"Drill (distributed practice) is bad. It is boring. It is not needed." [Baloney!]
"Tasks should be 'authentic.' Holistic. Teach the fundamentals of chemistry in the CONTEXT of chemistry experiments. Teach phonics skills in the context of reading." [This is the prescription for keeping kids ignorant and unskilled and for leaving them demoralized.]
"Since each student's learning is unique and INTERNAL, you cannot use quantitative and standardized methods of assessment. It should be qualitative--how students feel and think about what they are learning." [This makes no sense. Body temperature is also "internal," but you can measure it quantitatively and with a standard instrument. Likewise, you can easily count how many math problems kids do correctly. This is a cop-out to protect constructivists from data that would ruin them.]
And from this set of sophomoric beliefs, you get whole language, fuzziest math, inquiry science, literature without literacy, and history without moral and political lessons.
Constructivist "theory" is a mishmash of overlapping platitudes and absurdities--"empty words and poetic metaphors" (Aristotle, Metaphysics). Taken separately, constructivist "propositions" are merely simpleminded. Taken together, they are indistinguishable from the verbal behavior of a person suffering from chronic schizophrenia.
"Reality is a construction."
"Knowledge is a construction."
"Experience is a construction."
"Experience is constructed with constructs."
"Constructs are constructed out of experience."
"Reality is knowledge."
"Knowledge is reality."
"Experience is reality."
"There is no knowable reality external to the knowing subject (the constructor)."
"Individuals and groups construct meaning as they interact with environments."
"Therefore, no statement can be more than relatively true."
"A current body of knowledge ('reality') is a context that shapes the construction of knowledge."
"Therefore, environment, knowledge, experience, meaning and reality are the same thing."
In my lesson during the first block, we read a lot of the primary source documents out loud together, and then I led a discussion about them and we took notes together. This was roundly condemned as the wrong approach, and so the next period I had to let them read and interpret in groups. As usual, they wasted a lot of time and I don't really think they understood it. Not that I'm sure they had totally understood it in the first block, since they didn't have the proper historical background and I can't give them quizzes, but at least I got some reasonable answers out of the class discussion. In the second block, everyone got something different, depending on their group. It was so frustrating. I don't want to learn to teach like this because I don't think it's right. But I can't contradict the teacher. But I need the practice. It's an education grad school moral dilemma. The best kind.This is just the last paragraph of a fairly long post. Read the whole thing.
UPDATE #3: Here are more sources on constructivism:
What is Constructivism?These prescriptions would explain the surfeit of math cripples. I know from my own experience teaching math that students thrive when having things explained to them combined with guided practice and independent homework in the form of distributed practice and overlearning.
"Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to 'transfer' mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept." [Emphasis added].
- Calculus, Concepts, Computers, and Cooperative Learning (C4L)
Sunday, October 02, 2005
Here is an account from the frontlines of what is not happening in a high school math class. The account relates the experiences of a student in a math class in which the teacher won't teach. It was posted at Kitchen Table Math, a lively math site that has been called "the hippest online math ed community in the known universe."
Hello, my name is Colin Johnston and in this post I will describe the horrors of high school algebra.As Colin says, why not just take this class at home, over the internet? Maybe constructivists are on to something and this is the wave of the future. It would help save hundreds of billions spent on "education."
On the first day of my junior year, I stepped into my math class. I will leave names out so as not to offend anyone. I had heard mixed reviews about the math teacher that I would have this year, but people generally said he was a pretty good teahcer. As the bell rang, the class sat down and waited patiently for him to enter the room. He slowly stepped into the classroom. He looked like a smart enough guy. He then passed out the textbooks and walked to the front of the classroom. He began talking about the curriculum we would cover this year, his grading scale, etc. He then said something, however, that didn't go down as easily as the other things he had mentioned. He said "You kids have been told how to do everything in your math careers. That is, up until now. This year, you are going to learn how to teach yourselves."
