"Improving" education

.

One approach to improving the achievement of the United States of America in the Olympics has been to introduce American sports into it, sports that are not widely played outside the USA.  (This would certainly improve the profits of the TV channels that carry the Olympics.)

And now for something completely different.

A recent article in the NY Times by two quite respectable mathematicians and educators suggest some changes to the mathematics curriculum in American schools.

For instance, [the authors ask,] how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a 'group of transformations' or a 'complex number'? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood.

 The broad thrust of the article can be reduced to the following assumptions:

1. Every child doesn't need to be taught the same (science/engineering - type advanced) mathematics.
2. Concrete applications are more useful to students than abstract mathematics.
3. The useful mathematics (listed in the article) is not being taught now.

All this, of course, is being driven by poor results of American student samples on standard international tests.

The fact of the matter is that ALL THREE ASSUMPTIONS ARE WRONG.

Certainly, all children do not need to know the same mathematics (or the same social studies, or the same history, for that matter).  But there is no harm in teaching all students the same principles, while you allow for expected variations in interest.  It would be a big mistake to try to predict the precise sliver of mathematics a child is likely to need and teach him or her only that.  First of all, we can't predict needs that accurately, and people change careers so often that the prediction simply cannot be correct.  Finally, with the insistence that Education should cost society the very minimum it possibly can, (and that the majority of education dollars should be spent on building-beautification and athletics) we cannot afford to give a highly individualized education at lower levels.  But teachers can, and do know how to, adjust for individual interests in students, and the better teachers supplement their basic classwork with enrichment activities focused on student interest.  But, of course, that instruction cannot be easily tested in standardized tests.

Secondly, the concrete vs. abstract debate is so out of place here.  It is human to abstract; that is, to generalize.  Two chickens and two chickens is the same number of chickens--four--as two cows and two cows are the number of cows: four.  No one can possibly protest the most common abstraction of all, namely number.  Our parents tolerated quite well a large degree of abstraction (though, of course, it was a small elite that went on to college in their day).  In these times, we all recognize, we want the students to learn considerably more.  Why?  Because a lot of what our parents considered to be advanced knowledge has now been demoted to material that is accessible to kids, and which they must know.  A "complex number" might be regarded by Professor Sol Garfunkel as something mystical and specialized (though I know for certain that he is no stranger to them), but it is an easy enough concept for the typical student, and moreover, an easy way of teaching various topics in calculus.   [Easy for the teacher, but also easy for the student.]  Geometry is these days taught via the idea of transformation, where transformations was a topic reserved for mathematical black belts in the earlier part of the 20th century.  Abstraction is another way of killing several birds with the same stone, and hardly something to be deplored.

Finally, useful mathematics is being taught now.  As early as grade four, with the recommendations of the NCTM (National Council of Teachers of Mathematics) that were announced by a taskforce as early as 1980, and adopted by the full NCTM shortly thereafter, and widely adopted in schools across the country, basic descriptive statistics was to be taught to children of about the age of ten or eleven, and in classrooms across America you can find displays of various pieces of data in bar charts and pie charts.  These fellows should get out more.

The fact of the matter is that if we were to change the curriculum to be exactly what Garfunkel and Mumford recommend, the chances are that within a few years, this curriculum would be --in its essentials-- adopted by all foreign countries, or even taught in addition to their own, and foreign kids will be trouncing American kids once again.

Why is this?

In an insightful comment (Mike O'Shea?) says that a possible reason why academics in the US are weak for the majority of students is that excellence in academic subjects is valued less than excellence in athletics and sports.  He concludes with: "And if our teenagers aren't practicing sports, they're working at part-time jobs after school for pocket money for themselves. Competing against sports and money, academic subjects don't have a chance."

Mavis Tavis says, looking at the whole article:

Ah, yes, just what we need: a math for the masses and a math for their masters. This argument presupposes that the common people don't get it, don't need it, and don't want it. It echoes the argument that has gone on in the humanities and foreign languages for a generation now: why teach complex subjects and abstractions to the herd who don't need such instruction? Teach them what they need to know to become, at best, good Wal-Mart managers.

A time there was when math assumed not only a utilitarian function but also a theoretical function, teaching children not just what they need to know to get by, but also how to think logically--to make them better workers, neighbors, voters, parents, and citizens of a increasingly complex world.

Garfunkel and Mumfords's assertion suggests an unhealthy elitism. Worse, it smacks of classism.

