Making connections

In IF You Liked Whole-Word Reading, Open Classrooms & Fuzzy Math
You Will Love Inquiry-Based Science Charles Ormsby makes connections between modern fads dreamed up by ed gurus. What loony idea will come next? Suggestions welcome.

Teaching different achievement levels simultaneously is particularly obnoxious. It violates a basic law of physics that says that a body cannot be in different places at the same time. Consequently, teacher input is fragmented and rendered ineffective. But what are laws of physics to ed gurus who don't believe in a stable body of knowledge and instead conceive of knowledge only as "information" that keeps changing so rapidly that it need not be learned?

Guru advice that there is no need to learn anything because one can always look up the "information" somewhere is also fallacious. A lot of things we might know require extensive struggle to achieve understanding. I teach middle grades math and see daily that achieving an understanding of topics like ratios, proportions, percentages, unit rates, operations with integers, geometry, even ordering fractions, doesn't come easily. It's not a matter of looking it up when needed and grasping it instantly. It requires time and effort. What is true for math is also true for science and other subjects. Imagine trying to "look up" and understand topics in organic chemistry without a laboriously acquired firm grounding in chemistry. Or making sense of all the difficult terms in biology that were never memorized and understood if guru advice is followed.

See this hilarious video and see how handy "looking it up when needed" is.

[Note: There is certainly no dearth of grossly ignorant people. However, this video appears to be rigged by means of selectiveness to promote a biased point of view. The selection of people being interviewed is hardly representative. One could easily do the opposite: Interview a sizable number of people at random and then select only the knowledgeable ones to "prove" that the public is highly sophisticated.]

Here Ormsby:

As if deciding that we shouldn’t teach the magic code was not enough, professional educators decided to re-engineer the learning environment in the classroom. Again, we have thousands of years of experience in the design of learning environments. Past experience underlined the need for mental focus and concentration … a condition that is seriously hampered by distractions. Even parents who are not trained as educators seem to realize that children should turn off the TV and rap music while trying to absorb a history or math lesson.

But our education gurus had a deeper insight than the rest of us mere mortals could possibly appreciate. They figured that if you put classrooms together, without walls between them, the students would benefit from all the noise. It made sense to them, apparently, that understanding algebra or trigonometry would be enhanced by students reciting Shakespeare in the adjacent classroom! What were they thinking?

To make matters worse – is it even possible? – educators decided to give the teachers an extra challenge. Instead of having teachers teach a subject to a set of students who are roughly at the same achievement level in a subject, they decided to force them to teach to multiple levels simultaneously.

In a fourth-grade math class, teachers are required to teach simple addition and multiplication to some students while teaching division to others, and fractions to their most advanced students.

When it comes time for English Language Arts (read’n & write’n), they must simultaneously teach basic reading skills to some while discussing the classics with others.

Of course, they can’t actually do these things simultaneously, so they have to break up the class into more homogeneous groups and then split their time among the groups. Now students who could have had the teacher’s attention for the whole class, can only get it for a portion of the class time.

Brilliant!

Since the teacher splits the class up to make the sub-groups more similar in achievement level, one might ask, “WHY DIDN’T THEY DO THIS IN THE FIRST PLACE?” What were they thinking?

Last week I had occasion to witness a classroom in the inner city run by an admittedly incompetent substitute that was completely thrashed by pupils running wild like atoms flying around in a heated substance. It brought to mind the stark contrast between guru preachings about "inquiry," "discovery," "constructing knowledge and meaning," natural curiosity, and the reality of this classroom.

UPDATE: rightwingprof left a comment pointing out that we have a demonstration here of a student-centered classroom. Student centered indeed!

DOE to parents: Don't mess with the fuzzies

Occasionally slightly testy but mostly to the point text savvy takes issue with the Department of Education's recommendation that parents become a cog in fuzzy math schemes:

Try to be aware of how your child is being taught math, and don't teach strategies and shortcuts that conflict with the approach the teacher is using. Check in with the teacher and ask what you can do to help. Ask the teacher about online resources that you can use with your child at home.

(Via KTM II)

text savvy observes dryly that parents have a long history of passing on various skills to their offspring:

In case anyone (like the DOE) needs the obvious stated, parents have been successfully passing on low-order and high-order cognitive skills to their offspring long before there were schools, lesson plans, professional development seminars, research grants, or instructional philosophies.

text savvy even alludes to evolutionary roots explaining this parent behavior but is willing to make exceptions for certain tribes in a bow to the phenomenon of bongo-bongoism.

New math language

In a post called Math for poets, Linda Moran cites the comments from a mother and scientist that illustrate how traditional math terms are being swept away by fuzzy math. Apparently, terms like angles and degrees are too taxing:

In TERC it is
*joining not addition
*separating not subtraction
*bits and pieces and not fractions
*capacity and not volume
*it is what the calculator displays and not decimals.
*it is "landmarks" rather than ALL the numbers in the decimal system.
*it is turns and not angles and degrees.
*it is write a story and not write the equation.
*it is draw pictures and not show a true effective reusable strategy.

Fuzzy math was designed to make math "accessible" to large segments of the population which in the view of the fuzzy math creators were hitherto marginalized by rigorous math instruction. But by taking math out of "math", everybody loses.

Whole language debate

Who that?
Good debate about whole language vs. phonics at edspresso. Ken De Rosa, a phonics advocate, locks horns with whole language teacher Nancy Creech. Ken likens whole language advocates to the Japanese who were still roaming the jungles for years after the end of WW II, refusing to give up.

I have seen the sad victims of the psycholinguistic guessing game promoted by whole language. Words come out of the mouth of these victims that are nowhere in the sentence. Context clues are important for meaning but not for decoding, perhaps with the exception of words like read and lead. It does take a special zealotry to cling to this failed method.

See Martin Kozloff's A Whole Language Catalogue of the Grotesque for what whole language gurus actually believe. It's like entering a fun house with hideously distorting mirrors.

What I learned in PD today

From a professional development day inspired by an ASCD presentation by Dr. Jan Jones called Building Millennial Minds: Preparing Today's Students for Tomorrow's World I learned that:

Change is exponential. Gates says technology capacity doubles every nine months. Photonics leads to unimaginable data transmission rates. Semantic Web will be our new global brain.

The world is changing four times faster than schools (Dr. Willard Daggett).* Actually, the doctor is a bit fuzzy with the number. The exact number is 4.2651.

[The vision I have is of a globe spinning so rapidly that it'll throw everyone into space, including educationists].

Kids are immersed in fancy new technology (digital natives).

People will not earn a living, they'll learn a living.

21th century skills redefine core skills. What are those new core skills? Deep conceptual knowledge, critical thinking, creativity and problem-solving, innovation, imagination.

[I am afraid the mindless repetition of the critical thinking mantra will dull the senses and stop all thinking in its track. What's needed is critical thinking about "critical thinking."]

What are the implications for teaching of all this? I quote: "Learning can no longer be full, frontal lecturing or recall of data/facts, content."

[This is a spectacular non sequitur. Doubling technology capacity (whatever that is), faster data transmission rates and kids running around with iPods have no bearing on what content should be learned and how it should be taught. If it isn't dizzying technological change but the call for "deep conceptual knowledge" that necessitates the abandonment of content recall, then there is trouble, too. How is one supposed to have "deep conceptual knowledge" without engagement with content, i.e. assimilating or learning the content? Recall is another way of saying that content has been learned. A conceptualization is an abstraction from facts, a way to bring order to otherwise disparate facts. Conceptual knowledge, deep or otherwise, is impossible without that basis. So once again, educationists are blowing smoke, apparently enamored of the high-falutin' sound of these phrases without applying some critical thinking.]

What takes its place:

Big ideas

21th century learnings [note the plural]

Melding disciplines

Unique connections

Meta-cognitive options

Focusing instruction on relevance (don't fixate on minutiae, high-stakes testing)

Digital age literacies, e.g. health & wellness literacy, visual/performing arts literacy, information literacy, multicultural literacy... [Another example of educationist corruption of a good word that is now rendered meaningless].

So just go ahead, do the critical thinking and creating. No need to know anything.

*The sound of "change" makes educationists delirious. It's as intoxicating as a bottle of vodka. The change that whips them into a frenzy is mostly of a superficial nature, like faster data transmission rates and higher flash card storage capacity, kids adept at playing with new electronic gadgets and so on. From this they draw illogical conclusions about what and how things should be taught.

To calm them down from this frenzy and to rehearse critical thinking skills, I recommend that educationists be required to write a rigorous, lenghty and critical essay before Ed. D.'s are handed out. This essay could be called Change and Continuity. The objective of this essay is to examine what changes are occurring, whether these changes are profound or superficial and what, if any, effect they should have on the academic curriculum.

