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.

Wrong Again, Jonathan: Mr. Alter Doesn't Get Public Education (and neither does Obama)

Once upon a time, back in the Ronald Wilson Reagan era, I used to look forward to reading Jonathan Alter's column in NEWSWEEK. He seemed to be one of the guys who got it. I particularly remember what he wrote about Gary Hart during his rise and fall in the 1984 campaign.

Sad to say, Mr. Alter seems to have completely jumped the shark. Every post he makes on education is so blindly wrong, so clearly ignorant of what's going on with the current education deform movement in which Mr. Duncan and, at least passively, Mr. Obama, are willing partners, that as an educator who has worked most of his career with students, parents, teachers, and administrators in districts, schools, and communities devastated by extreme poverty, I cannot help but be appalled.

Looking at his latest education commentary ("Obama Shows Spunk Pushing Brave Education Plan"), there is simply no way that Mr. Alter could be truly in touch with what's going on in places like Chicago, New Orleans, Detroit, Los Angeles, Atlanta, Philadelphia, Boston, Miami, or New York City, given how shallow and erroneous is his analysis of education and what Obama's administration is up to. The recent waiver offer by Mr. Duncan is a classic case of figuring out long after everyone else has done so that a horrid piece of legislation like NCLB is about to crash and potentially bring loads of hard-working people down with it. This impending disaster was completely predictable for anyone who had a grasp of the nonsensical mathematics informing "annual yearly progress" and the absurd notion of 100% proficiency in math and literacy AT ANY POINT IN TIME. But I believe the authors of NCLB for the most part knew exactly what they were doing: creating a way to destroy public education and turn even the most outstanding public schools into "failing schools" through its impossible demands.

When Obama put Duncan in charge, we saw another strategic move, cynically called "Race To The Top," that was nothing more than openly bribing states to comply with anti-union, anti-teacher, anti-student, pro-testing, pro-charter, pro-privatization policies in exchange for the federal dollars, or otherwise be denied the funding to which ALL kids should have equal access, regardless of where they live. It doesn't get any more undemocratic, any less fair, any more patently wrong.

In light of NCLB and RttT, many people have correctly counseled states to refuse to take the waivers being "boldly" offered by Duncan/Obama. In fact, the absolutely sanest strategy for every state, district, administrator, school, teacher, parent, and student would be to say, "No!" to high-stakes testing abuse and insanity, to refuse to allow, administer, or participate in these heinous tests. Please look at the Bartleby Project and join those of us who will not bend to the forces of billionaires and politicians who care nothing about learning, kids, education, or democracy, but only about lining their pockets and those of their friends, colleagues, and masters. The folks pulling Mr. Obama and Mr. Duncan's strings (and one merely need look at how they operated in Chicago with public schools there to know that what's happened at the federal level since they took power was all too predictable) have to be rubbing their hands with glee at the "spunk" being shown in the US Dept. of Education. If this is the best Mr. Obama and his minions can come up with, we need a different nominee in 2012.

The Three Most Important Words in Education: Assessment, Assessment, Assessment.

Today (August 10, 2011), Alfie Kohn posted a piece entitled, "Teaching Strategies That Work! (Just Don't Ask 'Work to Do What?')"

As I read it (with the usual enjoyment and anger Alfie Kohn's posts elicit from me), I found myself thinking about this paragraph in particular: "Thus, 'evidence' may demonstrate beyond a doubt that a certain teaching strategy is effective, but it isn't until you remember to press for the working definition of effectiveness -- which can take quite a bit of pressing when the answer isn't clearly specified -- that you realize the teaching strategy (and all the impressive sounding data that support it) are worthless because there's no evidence that it improves learning. Just test scores." 

In countless arguments I've had on-line with people about education and assessment in general, and mathematics education and testing in particular, invariably my antagonists (and I use that word advisedly) would reject any curricular materials, pedagogical strategy, tool, task, theory, activity, etc., by stating, "Where is your gold standard research that shows that X is effective?" And as night follows day, when pressed, they would make clear that inside that "gold standard" was what for them comprised a platinum standard: only 'objective' (and hence machine-scored, multiple choice tests if given on a wide-scale, or, if the assessment was small and local (e.g., in one classroom), only tests that were scored with no partial credit, no discretionary judgment or rubrics for the scorer, but rather those that had single answers that were either 100% right or 100% wrong, so that the results couldn't be shaped by the scorer (who might, of course, be inclined to be subjective or, even worse, fuzzy!) 

Now, I think we all want reliable and valid tests, but I find it intriguing that these folks were SO suspicious of any test that allowed for a "human" factor in the scoring (let alone one that had human factors in the tasks themselves, of course!), and so absolutely convinced that given practicality, costs, and the fuzziness factor they so abhorred, only those nationally-normed, multiple-choice standardized tests would count. They were the true measurement of anything one might wish to measure in education. 

Alfie Kohn raises the opposite question: what good are your 'results' if all they are is improving test scores, not learning? And these ideologues I finally gave up arguing with about 15 months or so ago only want to talk about just that: test scores, and a very particular type of test at that. With no wiggle room at all. As an advocate for increased intelligent use of meaningful formative assessment (see the work of Paul Black, Dylan Wiliam, et al.), I find myself realizing with increasing dismay that everything I value about education is precisely what is dismissed by the folks I'm trying to either convince or, yes, defeat in the court of not only reason, public opinion, and school policy, but in the halls of government and the meeting rooms of the monied and powerful. If I and others who agree with my viewpoint are not able to get people to see that improving scores on lousy tests is an utter waste of time by ANY reasonable criteria one might choose to use, then US public education is doomed.

 And we cannot afford to let that happen, to allow control to be ceded to self-interested greedy profiteers and people with various political, social, or especially religious agendas that are at odds with our democratic core values. Assessment, what it means, and how we do it isn't the ONLY issue we need to struggle with, but it tends to be the one that touches upon where the rubber meets the road for a lot of folks.
Naturally, I agree with people like Alfie Kohn, Marian Brady, and others who want to focus clearly on WHAT we're teaching and why we are teaching it. There's no getting away from content and the curriculum that frames it. But I think assessment remains key because it is still the one thing that people are guaranteed to pay attention to: kids, parents, teachers, administrators, politicians, media, and the general public. If we can't win the assessment fight, we're in very deep trouble.