Perhaps Garfunkel and Mumford were careless in their writing, and laid themselves open to severe criticism because of a number of poorly-reasoned, or poorly thought-out remarks.  It is true that weaker students destined to be highway-repair laborers or construction workers will probably not get motivated to study mathematics that are in the least abstract, even at the level of, say, elementary geometry.  But they are butting their heads against cultural principles that dictate that every child must be considered to be potentially a professional or an artisan of some sort.  To relegate a child to an easy curriculum based on an assessment of his or her ability may make life easier for him or her, and for his or her teacher, but it is a choice that we cannot ethically afford.  We cannot both take the high road about the Equality of Man, and take the easy way to education, and get high scores for our kids in standardized tests.  I'm not saying our curriculum (and we do not have a national standard curriculum, but rather a core curriculum that is a sort of "back-to-basics" nucleus that, as G & M claim, has been adopted by at least 40 states) is perfect; it has to be adjusted from time to time.  But good teachers can do a better job within this curriculum, and they are doing so.  But statistically, they are a minority.

The vast majority of teachers are poorly-paid and poorly prepared underachievers.  You cannot improve the quality of teachers in the USA by picking on the weaker members of that profession and making life miserable for them.  I suspect that the better ones among our young people do not go into the teaching profession precisely because it is a scapegoat for all that is bad in society.  Let's stop bullying our teachers, and concentrate on rewarding the best of them, and appreciating all of them.

Arch

The Greatest Country In The World!

.

I just sat through what we call Freshman Convocation here, in my school; it is where we welcome the new students, and pump them up for the rest of the semester.  Our featured speaker was an alumnus who recently won a seat in Congress.  He described how he regularly meets people from other schools, and travels around the world (for the business of various committees he's on), and he attested to the fact that ours was just as good a school as any Ivy League school (which I'm willing to believe), and that The US is the greatest country in the world.

In some ways I have to agree to the latter sentiment as well.  I have met people in the US who are among the most broadminded, the best informed, the most flexible, the most willing to consider new ideas, the most culturally aware, the most generous, and most loyal.  Sometimes I'm tempted to believe that these people are just attracted to me because I am, of course, the greatest guy who ever lived.  But I quickly come back to earth; I realize that these people live here in the US either because they were born here, or came here because this country provided the greatest opportunities for the sorts of things they wanted to do.  An outstanding teacher can find a place to teach here; an outstanding athlete can pursue his craft; an outstanding artist can find a patron here.  Let's face it; there are a lot of people with a lot of money, who want to encourage a lot of the right things.

To an American who has emerged from a blue-collar background to become a US Attorney, and then win a seat in Congress, obviously there is no place like home.  But let's look at why this is ---or has been, until recently--- such an amazing place.

There are tremendous natural resources.

There has been great wealth, which meant that at one time anyone could get a sponsor or a financier to build a better mousetrap.  Today, there is greater wealth in the hands of some than there has ever been, and a few individuals have the ability to fund all sorts of creative schemes.  However, keeping possession of a large fortune is clearly becoming very difficult.  There are no books about How To Keep On Being A Billionaire Once You Become One.  There are Bernie Madoffs behind every shrub.  Your very assistants are probably waiting to bilk you out of your filthy lucre.  The only recognizable hostile party is the Federal Government in the shape of the IRS, which wants you to pay more tax than any of your friends seem to be paying.  (Your immediate family probably has an insatiable appetite for expensive necessities, and they probably find it very easy to confirm your suspicion about the evil intentions of the IRS.)

The wealthy class, however, is hard to herd.  It is amazing that the Republicans have succeeded in regimenting them so effectively for so long; at the present, they seem to be eying each other with deep suspicion.  As I have written before, the Tea Party and the mainstream old guard Republicans find it hard to agree on almost anything.  When the Republican majority meets on Capitol Hill, all they can agree upon are: NO TAXES, and AMERICA IS THE GREATEST NATION IN THE WORLD.  They cannot agree, I am sure, that it is precisely the taxes that make this country great.

What has also made this country great is the incredibly hard work of a few very unpopular people: FDR, who managed to establish common-sense social programs that were the envy of the rest of the world (until a whole pile of other countries found how to do the same job a lot better), Ralph Nader, who alerted a generation to the need for health and safety controls in a number of areas; Martin Luther King, who (reluctantly, we now know,) took up the fight against racial discrimination, so that black folk could have a stake in the society in which they lived, but is secretly despised today by many conservative bigots and not a few black racial extremists; Bill Clinton, who worked for and signed the Family Medical Leave Act; the much-hated State House of California that led the way to pollution control across the country.  I'm sure you can think of a half-dozen more individuals whom your friends love to hate, who made this a better society for all of us.