What? Then why don't we just take this class at home, over the internet? What is the point of having a teacher that doesn't teach? I made these same arguments to my friend after class, but he just shruged it off. "It will probably get better as the year goes on." He said. I guess I would give it a shot.
But as this year has gone on, things have gotten worse if anything. Now, the norm for the class is come in, sit down, spend an hour correcting last nights assignment (it takes so long because everyone has so many questions), get the new assignment, and puzzle over it for 10 minutes until you finally give up due to complete lack of understanding. Such is life in the new new math, Constructivism.
Thursday, September 29, 2005
We think Diane Ravitch and her fellow right-wing pundits have gotten multiculturalism -- and us -- all wrong.
In June Ravitch penned a Wall Street Journal opinion piece lambasting multicultural approaches to teaching mathematics. And she singled out our new book Rethinking Mathematics for special scorn.
Quoting from the table of contents -- in a manner that suggests she never bothered to read further -- she decried the book for trying to make math education culturally relevant to the children actually being served by U.S. public schools.
Ravitch accused Rethinking Schools -- and math teachers who believe in multiculturalism -- of abandoning academic rigor in favor of "political correctness."
Other right-wing pundits quickly took up Ravitch's chant and Rethinking Mathematics became a lightning rod for right-wing pundits and bloggers. Notably, Baltimore Sun columnist Gregory Kane -- who also seemed content to scan the book's table of contents and read no further -- blasted away at Rethinking Schools and multiculturalism.
Sunday, September 25, 2005
This point was driven home in spectacular fashion by a multi-billion grand experiment in Kansas City that resulted in abysmal failure:
For decades critics of the public schools have been saying, "You can't solve educational problems by throwing
money at them." The education establishment and its supporters have replied, "No one's ever tried." In Kansas City they did try. To improve the education of black students and encourage desegregation, a federal judge invited the Kansas City, Missouri, School District to come up with a cost-is-no object educational plan and ordered local and state taxpayers to find the money to pay for it.
Kansas City spent as much as $11,700 per pupil--more
money per pupil, on a cost of living adjusted basis, than any
other of the 280 largest districts in the country. The money
bought higher teachers' salaries, 15 new schools, and such
amenities as an Olympic-sized swimming pool with an underwater viewing room, television and animation studios, a robotics lab, a 25-acre wildlife sanctuary, a zoo, a model United Nations with simultaneous translation capability, and field trips to Mexico and Senegal. The student-teacher ratio was 12 or 13 to 1, the lowest of any major school district in the country.
The results were dismal. Test scores did not rise; the
black-white gap did not diminish; and there was less, not
Thursday, September 15, 2005
A nebulous title like that does not bode well and indeed the book is about all kinds of things except academic achievement. You'll find chapter headings and topics like Middle Grades Teacher Advisory System (this is big), Interdisciplinary and Interthematic Curriculum Designs (educationists are obsessed with interdisciplinary and thematic units, more often than not contrived), Morally Responsive Teaching, Team Teaching, Community Building...
The weirdest chapter was The Excluded Middle: Postmodern Conceptions of the Middle School. It's couched in thick postmodern jargon and obsessed with "power arrangements". It argues for a "fundamental shift away from the status quo power arrangements. The survival of the planet is at stake." Education must no longer serve "social structures" (whatever that is) and "unjust power arrangements" and embrace a "postmodern vision." The author urges that "society must be the function of education," as John Dewey and George Counts are said to have "insisted". Apparently this means that "the primary focus of education" must be the improvement of society and the creation of a "just, caring and ecologically sustainable community." Middle schools must adopt this vision or students and teachers will never be "empowered".
Schools must move away from "linear organization of curriculum on scope and sequence charts...mastering proficiency in discrete skills...memorizing officially sanctioned information (could the author mean academic subjects?)...accountability...written tests..." The author proclaims that we "have now entered a postmodern era" despite those who cling to "hegemonic schooling structures." Postmodern education "promotes diversity, understanding and a new social imagination with 'multiple points of consent.'"
