kitchen table math, the sequel

Monday, April 21, 2008

LooLoo




How did I come by this, you ask?

  • first stop: Wall Street Journal, under new management;
  • 2nd stop: "The Blogger Mom, In Your Face," (Lots of businesses get hate mail, but few owners react the way Heather Armstrong does. She prints out nasty emails, puts them in her driveway and drives over them with her car. "That's the attitude I have," she says, "and it's made my life a thousand percent better.")
  • and from there to dooce.com, et voilĂ .


These days, reading the Journal, I feel a bit like the shy kid on the first day of preschool:

Randy Bothwell, a police detective in Chester, Pa., considered and rejected a number of ways to rid his yard of bamboo: salt, an exorcism, shooting it with his service revolver. When he asked for advice at a local garden center, he says, they "laughed hysterically."

So Mr. Bothwell whacked the stand with a machete. It grew back. He bought a pickax and tried digging up the roots, a process that traced a 30-foot arc across his once-pristine lawn. One month and two broken shovels later, he rented a Bobcat minibulldozer and a big metal trash bin, acquired 14 gallons of poison and bought 24 cubic yards of dirt to fill the resulting hole. Total approximate cost: $1,500.

One year later, a single shoot appeared. "It gave me ... the final salute." Mr. Bothwell says. "I was like, 'Mother of God.' "

Call the Pandas: Bamboo Engulfs Defenseless Yards
by Matthew Rose


As fun as that sounds, I find myself thinking that what I'd like to do is just stand here by the cubbyholes and watch the other kids for the next six or seven months or so.

I don't know why.

Sunday, April 20, 2008

John McWhorter on "oral culture" and the direct quesstion

Have only skimmed Liz's post on Ruby Payne, on Ruby Payne, but it prompted me finally to get this passage from a John McWhorter column up. I had no idea -- none -- that "oral culture" was linguistically different from whatever culture it is I live in:
One wonders whether people .... truly understand what barriers poor kids face to learning how to read in a truly functional way. In countless American communities, flyers are routinely full of major misspellings, more than a few are only fitfully comfortable with e-mail, and few read newspapers above the tabloid level. Life is fundamentally oral.

Students from places like this — which include Appalachia and the rural white South as much as black and brown inner cities — get next to no reinforcement from home life in acquiring comfort with the written word. Eternally dismal reading scores make it clear that a school day ending at 3 p.m. is not alleviating the problem. We have become sadly familiar with every second black 8th grader reading below basic level.

Reading is not the only cultural hurdle. In black culture, for example, the direct question is not as central to normal communication as it is in mainstream culture (consult, for example, Shirley Brice Heath's "Ways With Words"). For kids from this kind of setting, getting comfortable with being asked point-blank "When was the Declaration of Independence written?" and answering clearly and directly takes work. Many black people of working-class or poor background mention how ticklish this kind of interaction felt when they first went to a decent school.

Direct questions as regular interaction are largely an epiphenomenon of the printed page. Most humans on earth lead fundamentally oral lives in the linguistic sense, and need to adjust to direct questions. Middle class American kids inhale them at the kitchen table. Poor kids learn how to deal with them in school, and it takes practice.

One objection is that supposedly, in the old days even poor kids just sat down in school and learned what they needed to know. But the grandparents who recount this were among the sliver of poor kids who even made it through school. A century ago, only 14% of native-born American kids even made it to high school, and more to the point, only 2% of Italian and Polish immigrant kids did.

Here is Betty Smith in "A Tree Grows in Brooklyn" on what poor children's schools were really like one hundred years ago this year:

"Brutalizing is the only adjective for the public schools of that district around 1908 and 1909. Child psychology had not been heard of in Williamsburg in those days. ... Few teachers had the true vocation for their work. They taught because it was one of the few jobs open to them; because they had a long summer vacation; because they got a pension when they retired."

Few children stayed around in places like this any longer than necessary. Today, however, even low-skill service jobs require a basic comfort with the written word. A school day that ends at 3 p.m., in the America that we live in, isn't enough to give that to people from bookless homes whose parents are unsure how to make the system work for their kids.

Fighting Words in Education Crowds
John McWhorter February 28, 2008
NY Sun
It never crossed my mind to think of "direct questions" as anything other than utterly natural and universal.

Saturday, April 19, 2008

Ruby Payne: Nine strategies help raise the achievement of students living in poverty

Educational Leadership, April 2008, | Volume 65 | Number 7
Poverty and Learning Pages 48-52

Students from families with little formal education often learn rules about how to speak, behave, and acquire knowledge that conflict with how learning happens in school. They also often come to school with less background knowledge and fewer family supports. Formal schooling, therefore, may present challenges to students living in poverty. Teachers need to recognize these challenges and help students overcome them. In my work consulting with schools that serve a large population of students living in poverty, I have found nine interventions particularly helpful in raising achievement for low-income students.

