Sunday, August 28, 2011

A Partial Bridge Over Troubled Mathematical Waters: Mumford and Garfunkel Try To Fix US Math Education

William R. Robinson

 William R. Robinson, my former mentor at University of Florida's Department of English, used to say that the further someone was from getting it right, the more useful it is to find something in what they have to say that is “heuristic” (by which he meant ‘thought-provoking’) and that the closer someone is to ‘getting it right,’ the more significant are the ways in which they ‘get it wrong.’

That useful binary construct came to mind again last week as I read NEW YORK TIMES opinion piece by Sol Garfunkel and David Mumford, "How To Fix Our Math Education."

Sol Garfunkel

David Mumford

Much of what Garfunkel and Mumford have to say is praiseworthy. Certainly, their main point - that a 'one-size-fits-all' approach to mathematics curricula is a bad idea - is mostly well-made and sensible. It is also true that many students would benefit by a more practical, applied approach to teaching and learning mathematics (though I would suggest that all students should have the chance to see the beauty of mathematics in itself, to see it as a living, growing, very human body of knowledge that not only has practical power, but also profound and stunning beauty. Neither the traditional American approach to mathematics for the vast majority of its students nor a strictly applied or modeling approach addresses the aesthetics of mathematics).

Nonetheless, my fundamental complaints regarding Garfunkel and Mumford's piece do not revolve around pure mathematics and mathematical aesthetics. Rather, my shock and disappointed came from  their failure to debunk some of the assumptions of the current educational deform movement that they raise and then pass over without any examination at the beginning of their proposed remedies.

First, the authors state unquestioningly that

widespread alarm in the United States about the state of our math education. . . can be traced to the poor performance of American students on various international tests, and it is now embodied in George W. Bush’s No Child Left Behind law, which requires public school students to pass standardized math tests by the year 2014 and punishes their schools or their teachers if they do not.

So much nonsense left unexamined in one paragraph. First, how widespread is this "alarm," exactly, and who accepts that the sky is falling when it comes to US mathematics education? While it is true that we are not doing justice when it comes to educating most of our students meaningfully about mathematics, this is not a recent problem and likely can be claimed about any era of American education one cares to examine closely. Readers of Gerald Bracey's work are familiar with the fact that our "Sputnik moments" in mathematics, science, and other areas are not limited to now or the late 1950s. Education punditry going back at least as far as 18th century America has found fault with public schooling, though the claimed consequences of the alleged failures have varied from the decay of the moral fabric of the nation to the current received wisdom that our economy and future ability to "compete in the global marketplace" are at risk because public schools are so poor and our youngsters so uneducated, ignorant, and intellectually lazy.

These notions have been debunked repeatedly by less credulous scholars, from Bracey to Richard Rothstein to Diane Ravitch; many others have or are starting to look more critically at such claims, including the ludicrous notion that economic success or failure depends directly and primarily on the quality of public education. Many have noted, too, that none of our successes are ever attributed by the critics to something that public education may have done right. Teachers, schools, colleges of education, and professors make increasingly-convenient scapegoats for sins that are more obviously attributable to people and institutions far removed from the world of public education and teacher preparation.

But even if there were truth to the causal linking of K-16 education to our economy (and even if one accepts the very arguable notion that the main or sole purpose of public education is to provide career preparation to and the winnowing of young people for the cost-free benefit of businesses - like many other historical facts the punditry and deform machine conveniently ignore, the fact that it used to be the responsibility of companies to train workers for their jobs and to figure out who was best fit for what kinds of work has be neatly pushed under the rug), the notion that comparative performance on international tests of mathematics and science gives sufficient and meaningful information about how well or poorly the schools in a country are doing is simply ridiculous. This is another bit of received wisdom that has repeatedly been debunked by a host of experts and scholars, going back at least as far as the criticism the mathematician Banesh Hoffman leveled in THE TYRANNY OF TESTING, his 1962 critique of standardized tests. For Mumford and Garfunkel to take at face value that these international tests are telling us anything of importance seems like another important opportunity missed.

Finally in the quoted paragraph, we have an accurate description of what NCLB is about: punishing public schools, teachers, administrators, students, their parents, and the communities that are their homes. But not a word of criticism from the authors to this shocking and cynical policy. Nothing about the deeply-flawed mathematics through which the inevitable branding of all schools as "failing," sooner or later, is the consequence, if not the outright goal of all of its authors and supporters. This oversight by two mathematicians is difficult to understand.

As stated earlier, Garfunkel and Mumford do a commendable job of outlining reasons to rethink and reorganize what mathematics should be available to students and how mathematics can be made more relevant and appealing to many young Americans. But then they offer near the end this disastrous assertion:

It is true that our students’ proficiency, measured by traditional standards, has fallen behind that of other countries’ students, but we believe that the best way for the United States to compete globally is to strive for universal quantitative literacy: teaching topics that make sense to all students and can be used by them throughout their lives.
The authors make two egregious errors here: first, they accept that we've fallen behind based on traditional standards. But in fact, many experts have shown that when apples are compared to apples, American students more than hold their own on such tests. The problem has been that the education deform movement has made much of results where we have a broad sample of American students, including those from the neediest, most impoverished urban and rural schools being compared with a far less representative sample of students and schools from many of the countries against which we are being judged and, ostensibly, found wanting. It simply makes no sense to draw conclusions about our schools, teachers, or students based on such invalid comparisons.

Second, Garfunkel and Mumford, sadly continue to accept the notion that we should make educational policy on a national level (a questionable notion in itself that I will not go into here) based on the idea that we educate students to compete (and, of course, conquer) in a global competition. This sort of social Darwinist, survival of the fittest nonsense is a huge key to how the education deformers get their agenda accepted by so many politicians and uncritical members of the public. Not only does it go against many of the basic principles of child-rearing and education, but it also undermines the collegiality among educators that is crucial to how many of the countries (Japan and Finland immediately come to mind) that are held up as "beating" us construct their schools.

Finally, let me make clear again that while I support the authors' suggestions about bringing applied mathematics and modeling much more deeply into what is commonly available to students, I don't think they suffice to give every student a fair chance at numeracy or at a variety of pursuits (not merely jobs) that can emerge from mathematics. I believe that they have properly tried to get more leverage for aspects of mathematics that have been mostly pushed aside over the last century or more in our schools, but they've left out some things of vital importance for enriching students lives. And of course, they've either overlooked or willfully ignored some key assumptions and myths that, left unchallenged, guarantee that the very changes Garfunkel and Mumford advocate will never be seriously considered by the real educational policy makers, let alone actually implemented.

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