What should education be about? Condemning "modern power structures." What will be "the hallmark of postmodern learning environments?" You guessed it! "Multiculturalism; eclecticism; cooperative practices; interdisciplinary experiences; community based projects; racial and gender inclusiveness; ecological and spiritual sensibilities; shared power arrangements; just economic structures that support health, nutrition and psychological well-being of all citizens..."
So education is all about welcoming some "structures" and condemning other "structures". The "structures" that education "must be prophetic" in condeming turn out to be, once again, "modern power structures."
I would have liked to learn some specifics about these nefarious "modern power structures," but apparently the author feels they are self-evident and that repeating the phrase endlessly is sufficient. This is odd since these "modern power structures" that education must not serve (how is education serving them now?) are evil incarnate and "have resulted in holocausts, genocide, starvation, ecological destruction, massive poverty, slavery, patriarchal domination, colonization, environmental degradation and other horrors of the twentieth century." They surely deserve to be described in great detail so we can recognize them and stare them in the face en masse.
The author issues this dire warning: "If education does not focus on these issues, then it is complicit in the continuing modern holocausts."
Adopt the ill-defined postmodern stew or you are a criminal!
This is some of the crap prospective teachers must endure to become "certified."
BTW, the author of this chapter is Patrick Slattery, Associate Professor of Education at Texas A&M University where he teaches "curriculum theory" and "foundations in education" among other things.
Wacky Wednesday: Several times per month, kids participate in a series of activities at lunch time designed to get them even more wired before they come into our afternoon classrooms. Examples include the notorious eat-the-candied necklace-off-a-member-of-the-opposite-sex contest, the raw-egg/ toss, water-balloon slingshot hit-the-kid contest, and Fun With Shaving Cream.
The Monthly Dance: Right after school, our 12-14 year-old students get to spend an hour-and-a-half bumping and grinding (and what they call freak dancing) in a darkened room while teachers and administrators blithely look on. (No parents are ever to be seen.)
And then there are those extra-curricular activities that are tailored to a more specific group of kids:
Annual Turkey Trot: This little time waster contest occurs right after lunch one day during the week before Thanksgiving. While the whole school is watching, our more athletic types run through an obstacle course. Students with the best times are awarded large trophies.There is much more. Read the whole thing.
What was once called "The Christmas Mile" then, "The Holiday Mile," and now, "The Winter Mile:" In the week before winter vacation, in the late morning, our student athletes once again get the opportunity to demonstrate their prowess in front of their lesser-fit classmates by running one mile around the school's track. The girls go first, and then the boys. Large trophies are awarded to the winners.
Powder Puff Football Game: This annual throwback spring-time homage to a time of more gender-specific roles innocence features our more popular girls on the field playing flag football while our male athletes perform cheerleading routines in short skirts, falsies, and pom-poms. Again, the entire school gets to watch right after lunch, usually on a Friday afternoon.
Now the veil is ripped off the ugly face of middle schoolism in a just-released
major study by the Fordham Foundation.
The study concludes that middle schoolism together with be lingering effects of the bizarre theory of "brain periodization" should be consigned to history's dustbin.
As a teacher of middle graders I know first-hand that early adolescents are perfectly capable of academic achievement and are not the dysfunctional monsters the movement would have us believe they are.
Excerpt from The Education Gladfly:
Fie on Middle Schoolism
If ever an education fad showed dreadful timing, reaching its intellectual and political pinnacle just as lightning struck the mountaintop, it's "middle schoolism." The key year was 1989, when the middle school bible, an influential Carnegie-backed report named Turning Points, was published. It hit just as the governors and then-President Bush gathered in Charlottesville to place the United States squarely astride the standards-based reform that is antithetical to the central message of this education religion.
In the ensuing decade and a half, the National Middle School Association (NMSA) and its acolytes, flying the banner of Turning Points and arguing that the middle grades are no time for academic learning, argued with great success that these schools should be devoted to social adjustment, coping with hormonal throbs, and looking out for the needs of the "whole child."