1. Build Relationships of Respect
2. Make Beginning Learning Relational (Collaborative)
3. Teach Students to Speak in Formal Register ("academic language")
4. Assess Each Student's Resources
5. Teach the Hidden Rules of School
6. Monitor Progress and Plan Interventions
7. Translate the Concrete into the Abstract
8. Teach Students How to Ask Questions
9. Forge Relationships with Parents

More detail:
Update:
(a) the following has been misread by more than one commenter. As I understand Payne's work, the point of the "Assess Each Student's Resources" strategy is for the teacher to
examine, not assume, the extent of the student's resources in each of the eight domains. Let us take the "physical health" domain--a teacher may assume that the child's vision is excellent, because the child doesn't wear glasses, when in fact, the child's vision is poor and has never been evaluated.

(b) the "spiritual domain". Not to my preferences. However, let us take a non-trivial example: in the United States, a high-school student who had never even heard of Adam and Eve, the Garden of Eden, Cain and Abel, Abraham and his son, Moses, or any of the New Testament stories will struggle in both history and literature classes.

4. Assess Each Student's Resources

School success, as it's currently defined, requires a huge amount of resources that schools don't necessarily provide. Teachers need to be aware that many students identified as "at risk" lack these outside resources. Interventions that require students to draw on resources they do not possess will not work. For example, many students in households characterized by generational poverty have a very limited support system. If such a student isn't completing homework, telling that student's parent, who is working two jobs, to make sure the student does his or her homework isn't going to be effective. But if the school provides a time and place before school, after school, or during lunch for the student to complete homework, that intervention will be more successful.

  • Financial: Money to purchase goods and services.
  • Emotional: The ability to control emotional responses, particularly to negative situations, without engaging in self-destructive behavior. This internal resource shows itself through stamina, perseverance, and good decision making.
  • Mental: The mental abilities and acquired skills (such as reading, writing, and computing) needed for daily life.
  • Spiritual: Some belief in a divine purpose and guidance.
  • Physical: Good physical health and mobility.
  • Support systems: Friends, family, and resource people who are available in times of need.
  • Relationships and role models: Frequent contact with adults who are appropriate role models, who nurture the child, and who do not engage in self-destructive behavior.
  • Knowledge of unspoken rules: Knowing the unspoken norms and habits of a group.
5. Teach the Hidden Rules of School

People need to know different rules and behaviors to survive in different environments. The actions and attitudes that help a student learn and thrive in a low-income community often clash with those that help one get ahead in school. For example, when adult family members have little formal schooling, the student's environment may be unpredictable. Having reactive skills might be particularly important. These skills may be counterproductive in school, where a learner must plan ahead, rather than react, to succeed. If laughter is often used to lessen conflict in a student's community, that student may laugh when being disciplined. Such behavior is considered disrespectful in school and may anger teachers and administrators....

The simple way to deal with this clash of norms is to teach students two sets of rules. I frequently say to students

You don't use the same set of rules in basketball that you use in football. It's the same with school and other parts of your life. The rules in school are different from the rules out of school. So let's make a list of the rules in school so we're sure we know them.

8. Teach Students How to Ask Questions

When you have asked a student what part of a lesson he or she didn't understand, have you heard the reply, "All of it"? This response may indicate that the student has trouble formulating a specific question.

Questions are a principal tool to gain access to information, and knowing how to ask questions yields a huge payoff in achievement (Marzano, 2007). In their research on reading, Palincsar and Brown (1984) found that students who couldn't ask good questions had many academic struggles.

To teach students how to ask questions, I assign pairs of students to read a text and compose multiple-choice questions about it. I give them sentence stems, such as "When ___________ happened, why did __________ do ___________?" Students develop questions using the stems, then come up with four answers to each question, only one of which they consider correct and one of which has to be funny.


I highly recommend that you read the whole article. Of course, the Nine Strategies are also useful in all classrooms.


update - Catherine here, parachuting into Liz' post. (I hope she won't mind.)

Just thought I'd put in a link to the Times article on Payne along with a link to my follow-up on oral cultures and direct questions.

The NMP recognizes giftedness -- Part 1


(Cross-posted from After The Math Panel, a blog originating from Ridgewood, New Jersey which analyzes the findings of the Presidential National Math Panel.)

Gifted. It's a simple word that evokes strong reactions. But what is it?

According to the National Association for Gifted Children, it's hard to pin down:

National Association for Gifted Children:

The quick response is that there is, as yet, no universally agreed upon answer to this question. Giftedness, intelligence, and talent are fluid concepts and may look different in different contexts and cultures. Even within schools you will find a range of personal beliefs about the word "gifted," which has become a term with multiple meanings and much nuance.

NAGC does not subscribe to any one theory of the nature of human abilities or their origins. We assert that there are children who demonstrate high performance, or who have the potential to do so, and that we have a responsibility to provide optimal educational experiences for talents to flourish in as many children as possible, for the benefit of the individual and the community.



So, giftedness is hard to define, hard to test, has many philosophies and contexts. Add to that our current culture of keeping everyone label-free, plus a valid concern with assigning unlimited potential to all, and strong parental feelings about their own child's abilities, and it's a slippery slope at best.

Then why do well-established organizations such as the NAGC and our local Gifted Child Society of Northern New Jersey exist?

The short answer is because it's important, and throwing the baby out with the bathwater will not solve the problem. Better to address the issue, stated above: "We assert that there are children who demonstrate high performance, or who have the potential to do so, and that we have a responsibility to provide optimal educational experiences for talents to flourish in as many children as possible..."

