Category Archives: standardized tests

How do you figure the circumference of a circle ?

And why would you want to do that ?

In his final week as Chancellor of New York’s public schools, Mr. Joel Klein was interviewed on TV about his educational philosophy. Well, he opined, a child certainly must know how to figure the circumference of a circle.

Now I bet that Mr. Klein himself, a lawyer and educational administrator, never once had to figure the circumference of a circle after leaving high school. Perhaps he needed this knowledge for higher math in college, and perhaps not. I myself happen to remember the idea: 2πR, and of course I needed this knowledge when I studied trigonometry and calculus. So yes, I am not against teaching 2πR somewhere in high school, or, better yet, teaching how to find the formula if you happen to need it.

But compare this to mathematical ideas that everyone truly needs, and that are not taught in high school, at least not on a regular basis. Take the basic ideas of statistics, in particular the idea of sampling and the often-abused idea of “statistical significance.” These concepts are essential to all citizens because they enable a person to evaluate the (frequently false) claims made in the media about medical research, public opinion polls, and much else. (For a recent account of the misleading nature of scientific reporting — in the absence of an understanding of the basic ides of statistics — see the important article by Jonah Lehrer in the New Yorker of December 13, 2010.)

Here is one more example of the mindlessness of the current crop of “educational reformers” who preach the gospel of testing, large classes, charter schools, firing of teachers, and. overall, a disregard of Dewey’s concern for “the child and the curriculum.” See my previous posting here.

Let there be better teachers ..


John Dewey

What are the problems of education ? Are they complex, calling for thought to be given to a number of factors, or are they, as current fashion would have it, so simple that they can be reduced to a single factor ?

From the White House down, and most certainly including City Hall in New York and its brand-new Chancellor of Education, there is now a simple mantra: let there be better teachers and all will be well, in the schools, in the country, in the world. Ninotchka had similar ideas (“The last mass trials were a great success. There are going to be fewer but better Russians.”), but let that pass.

Michelle Rhee, until recently the Chancellor of the District of Columbia schools, was perhaps the most vocal and the most active proponent of this doctrine. She came into office, she fired teachers, she got tremendous acclaim from politicians (including the current incumbent at the White House), and, voilà, the District schools are, well, in turmoil politically but, insofar as anyone can tell, academically no better than before.

No matter. Rhee may be gone, but her ideas still carry in the halls of power. Diane Ravitch (The Death and Life of the Great American School System) describes Rhee’s program:

As a member of Teach for American, Rhee taught for three years in a Baltimore elementary school managed by Education Alternatives Inc., a for-profit organization that received a contract as part of an experiment in privatization. According to Rhee, during her second and third years of teaching, the proportion of her students who read on grade level leapt from 13 percent to 90 percent (critics were doubtful since the Baltimore records could not be located). From her experience, she concluded that effective teachers could overcome poverty and other disadvantages….”Those kids, where they lived didn’t change. Their parents didn’t change. Their diets didn’t change. The violence in the community didn’t change. The only thing that changed for those 70 kids was the adults who were in front of them every single day teaching them.”

So here we have it: the teacher is the thing, nothing else matters. Nothing. And, to judge from Rhee’s administration in D.C., let these teachers be few, young, inexpensive, and, above all, “good.” How do we know when a teacher is “good,” or as it is sometimes put, “effective” ? Not a problem. Just administer tests to students, and those teachers whose students do best on the test are the best teachers. And how do we know whether the tests are any good ? Not a problem. Tests are good if their results can be quantified.

Well, a beginning — and only a beginning — of appreciating the problems with the Rhee doctrine is to look at how these attempts at measuring student and teacher performance have worked. As Diane Ravitch has shown in her book, the testing of student achievement by standardized, bureaucratized instruments has been almost uniformly unreliable. She cites the “law” promulgated by the social scientist Donald Campbell: “The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and more apt it will be to distort and corrupt the social processes it intended to monitor.”

If the prevailing standardized tests for student achievement have proven unreliable, the attempts to measure “teacher effectiveness” by such measures have been a complete failure. The New York Times has published an unusually good accounting on December 26. Despite very considerable number-crunching by statisticians, nobody has been able to find coherence in these ostensible measures of teaching quality. Even after overlooking such obvious absurdities as grading teachers who weren’t teaching for the period in question and failing to grade those who were, these reports undermine their own premise when they indicate that a “good” teacher one year is, almost as often as not, a bad one the next and then back again.

There is no rhyme or reason in this kind of quantitative “accountability” of the teaching profession. For anyone who has given thought to the complexity of the teaching enterprise, the reason is obvious: the problems of education are far more complex and far more profound than are dreamt of in the philosophies of Ms. Rhee’s Teach for America (a three-year program), or Ms. Black’s Hearst Publishing (executive suite).

John Dewey, the great American philosopher of education, published a little booklet in 1902: “The Child and the Curriculum,” calling attention to two of the complex factors that need to be considered in any discussion of education. Let me run down a few:

1. The child. Obviously, every child differs from all the others, as every snow flake differs from all its peers. But there are some regularities in this variance that the school must accommodate. It is a truism of the social science research that children from lower economic strata, as a group, come to first grade with far less (formal) verbal equipment than their peers from the more advantaged classes. To say, as Ms. Rhee does, that the heterogeneity of the students doesn’t matter is to say that the moon is made of green cheese. To everyone else, it would appear that the school must take careful account of heterogeneity and that, for that reason, class size — and the time a teacher can spend with an individual child — is too obvious a factor to sweep under the rug.