Educationists should then compare and contrast these changes to what stays the same in the various subject areas, 21th century or not. Educationists could ask themselves a long list of questions pertaining to the various disciplines. For example, do faster data transmission rates and high-capacity flash cards alter the laws of gravity and motion, planetary orbits and atom bonding, or the electromagnetic spectrum and Fraunhofer lines? Do these technological changes impinge on photosynthesis and animal cell structure? Or refraction and the Doppler effect? Do they make 2 + 2 = 4 untrue? Is pi no longer the ratio of circumference to diameter because of dizzying 21th century changes and yet-unheard of electronic gadgets? Did Caesar suddenly not cross the Rubicon because Gates predicts a doubling of technological capacity every nine months?

Requiring educationists to pose and answer these questions could have a sobering effect. But I wouldn't count on it.

So that's what it is!

Maybe one day I'll pin down what this "constructivism" is. Is it a theory of knowing as some claim? Or is it an approach to teaching as the influential Association for Supervision and Curriculum Development claims:

The Definition of Constructivism

Constructivism is an approach to teaching based on research about how people learn. Many researchers say that each individual constructs knowledge rather than receiving it from others.

Although people disagree about how to achieve constructive learning, constructive teaching is based on the belief that students learn best when they gain knowledge through exploration and active learning. Hands-on materials are used instead of textbooks, and students are encouraged to think and explain their reasoning instead of memorizing and reciting facts. Education is centered on themes and concepts and the connections between them, rather than isolated information.

Source: From The Language of Learning: A Guide to Education Terms, by J. L. McBrien and R. S. Brandt, 1997, Alexandria, VA: Association for Supervision and Curriculum Development.

So, many researchers say that each individual constructs knowledge rather than receiving it from others. Ain't that grand. How did these researchers figure this out? Did they research how each individual constructs the periodic table, how atoms bond, how the sun produces energy? How individuals construct knowledge about the Renaissance period? Ah, I forgot. Through hands-on materials instead of textbooks.

More intense, instead of longer school day

The New York Times reports that many states and school districts with failing schools are seeking salvation in a longer school day. Failing Schools See a Solution in Longer Day. Prodigious amounts of money are once again being made available for a solution that is likely to yield negligible results:

FALL RIVER, Mass. — States and school districts nationwide are moving to lengthen the day at struggling schools, spurred by grim test results suggesting that more than 10,000 schools are likely to be declared failing under federal law next year.

In Massachusetts, in the forefront of the movement, Gov. Deval L. Patrick is allocating $6.5 million this year for longer days and can barely keep pace with demand: 84 schools have expressed interest.

Gov. Eliot Spitzer of New York has proposed an extended day as one of five options for his state’s troubled schools, part of a $7 billion increase in spending on education over the next four years — apart from the 37 minutes of extra tutoring that children in some city schools already receive four times a week.

And Gov. M. Jodi Rell of Connecticut is proposing to lengthen the day at persistently failing schools as part of a push to raise state spending on education by $1 billion.

[snip]

And of all the steps school districts take to try to improve student achievement, lengthening the day is generally the costliest — an extra $1,300 a student annually here in Massachusetts — and difficult to sustain.

Schools would do better to focus on wasted time during the existing school day rather than lengthening the school day. Schools should work more intensely, instead of longer. Schools should ask themselves: Do we really need all these endless blocks for sustained, silent reading of vapid fiction? Shouldn't we perhaps also be reading some science stories, biographies, history? What about this time-consuming bean-counting project? Do kids really need to be spending a week to count a million mung beans? Another papier-mâché dinosaur?

I propose a different model.

For a fraction of the additional funds the states are willing to dish out, the districts could try a much more effective model: Offering intensive academic support (IAS) to small groups (not more than ten) during regular school hours in failing schools. This support can be offered for math and science, for example, two areas in which the disadvantaged fail spectacularly. It would require hiring a few new teachers with expertise in the respective subject areas per struggling school. These intensive academic support sessions could be held during the prep times of regular classroom teachers.

Such an approach would do wonders to the math and science education of the disadvantaged. Because of large classrooms and frequent disruptions, regular classroom teachers cannot offer the individualized and sustained attention the disadvantaged need to succeed in math and science. Many are so far behind and have such poor work and study habits that only intensive and sustained academic involvement will bring them up to speed.

It can be done.

What to do with disruptive students

I wrote a deliberately provocative post on the huge problem of disruptive students (Segregate non-students). This has generated a series of very thoughtful exchanges by Diana, NYC Math Teacher and Larry Strauss. The responses add much more complexity and subtlety to this problem than expressed in my prescription. I encourage everyone to read the comments.

I particularly like Larry Strauss' suggestion:

If you are going to remove disruptive students, do so for a positive reason, some form of behavioral intervention; call it a good manners academy and get a well-paid tattooed drill sergeant to conduct it.

How issues are framed and formulated is crucial when seeking solutions.

History is knowable, teachable and testable

Less than a year ago, the Florida legislature caused a sharp outcry by requiring that the U.S. history taught in the state's schools "shall be viewed as factual, not as constructed" and "shall be viewed as knowable, teachable and testable."

For example, there was this Op-Ed in the NYT that made the case that facts need to be interpreted. The folks at Common Dreams seemed to believe that the sky was falling and the end of "critical thinking" had arrived:

Florida's Fear of History: New Law Undermines Critical Thinking
by Robert Jensen

One way to measure the fears of people in power is by the intensity of their quest for certainty and control over knowledge.

By that standard, the members of the Florida Legislature marked themselves as the folks most terrified of history in the United States when last month they took bold action to become the first state to outlaw historical interpretation in public schools. In other words, Florida has officially replaced the study of history with the imposition of dogma and effectively outlawed critical thinking.

Instead of being terrified of history as the Common Dreamers claim, according to the Tampa Tribune the proponents of the law were simply perturbed by the "widespread lack of knowledge about U.S. government and history." So the Dreamers have it backwards: The lawmakers don't fear history. They want more of it.

I also found talk about meaning and significance in the Florida statute. This does not sound like a ban on critical thinking:

(b) The history, meaning, significance, and effect of the provisions of the Constitution of the United States and amendments thereto, with emphasis on each of the 10 amendments that make up the Bill of Rights and how the constitution provides the structure of our government.

There were also voices that derided such apocalyptic visions:

Construction Deconstructed
Facts and snippy academics.

By Matthew J. Franck
Academics are touchy people — especially when mere mortals presume to speak for themselves on matters where the professors claim expertise. So Cornell historian Mary Beth Norton lashed out, in the Sunday New York Times, against the Florida legislature for daring to make law on a subject squarely within its responsibility — educational standards in history — without apparently consulting the most enlightened members of the history professoriate, like, say, Mary Beth Norton. Oh dear, what trouble those poor legislators bought themselves. I’m sure they’re all slapping their foreheads and saying “Dang! Why didn’t we ask this Norton woman for advice!”

For Norton, the first cardinal sin the legislature could have avoided was its statement, in a revision of Florida education statutes, that “American history shall be viewed as factual, not as constructed.” Tsk, tsk. “Facts,” Norton says, “mean little or nothing without being interpreted — another word for ‘constructed.’ All historians know that facts never speak for themselves.” Somehow I think people who have made it their work to write laws didn’t need to be told about the importance of interpretation, of facts or anything else. So Norton’s preening and condescension are certainly misplaced here. Her assertion is a half-truth anyway. Facts are what they are. (The Second Continental Congress did vote for independence on July 2, 1776, to use an example of Norton’s. That speaks for itself whether anyone is listening or not.) “Meaning” is another matter, and facts rise and fall in our estimation with the uses we make of them. This much is true too — one might say it’s a fact — and if that’s all Norton wants to claim, she surely has no quarrel with the Florida legislature.

This controversy seems strange at first but becomes clearer when one considers the inroads postmodernism has made into the field of history. Matthew J. Franck continues:

But let’s do a little interpretation ourselves. It seems not to have occurred to Norton that when the Florida legislature decreed that in the state’s schools history shall be treated by teachers “as factual, not as constructed,” it was evidently taking sides in a debate in Norton’s own discipline. (I say “evidently” because I have no inside dope from Tallahassee — only the eyes of a reader of the statute.) As the Australian historian Keith Windschuttle observed a decade ago in The Killing of History, postmodern social theory has been invading the historical profession, reducing “the belief that there are ‘facts’ about history” to the status of “an ideological position” with no privileged status over the competing view that “history is nothing more than a form of literature.” Perhaps Norton, who declares that she “love[s] facts,” hasn’t heard of this crisis in her own discipline. But someone in Florida seems to have heard of it. And that “not as constructed” language in the new state law was surely aimed at such fashions of postmodernism, with the intent of keeping the state’s history teachers from donning those new clothes.