Don't our schools do that? comes the question. No, they don't. When you consider that public school must meet certain minimum standards, must cater to the middle, and is designed not for individuals but for groups, you can see where kids with high potential, intense interest, or unusual ability will fall through the cracks.

In their defense, many schools do better than ever today to individualize instruction. But alas, even in the best schools, some kids methodically learn to be underachievers. When you consider that our best and brightest are needed to compete in a global economy, this is a terrible fact to face.

Thankfully, for the purposes of this blog, we can at least restrict our concerns to that of mathematical giftedness. But even that is a quagmire.

The National Math Panel's view of giftedness cannot be covered in one day. This topic will stretch out over a few entries.

Suffice it for today to say that despite our era of political correctness, and all the difficulties outlined above, the National Math Panel--a government entity--has done the bold thing, and set giftedness back on the map. Mathematical giftedness must be really, really important.

That in itself is something for our public schools to chew on. So much for certain public school teachers lecturing the kids that there is "no such thing as giftedness." That must stop immediately.





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Friday, April 18, 2008

reason, beauty, and errors of pragmatism

Much of the written history of Catholic schooling focuses on how its institutions developed in interaction with a politically dominant Protestant America. In some cases, Catholics directly imitated public initiative, often shaping schools out of a desire to accommodate. Sometimes, however, they took a different course in sharp rejection of the dominant culture. The debate over high school curriculum in the first quarter of this century exemplifies this dynamic.

At the beginning of the twentieth century, Catholic secondary schooling, like public secondary schooling, was limited to a relatively small percentage of the population. As opportunities for Catholic secondary schooling expanded, a more comprehensive educational philosophy, with an expanded life studies curriculum, was increasingly espoused as an alternative to the academic curriculum found in the older boys' preparatory schools and girls' academies.

In considering a new high school curriculum, Catholics were responding to movements in the larger society. The Cardinal Principles of Secondary Education, published in 1918 by the National Education Association (NEA) conceived of the high school as a more universal institution with a different, more vocational, emphasis. Although some Catholic high schools embraced the philosophy of the Cardinal Principles, this bulwark of the contemporary comprehensive public high school was eventually rejected by Catholics owing to the interaction of several forces.

Much of the vigorous debate among Catholics [hark! did I just read the words "vigorous debate"?] about the purposes and methods of their high schools was played out in the proceedings of the National Catholic Educational Association. In the spirit of pragmatism, voices were raised in favor of eliminating Greek from the curriculum, reducing the amount of Latin, and adding commercial and vocational courses. Considerable discussion ensued about the merits of the classics and about the need for more industrial training to better prepare future workers.

The reaction against these pragmatic voices was vigorous and forceful. Critics argued that the classics were the languages of Western civilization. Their study had moral and aesthetic value; they provided intellectual discipline and encouraged inventiveness.* The overwhelming response from NCEA members was that the study of classical humanism served every student well.

This rejection of life studies and vocationalism was predicated on fundamental philosophical premises. Developing the student's ability to reason was a central tenet of Catholic educational philosophy, beginning with the Ratio Studiorum and further affirmed in Neoscholastic thought...Such intellectual development was deemed necessary in order to grasp fully the established understandings about person, society, and God. Although universal secondary education had expanded the base of people to be educated, the purpose of education should not change. Practical education deviated too far from the central moral aims of schooling.

Institutional status and social class dynamics were also at work in the debate. The NCEA had grown out of the Association of Catholic Colleges of the United States, and these institutions of higher education exerted a major influence on Catholic secondary education through the 1920s. The colleges maintained close relationships with the boys' preparatory schools and girls' academies and tended to deprecate the weak academic programs in parochial and diocesan high schools. The latter schools were determined to prove their worth before the Catholic educational elite: the higher educational institutions. To secure such recognition and respect, diocesan schools increasingly put the college-preparatory curriculum first, with life studies offerings becoming ancillary. Catholic colleges themselves added to this pressure in 191 by instituting strict academic admissions requirements, including 16 credits in specific academic subjects.

The value of education as a vehicle for social mobility was also increasingly apparent to both Catholic educators and immigrant parents. This idea was raised in early discussions of the Association of Catholic Colleges, as leaders "cried out that Catholic youth should not be the 'hewers of wood and drawers of water,' but should be prepared for the professions or mercantile pursuits." The classical curriculum was the curriculum for the attainment of status. Catholic educators were urged to point out to parents the greater earning power of students who finished high school. An academic education in high school and then college paved the way for social position, the professions, and Catholic leadership in society.

Last, Rome placed its seal of approval on a conservative educational philosophy in 1929 in a statement by Pius XI, Divini Illius Magistri (On the Christian Education of Youth). Arguing that true education is directed toward the ultimate ends, Pius XI cautioned against errors of pragmatism in the curriculum. The Church was a conserver of humanity's cultural heritage.** Though supporting efforts to discern what is of worth in modern systems, Pius XI cautioned against "hastily abandoning the old, which the experience of centuries had found expedient and profitable." Two important features were signaled out and affirmed by the Pope: the teaching of Latin and single-sex rather than coeducational schooling.