That is the essence of middle schoolism as set forth in a stunning new Fordham report by Cheri Pierson Yecke. It's a jeremiad drawing upon gobs of evidence that show the middle grades are where U.S. student achievement begins its fateful plunge and where a growing number of other nations begins to outpace us.
You can access the middle school report here.
Sunday, September 11, 2005
It's about something totally different:
The underlying goal of multicultural education is to affect [sic] social change. The pathway toward this goal incorporates three strands of transformation:
the transformation of self;
the transformation of schools and schooling; and
the transformation of society.
Saturday, September 10, 2005
"....Teach the subject matter in depth".A much better approach would be to spread out the teaching of history over many grades, beginning in the early grades. But this would run smack into one of the most sacred and pervasive dogmas of progressive/constructivist ideology: the dogma known as expanding horizons and any number of other names. As a result, the early grades are a content-free wasteland as far as the teaching of history (and geography for that matter) is concerned.
This would be nice. But, here in California (and I am sure many teachers in other states are subjected to this), I have to teach what is mandated by our State Dept. of Ed. via their frameworks.
I am currently teaching Grade 7 History, which, according to the framework, includes the end of the Roman Empire, Byzantine Empire, European Middle Ages (including the history and influence of the Christian Church, Medieval life and institutions, the Crusades, the Renaissance, Reformation, Scientific Revolution, Age of Reason, Age of Discovery, Age of Revolutions), Survey of Islam and development of Islamic Empire and its Contributions, 'Medieval' African Empires and Cultures, 'Medieval' China and Japan and the major PreColumbian Native cultures of Middle and South America.
This is a ton of material to try to cover with my 175 mostly 11-13 year olds, most of whom did not study early US History in Grade 5 or Ancient History in Grade 6 (also as per State framework) because "they are not tested on social studies" while in grade school. BUT, they are tested on this material in Grade 8.
It would be great to teach some of the above in depth.....especially such personally interesting topics as the Crusades, Black Death, Vikings, Chinese Inventions and Discoveries, the Mongols and their Empire, etc. But I can't teach any of this in depth. I have to 'get through the standards'. They have to be ready for THE TEST.
This problem is compounded by the lack of history testing in earlier grades.
As Polski3 points out, although the framework requires history in earlier grades it doesn't get taught because "they are not tested on social studies." No tests, no teaching. This points up the need for testing on the one hand and explains educationist hostility to testing on the other. Hostility because it would force educationists to do something they don't want to do: teach content. (Educationist is my shorthand for followers of the progressive/constructivist faith).
From the Fordham Foundation's study called Where Did Social Studies Go Wrong?:
The same is true in education, and specifically in the social studies: you have to possess some basic skills and knowledge before you can begin to tackle the higher tasks of analysis and critical thinking. Content knowledge is also the backbone of good teaching. To be effective, pedagogy must begin by identifying the specific knowledge a teacher expects students to learn and establishing clear assessment procedures. Only then can teachers begin to determine how to teach content to their students.
Unfortunately, the delivery of content in elementary social studies is frequently hampered by two popular but misguided theories— "expanding environments" and "constructivism." Both are ineffective because they focus on how social studies should be taught in elementary classrooms rather than on the content knowledge that should be the centerpiece for teaching and learning.
Expanding environments is the basic curriculum that most states, textbook companies, and curriculum leaders use to organize elementary (K-6) social studies, and it has dominated elementary school social studies for nearly 75 years. The basic premise is that at each grade level, each year, students are exposed to a slowly widening social environment that takes up, in turn, self/home (kindergarten), families (1st grade), neighborhoods (2nd), communities (3rd), state (4th), country (5th), and world (6th). While this approach appears to provide an organized curricular sequence, it lacks substantial content, especially in the early elementary grades, and children tend to find its narrow focus deeply boring. In fact, expanding environments actually impedes content knowledge because of its trivial and repetitious sequence. For example, students in grades K-3 are taught about "community helpers" like mail carriers, milkmen, and fire fighters. Such lessons are superfluous (what kindergartener does not know about firefighters?) but more damagingly do not even begin to lay the groundwork for later study of history, heroes, struggles, victories, and defeats. Instead, they limit children's instruction to persons and institutions with which children are already familiar.