Those who fought for a better America are cheerfully reviled by the people at large.  So how can we claim that this is such a wonderful place to live, if the cost of improving things for your fellow-countrymen is to be cursed for years?  Each of us thinks of those who (privately, I suppose,) express disgust at the names of some of these patriots, as misguided.  So if this country is the greatest in the world, it is populated by a majority of misguided citizens.  It is great despite the majority of Americans, and not because of them.

What I did over The Summer

.

I can now reveal ---albeit in a limited way--- what has kept me from posting up a storm over the last several weeks.

Firstly, of course, in the political arena, nothing really interesting and substantial has been happening.  The White House has been curiously inactive, but it is a tricky endgame leading up to the elections and the sort of gambling that takes place at this time is difficult to second-guess, especially since the various assumptions they might be working on are a sort of discontinuous set, possibly wildly differing from each other and from our own guesses.

Secondly, I haven't been listening to music very much.  And why is this?

Because I have been busy.  I was seeing a lady friend, and the sight was getting more intense as the weeks went by.  We decided to marry around midsummer ---which was a lot of excitement, but not of the sort you might expect; it was a quiet ceremony at a country Magistrate's office, in between petitions for zoning variances and evictions, etc, the actual "swearing in" attended only by the two of us and the Judge--- after which we planned to have a nice big party for a few of our friends.

The Party was planned over a couple of months.

We first rented a room.  It was a small ballroom at the school where I teach, the perfect size for a party of forty people.  The most exciting piece of the arrangements was that we had to obtain an event insurance policy for a million dollars!  It only cost us $50, but we walked around for a couple of weeks, pale beneath our tans, pondering the enormity of the undertaking.  We were also forbidden the use of alcohol, and we knew many of our friends would have trouble loosening up without alcoholic inspiration.  But I figured that if alcohol had been found on the premises after a major fire had broken out, I would be in roughly a million dollars' worth of trouble.  But we held firm, and decided to have a certain modest amount of liquid entertainment at our home ---a mere 100 yards from the party--- for Afters.

Next, we got some music together.  Since we couldn't afford a disc jockey or a professional master of ceremonies (or even an amateur one), we decided to compile a collection of pieces we both liked, jointly and severally.  She liked most of my choices, but she wanted additional tunes that I did not have.  So the compilation was partly complete some weeks before.

We then compiled the list of invitees, a most amazingly wonderful collection of people in our separate estimates.  I had met a half-dozen of her friends who lived close by, and a couple who lived in New York, and liked them right away.  She had met my daughter, and the two of them had struck up a roaring friendship.  Junior was having her own romantic adventures (which I am not at liberty to report on), but managed to organize a frighteningly complicated itinerary for her 10-day visit from distant parts.

As my readers might know, Junior is an amateur musician of sorts, and it turns out, so are the daughters of my new wife, Katie.  Of course, therefore, we must have the girls sing!  The kids had never met, but began a tentative correspondence via the evil FaceBook.  My girl, being older, was much more relaxed about the whole thing.  The other girls were much younger, and therefore more uneasy about matters.  Still, they responded, and I really cannot tell you much about what they discussed.

Meanwhile, down at the farm, friends were e-mailing me, asking what they were to wear.  We were determined not to have a formal event, so we had to first decide what we would wear.  I finally settled on a sort of Hawaiian shirt, and a nice pair of pants---until I saw the most brilliant T-Shirt, with a fake Tuxedo printed on it!  So, of course, that's what I decided to wear.

We forbade any presents, mostly because we live in a small house, and there just isn't enough room for any more Stuff.  (Thankfully, all but five families abided by our request.)

Finally, Junior arrived, and we picked her up in Baltimore.  The next day, she spoke directly to Katie's youngest daughter on the phone, and they began a brain's trust about what to sing together.  They simply could not agree on anything, but with some nudging, I made Junior suggest a song by The Seekers: I'll Never Find Another You.  Now she had to teach that to Katie's youngest daughter, who was going to arrive a couple of hours before the party.