In a review of Keith Windschuttle's book in The New Criterion, Roger Kimball chronicles the strange things that have been happening to the study of history. At bottom, it is an abandonment of the commitment to truth:

One depressing sign of this situation is the absolute horror with which the idea of “objective truth” is regarded in chic academic circles today. Another is the widespread tendency to downgrade facts to matters of opinion—a tendency that follows naturally from the rejection of objective truth. This shows itself in the amazingly prevalent assumption that truth is “relative,” i.e., that the truth of what is said depends crucially upon the interests, prejudices, even the sex or ethnic origin of the speaker rather than—well, than the truth or falsity of what the speaker says. The basic idea is that truth is somehow invented rather than discovered. Typical of this position is the feminist complaint about “male-centered” epistemologies that make false claims to universality (another word that inspires panic) or objectivity.

So I say, let's first get a factual foundation in history. Then interpretation can follow. Interpretation without a factual foundation is just empty palaver.

Critical thinking and creativity watch

It's been said that if fascism comes, it will come in the name of anti-fascism.

I am reminded of that aperçu every time an educationist, business-type or politician sings the praises of critical thinking, higher-order thinking skills, creativity and innovation.

These are all lofty aspirations. What bothers me is that the advocacy of these worthy goals is frequently accompanied by a disparagement of subject matter knowledge. These advocates seem to believe that these qualities can be taught in a vacuum. It's questionable whether they can be taught at all. More likely they develop incidentally through a struggle with subject matter. They are certainly not free-floating entities without moorings. So to get back to the fascism case, in edland anti-intellectualism comes in the name of "critical thinking" and "creativity".

I found new evidence for this phenomenon in a fight over educational legislation in Colorado as presented by the blog Mount Virtus:

On a party line vote today, the Senate Education Committee passed a bill sponsored by Senator Sue Windels (D-Arvada) to mandate standards on Colorado schools that teach sex education. Three committee members, all Democrats - Windels, Bob Bacon, and Ron Tupa - voted to support the House Bill 1292 mandate six weeks after voting against a mandate setting higher state graduation requirements for math and science (Senate Bill 131), and eight weeks after voting against a requirement that high school graduates have basic competency in English (Senate Bill 73). Suzanne Williams (D-Aurora) was the only committee member to cast votes for all three measures.

Last week the House Education Committee, chaired by Mike “Give ‘Em Hell” Merrifield, shot down the math and science requirements after hearing support from a Jefferson County teacher, a university president (could have been two if Merrifield hadn’t rescheduled the hearing at the last minute so CU’s Hank Brown couldn’t testify), and a Lockheed engineer. Said Merrifield:

And here is the kicker:

“My contention is by forcing every child into this narrow curriculum, we are not making them more innovative, we are not making them more creative,” the Colorado Springs Democrat said, citing a national report that calls a well-rounded education the “passport to a job in which creativity and innovation are the key to a good life.”

The Witwer plan, Merrifield said, would make students “more regimented and more lock-step (with) less ability to think outside the box.”

(Hat tip to Myrtle Hocklemeier commenting at KTM II.)

The twisted thinking exhibited by this chairman of the House Education Committee (of all things!) frankly leaves me speechless. It's easy to utter a stupidity. It takes considerable effort to describe the nature of a stupidity. For example, would I have to brandish logical notions like denying the antecedent or affirming the consequent to tackle this inanity?

Another juicy example comes via D-EDRECKONING. Highly prolific blogger Ken deRosa cites a Daily Mail article in which some Association of Teachers and Lecturers suffers paroxysms of anti-intellectualism:

Schools should teach children the key skills they need for life - like walking and thinking - not set subjects such as history or French, teachers' leaders have said.

The Association of Teachers and Lecturers called for the National Curriculum to be torn up and the testing system abolished.

The union said teachers in local schools should be able to adapt lessons to fit a new framework focusing on important skills for life, rather than academic subjects.

Martin Johnson, ATL's acting deputy general secretary, said prioritising academic education over other types of knowledge was "totalitarian".

"A curriculum is a selection from the total sum of knowledge, which is exploding," he said.

"For the state to suggest that some knowledge should be privileged over other knowledge is a bit totalitarian in a 21st century environment. We are arguing that knowledge which traditionally has high status should not be privileged over other kinds of knowledge.

Schools should teach children the key skills they need for life - like walking and thinking?

Walking?

Now I am waiting for an educationist to point out breathlessly that walking is an important 21th century skill.

UPDATE:
In the meantime, Rory has left a comment at D-ED RECKONING in which he reviews the massive amount of research confirming the importance of walking:

I am finally glad someone has finally decided to address the walking achievement gap.

Study after study has confirmed that the ability to walk is a critical aspect of employment.

Our new information based society heavily depends on consumption of coffee. A recent study by a leading University determined it is much more economical to provide centralized coffee pots in office environments. Without the ability to "walk" to these coffee pots, employees will soon suffer from coffee withdrawal causing severe detrimental effects on worker productivity.

L.B. Ral from Progressive University cautions against a biased approach to walking instruction though. He notes that different cultures have different styles of walking.

Meanwhile, disabled activists have called the new emphasis on walking instruction discriminatory. They point out that thousands of wheelchair bound people across the country are able to get around quite well without walking. They recommend "walking" classes be replaced with inclusive instruction on "moving".

Segregate non-students

A New York City teacher writes about the horrendous discipline problems she faces every day:

Most recently, a student threatened a student and a teacher in the same day, yet is still sitting in class. Not even a suspension! Rumor has it that the principal feels we have too many suspensions and is using shady means to cover up that fact. Either our school totally lacks the infrastrucutre to handle unruly students, or there is major corruption going on at the administrative levels. Last semester, there was a fight in my classroom. As per protocol, I called security. The line was busy. One of the two security guards in the building (yes, we only have to for two whole schools) sits on the phone all day, making personal calls. Another time, a teacher called for a student making threats, and the guard told her she simply wasn't coming! In any case, we all know students must feel safe to be able to learn. Students should not feel safer outside the school than within. How can I protect my students when I have no recourse to discpline students effectively? How can I protect my students when I myself don't even feel safe?

[snip]

The one thing I know for sure is that I am totally burned out. Battling disruptive and extremely disrespectful students every single day, being totally taken advantage of in terms of the contract, and walking on eggshells with administrators so as to remain on their "good side" has really been an exhausting experience. As a result, I have lost my belief that I am actually making a difference. The problems that plague NYC schools are so beyond the scope of one person to fix. It is really overwhelming.

There is something fundamentally wrong with a culture that produces so many disrespectful, unruly students. Nevertheless, no matter how bad the school, there are always well-behaved students willing to learn. We owe it to them to create a propitious learning environment. That means we have to get serious about segregating dysfunctional non-students. This is a first step toward achieving quality education. It runs counter to entrenched dogma, but it needs to be done.

How should reading be taught?

A little gem of an article that appeared in Scientific American called HOW
SHOULD READING BE TAUGHT?

A scientific consensus should be nigh. But then there are those fans of the psychotic guessing game who think that learning how to read is as natural as learning how to speak. A pervasive misconception. See also how whole language hurts the disadvantaged.

Whole language raises the question whether a theory that is largely grounded in crackpottery can be said to be upsetting the scientific consensus. I say it does not.

Boxed-in creativity

When educationists don't want to impart knowledge (which they don't by definition), they mumble something about "critical thinking" and "creativity".

In the Comments section of Education Week and in response to an article in Education Week, writer SteveH argues persuasively that you cannot think outside the box if you don't know what's inside the box:

Creativity is even more poorly defined, but many toss it out like everyone knows what it means. What is creativity in math? It's something that is only possible when it is built on mastery of a whole lot of basic skills. It is not something learned top-down. You have to know what is inside the box before you can think outside of the box. There is nothing worse in the scientific world than a technical report whose authors do not cite (or even know about) other work in their field.

Here is a problem that I had to solve a number of years ago. Find, as fast as possible, the intersection line segment of two triangles. The triangles are each defined by three [X,Y,Z] points and you have to be able to eliminate triangles that are not close very quickly.

Employers do not want "creative" employees who want to rediscover the wheel. They want employees who know the literature and can look it up. When they have to look it up, they need to know where to go and they need to implicitly know the difference between a dot product and a cross product. They need to know what a box check is; not creatively discover it. Only after reviewing the literature and finding no solution that meets the need, do you begin to get creative. But creativity takes knowledge and mastery of the basics. Real creativity is only possible by standing on the shoulders of those who have gone before you. Creativity is not sheer dumb luck. Knowledge and mastery do not reduce creativity, they enhance it.