Constructivism is a theory that holds that humans learn when they analyze, interpret, create, and construct meaning from experience and knowledge. At its root is a belief that only self-discovered knowledge is understood and remembered. Constructivists believe that students must be self-directed while learning in order to create their own meaningful experiences that will be retained when moving forward in life. While there is no doubt that some worthwhile learning may occur this way, it is difficult, if not impossible, to achieve self-created meaning unless specific content knowledge is a prerequisite.
Proponents of both approaches—expanding environments and constructivism—stress the importance of active learning over content knowledge as a necessary component of historical or geographical understanding. Yet just as the chess player needs to know how to move the pieces before he or she can begin the process of mastering chess, the elementary student needs content knowledge as the basis of thinking critically about history, civics, geography, economics, and all the other disciplines that make up the social studies. Content knowledge, we argue, must come first when making teaching and learning decisions.
Tuesday, September 06, 2005
Let's hope this forthcoming book by E. D. Hirsch will help curtail the prevailing worst practices.
New Book on Reading by E. D. Hirsch, Jr., to Be Called The Knowledge Deficit
Charlottesville, VA August 25, 2005 —This March, Houghton Mifflin will publish a new book by E. D. Hirsch, Jr., that will answer questions plaguing educators all across the country. Why do American children fail to perform as well as children in other industrialized countries? Why, after fourth grade, do students experience a slump in reading comprehension? Why, despite federal government spending of a billion dollars a year on the Reading First program, do so many schools fail to meet the goals established by the No Child Left Behind Act (NCLB)?
The book, entitled The Knowledge Deficit, answers these questions not by looking at funding or legislation, but by looking at what children are actually being taught. This, says Hirsch, is where the problem lies. Our children are not learning how to read because they are subjected to a watered-down curriculum that fails to build the background knowledge essential to reading comprehension. Many schools excel at teaching the mechanics of reading, at giving kids the decoding skills they need to make out individual words. However, by fourth grade, students’ deficit in background knowledge trips them up. A steady diet of fictional stories and instruction in abstract thinking skills leaves students starved for facts ─ facts about history, geography, science, literature, mathematics, music, and art. Because of their knowledge deficit, students cannot comprehend the texts they are asked to read in fourth grade and beyond.
Hirsch not only diagnoses the problem with reading in America and explains why students are failing to make adequate yearly progress under NCLB, he also shows how these problems can be corrected. This book builds upon decades of research into school curricula that Hirsch has conducted since his best-selling Cultural Literacy captured the American imagination in the 1980s. The new book is likely to be a bombshell, blasting to smithereens the received ideas of the education school thoughtworld that determine what and how kids are being taught in America today.
Drawing on extensive scholarship and vast knowledge of cognitive psychology, as well as on recent practical experience in school reform, Hirsch points the way out of our current morass, showing educators, policy makers, and parents how we can overcome the achievement gap that leaves poor students, who are disproportionately black and Hispanic, behind. Only by doing this, says Hirsch, can we fulfill the democratic imperative that first drove the creation of America’s public schools.
