Education and algorithms, and a Teacher in America

View 778 Tuesday, June 18, 2013

I had several possible leads today but this mail really got my interest.

I came across this blog today on math education, it is not behind a paywall:

http://opinionator.blogs.nytimes.com/2013/06/16/the-faulty-logic-of-the-math-wars/

I don’t any formal experience with evaluating ideas, but this makes sense to me. For instance, back in the 8 bit world when I was teaching myself programming, I could flounder around and figure out a routine for myself, that took a lot of lines, took a lot of processing time, and kind of did want I wanted, a friend of mine, who was from the magnetic drum era, knocked it out in 3 lines. He then gave me a book on algorithms which both saved me a huge amount of time and made me a much better programmer.

tonyb

The article by Alice Crary and W. Stephen Wilson is very much worth your attention. My children are long out of school, and while I have been following the repeated disasters in public education as education theory takes over from experience to produce teachers with credentials who can’t teach I hadn’t seen this one.

At stake in the math wars is the value of a “reform” strategy for teaching math that, over the past 25 years, has taken American schools by storm. Today the emphasis of most math instruction is on — to use the new lingo — numerical reasoning. This is in contrast with a more traditional focus on understanding and mastery of the most efficient mathematical algorithms.
A mathematical algorithm is a procedure for performing a computation. At the heart of the discipline of mathematics is a set of the most efficient — and most elegant and powerful — algorithms for specific operations. The most efficient algorithm for addition, for instance, involves stacking numbers to be added with their place values aligned, successively adding single digits beginning with the ones place column, and “carrying” any extra place values leftward.

What is striking about reform math is that the standard algorithms are either de-emphasized to students or withheld from them entirely. In one widely used and very representative math program — TERC Investigations — second grade students are repeatedly given specific addition problems and asked to explore a variety of procedures for arriving at a solution. The standard algorithm is absent from the procedures they are offered. Students in this program don’t encounter the standard algorithm until fourth grade, and even then they are not asked to regard it as a privileged method.

The battle over math education is often conceived as a referendum on progressive ideals, with those on the reform side as the clear winners. This is reflected, for instance, in the terms that reformists employ in defending their preferred programs. The staunchest supporters of reform math are math teachers and faculty at schools of education. While some of these individuals maintain that the standard algorithms are simply too hard for many students, most take the following, more plausible tack. They insist that the point of math classes should be to get children to reason independently, and in their own styles, about numbers and numerical concepts. The standard algorithms should be avoided because, reformists claim, mastering them is a merely mechanical exercise that threatens individual growth. The idea is that competence with algorithms can be substituted for by the use of calculators, and reformists often call for training students in the use of calculators as early as first or second grade.

Reform math has some serious detractors. It comes under fierce attack from college teachers of mathematics, for instance, who argue that it fails to prepare students for studies in STEM (science, technology, engineering and math) fields. These professors maintain that college-level work requires ready and effortless competence with the standard algorithms and that the student who needs to ponder fractions — or is dependent on a calculator — is simply not prepared for college math. They express outrage and bafflement that so much American math education policy is set by people with no special knowledge of the discipline.

There is considerably more, and all worth your time.

The problem is that we no longer know what the public schools are for, and we no longer recognize that a good public school system would make high school the normal education for citizens, with junior colleges to teach skills not so easily learned in apprenticeships, colleges as the place for those who want more education or need some credentials to make a living (teachers, accountants) and universities for those who are seriously going into professions needing high levels of technical competence. Liberal arts colleges we will leave for another discussion – there are many publications on that.

But the essential point is that public education can’t give everyone the same education. We need not go to the extremes they have in Japan and other places where early examination scores determine the course of your education and your life from then on; but we do need to recognize that not everyone needs to know algebra and calculus, and trying to bestow that as a right is to doom the ones who should know it to being forced to learn at the pace of those who never will learn them.

Jacques Barzun dealt with much of this a very long time ago in his Teacher in America, and anyone who hasn’t read that has both a treat and an epiphany in store. http://www.amazon.com/Teacher-America-Jacques-Barzun/dp/0913966797 alas not in Kindle, at least as yet.

I have errands but I recommend the Crary and Wilson essay to everyone and strongly urge it on all those with children in grade school.