With a fine touch for the comical, Education Week encourages readers to comment on the effect of "school reform."

What do you think? Does the current approach to school reform favor the regurgitation of random facts over the development of critical and creative thinking?

It doesn't say which school reform but I am assuming Education Week is referring to NCLB's accountability schemes. If holding educationists accountable for educating kids is likely to result only in a "regurgitation of random facts," then the state of education is in even worse shape than I had previously assumed. The conclusion I reach is that educationists simply don't know how to educate, if holding them accountable for minimal standards results in a regurgitation of random facts. I suggest they vacate the field and leave education to others.

A tale of three math books

This is a hoot!

Here is an example from the fabulously encyclopedic old Kitchen Table Math of the quality of different textbooks. The first two problems are from Singapore Math and Saxon, respectively. The last "problem" is from the egregious and execrable fuzzy math text Trailblazers. Compare and contrast indeed!

CompareAndContrast
Posted on May 26, 2005 @ 20:05 by CatherineJohnson

problems in three grade 5 textbooks

from the last page of Primary Mathematics 5B (U.S. Edition):

18. A fish tank is 2/5 full after Sara poured 14 gal of water into it. What is the full capacity of the tank in gallons?

final problem in Saxon Homeschool Math 6/5 3rd Edition:

Change each of these base 10 numbers to base 5:
a. 31
b. 51
c. 10
d. 100
e. 38
f. 86

from the last page of Math Trailblazers Grade 5:

4. Write a paragraph comparing two pieces of work in your portfolio that are alike in some way. For example, you can compare two labs or your solutions to two problems you solved. One piece should be new and one should be from the beginning of the year. Use these questions to help you write your paragraph:

Which two pieces did you choose to compare?

How are they alike? How are they different?

Do you see any improvement in the newest piece of work as compared to the older work? Explain.

If you could redo the older piece of work, how would you improve it?

How could you improve the newer piece of work?

With "math" instruction like that, the U.S. is sure going to remain competitive with the rest of the world.

Parents, don't let educationists ruin your child's opportunities in life. Fight the fuzzy math plague!

Educationist misconceptions

Good discussion at KTM II on constructivism. ("Constructivism attacks the immune system that saves us from silliness")

I even managed to deliver myself of an opinion that then accidentally turned into a brief statement of my teaching philosophy:

I cannot understand for the life of me how construction and discovery can be compatible. If knowledge is just lying around the kitchen table or on the floor to be discovered, then why does it need to be constructed? If it is to be constructed, why does it need to be discovered?

I can understand construction in the banal sense that we must somehow integrate external input (from observations, books, sage on the stage, etc.) into our knowledge apparatus, but the external input must still be there. This type of integration is necessarily always active, contrary to educationist palaver. So-called "constructivists" militate against this external input and disparage textbooks, explicit and expository instruction, etc. [All based on a misconception of constructivism. See below.]

My own favored teaching/learning model is one I dubbed the Optimal Electrode Gap model [spark gap might be better], or OEG model (somehow I feel I must turn this into an acronym. Acronyms lend legitimacy even to screwball ideas. Not that I consider the OEG model to be a screwball idea).

The analogy is taken from physics. When relatively high voltage is applied to electrodes, three things can occur depending on the electrode gap:

a) no sparks fly if the electrodes are too far apart

b) a short-circuit is created if the electrodes touch each other

and c) sparks begin flying if the gap is just right.

This technical bit lends itself beautifully as an analogy and even metaphor for education where it has major implications for teaching and learning. The flying sparks are a metaphor for true learning and understanding. The electrode gap stands for the kind of pupil/teacher interaction. Finding the right gap is at the heart of a teacher's teaching ability and skill.

If a teacher talks above the head of the pupil without connecting with the pupil's prior knowledge, then the gap is set too wide and no sparks fly. If the teacher tells the student (who may not be paying attention as is most often the case) everything without allowing for creative tension and some student struggle, then we have a short-circuit (the electrodes touch each other) and the voltage is for nought.

On the other hand, finding the right gap prevents pupil frustration on the one hand and wasted energy on the other, and can lead to student excitement and enthusiasm, and a real sense of accomplishment. [I presume Vygotsky's zone of proximal development is something along those lines, but note below how educationists manage to turn a good idea into an absurdity].

This is my teaching philosophy in a nutshell. I am not sure how all of this ties in with prevailing theories, but I suspect it incorporates elements from a variety of philosophies.

In the Comments section of the post, Barry Garelick cites a quote that addresses one of the major misconceptions under which educationists are laboring, namely that the constructing pupil needs no external input:

I was referring to a paper by Anderson, Reder and Simon called "Radical Constructivism and Cognitive Psychology" which appeared in a collection published by Brookings Institute in 1998. In the paper, they state:

“A consensus exists within cognitive psychology that people do not record experience passively but interpret new information with the help of prior knowledge and experience. The term “constructivism” is used in this sense in psychology, and we have been appropriately referred to as constructivists (in this sense) by mathematics educators. However, (AND THIS IS A BIG ‘HOWEVER’ FOLKS) denying that information is recorded passively does not imply that students must discover their knowledge by themselves without explicit instruction, as claimed by radical constructivists. In modern cognitive theories, all acquisition of knowledge, whether by instruction or discover, requires active interpretation by the learner. The processing of instruction can be elaborate, its extent growing with the amount of relevant knowledge the learner brings to the task.”

Catherine Johnson of KTM I and KTM II fame contributes a terrific quote that further elaborates on this enormously damaging and widespread educationist misconception:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.

Barry Garelick points out that my spark gap analogy fits in nicely with Vygotsky's ZPD:

Yes, the spark gap analogy is quite good. It fits in with the Vygotsky theory of Zone of Proximal Development or ZPD. You want to teach children in that zone (i.e., the spark gap is not too wide) and provide the scaffolding or guidance to help bridge that gap.

BeckyC cautions that constructivists go off the deep end when it comes to defining the pivotal term "scaffolding". Scaffolds are usually high up next to a building and I am speculating that educationists begin to suffer from a case of vertigo when they are on a scaffold and fall off. How else to explain this educationist fall into the abyss of absurdity?

It's in trying to define what constitutes scaffolding that the constructivist mischief begins again in earnest.

Constructivists deny the possibility of scaffolding by directly instructing or directly telling the child how to bridge the gap between what he knows and what we know he could know next. They allow indirect methods only, and they are even uncomfortable with presuming to know what the child should know next. They wait patiently, and they wait and wait. After all, it's not their child, and the child goes away at the end of the school year.

Let's hope that through repeated exposure one or the other educationist will come to recognize the terrible misconception under which they have been laboring.

More parents fighting fuzzy math

Another parent group has formed to fight the fuzzy math plague. This time in Plainfield, NY.

Among the complaints:
Kids don't have basic skills.
Homework is unrecognizable.
Oodles spent on tutors.

Hat tip to Linda Moran.

Teaching fractions

There is more to knowing and teaching fractions than meets the eye. Paper by H. Wu.

1 Definition of a Fraction . . . . . . . . . . . . . . . . . . . . . . 4
2 Equal Division of a Segment by Ruler and Compass . . . . . . 20
3 Equivalent Fractions (Cancellation Law) . . . . . . . . . . . . 22
4 Fraction as Division . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Ordering Fractions (the Cross-Multiplication Algorithm) . . . 38
6 Addition and Subtraction of Fractions . . . . . . . . . . . . . 46
7 Multiplication of Fractions . . . . . . . . . . . . . . . . . . . . 62
7.1 Formula for the product, and first consequences . . . . . . . . 64
7.2 The first alternative approach . . . . . . . . . . . . . . . . . . 74
7.3 The second alternative approach . . . . . . . . . . . . . . . . . 78
8 Division of Fractions . . . . . . . . . . . . . . . . . . . . . . . 80
9 Complex Fractions . . . . . . . . . . . . . . . . . . . . . . . . 88
10 “Of” and Percent . . . . . . . . . . . . . . . . . . . . . . . . . 93
11 Ratio, Rates, and the Fundamental Assumption of School
Mathematics (FASM) . . . . . . . . . . . . . . . . . . . . . . . 99
12 Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 108
13 APPENDIX: Some Remarks on the Teaching of Fractions in
Elementary School . . . . . . . . . . . . . . . . . . . . . . . . 117

Curtain call for Zig's book

NEW PLAN: Curtain Call for Earlier Chapters
The original schedule called for each chapter being on Zigsite.com for two weeks without ever returning. Several people have indicated that they did not access the earlier chapters. So there will be something of a curtain call:
DURING THE WEEK OF MONDAY, MARCH 12, ALL CHAPTERS WILL BE ON FOR ONE WEEK, THROUGH SUNDAY MARCH 18. Then, for sure, they will not return.