Wednesday, August 31, 2005
As the video opens, Klein announces, “This CD will walk you through the research upon which we based our decisions regarding our program choices.” The implication is that the city’s search for the “best practices” was intellectually serious. Not so. Otherwise, this instructional guide would not be dominated by the pedagogical principles of a radical education guru from Australia named Brian Cambourne, who believes that teachers ought to encourage their students to achieve a “literacy for social equity and social justice.”Educationists pay lip service to "critical thinking" but any critical thought gets you denounced:
Professor Cambourne says he came to his theories when he discovered that many of his poorly performing students were actually quite bright. To his surprise, almost all demonstrated competence at challenging tasks in the real adult world, including poker. This led to the brainstorm that children learn better in natural settings with a minimum amount of adult help. So important does Joel Klein’s education department deem Cambourne’s theories to be that it instructs all city teachers to go through a checklist to make sure their classroom practices meet the down-under education professor’s “Conditions for Learning.” Which of four scenarios most accurately describes how your classroom is set up? teachers are asked. If the teacher can claim “a variety of center-based activities, for purposeful learning using different strategies, and for students to flow as needed,” she can pat herself on the back. But if her classroom is set up “for lecture with rows facing forward,” she must immediately change her practice.
You might ask whether there’s any evidence for such pedagogy. It’s “weak to nonexistent,” according to Reid Lyon, former head of all reading research at the National Institutes of Health. “The philosophical and romantic notion that children learn to read naturally and through incidental exposure to print and literature has no scientific merit whatsoever.”
That hasn’t deterred Chancellor Klein in the least. Constructivist pedagogical guidelines are forced on classroom teachers in weekly “professional development” sessions that are closer to a military boot camp than any serious inquiry into the best classroom practices. No dissent is allowed. Teachers are given lists of “nonnegotiables,” a strange and embarrassing concept for any education enterprise. Thus students must not be sitting in rows. Teachers are forbidden to stand at the head of the class and do “chalk and talk” at the blackboard. There must be a “workshop” (students working in groups) in every single reading period. Teachers are also provided with classroom maps indicating the exact location of the teacher’s desk, the students’ writing stations, and exactly how much of the wall space should be set aside for posting student work. Also nonnegotiable is that every elementary school classroom must have a rug.
Is it surprising then that Chancellor Klein is facing a revolt from teachers like 13-year veteran Jackie Bennett, from a Staten Island high school? Ms. Bennett’s problem is that she believes it’s not a sin to bring her knowledge of great literature to her students, even if she occasionally lectures. After all, Bennett has a master’s in English literature from Columbia University, exactly the kind of academic attainment we supposedly want more of from our teachers.
“DOE administrators talk about balance,” Ms. Bennett recently wrote in an unpublished letter to the New York Times.
"What they really want is all-group, all the time. What’s more, the message is clear: when we visit your classes and the kids are not in groups, you have one strike against you.
My recent experience at staff development is illustrative of just how clear that message is intended to be. After spending the morning working with my colleagues on a small group activity that entailed busywork that did nothing to further our development as teachers, we returned to a whole-class discussion to briefly assess what we had learned. I raised my hand and asked if there was any research tying group work to better test scores. The answer was no.
My behavior was reported to the Local Instructional Superintendent, and two days later, my assistant principal asked me to forgo attendance at the remaining meetings. I had, it seems, been kicked out of staff development. Had I made a ruckus? No. But I had asked uncomfortable questions. I had thought critically. Though the City’s Department of Education gives lip service to teaching kids to think critically, it is clear they want those critical thinking skills taught by drones."
Sunday, August 28, 2005
The ‘Crayola Curriculum’
By Mike Schmoker
We may have the reading crisis all wrong. It may have far less to do with the "reading wars" than we presumed. I am convinced that the following explanation is, without doubt, the least recognized but most salient explanation for why there is a reading gap between rich and poor, for why so many kids reach upper-elementary and middle school with less than even minimal ability to read and make sense of text. The explanation is both simple and shocking. But the evidence for it is compelling. Best of all, this explanation holds out enormous hope for dramatic, near-term improvements at every level of education.
A couple of years ago, I found myself touring a school that had received an international award for excellence in staff development. Roaming from class to class—on what was clearly a "showcase day"—I went from being puzzled to astonished by what I saw.