2. The neighborhood. Variable neighborhoods are obvious to all serious observers. Educational planners cannot ignore them.

3. The curriculum. The current fad of emphasizing only language comprehension and mathematics, at the expense of a great world of other topics, rules out the necessary and continuing debate about what it is that our children need to experience in the school. There really should not be final answers about what is and what is not important to the curriculum. We need to learn from evolving research — both into the state of scientific knowledge and the state of children’s needs — how the curriculum is to evolve.

I had planned to make this posting one in which I say everything that I can I think of on the topic of education. But I will not go that route; I can see too well all the obvious reasons that would make such an effort both shallow and futile. Instead I will close by recalling two mathematics teachers with whom I studied at City College between 1948 and 1949:

A. Mr. Zeig, instructor in Plane and Spherical Trigonometry, using the 1936 text by Rietz, Reilly, and Woods, which is before me as I write. It was a class of tremendous energy, with a teacher better organized than anyone I have met before or after. Every week, without fail, there was a test. Everyone, I believe, kept up with the material, everyone did well. I certainly did. I got an A. I memorized the trigonometric functions, I could perform all the required operations, and I mastered all this to its very maximum, as far as the class was concerned.

B. Professor Bergman, Professor of Calculus. The text by Sherwood and Taylor, dated 1942, is also before me now. I remember Professor Bergman standing in front of the class, scratching his head, trying to write a proof on the board, muttering: “I am not sure I’m quick-witted enough to get this right here….” I felt bewildered, as did, I suspect, much of the class. I worked very very hard in the class, but I did not have the neat structure — a test every week, etc. — that Mr. Zeig had provided in trigonometry. Moreover, much of calculus, I knew then and I know now, was beyond me. I managed to get a B for the course, which in those days was considered an achievement.

Who was the “better,” the “more effective” teacher ? By Ms. Rhee’s lights, it undoubtedly was Mr. Zeig who performed better: more of his students, no doubt, would pass a Rhee-devised test. But it was Professor Bergman’s difficult calculus that I remember, and it is Professor Bergman, from my perspective today, who has contributed far more to my education. Of course it is not an entirely fair comparison because Mr. Zeig’s trigonometry may be an inherently less profound subject. Still, Mr. Zeig made no attempt to convey to us whatever profundity that, surely, could have been found, even in trigonometry.

Final tally: I give Professor Bergman an A as a teacher. I will not grade Mr. Zeig ….

Standardized Testing and Mayor Mike

New York’s Mayor Michael Bloomberg has just announced that he will place still greater emphasis on the use of standardized testing in his administration of the public schools.

There are people, easily located on the Web, who oppose any and all use of standardized testing in the schools. I am not one of these. There is and there will continue to be an important place for the intelligent and critical use of standardized testing in education. But as I read the recent pronouncements from City Hall and the White House, I fear that the trend is away from intelligence and critical examination of these tests, toward an ever increasing acceptance of them at face value, as completely reliable measures of success in the schools. The about-face by Obama, from pre-election statements that signaled a much more critical approach, is especially worrying.

Much of the political language pushing the primacy of standardized testing borrows from economic notions of “efficiency.” As Henry Ford found, an assembly line, based on interchangeable parts, allows for the building of more and cheaper automobiles. Make sure the line runs smoothly, make sure the right worker tightens the right bolt at the right time, and out it comes: the well-running Model T. Why not use such methods to get Johnny to produce mastery of the Three R’s, efficiently, thoroughly, and without the bothersome interference of teachers’ unions ? (Henry Ford thought of the UAW much as the standardized-test enthusiasts of today think of the UFT.)

Some standardized tests are better than others, some test more, others less, for underlying abilities that are relevant to what we want from education. In any case, each test, and each use of a test, needs to be critically examined: does it do what we want ? To what extent does it do this ?
But beyond the virtues, or otherwise, of specific uses of these tests, there are some inherent limitations to which its critics point. Here are just some of these:

1) Experienced teachers say that it is almost impossible to eliminate widespread cheating on standardized tests, by students, teachers, and even administrators. This does not mean that these tests should be abolished, but it does mean that greater caution needs to shown in their interpretation.

2) It is probably impossible to test, in the context of these standardized measures, for some of the most important results of a humane education:

a. A critical approach to book learning. No, it’s not only Wikipedia that can mislead you — any established source is error-prone, bias-prone. Our children need to learn, as a matter of intellectual habit, to check one source against many others.

b. A realization that appearance is not necessarily reality. A man has degrees, titles, positions; another has none. The two get into an argument. Who is right, and why ? Our children should learn, more and more as they progress through the grades, that not everything that glitters is gold.

3) The more there is an emphasis on standardized tests, the more teachers will be pressured to “teach for The Test.” Here is a teacher, say of American history, who knows that a deeper and better understanding of the Civil War requires generous side-glances at European society, at the American and European literature of the day, at Africa and its cultures. But these things will not be “on The Test.” What is he to do ? Furnish what he knows is the better education, or teach, as Henry Ford would no doubt counsel, to “produce results,” efficiently, i.e. results on The Test ? What do you think he will do ?

Read statement by United Federation of Teachers