Although Catholics made some accommodation to the philosophy of the Cardinal Principles, they never moved as far or as firmly in that direction as did the public schools. The end result was to reaffirm the position articulated at the third Baltimore Council in 1884: "The beauty of truth, the refining and elevating influences of knowledge, are meant for all, and she [the Church] wishes them to be brought within the reach of all. Knowledge enlarges our capacity both for self-improvement and for promoting the welfare of our fellow men; and in so noble a work the Church wishes every had to be busy." Catholicism's uneasy relationship to secular society thus continued. Much but not all of the modern world could be embraced by Catholic liberals. Practical concerns would increasingly enter its debates and be given their due, but ultimate principles could never be compromised.

Catholic Schools and the Common Good by Anthony S. Bryk, Valerie E. Lee, & Peter B. Holland
p. 30-31

The Church was a conserver of humanity's cultural heritage.
reason

beauty

errors of pragmatism

It is inconceivable that a public school would speak of conserving humanity's cultural heritage. When I read this passage, I think I should forget about the public schools and put my energies into figuring out how I can help save urban Catholic schools.


* Howard Gardner agrees.

I would like to overthrow dissension




Didn't Toqueville call this kind of thing the tyrrany of the majority?

I believe he did.

This woman's election is bad news for Ridgewood. Ms. Goodman, like most of us, does not know the first thing about the "overthrow of dissension," the first thing being: only a totalitarian state can overthrow dissension. (I know this because I happen to be married to a historian.)

A simple dictatorship, of the kind enjoyed by school boards and school superintendents, won't do. A simple dictatorship, of the kind enjoyed by school boards and school superintendents, breeds dissension.

oh good

Ed is back from his run.

Ed speaking: Supporting a constructivist superintendent's reform agenda won't overthrow dissent. Supporting a constructivist superintendent's reform agenda will provoke dissent. If a school board member wishes to overthrow dissent, she will have to support policies to which everyone agrees. Or else move to Irvington, where dissent is frowned upon.

Thursday, April 17, 2008

Lost in Time




Here is Oliver Sacks' article about Clive Wearing in The New Yorker: The Abyss.

In March of 1985, Clive Wearing, an eminent English musician and musicologist in his mid-forties, was struck by a brain infection—a herpes encephalitis—affecting especially the parts of his brain concerned with memory. He was left with a memory span of only seconds—the most devastating case of amnesia ever recorded. New events and experiences were effaced almost instantly. As his wife, Deborah, wrote in her 2005 memoir, “Forever Today”:

His ability to perceive what he saw and heard was unimpaired. But he did not seem to be able to retain any impression of anything for more than a blink. Indeed, if he did blink, his eyelids parted to reveal a new scene. The view before the blink was utterly forgotten. Each blink, each glance away and back, brought him an entirely new view. I tried to imagine how it was for him. . . . Something akin to a film with bad continuity, the glass half empty, then full, the cigarette suddenly longer, the actor’s hair now tousled, now smooth. But this was real life, a room changing in ways that were physically impossible.

In addition to this inability to preserve new memories, Clive had a retrograde amnesia, a deletion of virtually his entire past.

When he was filmed in 1986 for Jonathan Miller’s extraordinary documentary “Prisoner of Consciousness,” Clive showed a desperate aloneness, fear, and bewilderment. He was acutely, continually, agonizingly conscious that something bizarre, something awful, was the matter. His constantly repeated complaint, however, was not of a faulty memory but of being deprived, in some uncanny and terrible way, of all experience, deprived of consciousness and life itself. As Deborah wrote:

It was as if every waking moment was the first waking moment. Clive was under the constant impression that he had just emerged from unconsciousness because he had no evidence in his own mind of ever being awake before. . . . “I haven’t heard anything, seen anything, touched anything, smelled anything,” he would say. “It’s like being dead.”

Desperate to hold on to something, to gain some purchase, Clive started to keep a journal, first on scraps of paper, then in a notebook. But his journal entries consisted, essentially, of the statements “I am awake” or “I am conscious,” entered again and again every few minutes. He would write: “2:10 P.M: This time properly awake. . . . 2:14 P.M: this time finally awake. . . . 2:35 P.M: this time completely awake,” along with negations of these statements: “At 9:40 P.M. I awoke for the first time, despite my previous claims.” This in turn was crossed out, followed by “I was fully conscious at 10:35 P.M., and awake for the first time in many, many weeks.” This in turn was cancelled out by the next entry.

[snip]

Clive’s loquacity, his almost compulsive need to talk and keep conversations going, served to maintain a precarious platform, and when he came to a stop the abyss was there, waiting to engulf him. This, indeed, is what happened when we went to a supermarket and he and I got separated briefly from Deborah. He suddenly exclaimed, “I’m conscious now . . . . Never saw a human being before . . . for thirty years . . . . It’s like death!” He looked very angry and distressed. Deborah said the staff calls these grim monologues his “deads”—they make a note of how many he has in a day or a week and gauge his state of mind by their number.

[snip]

Back in his room, I spotted the two volumes of Bach’s “Forty-eight Preludes and Fugues” on top of the piano and asked Clive if he would play one of them. He said that he had never played any of them before, but then he began to play Prelude 9 in E Major and said, “I remember this one.” He remembers almost nothing unless he is actually doing it; then it may come to him. He inserted a tiny, charming improvisation at one point, and did a sort of Chico Marx ending, with a huge downward scale. With his great musicality and his playfulness, he can easily improvise, joke, play with any piece of music.