Everything went smoothly.  My Canadian friends, father and daughter, had arrived the previous day, and very ingeniously kept us distracted, and helped get the house ready for the after-party party!  On the day of the party, it began to rain, but the tribes gathered notwithstanding, and before we knew it, it was under way.  The food was wonderful, the music was apparently satisfactory to all---Junior had helped supplement my folder of music with Katie's more rhythmic, bluesy selections from the fifties and sixties.

When everyone had eaten, Junior and Katie's youngest daughter went over to the microphone, and sang.  That broke the ice, and then Katie's oldest sang one of her own compositions, followed by Junior, who writes her own songs too, and Katie's youngest, who first sang a song of her own, and then, to my astonishment, gave a fabulous rendering of Me and Bobby McGee, in Janis Joplin style.

Shortly afterwards we brought the party to a close, and everyone headed either to their homes, or to our small home, especially those who could stay overnight.  After the rest of us had beer or wine, respectively, Katie's oldest and her young man sang a lovely duet, and the young lady sang alone, followed by Junior with one of her own, and then we all began to sing songs from the sixties: notably Mrs Robinson [Simon and Garfunkel], If I had a hammer [Pete Seeger], and Blowing in the Wind [Bob Dylan]!  (If photos become available, I'll post them.)

Hopefully, my regular rants will resume in the Fall, though Katie keeps me steadily distracted.  [Added later: a few photos of all of us, including some taken later in the week, when we visited some relatives in New York and New England.]

Arch

Music Lists

.

What is a discussion list?
A "discussion list" is a loose organization of people who like to discuss topics on a particular subject.  It was one of the oldest recreational uses of the Internet, powered by e-mail.

A piece of software called a Listserv resides on a central computer somewhere, and when you join the list, it adds your e-mail address to its internal list.  You make a post to the list (by simply sending email to a special address), and the e-mail is copied by the software to everyone on the list.  You reply to a post, if you wish, and the reply is sent out to everyone on the list.  The nice feature is that you do not have to go out on a browser to a website; the stuff arrives in your mailbox.  You can make a complete fool of yourself on the list, knowing that only your discussion-list friends can see it!

I belong to several mailing lists, and here they are:

• The Bach List.  This one is hardly active at all, especially since the lady who was in charge of it seems to have fallen ill.  To join, go to this website and follow instructions: The Bach List.  Once you join, you post to the list by simply sending mail to bach-list.
• The Classical Music List, classm-l.
  This list was my earliest education on the Internet, and e-mail, generally speaking.  It has been around since the late 80's, and though it takes as its domain all of classical music, the members have been a close-knit group of friends that enjoy talking about matters that are very much on the periphery of the subject.  A great list to start with.  Go to CLASSM-L
• The Bach Recordings List, BachRecordings.
  This list is the most active of the lists mentioned above (though that could change at any moment, depending on response to a particular post).  It is one of three sister groups, and can be joined at this location.  Though, on the face of it, their subject is recordings of Bach works, it is in effect a list on which you can discuss most topics related to Bach, except for the Cantatas, which have their own list.

The proliferation of mailing lists is, on one hand, regrettable, especially in times when the discussion in all of them is inactive.  When the posts are flying fast and furious, we are thankful that everyone is not posting to the same list, since we can choose which particular flavor of topic and discussion we would like to join.

A Closer Look at Distrust of Government

.

I was puzzling over the failure of the Democratic Congress of 2008 and President Obama to pass Healthcare Reform Legislation.  Why, I asked myself, is there such suspicion of government sponsored healthcare?

The upper-middle-class really has a reason to view healthcare reform with dislike: it would seem to be accompanied by higher taxes.  The reform was presented as being tax-neutral, but over the years, as the country got a taste for the service, one could imagine Government Health Service expanding, with an ever-increasing load on taxpayers.  Healthy taxpayers would hate it, but the average taxpayer would benefit, since most basic services would be performed for free: your annual or half-yearly checkup: free; basic emergency room visits for simple surgery: free; family planning, neonatal care, elective and compulsory inoculations: free; preventive medicine related to diet, exercise, lowering health risks such as cholesterol, high blood pressure, high blood sugar: free.  Most Americans pay for all this anyway.

But ordinary middle class, and working class folks are against health reform!!  These people's share of the tax burden for health care will be negligible, but they are deathly afraid of it.  In heaven's name, why?

The suspicion must come from Government Services that are presently provided, but, at least in the view of common people, badly carried out.  The example that pops into mind is: Education.  Is it possible that the Face of Government for many folks ---and most certainly, the Face of Authority--- is the schoolteacher.  Even though it is the local government that ultimately controls the schools, it could well be that in the minds of many, Washington looks like the school: a place from where you get your education, a place which dominates your spare time with homework and other tedious responsibilities, and over which you have very little control.