When disaster strikes

I tried to make upgrades to this site and was promised by Blogger that my template would be saved. I cannot find the location where it was supposedly saved and now I lost my blogroll and all the other information on the left margin.

Sometimes it is better to leave well enough alone.

Buzzword education

(Cross-posted at KTM II)

Wikipedia has an interesting entry on buzzwords. Buzzwords may sound impressive but have an unclear meaning. Wikipedia says: "Buzzwords are typically intended to impress one's audience with the pretense of knowledge. For this reason, they are often universal. They typically make sentences difficult to dispute, on account of their cloudy meaning."

Buzzwords should not be confused with jargon. For the most part, jargon has a well-defined technical meaning, at least to the initiated. On the other hand, buzzwords not only obscure meaning, but "can also function to control thought by being intentionally vague." As Wikipedia puts it: "In management, stating organizational goals by using words with unclear meanings prevents anybody from questioning the directions and intentions of these decisions..."

What is true for management is true for education to a high degree. Education presents a veritable cornucopia of buzzwords with vague meanings. They form the feeble corpus of the educationist Thoughtworld that would be a corpse in a more rational world. (Thoughtworld is a term coined by E. D. Hirsch to describe the nebulous educationist thought complex).

Ed schools are a rich generator of educationist fog, blasting prodigious quantities of fog into the air the way Mount Pinatubo might spew massive amounts of ash into the air until the sun is reduced to a faint glow.

And yet, astonishingly and improbably, we are asked to believe that the massive amounts of fog mixed with toxic fumes emitted by ed schools magically stop at the schoolhouse door.

It's been claimed by some, including Washington Post education writer Jay Mathews (see The Ed School Disease, Part Two) commenting on educational historian David F. Labaree's new book, "The Trouble With Ed Schools," that ed schools may be pitiful institutions and the butt of jokes, but there is no need to worry. They are not doing any harm: "Why worry about ed schools if they don't do any harm, or any good?" Mathews avers:

What I said in that column was that I had been in a lot of classrooms and had rarely seen much of this guide on the side stuff. I wasn't saying I was happy about it. We have never given the Deweyites a fair test of their theories, and I know of a few schools that have used child-centered learning to good effect. Labaree's insight is powerful and useful all the same: why worry about ed schools if they don't do any harm, or any good?

The blindness revealed in this statement is astonishing. Could armies of new teachers and educational leaders who go through the rigorous ed school indoctrination process really emerge unscathed? Not very likely.

When attempting to write about the harm done by ed school ideology, it is hard to know where to begin. One could start with relatively minor topics like the preachments about the unimportance of correct spelling and the alleged benefits of invented spelling. One could start with the promotion of disastrous creeds like constructivism that are reflected in curricula and teaching methods, and form the core of ed school ideology.

A perusal of mission and vision statements of schools show how deeply entrenched ed school ideology is in the thinking of educationists who run the schools. Take, for example, Chicago's so-called Renaissance schools. Classrooms need to be heterogeneous, disciplines must be integrated, collaborative groups must engage in peer teaching, math and science must be learned by inquiry and discovery without coherent textbooks and so on. Among my many favorites is the Al Raby school:

Educational Philosphy [sic]
The Al Raby School will embody a constructivist approach to learning. Learning will be an active process; our teachers will use lecture style instruction and worksheets sparingly. All teachers will stress collaborative groups as well as individual initiative, striving to make the classroom a model democratic community where students have choices and responsibilities. Based on a large body of research, we believe that for true comprehension and retention to occur the learning must be relevant, active and reflective.

Many of these new Chicago schools receive money from the Gates Foundation.

It is also wrong for Mathews to presume teacher autonomy. Teachers are not free agents. They must work under the contraints imposed from above. In many schools, this means having to work with fuzzy math textbooks like TERC, Trailblazers, Connected Math, CorePlus, all execrable fuzzy math programs. The CMP teacher manual tells teachers not to provide explicit instruction. Math teachers I've talked to either follow this dictum or are agonizing over it. Often it can mean working with no textbooks at all. Periodically, an ed school-indoctrinated leadership comes in and orders the removal of textbooks and workbooks from classrooms. These are then given away or end up in the trash.

Even if teachers manage to defy ed school indoctrination, the obstacles they face in actual practice are formidable. They face not only institutional constraints (e.g. constructivist materials and approaches mandated from above), but they are also facing a student body that has been conditioned to expect to be entertained and to be resistant to expository instruction.

One of the pernicious effects of ed school ideology is how it produces an indoctrinated cadre for top leadership positions which then has the power to impose constructivist texts and practices on schools, like Chicago's CMSI. This cadre could be anything from superintendents to board members to curriculum and instruction experts to principals and supervisory bodies.

The message from this cadre is that explicit instruction should be minimized or avoided altogether; that worksheets (one of the hands-on activities that make sense) should be avoided like the plague [one reason for the highly restricted photocopying allotment given to teachers here in Chicago]; that textbooks are evil incarnate and prevent teachers from being "creative". On top of everything, overworked and frazzled teachers are expected to reinvent the wheel every day. Since many elementary teachers are not well-educated to begin with (e.g. a pathetic knowledge of history, geography and science), the one source of knowledge (textbooks) that could be a corrective is foreclosed. So you have instances of textbook-free schools. Schools without basals (hated by educationists), history and science textbooks, except for science "inquiry" manuals.

Part of this hatred for textbooks is the belief -- a component of ed school ideology -- that "information" (this is how educationists view knowledge) is exploding like supernovae, and what is true today is hopelessly obsolete tomorrow. Another reason is plain educationist disdain for facts. It interferes with "critical thinking" and "creativity" and stunts the mind.

One can see the hand of ed school ideology everywhere in school. At least I see it everywhere. I see it when DEAR (Drop Everything and Read insipid, vacuous and vapid fiction) is the first thing on the agenda in the morning when students are most receptive for more substantial stuff. This reading then takes place silently for an hour without teacher feedback. I see it in block scheduling to provide ample opportunity for time-wasting activities. I see it in contrived interdisciplinary instruction and in coloring and more coloring. I see the hand of ed school ideology indirectly when new elementary teacher candidates are released from the citadels of anti-intellectualism with scant knowledge of math, science, history, geography, grammar and languages, and subsequently validated by laughable state "content" tests.

The list goes on and on. I haven't even adressed ed school staples like learning styles, multiple intelligences, developmentally appropriate injunctions that often slide into low expectations, project and activities mania, heterogeneous grouping, expanding horizons, the travesty form of Bloom's taxonomy, and the disdain for factual knowledge. Moreover, once out of ed school, teachers continue to be assaulted with ed school ideology in the form of professional development requirements.

Dimensional analysis

A reader of this site signing as Anonymous has left this fantastic comment modeled on Vern Williams' 4 3/8 dimension:

One morning as I was walking my kids up to school, the sidewalk ended and we fell into the Sevenths dimension and I actually believed the following:

All my child will ever need to know about sevenths is that they are a little bit bigger than eighths, and a little bit smaller than sixths.

It is not my job to teach my child.

It is my job to support my child's learning.

My child should never be bored in class.

My child isn't just wandering around his classroom chatting with classmates, he's a kinesthetic learner with high verbal intelligence.

Children don't mindlessly copy from each other in small groups; they richly create meaning in conversation with their peers.

My child will discover efficient mathematical algorithms on his own in a way that makes sense to him.

Learning by rote is bad.

If my child hasn't memorized his basic addition facts in first grade, he'll have another chance in second grade.

If my child hasn't memorized his basic addition facts in second grade, he'll have another chance in third grade.

I should drill my child on his basic addition facts at home in order to support the conceptual learning that takes place at school.

If my child hasn't memorized his multiplication facts in third grade, he'll have another chance in fourth grade.

If my child hasn't memorized his multiplication facts in fourth grade, he'll have another chance in fifth grade.

I should drill my child on his multiplication facts at home in order to support the conceptual learning that takes place at school.

I should be more active in the PTA.

I should buy more gift wrap.

I should go to a school board meeting and see real decisions being made.

I should feel guilty questioning the curriculum even if I have a college degree in the field of interest.

A 25 year-old teacher is a licensed professional who is fully qualified to teach my child.

Children should write about math a lot.

Teachers will lovingly read everything my child writes because, as teachers, they look forward to creating an authentic portfolio that assesses my child's true mathematical learnings across thematic units.