His eye fell on the book about cathedrals, and he talked about cathedral bells—did I know how many combinations there could be with eight bells? “Eight by seven by six by five by four by three by two by one,” he rattled off. “Factorial eight.” And then, without pause: “That’s forty thousand.” (I worked it out, laboriously: it is 40,320.)

Wednesday, April 16, 2008

My Kind of Town...

In animal news a cougar was just killed about 2.5 miles away from my apartment building.


View Larger Map

Question:

If George can run at a maximum velocity of 6 mph for about 10 minutes before collapsing into an exhausted heap, and an adult cougar can sprint up to 30 mph, how much of a running head start does George need to avoid becoming cat food? Answers may be expressed in units of either time or distance.

Monday, April 14, 2008

Fractions: An Example

We're up to 5 in our series of posts fleshing out the material written by Hung Hsi Wu in Critical Concepts for Understanding Fractions. See also Part I ,Part II, Part III, and Part IV.


Here, we go to a concrete example of all of the elements we've discussed: definitions of fractions, use of the number line, equivalent fractions, and some simple operations on fractions--comparing fractions and addition of fractions.

We consider Decimal Fractions. Decimal Fractions are a particular kind of fractions: fractions whose denominator is a power of 10: 10, 100, 1000, or any number represented by 10^n, where (for simplicity) n is a non negative integer.

here are some examples: 1489/100, 24/100000, 58900/10000

Decimal fractions have another convenient representation: as numbers that can be abbreviated into decimals: 14.89, 0.00024, 5.8900

Specifically, the above are finite decimals, though they are usually referred to simply as decimals. The number of digits to the right of the decimal point tells us the number of zeros in the denominator: 2 in 1489/100, 5 in 24/100000, 4 in 58900/10000. In this form, the convention is that zeros are added to the left of numbers as necessary to indicate the number of zeros in the denominator: in the case of 24/100000, we added three zeros to the left of 24: .00024.

The example 5.8900 shows that our decimal convention is not enough for explaining that we can remove the trailing zeros to the right of our number and decimal point. to show that, we need to invoke equivalent fractions:

for all whole numbers k, m, and n, where n and k are non-zero,
m/n = km/kn.


In this case, we can show that 5.8900 is the same as 5.89 by going back to the fraction form:

5.8900 = 58900/10000 = (589 * 100)/(100 * 100) = 589/100 = 5.89


This invocation of equivalent fractions works for in general, so any number of trailing zeros on the right can be shown to be equivalent to their absences:
12.700000 = 12.7 = 12.70 = .... etc.

After equivalent fractions, we moved on to comparing of fractions. Here, we show how to compare decimals.

Example: given 0.0082 and 0.013, which is bigger? We can compare these decimals easily by first converting them to fractions, giving them common denominators, and then comparing the numerators.

Converting to fractions, we see that we are comparing 82/10000 and 13/1000. To compare fractions, we then invoke again the rule that any two fractions may be represented by the same denominator:

m/n = ml/nl and k/l = nk/nl.


If m = 13 and n = 1000, then l = 10, and we have 13/1000 = 130/10000.Now we can compare 82/10000 and 130/10000 by comparing numerators. 130 is larger, so .013 > .0082.


Now, we move onto an application of fraction addition: to understand the algorithm for adding decimal fractions.

Example: 4.0451 + 7.28

Looking at our example and recalling what we know about fractions, the decimal fractions are just short hand for these numbers as fractions: 4.0451 = 40451/10000, and 7.28 = 728/100. We can then add them as we add any fractions, by giving them the same denominator. In this case, we call m = 728 and n = 100. If l = 100, then ml = 72800 and nl = 10000. Now, adding the whole numbers is the same as adding the numerator: we add

40451/10000 + 72800/10000 = (40451 + 72800)/10000 = (113251)/10000.

This leads us to an algorithm for adding decimals is:
1. line up the numbers by their decimal point
2. add the numbers just as you would "normal" whole numbers
3. put the decimal point in the number, based on where it "lined up" with the decimals in the additions.

When we line up the numbers by their decimal points, we are essentially rewriting the two decimals so they have the same number of digits to the right of the decimal point. This is the same as giving both of the decimal fractions the same denominator.

Then, we add the numbers, just as we would add the numerators.

Then, we determine the appropriate location of the decimal point just as we do by convention: we count the number of zeros in the denominator, and place the decimal point so that the number of digits to the right of the point matches the number of zeros in the denominator: 11.3251.

The point here is to stress that decimal fractions are really just fractions, and that we know how to perform elementary operations on fractions just as we do on whole numbers. Everything we understood about how to manipulate whole numbers on the number line mapped to fractions on the number line, and decimals are just a convenient notation for a certain type of fraction. The point is to underline how similar the processes are.

We'll get into more complications, like multiplication of decimals, later, after we advance a bit more with fractions themselves. Onto understanding fractions as division, then to multiplication and division operations!

memorize this!

At Out in Left Field.

water rope

Yesterday Andrew wrote “I want water” on his Dynamo.

Ed got him a bottle of water.