I looked up on the Internet for a ranking of student achievement averages by State, and found only one site that was willing to provide the figures for 2003 for free, but wanted me to take a subscription in order to be given more recent data.  I just went with the data for 2003.

The table is at right, in the form of an image.  Here is a link to the actual page for the first table.

Let's look at the achievement in Elementary School, i.e., the Grade Four reading and mathematics scores.  The last several states are Hawaii, Mississippi, Alabama, and New Mexico, with Louisiana and California not doing much better.  A little higher up come Florida, Georgia, Arizona, Tennessee, and Arkansas.  These are the states whose students fared worst in these tests.

Is it possible that the residents of these states would expect that Government Health Care will stink as badly as Government Education?

The top achievers are Massachusetts, Connecticut, New Hampshire and Vermont.  I don't know about NH; perhaps their State Health Care motto is Private Health Care Or Die, but Massachusetts is certainly for Healthcare Reform, despite all the energetic efforts of the Tea Party to confuse Massachusetts residents.

When it comes to Middle School achievement, the top scorers are again Massachusetts, New Hampshire, with Minnesota and North Dakota.  The low scorers are, again,MS, AL and NM, joined by Hawaii.

It's difficult to tell what drives these variations in state achievement.  States with many families living below or close to the poverty line can be expected to have low average achievement: a child needs family support, a home environment conducive to grappling with ideas introduced in school even briefly each day, nutrition, rest, security, all of which impinge school performance, and all of which are threatened by poverty.

A large proportion of ethnic minorities might seem to influence achievement, but belonging to a minority alone should not influence school achievement, except via the poverty factor.

Latitude does seem to have a mysterious effect on achievement; it remains to be shown whether it has a corresponding effect on suspicion of government!

Arch

Honeybee

.

This post is completely devoted to my dog-in-law, Honeybee.  Honeybee is a mixed-breed (a.k.a. a mutt), with a lot of character.  To illustrate I would have to post a million anecdotes of goofy things that she does, but that would bore you.

Honeybee is a silly dog, but has a lot of dignity.  She tends to look at you through the corner of her eye, just as in the photo above.  It is as though she is thinking deep and beautiful thoughts, but wants to keep an eye on you all the same just in case you're going to do something amusing.  This glance looks flirtatious sometimes, but I haven't succeeded in capturing it perfectly on camera.

Honeybee loves to go on walks, and gets quite excited when she sees her owner put on her sneakers.  She wears a huge grin while she gallops along on the trails we take when walking her.  She likes to visit her doggie friends next door (this is in the country, so the doggies next door live a quarter-mile away).  They are kept in a cage (a nice roomy one, so it's not a hardship).  Honeybee goes and barks at them furiously, her tail wagging, and then comes home smiling.  I suspect that she knows that if the neighbor dogs were out of the cage, she would be nursing some painful bites.  She's 11, but they're much younger.  In this next one Honeybee is pretending to be mad and snarling.  You can tell from her eyes that she's a terrible actress.

[2011/8/8]

Well, here's a new story that emerged over the weekend.

Honeybee is left home by herself, now since the family is growing up and leaving home.  She does have her pet cat, Bigfoot, but he isn't much company for an intelligent dog, really.  Honeybee is left to gobbling up any food Bigfoot happens to knock off the kitchen table, and that's the extent of their voluntary interaction.

One morning, the gentleman who, apart from Honeybee and Bigfoot is the sole occupant of the house, decided to lock up the house when he left for work.  Now it came to pass that, later that day, the young lady, his sister, who had just moved out into her own apartment, came home to ferry out a few additional items that she needed, and found the place all locked up.  She had, much to her frustration, to gain entrance via the kitchen window.  However, she caught the leg of her pants on the toaster oven, and fell unceremoniously to the floor.

As was her custom, on occasions when she was precipitated onto the floor unexpectedly, she cursed all of nature and mankind at length, before she noticed Honeybee.  "I swear," she recounted to us, "that dog was laughing at me!"

I have to agree; I have never seen a dog with a broader grin than this particular one, and it is with deep regret that I find myself without a single photo of her laughing.  The minute you take out a camera it seems that the dog composes herself into a semblance of great seriousness.  I declare she knows that a photo is being taken, and that it behooves her to look as solemn as a deaconess.

Arch