Two things were terribly wrong: One, a majority of students were sitting in small, unsupervised groups, barely, if at all, engaged in what were supposedly learning activities. Many of the children were chatting. Second, but more important, was that the activities themselves seemed to bear no relation whatsoever to reading, the presumed subject being taught at the time. After seeing this pattern in several classes, I finally asked my host what kinds of gains had been made in this award-winning but high-poverty school. I was regretfully informed that there had been no gains, what with the hardships these children faced at home and in their neighborhoods.
After a few such tours, I became more convinced that something was truly awry, something more profound than the debates that perennially rage about such matters as phonics vs. whole language. After touring about 50 classrooms in several schools in several states—always with others from that same school or district—I became doubly convinced. I am now up to about 300 classrooms, and the pattern still holds.None of this is really surprising since non-instruction and hands-on activities are major components of the dominant progressive/constructivist ed ideology.
What is actually going on during these early-grade reading periods? A number of things, but the activity that overwhelmed all legitimate literacy activities may surprise you. Students were not reading, they weren't writing about what they had read, they weren't learning the alphabet or its corresponding sounds; they weren't learning words or sentences or how to read short texts.
They were coloring. Coloring on a scale unimaginable to us before these classroom tours. The crayons were ever-present. Sometimes, students were cutting or building things out of paper (which they had colored) or just talking quietly while sitting at "activity centers" that were presumably for the purpose of promoting reading and writing skills. These centers, too, were ubiquitous, and a great source of pride to many teachers and administrators. They were great for classroom management—and patently, tragically counterproductive.
Friday, August 26, 2005
Read the entire list at illinoisloop
The Illinois State Board of Education would have you believe that our official state standards for science education are tough and demanding.
But what could possibly be the point of a science standard that doesn't even mention "mammals", "machine", "electronics", "acid", "radiation", "reptile", "dinosaur", "evolution", "pollution", "oxygen", "organ", "muscle", "brain", "lung", "heart", "smell", "taste", "touch", "skin", "fat", "sugar", "salt", "volcano", "geology", "meteorology", "astronomy", "eclipse", "sunrise" or "sunset"?
I have taken the trouble to look at the Illinois Learning Standards for Science. It's pathetic! There is no there there.
The "standards" turn out to be three goals for science education covering the whole gamut from "early elementary" to "late high school." These goals are:
STATE GOAL 11: HAVE A WORKING KNOWLEDGE OF THE PROCESSES OF SCIENTIFIC INQUIRY AND TECHNOLOGICAL DESIGN TO INVESTIGATE QUESTIONS, CONDUCT EXPERIMENTS AND SOLVE PROBLEMS.
STATE GOAL 12: HAVE A WORKING KNOWLEDGE OF THE FUNDAMENTAL CONCEPTS AND PRINCIPLES OF THE LIFE, PHYSICAL, AND EARTH/SPACE SCIENCES AND THEIR CONNECTIONS.
STATE GOAL 13: HAVE A WORKING KNOWLEDGE OF THE RELATIONSHIPS AMONG SCIENCE, TECHNOLOGY, AND SOCIETY IN HISTORICAL AND CONTEMPORARY CONTEXTS.
I clicked on the goals to see if any factual knowledge is specified for individual grades. Not at all. No specific grades, no specific knowledge. Instead there is a verb salad of things to do, all in the constructivist mold. It's all about collecting and recording data, constructing charts, identifying a design problem, assessing results, reporting test design, building a prototype, developing a plan, design and procedure, formulating a hypothesis and so on.
Under understanding concepts each item starts with a verb. It's compare, identify, describe, explain, demonstrate ad nauseam.
I wouldn't be surprised at all to learn that the situation is similar in most other states.
Thursday, August 25, 2005
o A New York Times article ( Fuzzy Answers: The New, Flexible Math Meets Parental Rebellion) includes this wonderfully delicious look at a Chicago school where Math Trailblazers was used:I suspect this pollution of fuzzy math goes on quite a bit. Teachers might sneak in real math, parents may do real math with their kids (on the kitchen table if necessary) or hire tutors.