That wasn't what he meant, so he wrote “I want water rope.”

He wanted Ed to squirt him with the hose.

.......................

Andrew's speech therapist tells me he desperately needs to learn grammar, which she is working on.

Here at home, assuming the demo lessons pan out, I'm probably going to use a program I stumbled across just two weeks ago: GrammarTrainer.

If you spend some time on the web site you might spot something interesting.


smarter than your average bear

last of the Mohicans

Earl Smith of Colby College:

You may have read of the death of Marie Smith Jones, the last native fluent speaker of Eyak, once used along the Copper River in south Alaska. The notice set me to wonder if perhaps the day is not far off when we will be informed of the demise of the last known defender of the King’s English.

When that day comes, we might read in the New York Times (by then undoubtedly a weekly) an obituary that reads something like this:

PIORIA, Ill. – Harvey “Picky” Stickler, the last stout defender of proper English usage, has died. Many will remember him as an inveterate writer of letters to the editors of many now defunct large daily newspapers, carping about misspellings and violations of arcane grammar rules. He had recently turned his attention toward the Internet and its blog writers, a task that caused his health to deteriorate rapidly. He was 92 and discouraged.

His daughter and lone survivor, Lucy, had been estranged from her father for several years. “He wasn’t nicknamed ‘Picky’ for nothing,” she said from her home in Boston. “When I lived with him he was always, like, well, you know, correcting me. After my daughter was born, her and I just moved out.”


the project method redux
It is common belief that the decline of the language is the fault of the facility of the computer. This is not true... proper English usage first began to slide long ago when educators replaced old-fashioned English courses (boring topics like parts of speech and punctuation) with courses called Language Arts.

I made this discovery one evening several years ago when I found my daughter, a student in secondary school, wrestling with our young Golden Retriever named Colby (for Colby College of course) on the kitchen floor. She explained she was making a Plaster of Paris cast of one of the dog’s paws. The kitchen was a mess. The dog was not amused. “What for?” I said. “For Language Arts,” she said.

Which reminds me. It's getting to be time for our second annual Worst School Project awards.

Taking entries now.

the Harvard Education School

Harvard Education School is kind enough to offer, on its website, an insight into the research interests of its faculty. Their centers for research include: “The Center on the Developing Child; Change Leadership Group; Chartering Practice Project; Civil Rights Project; Collaborative on Academic Careers in Higher Education; Dynamic Development Laboratory; Everyday Antiracism Working Group; the GoodWork Project; Harvard Family Research Project; Language Diversity & Literacy Development Research Group; National Center for the Study of Adult Learning and Literacy (NCSALL); NICHD Study of Early Child Care & Youth Development; Project IF; Project on the Next Generation of Teachers; Project Zero; Projects in Language Development; Project for Policy Innovation in Education; Public Education Leadership Project (PELP); and Understanding the Roots of Tolerance and Prejudice.”

The mission of some may be less clear. The “GoodWork Project” explains that: “The GoodWork® Project is a large scale effort to identify individuals and institutions that exemplify good work—work that is excellent in quality, socially responsible, and meaningful to its practitioners—and to determine how best to increase the incidence of good work in our society.” There is no indication that they are interested in good academic homework. Project IF is about “Inventing the Future.”

[snip]

Perhaps academic schoolwork has comes to seem mundane, banal—really beneath them—so they decide to give their attention to “higher” concerns like multiple intelligences, child care, everyday antiracism, inventing the future, and "dynamic development." To some, it may appear that many of these topics might better be studied in a school of social work or in a graduate department of psychology, but if Harvard Education School feels that academics are not that important for teachers and students in the schools, they have to do research on something, I suppose, and to me it seems that what has occurred as a result might be called the psychologyzation of an education school.

Now, if our public school students were already doing splendidly in academic work, perhaps there would be a need to look beyond plain academics as a subject of study, but my impression is that this is not yet the case in the United States.

I think it would be great if Harvard Education School, and others, would, until our students are more proficient academically, spend more time working on ways to teach academics and to encourage our students to do academic work in the schools. Then, when our students are doing a lot better in academics, the Ed Schools can go back to roaming around in social justice, everyday antiracism, child development, inventing the future, and all the other subjects to which they are now devoting themselves.

Will Fitzhugh at School Information System
The Concord Review

Sunday, April 13, 2008

Bleg: rules about school overcrowding ?

I am posting a bleg because maybe KTM readers know people who know the answer, or know how to find out the answers.

Short version, wherever you are: do you know what the law says in your city/state/district when your neighborhood school is over capacity? Does the school district have the legal right to move your child to any school they see fit? What recourse, if any, do you have, to keep your child in your neighborhood school? Can they be sued to expand? Sued for denying your kid a space there? What are the rules? I'd hate to be in the position where I mortgaged my future to buy a house in a specific district/neighborhood, thereby preventing me from affording private school, only to find out my kid can't go there after all.

Someone I'm close to is in that position. They recently moved their family to a house in Los Angeles because it was specifically within a certain LAUSD school's neighborhood, and they wanted to send their child to that school. The school is Fairburn Avenue Elementary. The child in question will be starting kindergarten in the fall.