My child's teacher will be so proud of him when he graduates from high school that we should planning on buying her a ticket for the commencement ceremony so she can sit with us.

I finally woke up in a cold sweat from this nightmare and asked myself, does anyone actually believe those things? The answer is a resounding yes. Every parent of every kindergartener I have ever met, myself included.

Fever and recycling

Global warming hysteria is causing kids to freak out:

Global warming concerns are keeping children awake at night
Half of young children are anxious about the effects of global warming, often losing sleep because of their concern, according to a new report today.

A survey of 1,150 youngsters aged between seven and 11 found that one in four blamed politicians for the problems of climate change.

And then there is this line that had me rolling in the aisles and prompted me to post this story:

Most of those polled understood the benefits of recycling, although one in 10 thought the issue was linked to riding a bike.

Elsewhere I read that GW will cause fever in half the child population. I grew up in the subtropics where it was really hot and don't remember having had an unsual share of fevered days.

This site called live science has different views on GW. I has links to related topics that seem like a good source for teachers who want to have kids do research projects.

Math research hoax

Fuzzy math enthusiasts and curanderos like to point to alleged "research shows" to help peddle their wares.

Let the colonel explain.

Excerpts from a stunning report from the National Research Council posted on KTM II show that there is no there there.

Among other things, the committee finds that:

The corpus of evaluation studies as a whole across the 19 programs studied does not permit one to determine the effectiveness of individual programs with high degree of certainty, due to the restricted number of studies for any particular curriculum, limitations in the array of methods used, and the uneven quality of the studies.

As a bonus, there is a list of rogue fuzzy math programs, most of them financed with tax dollars through the EHR directorate of the National Science Foundation:

Elementary School:
• Everyday Mathematics (EM), Grades K-6 (SRA/McGraw-Hill)
• Investigations in Number, Data and Space, Grades K-6 (Scott Foresman) [ed.: also called "TERC"]
• Math Trailblazers, Grades K-6 (Kendall/Hunt Publishing Company)

Middle School:
• Connected Mathematics Project (CMP), Grades 6-8 (Prentice Hall)
• Mathematics in Context (MiC), Grades 5-8 (Holt, Rinehart and Winston)
• MathScape: Seeing and Thinking Mathematically, Grades 6-8 (Glencoe/McGraw-Hill)
• MathThematics (STEM), Grades 6-8 (McDougal Littell)
• Middle School Mathematics Through Applications Project (MMAP) Pathways to Algebra and Geometry, Grades 6-8 (currently unpublished)

High School:
• Contemporary Mathematics in Context (Core-Plus), Grades 9-12 (Glencoe/McGraw-Hill)
• Interactive Mathematics Program (IMP), Grades 9-12 (Key Curriculum Press)
• MATH Connections: A Secondary Mathematics Core Curriculum, Grades 9-12 (IT’S ABOUT TIME, Inc.)
• Mathematics: Modeling Our World (MMOW/ARISE), Grades 9-12 (W.H. Freeman and Company)
• Systemic Initiative for Montana Mathematics and Science (SIMMS) Integrated Mathematics, Grades 9-12 (Kendall/Hunt Publishing Company)

This list can help parents spot the offending and immensely damaging voodoo math programs in their schools so they can raise hell.

The long story of gold

Cross-posted at KTM II

Gold is a rare, odd-numbered atom with 79 protons. Common atoms have an even number of protons.

Here is something for science buffs. Where did gold come from?

Robert Krulwich of NPR asks this question apropos Valentine's Day and receives a long answer.

Ever since taking earth science courses in college I have been fascinated by the fusion processes in distant stars that produce different elements. This gold story explains why gold is so rare, as rare as a good education.

Fuzzy math cartoon

UPDATE: In the latest, Steve advises Bill on where to find designers for Bill's latest project. Get them from the discovery schools Bill supports. Good advice for a competitor. If Bill takes the advice, I recommend shorting MSFT.

Check out this fantastic cartoon series at Weapons of Math Destruction. It's all about the ravages of fuzzy math.

I like the one where Einstein goes on a discovery journey and discovers the Pythagorean Theorem. Yeah, keep reinventing the wheel. That should be the motto of the fuzzies.

A better mousetrap

In the latest issue of Education Next, Diane Ravitch reviews a book on the sad story of how Open Court died the death of a thousand cuts:

Henderson tries to persuade the reader that the books should have been congenial to whole-language teachers because of their superior literature selections and should have been embraced by progressive educators because they blended the best of both approaches, including workshop activities, so-called reciprocal teaching (where the teacher and the students take turns as teacher), and other practices that were embraced by progressives. He never adequately explains why progressives did not see the obvious virtues of the Open Court readers (my guess is that any reader that paid any attention to explicit phonics was doomed in the eyes of progressives, at that period in history).

Henderson even buys the canard that the Caruses’ efforts to promote “high culture” were doomed by mass enrollments, as though it were an obvious truth that the children of the poor could never appreciate classic fairy tales and myths, a rather questionable assumption. Even so, Let’s Kill Dick & Jane is a fascinating and rather depressing read, explicating for all the world to see how an ambitious textbook series with rich content and beautiful illustrations died the death of a thousand cuts, administered by ideologues, bureaucrats, and the dumbed-down culture of American education.

Ultimately, the life and death of the original Open Court readers demonstrate that American education is a challenging environment for the industry that supplies its needs. Ralph Waldo Emerson said that if you build a better mousetrap, the world will beat a path to your door. Blouke and Marianne Carus learned that this is not true, that the market is shaped more by fads and ideology than by evidence about what works best for children.

Free book on Project Follow-Through

UPDATE II: Don't miss Chapter 4. It really goes away as promised.

UPDATE I: Chapter 3 of Zig's saga is now available for downloading.

You've got only one more week to download the first chapter of Siegfried Engelmann's opus The Outrage of Project Follow Through: 5 Million Failed Kids Later for free. Project Follow-Through was the nation's most extensive, ambitious and costly study of what works in education ever conducted. Its findings did not sit well with the educational establishment's pet notions and beliefs, and the establishment did its best to either ignore or disparage the study.

Helpful hint on downloading: When the text appears in the Adobe Reader, go to the top left and find Save a Copy. Click and the file will download to the designated folder.


Sometimes I wish PDF files had never been invented.

From Zig's site:

Schedule for Chapters of Zig's Latest Book

The Outrage of Project Follow Through:
5 Million Failed Kids Later

Here's the plan: Every week for the next seven weeks, starting January 22, I will post one chapter of the trade book I have written, The Outrage of Project Follow Through: 5 Million Failed kids Later. Each chapter will remain on Zigsite.com for two weeks. Once it's off, it's off and will not return. There are seven chapters

Chapter 1: Before Project Follow Through (January 22) click for print friendly version
Chapter 2: Project Follow Through Begins (January 29)
Chapter 3: Follow Through Continues (February 5)
Chapter 4: During Follow Through (February 12)
Chapter 5: Follow Through Evaluation (February 19)
Chapter 6: Follow Through Aftermath (February 26)
Chapter 7: The New Millennium (March 5)

You may download chapters, but understand that the material is copyrighted by me and is not to be distributed or published without consent. I still have some hopes of getting it published, but so far I've petitioned 5 literary agents, and none was interested in even reading the book. I'm going to keep trying to find a major publisher that will take the work and publicize it, but in the meantime I figured I'd put out the material for those who are interested. All chapters except the one on evaluation are at least 80 pages.

Prologue to Zig's Latest Book
The book is not designed for educators but for the general public. The events start in 1964, when I got my first job in education (at the Institute for Research on Exceptional Children at the University of Illinois) and proceed from there to the present through a series of first-person vignettes and episodes that present the human side of what we did and why we did it. I think it delivers a powerful message.

Many episodes are dramatic—at least they were when we experienced them. I believe they show that we knew what we were talking about because we'd done more than theorize or observe through the sterile literature. We were completely involved in working with teachers, kids, and schools for more than 20 years in different manifestations of Follow Through. The book also provides short tours of work we've done with various types of learners, from the autistic, those with traumatic brain damage, and the deaf, to preschoolers, at-risk high school students, and the gifted.

The theme of the book is that urban school districts, as they are currently configured, can't possibly work because their structure, logic, and philosophy are anti-scientific. Overall, the book will probably sadden you, but hopefully, it will provide an interesting journey and won't discourage you.

UPDATE: Chapter Two is now available. It won't stay on for long.