The Daniel Boone School, in West Ridge, a tidy working class part of Chicago brightened by magnolia trees and the babushkas of Russian grandmothers, has been a laboratory for the development of TIMS Math Trailblazers, a constructivist program created by the University of Illinois. Math scores have risen since the program was put into effect. The principal, Paul Zavitkovsky, credits the program, but does not rule out increased attention to math, teacher training and collaboration.
In fifth grade the other day, Mila Kell, a Russian immigrant, taught a crisp lesson in probability, improvising riffs on the probability that the sun would rise in the morning and that she would fly to the moon. The class was enchanted.
Mrs. Kell said she loved the freedom and creativity of the new math. But on her desk was a secret weapon: a stack of worksheets -- the antithesis of constructivist math -- pages of classic problems in long division, the addition of fractions and reducing the sum of fractions to its simplest terms.
Of course, if pupils fed fuzzy stuff test well on real math tests, credit will be given to the fuzzies.
TOPEKA, KS—As the debate over the teaching of evolution in public schools continues, a new controversy over the science curriculum arose Monday in this embattled Midwestern state. Scientists from the Evangelical Center For Faith-Based Reasoning are now asserting that the long-held "theory of gravity" is flawed, and they have responded to it with a new theory of Intelligent Falling.
"Things fall not because they are acted upon by some gravitational force, but because a higher intelligence, 'God' if you will, is pushing them down," said Gabriel Burdett, who holds degrees in education, applied Scripture, and physics from Oral Roberts University.
Burdett added: "Gravity—which is taught to our children as a law—is founded on great gaps in understanding. The laws predict the mutual force between all bodies of mass, but they cannot explain that force. Isaac Newton himself said, 'I suspect that my theories may all depend upon a force for which philosophers have searched all of nature in vain.' Of course, he is alluding to a higher power."
Founded in 1987, the ECFR is the world's leading institution of evangelical physics, a branch of physics based on literal interpretation of the Bible.
Tuesday, August 23, 2005
As advertised, a NEW (improved) learning style has been added to the ever-growing list (of things that don’t exist)Now I am realizing the modality folks are hurling another stink bomb and are quite serious about schnoz-based learning.
* Learns best though the sense of smell and taste [Yeah, lots of kids learn calculus this way. It’s called schnoz-based learning.]
* Smells have a special significance [Is there ANYone for whom this isn’t true?]
* Associates a particular smell with specific past memories [Is there anyone who doesn’t?]
* Is frequently able to identify smells [Is there anyone who CAN’T?]
* Finds that smells add to learning [This is precise! “Finds”… And what exactly do smells add? Smell is pretty much all I can see, or smell.]
I guess this means that teachers who feel obliged to “adapt instruction to each child’s learning styles,” will be shoving things up their students’ noses or letting them taste the pages.
“Look, boys and girls. This is the letter m. It says mmmm. Smell it?”
“Now. let’s examine the Declaration of Independence. All you olfactory learners lick the text a few times to get the flavor of the argument.”
But there is an antidote. Cognitive science is coming to the rescue of the cognitively challenged.
The latest issue of American Educator has an extraordinary article by cognitive scientist Daniel T. Willingham called Do Visual, Auditory, and Kinesthetic Learners Need Visual, Auditory, and Kinesthetic Instruction? that throws cold water on one of the educationists favorite fads:
What cognitive science has taught us is that children do differ in their abilities with different modalities, but teaching the child in his best modality doesn’t affect his educational achievement. What does matter is whether the child is taught in the content’s best modality. All students learn more when content drives the choice of modality. In this column, I will describe some of the research on matching modality strength to the modality of instruction. I will also address why the idea of tailoring instruction to a student’s best modality is so enduring—despite substantial evidence that it is wrong. [Emphasis added]The "content’s best modality!" That is so commonsensical, and yet must be regarded as a revolutionary insight in today's ed climate. Let's hope this important article drives a stake through the heart of the "learning styles" craze.