That school has been crowded recently. Last year, they added an additional K class, but still did not accommodate the numbers, and an entire class were moved to another school. This year, the school has decided not to bother. Their argument? They can't accommodate them in the higher grades (2nd, 3rd... the school goes up to 5th) in those facilities anyway. BTW, LAUSD recently decided that classroom size matters, so no k-3 will have more than 20 students. look how well that's working!

Here was the statement by the school:
"LAUSD will allow 300 students in K through 3 and due to the large class sizes for next years 2nd and 3rd grade classes, we will have only 3 K classes next year. That means only 60 Kindergarten students. They will be admitted first come first serve so if you have incoming Kindergarteners next year, please show up on the first Monday in May to pick up the paperwork to enroll your children.... If more than 60 children enroll in Kindergarten, Warner is projected to be able to take up to 16 of the latest to enroll. Any kids enrolling beyond those 16 will be accommodated at another, not yet decided upon, school."

how nice. so, is this common? Is this well known when it does occur? How often do parents find themselves in this kind of predicament? And is there anything that can be done about it?

Fighting Back Against "The World Is Soooo Dangerous Now": Free Range Kids

Lenore Skenazy let her son Izzy make his own way home from Bloomingdale's in New York City a couple of weeks ago, and wrote about the experience in the New York Sun. It was a man-bites-dog story, as Izzy is only nine--. Lenore wrote another column for the Huffington Post:

Last week I wrote a column for my newspaper, The New York Sun, titled, "Why I Let My 9-Year-Old Ride The Subway." It basically said that I let him do this because he wanted to take a trip solo, he knew how to read the map, and I had every confidence that he could find his way home.

Two days later, said son and I found ourselves on the Today Show, MSNBC and FoxNews, trying to convince anchor after anchor after anchor that:

1) This was not a crazy idea - as they could see from the fact the kid was sitting there, grinning. And

2) I am not a crazy mom, as they could see from...

Well, that's the point. Not all of them could see. The mere fact that I'd let my son out of my sight made me seem nuts to more than a few people, who wondered why didn't I follow him, or keep checking in with a cell phone, or wait until he was 34 and balding before I let him go out on his own.

Skenazy is looking to give her son "a longer leash."

But here's what I've learned from all the folks who don't want to do that, and send bile-filled notes instead: For some reason we live in a society that sees little difference between letting a child frolic in the front yard and letting a child frolic in front of a firing squad. It's impossible for people to calculate the difference between real and remote risks.

So she's started a blog, Free Range Kids, to counter the coddling and hypervigilance -- even countering the helicopter parenting phenomenon.

At Free Range, we believe in safe kids. We believe in helmets, car seats and safety belts. We do NOT believe that every time school age children go outside, they need a security detail.

Go and tell your story of raising Free Range Kids.

(will be cross-posted at I Speak of Dreams)

Saturday, April 12, 2008

core knowledge




Have I ever mentioned the fact that I won $9,000 cash on a game show two days before I got married?

Well, I did.

My winning answer: Who is Norman Lear's producing partner?

title-nining science

Math 55 is advertised in the Harvard catalog as “probably the most difficult undergraduate math class in the country.” It is legendary among high school math prodigies, who hear terrifying stories about it in their computer camps and at the Math Olympiads. Some go to Harvard just to have the opportunity to enroll in it. Its formal title is “Honors Advanced Calculus and Linear Algebra,” but it is also known as “math boot camp” and “a cult.” The two-semester freshman course meets for three hours a week, but, as the catalog says, homework for the class takes between 24 and 60 hours a week.

Math 55 does not look like America. Each year as many as 50 students sign up, but at least half drop out within a few weeks. As one former student told The Crimson newspaper in 2006, “We had 51 students the first day, 31 students the second day, 24 for the next four days, 23 for two more weeks, and then 21 for the rest of the first semester.” Said another student, “I guess you can say it’s an episode of ‘Survivor’ with people voting themselves off.” The final class roster, according to The Crimson: “45 percent Jewish, 18 percent Asian, 100 percent male.”

Why do women avoid classes like Math 55? Why, in fact, are there so few women in the high echelons of academic math and in the physical sciences?

Why Can’t a Woman Be More Like a Man?
By Christina Hoff Sommers
From the March/April 2008 Issue
The American

Oh, I don't know....

Possibly because they're not insane?

Just kidding.

Women now earn 57 percent of bachelors degrees and 59 percent of masters degrees. According to the Survey of Earned Doctorates, 2006 was the fifth year in a row in which the majority of research Ph.D.’s awarded to U.S. citizens went to women. Women earn more Ph.D.’s than men in the humanities, social sciences, education, and life sciences. Women now serve as presidents of Harvard, MIT, Princeton, the University of Pennsylvania, and other leading research universities. But elsewhere, the figures are different. Women comprise just 19 percent of tenure-track professors in math, 11 percent in physics, 10 percent in computer science, and 10 percent in electrical engineering. And the pipeline does not promise statistical parity any time soon: women are now earning 24 percent of the Ph.D.’s in the physical sciences—way up from the 4 percent of the 1960s, but still far behind the rate they are winning doctorates in other fields. “The change is glacial,” says Debra Rolison, a physical chemist at the Naval Research Laboratory.