I will also point out that many elementary schools no longer require learning the plus and times – addition and multiplication – tables by heart in first grade (an age at which it’s easy to learn such things by heart). Not knowing the plus and times tables by heart is a great handicap for the rest of one’s life. Like being able to read from an early age on, knowing those algorithms – I recommend learning them to 20 rather than the traditional 10, largely because if you know them to 20 you will inevitably notice some patterns that will make learning some other things about number easier – is a great gift. It saves time in everything from counting change to calculating the tip in a restaurant, and a hundred other things you do daily.

If you are involved with elementary education, either as a teacher or a parent, read the Crary and Wilson essay – and go read Barzun. And if you have read Barzun it won’t hurt to read him again.

"Playing balance of power games, subsidizing one enemy to fight another, is a game of high risk and high skill."

Does anyone really think the current administration possesses the talents to manage this?

s/f

Couv

David Couvillon

Colonel, U.S. Marine Corps Reserve, Retired.; Former Governor of Wasit Province, Iraq; Righter of Wrongs; Wrong most of the time; Distinguished Expert, TV remote control; Chef de Hot Dog Excellance; Avoider of Yard Work

I have no evidence to suggest that we have those skills at the cabinet level in the United States, nor have we politicians who understand their own limits at such matters of state.  This has always been a defect of a republic: it has to go to war to develop long term professionals in such matters.  We are at a war without such development, and the result is that it appears to be war without end.  We do not have a Richelieu or a Metternich, nor indeed a Pitt or a Palmerston. We have people capable of such finesse but they are not likely to be put in power, nor left there if they get there. 

It was not from lack of understanding of political history that many of our Framers concluded that America’s best course was to be the city on a hill, a shining example of the fruits of liberty.  We are the friends of liberty everywhere but we are guardians only of our own.

 

Thor

Hi,

A friend sent me a link. I’ve seen THOR referenced in a couple of science fiction books, sure, but in a comic about 20-somethings working in a coffee shop?

http://questionablecontent.net/view.php?comic=2468

Ed

Ed Hahn

Complete with tungsten.  Well, my original papers were never classified.  The proposals that were generated by them were, but I suspect that even they have long been declassified.

Subject: Educating Educators Lost

A new study rates almost all U.S. college programs that try to prepare persons to be teachers at mediocre or below.

One quote, "We don’t know how to prepare teachers"

I guess, at one time, we did know how to prepare teachers. We must have forgotten along the way.

http://www.washingtonpost.com/local/education/university-programs-that-train-us-teachers-get-mediocre-marks-in-first-ever-ratings/2013/06/17/ab99d64a-d75b-11e2-a016-92547bf094cc_story.html?hpid=z2

—

Dwayne Phillips

Go to any college campus and ask the first 20 people you meet which department is toughest and which is easiest.  Ask the next 20 if they have any Mickey Mouse majors.

Teaching is part knowledge and part skill.  The knowledge should come from the same place that other students get it. To teach math one ought to know some math. Etc.  The Ed Dept. courses in math and science are generally taught by education theorists, so the result are expected.  Of course there are exceptions.  There are some good education schools.

When the Rev. Moon bought Bridgeport University they asked me as one of a list of consultants what they ought to do with it.  I suggested starting a University Grammar School that took in neighborhood kids – it is not in a university district so there would be plenty of diversity – and had the classes taught by teachers who actually could teach, and who were the advisory council for the department of education and had full control of it. A different picture.  I pointed out that we could get a number of people involved in this including Barzun and Annette Kirk who was one of the principal authors of the 1983 National Commission on Education “Seybold Report”.  We could probably get Seybold himself – he had just attended one of Moon’s International Society for the Unification of the Sciences meetings in Seoul and I had actually discusses this with him.  We could in other words get things started well and use the actual school results as the criteria, and perhaps change the world.

Alas it didn’t happen, in part due to opposition of the Bridgeport faculty who were afraid of Moon and his interference:  I tried to point out that not a single one of the consultants he had brought in to try to organize this was a member of the Unification Church.  Some were Catholic, some were Protestant, some were Jews, and at least one public atheist.  Ah well. It would have been a lot of work for me, and for my wife who would have had to organize the reading instruction program for first and second grade and probably would have worked directly with the first teacher class. 

It didn’t happen but it still could, somewhere.  We used to do that sort of thing. Look what I learned in Capleville with 2 grades to the classroom in the Depression.  It can be done but we have to want to do it, and the progressives  — well, we’ve been through all this before.;