Here are the opening lines of Chapter Two:

Project Follow Through Begins

Devious Logic of the 1960s
Project Follow Through, a creation of the ‘60s, was the largest
educational experiment ever conducted, the most responsive effort ever
designed to find out what works well and how to serve at-risk children
effectively. Yet, Follow Through is not recognized as a landmark study or a
source of revelation about how to educate children of poverty effectively. It
remains a secret, both to the public and to the educational community. In
fact, its results have never been used to fashion even one urban school
district, and the project has been all but erased from what serves as the
current idiom of the “history of compensatory education.”

Test your math knowledge

The Fordham Foundation's The State of State Standards 2006 has given California's math standards a top rating. (CA shares an A with MA and IN).

Here you can test your math knowledge with Practice Problems for the California Mathematics Standards Grades 1-8

An example from 7th grade:

A jacket is on sale for 70% of the original price. If the discount saves $45, what was the original price of the jacket? What is the sale price?

Let's see...

Here is an example from fourth grade:

What is the length of the line segment joining the points
(6, -4) and (21, -4)?

So the kids are already expected to know early algebra at that grade level? Pretty amazing!

Fuzzy math video

Parents who are bewildered by the kind of math their children are exposed to in school should watch this video. A parent who is also an atmospheric scientist demonstrates how multiplication and division problems are done with this new-fangled math. Incredibly confusing stuff for a kid, done to avoid standard algorithms.



This link of the video called Math Education: An Inconvenient Truth takes you to the YouTube site. The video has sparked a lively discussion at YouTube that includes a few defenders of fuzzy math. This is an example:

Kids will "learn math" if they are given an opportunity to discover. Kids want to explore things. If you tell them that this is the way to do it, you have (for many, but not all) squelched their creative energy. They are reduced to just finding the answer. Kids want to understand the language of math. In the standard division algorithm, we use the term "goes in to". What does that mean to a kid just beginning to learn the concept of division? What is a "remainder"?

This is what I don't understand. If kids are so eager to discover, why are they not discovering on their own outside school? If this were true, nearly every child would be math proficient.

Ed school nuttiness

One of the major travesties in education are the education schools. One of my recommendations for a new and improved NCLB law would be to declare an education major a disqualification for teaching. Prospective elementary teachers should be required to major in an academic subject. Education courses can be tagged on if they meet a set of criteria to be determined.

This radical solution I am proposing received a new impetus when I was looking around other education weblogs and came across this post at Right Wing Nation. The good prof unearthed samples of course offerings at an ed school in Indiana that are geared more to political indoctration in a particular ideology than to turning out effective, knowledgeable teachers. Theses examples could be replicated countless times at other ed schools.

Here is what ed majors can choose from:

E 305 Infusion of Technology (3 cr.) B One of the goals for the Democracy, Diversity, and Social Justice Program is to infuse the study, use, and teaching about technology throughout the entire program. Rather than being a tool that preservice teachers learn about, technology will be studied as a subject and a means to expand research opportunities, stimulate and enhance models of inquiry, and broaden teaching abilities.

What on earth does technology have to do with Democracy, Diversity, and Social Justice?

E 320 Envisioning, Exploring, and Creating Our Social Worlds Through Multiple Literacies in the Elementary School (9 cr.) B This interdisciplinary course explores the social studies as ways of knowing about our world; the language arts and language learning theory; aesthetics and the arts; and the multiple roles of the teacher as facilitator of learning, social researcher, and curriculum creator. A field experience is included.

Here we have another example of the corruption of language. Literacy is now literacies and can mean anything under the sky. How about concentrating on turning out fluent readers and writers who can put together coherent, articulate and error-free sentences and paragraphs?

E 322 Diversity and Social Justice I (3 cr.) B Students will develop curricula for social studies, language arts, aesthetics, and the arts that responds to multicultural and disability concerns. Curriculum planning and teaching strategies will attend to issues of student diversity in home and community contexts and school settings.

E 326 Diversity and Social Justice II (3 cr.) Students will develop curriculum for mathematics and science that responds to multicultural and disability concerns. Curriculum planning and teaching strategies will attend to issues of student diversity in home and community contexts and school settings.

In all this responding to multicultural and disability concerns the concern for what these students should know is lost. Are these multiculturals really from another planet that makes them unsuitable for a core, agreed-upon curriculum good for non-multiculturals?

E 324 Teaching Mathematics and Science for All Students (9 cr.) This course prepares prospective elementary school teachers to teach mathematics and science in an integrated, discovery-based environment. A major goal of this course is to promote student familiarity with the conceptual understanding and skills necessary for teaching in a manner that promotes the inclusion of all pupils. Constructivism, the History and Philosophy of Science, and Technology and Society comprise three strands that further the aim of democratic teaching as applied to mathematics and science.

I'll bet the "democratic" discovery-based environment excludes a lot of students who need special attention and explicit instruction.

David Klein video

I had great fun watching a video of David Klein and James Milgram speaking at an event hosted by Where's the Math?


As a bonus you get to see Ma and Pa Kettle doing innovative division and multiplication. I guess the Kettles discovered their own algorithm and could become poster boys and girls for the fuzzies.

Perversity in Chicago

Like so many big cities, Chicago has a huge number of underperforming schools who get placed on a probation list, thanks to NCLB. What is the school board's answer to ailing schools? Administer a massive dose of poison!

In what can only seem to be head-shaking perversity, the board forces something called the Chicago Math and Science Initiative on ailing schools, enforced by its network of so-called Area Instructional Offices.

As can be seen from the instructional materials used by CMSI, it's all of the worst fuzzy type:

Purpose: To promote instructional coherence across K-8 mathematics classrooms by recommending and supporting specific research- and inquiry-based instructional materials.

Description: The mathematics instructional materials designated for grades K-8 in the Chicago Public Schools are:

Primary Grades Mathematics: Math Trailblazers and Everyday Mathematics

Middle Grades Mathematics: Connected Mathematics and Math Thematics

This information can be used as a resource by other elementary schools that seek to align their use of instructional materials with that supported by CMSI.

Students who desperately need structure, coherence, instruction and solid foundational knowledge are fed this fuzzy crap, guaranteed to perpetuate failure.

The science component is of a similar vein. All "inquiry" and discovery and no foundational knowledge.

Bad advice

Over at edspresso there is a fascinating series of articles written by an ed student using the pseudonym John Dewey. In one of the installments, the student quotes from the textbook the class is using:

A case in point is the textbook we are reading in my math teaching methods class. The textbook is "Teaching Mathematics in Secondary and Middle School" by James S. Cangelosi. Excerpt from Chapter 4:

"Because mathematics is widely misunderstood to be a linear sequence of skills to be mastered one at a time in a fixed order, some people think teaching mathematics is a matter of following a prescribed curriculum guide or mathematics textbook. ... “

This statement makes me shudder. Math is brutally cumulative and a linear sequence of skills is often necessary. For example, how can you reduce fractions without having learned division? Leave it to ed schools to mistrain teachers in such an egregious fashion. One can only hope math continues to be "widely misunderstood."

Long division

If you listen in on the math wars, you'll notice that long division is one of the more divisive issues in this war. It's hard to comprehend why fuzzy math zealots are so opposed to teaching long division and making such a fuss. For example, NCTM in its so-called standards calls for "decreased attention" to long division. I've taught long division and the kids caught on quickly.

In a paper called The Role of Long Division in the K-12 Curriculum that should be must-reading for educationists, David Klein and R. James Milgram show that long division is a crucial skill necessary to understand more advanced math concepts:

Abstract
We discuss the role of long division in the K - 12 mathematics curriculum. We begin by reviewing the reasons that most math educators today depreciate the topic and other topics in the curriculum that derive from it, such as polynomial long division or polynomial factorization. Later we show that this view is simply wrong mathematically. The role of long division is not just to divide one rational number by another, but the algorithm itself contains the initial exposure of topics which become crucial in the core
applications of mathematics in our society today. Following the introduction, we discuss methods for teaching long division in such a way that the underlying concepts can be understood by students. We then provide more details about the ways in which these concepts develop in later mathematics course, and why they are so important.

After reading this, the mysteries of real numbers and the conversion of fractions to decimals will become much clearer. Isn't conceptual understanding what the fuzzies purport to be after? So why are they opposing a tool that leads to a conceptual understanding of major math topics?

UPDATE: Reader Katie has left an incredible link to an actual conversation between a phone customer and a number of customer reps (supervisors) that sounds more like an Abbott and Costello routine. It's about telling the difference between dollars and cents expressed in decimal form. The reps never get it and instead rely on a calculator without realizing what they are doing. This should give pause to NCTM and fellow fuzzies and their enthusiasm for calculators.

What is absolutely hilarious is that at the end the rep (supervisor) declares that the difference between the customer's correct math and the rep's fuzzy math is a matter of opinion.

More here.