Rolison, who describes herself as an “uppity woman,” has a solution. A popular anti–gender bias lecturer, she gives talks with titles like “Isn’t a Millennium of Affirmative Action for White Men Sufficient?” She wants to apply Title IX to science education. Title IX, the celebrated gender equity provision of the Education Amendments Act of 1972, has so far mainly been applied to college sports. But the measure is not limited to sports. It provides, “No person in the United States shall, on the basis of sex...be denied the benefits of...any education program or activity receiving federal financial assistance.”

While Title IX has been effective in promoting women’s participation in sports, it has also caused serious damage, in part because it has led to the adoption of a quota system. Over the years, judges, Department of Education officials, and college administrators have interpreted Title IX to mean that women are entitled to “statistical proportionality.” That is to say, if a college’s student body is 60 percent female, then 60 percent of the athletes should be female—even if far fewer women than men are interested in playing sports at that college. But many athletic directors have been unable to attract the same proportion of women as men. To avoid government harassment, loss of funding, and lawsuits, they have simply eliminated men’s teams. Although there are many factors affecting the evolution of men’s and women’s college sports, there is no question that Title IX has led to men’s participation being calibrated to the level of women’s interest. That kind of calibration could devastate academic science.

But unfortunately, in her enthusiasm for Title IX, Rolison is not alone.

On October 17, 2007, a subcommittee of the House Committee on Science and Technology convened to learn why women are “underrepresented” in academic professorships of science and engineering and to consider what the federal government should do about it.
As a rule, women tend to gravitate to fields such as education, English, psychology, biology, and art history, while men are much more numerous in physics, mathematics, computer science, and engineering.

There are many days when I think that one of the worst problems in education is the complete and total domination of the field by women. We desperately need some guys in the schools and running the schools.

Interestingly, Ed says that the field history continues to be a guy thing. Every other field in the humanities has been taken over by women, but men continue to outnumber women in the study of history. There are many more female historians than there once were, but the field hasn't "flipped," the way literature and art history fields have.

I don't know what to make of that.


Needed in class: a few good men
Are male teachers on the road to extinction?

U = E x V / I x D

Steel developed the equation U = E x V / I x D, where U is the desire to complete the task; E, the expectation of success; V, the value of completion; I, the immediacy of task; and D, the personal sensitivity to delay, as a way of mathematically mapping a given individual's procrastination response. So, for example, my desire to finish this article is influenced by my relative confidence in writing it well and the prospect of a paycheck as well as a looming deadline and my inherent desire to go home at the end of the day. "You're more likely to put something off if you're a very impulsive individual," Steel says. But, "if you only work at the last minute, time on task tells."

Of course, this does not explain why humans would procrastinate in the first place, but it is certainly not a new problem. The Greek poet Hesiod, writing in 800 B.C., averred "a man who puts off work is always at handgrips with ruin" and the divine incarnation Krishna singled out procrastinators for special scorn in the Bhagavad Gita. Nor does it explain why procrastination seems to be on the rise--afflicting as many as 95 percent of students and at least 15 percent of adults, according to two recent surveys.

Why Do Today What You Can Put Off Until Tomorrow
by David Biello
Scientific American
January 15, 2007

Hah!

I can tell you exactly why procrastination is on the rise.

projects

Projects are long-duration behavior. Everyone procrastinates long-duration behavior, even chickens. Maybe especially chickens; who knows? Turn K-12 into 13 years of project-based, collaborative learning, et voilĂ ! Epidemic levels of procrastination! This generation will emerge from high school suffering the customary math phobia, and on top of that they'll have writer's block and chronic problems with procrastination and time-management.

Once they're all settled into lifelong therapy and/or AA, we'll need a whole new slew of child-centered reforms to fix the schools.


Procrastination Central

The Educational Industrial Complex

Today I came across a great blog entry over at The Daily Kos by Nanoman, "a professor of electrical and computer engineering in Louisville, Kentucky and a parent who has had children attending K-12 public schools." He's taken the liberty of welcoming Education to "the old familiar Military, Tobacco, Pharmaceutical and Medical Insurance Industrial Complexes."

He prefaces a fabulous chart, a centerpiece of the blog entry, with this:
Please forgive the hyped intro, but the story that follows (which is summarized in the blue and yellow chart) is worth reading because it is being repeated in school districts across the country where choreographed ploys are used to bypass parent concerns about poor math texts.

Just take a look at Math Wars: The Educational Industrial Complex. The chart with Steve Leinwand at the center of all the hullabaloo is certainly worth the price of admission.

When you're done with that, you might want to check out "Is Our Children Learning" Math Texts too.

"another contraption"

in the Sun yesterday:

The schools chancellor, Joel Klein, and the president of the teachers' union, Randi Weingarten, are locked in a bitter debate over whether test scores should be used to evaluate teachers. Mr. Klein thinks they should and Ms. Weingarten thinks they shouldn't. The legislature and the governor have sided with Ms. Weingarten, and it looks like New York is going to be the only state in the union that will forbid using test scores to evaluate teachers. As it happens, we're not terribly excited about this fight one way or another, because we don't think test scores should be the device for evaluating teachers. We have another contraption we favor for evaluating teachers. It's called parents.

How To Evaluate Teachers
NY Sun April 11, 2008


That's what I call upping the ante.