Scores and class size

The Chicago Sun-Times reports the astonishing news that some of the highest-scoring Chicago public schools also have the largest class sizes:

Small, medium or large. What class size would you choose for your child? Today, in the second of two parts -- what may seem counterintuitive: Some of the best test scores are being racked up by Chicago schools with some of the largest primary class sizes.

If you're looking for a high-scoring Chicago public school, be prepared to accept larger class sizes in the early grades, just when some experts say smaller classes count the most.

The 25 highest-scoring schools in CPS average roughly seven more kids in their primary classrooms than the 25 highest-scoring suburban schools, or about 27 kids vs. 20, a Chicago Sun-Times analysis of state public school data indicates.

That's seven more kids in a CPS room just as children are learning everything from how to read to how to sit quietly at a desk and do classwork. Compared with the statewide primary average, it's roughly six more kids.

At top Chicago public schools, K-3 classrooms with at least 30 students aren't unusual. Meanwhile, many kids in top suburban schools enjoy the intimacy -- and efficiency -- of 16, 18 or 19 kids in a class.

Rising scores in some Chicago neighborhood schools -- among the system's most affluent -- have brought a rising tide of students, jamming classes to the point where some parents want relief. Even some of the city's most popular magnet schools have 30-plus classes, often because of the extra teacher bigger classes bring.

At first glance, the results at Edgebrook School, on the Far Northwest Side, seem to stand common sense on its head.

In 2004-2005, Edgebrook's sole first-grade room held a whopping 40 students. That year, the school posted the highest test score among the city's neighborhood schools, yet it had the largest primary class sizes in the six-county area. At least two of its tested grades that year -- third and eighth -- held 30 or more students.

At first glance this would seem to give ammunition to those who contend that class size doesn't matter. However, it would be a mistake to generalize from the cases reported above. The crucial element that allows large class sizes is the quality of the student body. Edgebrook School is a case in point. The school is located in an affluent area and peopled by students enjoying a high socio-economic status. This success could not be replicated in large classrooms filled with the disadvanted, many of whom suffer from behavior disorders. Such students need more intensive teacher attention.

Via Joanne Jacobs.

Reading instruction breakthrough

The Chicago Tribune has a report on innovative reading instruction methods. I expect reading scores to be boosted significantly as a result.

In Leah Coffey's kindergarten class, learning to read means breaking a sweat and getting your hands dirty.

One morning last week, Coffey put in a CD with infectious drumbeats and pupils repeated the names of different instruments. "T-T-T-Tambourine," they sang as they danced and smacked invisible tambourines.

Later, Coffey and four pupils dipped their hands into a can of clay. First, they molded the letter T. They then flattened the clay into discs.

"T-T-T-Tambourine," they said and tapped the clay tambourines against their hands.

Westcott Elementary School, 409 W. 80th St. on the South Side, has joined 17 other Chicago public schools in implementing a curriculum from Reading in Motion, a Chicago agency that uses music, drama and dance to teach reading.

Coffey is sold on the concept. "I think that every lesson should be put to music," she said.

Reading in Motion is one of several organizations supported by Chicago Tribune Holiday Giving, a campaign of Chicago Tribune Charities, a McCormick Tribune Foundation fund.

The way I learned to read way back then was so incidental that I can't even remember how it was done.

Glue guns shoot down real studying

Time-consuming and often pointless projects are not only devouring students' time but also rob parents of whatever free time they have. Acquiring substantive subject matter knowledge must inevitably take a back seat.

Ken DeRosa has found a mother's plea that calls for an end to this educationist extravaganza:

It can wreck marriages and destroy family life, and it's more burdensome than travel soccer, football practice, or the Boy Scouts: It's the school project.

Ask a bunch of mothers how they spent their week, and they will tell you that they built the Parthenon with sugar cubes, the Pyramids from milk cartons, and Mount Olympus using Cocoa Puffs.

Consider a recent Sunday evening at my house. The kids had gone to bed, and Mom and Dad were relaxing in the living room. But suddenly, a voice cried out from upstairs.

"Mom, I forgot I need to bring a hot glue gun to school tomorrow for a project. We are making African masks in social studies. And, oh yeah, Mom, I also need pipe cleaners, a box of sugar cubes, and some wooden spoons - you know, the kind they use with those little ice cream cups."

Half-dressed, I hopped into my minivan and searched for a hardware store open late on a Sunday. Thank goodness for the 24-hour Walgreens, where aisles are filled with construction paper, glue sticks, and pipe cleaners - but, alas, no hot glue guns.

Please, oh please, dear curriculum developers, give us parents a break: Ban all make-work projects. Parents have jobs, too, you know. We do our children's homework. We serve on school boards, coach basketball, and volunteer with the Boy Scouts. Now you want us to be creative?!

The project method was widely acclaimed by progressive educationists upon its publication by William H. Kilpatrick in 1918. It has become a mainstay in education thanks to a convergence of educationist fads, tenets and theories. Illinoisloop has one of the best explanations of this mania that I have ever seen:

• Constructivism:
The pervasive education religion of "constructivism" holds that a child learns best through active "doing". To some extent, this is of course true. However, the Achilles heel of constructivism is that this is a painfully plodding and tedious way of learning, while forcing a drastic reduction (dumbing down) of the content of a course. While an active project may often be a good technique for making a difficult concept clear, it is often used when a simple direct method would be just as effective and far more efficient.

• Groups:
The pressure for "collaborative learning" or "cooperative learning" is frequently met with more projects and activities.

• Interdisciplinary curriculum:
Teachers are under pressure to find "thematic" or "interdisciplinary" links between subjects. There is nothing inherently wrong with that -- the Core Knowledge Sequence used in the Core Knowledge schools is carefully constructed to encourage learning in this way. But without a rigorous, well-reasoned curriculum like the CK Sequence, the result too often is time-wasting art or writing projects linking vague language arts goals with minimal content points.

• Multiple Intelligences:
The fevered success of another fad, Howard Gardner's Multiple Intelligences (click for much more info on that), pressures teachers into coming up with separate projects for each of this theory's supposed categories. So, we have one project to appeal to "kinesthetic" children, another project for the "intrapersonal" learners, we sing a song for the "musical" learners, and so on. Of course, since the MI mindset offers no method to identify or quantify these supposed differences, the bottom line is lots and lots of projects for all the children in the class.

• Anti-Fact Mentality:
Starting in ed school and throughout their careers in most schools, teachers are subjected to a barrage of rhetoric about the dangers of teaching facts. They are told not to teach "mere facts" to be "regurgitated." Learning of specific content knowledge is called "low level" and nothing more than "memorization." What used to be called "learning" is now disparaged as "brain-stuffing". A teacher is to be "a guide on the side" rather than "a sage on the stage." This drumbeat from the ed schools and education orthodoxy is pervasive and relentless, and teachers are drilled incessantly (ironic, isn't it?) that direct teaching is to be avoided. So, if the teacher isn't teaching, what are the kids likely to be doing? Yup, more projects.

• Anti-Fact Assessments:
If facts are bad, then testing whether children know facts is even worse -- or so teachers are told. Thus, chapter tests and other quantitative measures of learning are deemphasized in favor of so-called "authentic" assessment, in which we look at a whole "portfolio" of a child's "work" which largely consists of (ta da!) projects.

• "Authentic" Skills:
If the purpose of a school is not to build knowledge, then what is a school for? The progressivists have a ready answer for that: to learn supposed "skills." They argue that since knowledge is always increasing, it is hopeless to try to teach very much at all (using a twisted logic that defies comprehension). What kids need, they say, is to learn how to look things up. Well, guess what? Projects give them an "opportunity" to look things up instead of being taught.

• Innovation:
School administrators suppose themselves to be seen as "creative" or "innovative." We often read of a school calling itself "innovative" or a teacher said to be "creative" ort "imaginative." Those are fine attributes, but not when they take the place of words like "effective" or "knowledgeable." One teacher might be extraordinarily effective and captivating in teaching children a rich, detailed and memorable introduction to American history, while another teacher gains more recognition from parents and maybe the local newspaper not by teaching much of anything but by staging a marathon dress-up pageant, puppet show or enormous craft project.

• Finding a Use for Computers:
Projects provide a convenient raison d'etre for the expensive computers that schools have been buying in bulk.

• Smaller Class Sizes:
For all of the above reasons, the teaching industry is obsessive about urging more dubious classroom projects. But when class sizes are large, it's extremely difficult to manage the hubbub of activity and to try to keep a semblance or order. But as class sizes shrink, it becomes ever more practical for a teacher to assign more and more projects.

On that same page, Illinoisloop has many links to important articles dealing with this project mania.