What can you say about an eighty-eight year old organization that died? That it was arrogant and complacent? That it loved power, money, and influence (or at least the illusion of them) more than being effective, and blew it all anyway?
Put them all (and more) together and you may get a sense of why I am so disenchanted with NCTM as an effective organization we need to lead us towards meaningful change in mathematics education. Though it us the favorite target of the various anti-reform spokes-holes, nay-sayers, and prophets (profits?) of doom, both individuals and groups who decry every new idea about math content, pedagogy, curriculum, and especially technology, NCTM just doesn't get the job done. When I contemplate the waste of time, energy, and resources that has occurred during just the last 15 or so years of the MATH WARS, I'm increasingly tempted to state: "A plague on both your houses." Stick a fork in these turkeys: they're done. And yes, I mean NCTM at least as much as its critics.
Let 'em dangle
Despite my reputation in some quarters as an apologist for NCTM, I have long been privately and publicly critical of the organization (especially its for the most part shamefully conservative board). Some of my strongest criticisms have centered around its continued failure to support districts, schools, administrators, teachers, parents, and students where the very kinds of reform NCTM started calling for in 1989 were implemented and then came under scurrilous attacks from the educational right wing. Rather than taking both defensive and proactive measures to support districts that had the courage to try to reform their mathematics educational practices, NCTM first stood around like a bunch of effete prep school boys who were shocked to discover that their critics weren't going to play by gentlemen's rules.
The first shots were fired by the late John Saxon, who bitch-slapped NCTM repeatedly in combative advertising "position papers," in which he claimed to have the one true implementation of the 1989 Standards; he then began trashing that same series of documents in no uncertain terms. The fun part was seeing these ads appear in NCTM publications for teachers, who often don't know what all the philosophical and political shouting is about, but do tend to like books that bring up test scores, don't require that they learn new ways of thinking about and teaching mathematics, and which make them look good to administrators and parents without having to work too hard. If Saxon had the goods (and from a certain perspective, he did), and made a lot of noise to get everyone's attention, he was sure to gain a hard-core following among the rank-and-file in the classroom. And of course, he did so, quite profitably.
"Non-Political" is political
How did NCTM, ostensibly the most powerful and influential organization of mathematics teachers in the Americas, allow a poseur like Saxon to repeatedly steal its thunder? And more importantly, why? Purportedly, NCTM is "apolitical." But as most people whose heads aren't stuck firmly in the sand (or somewhere else dark and warm) are aware, there's nothing that isn't political to some extent. Every non-decision is in fact a decision. Every passive response to attacks from the educational right is a choice that is complicit with their demands. And NCTM, which let itself be bullied by an educational "maverick" like John Saxon (the John McCain of mathematics education, perhaps?) acted the 98-lb weakling when confronted with tiny but openly political groups like Mathematically Correct, NYC-HOLD, and their many smaller versions that arose (and continue to pop up) locally throughout the country. Had NCTM decided to put its (or should I, as a paying member since 1992, say, MY and OUR) money where its mouth was, I think it would have been trivially easy for it to find a principled way to support those who had the vision (or gullibility) to take the 1989 Standards seriously by using innovative curricula and reform pedagogy. Instead, despite repeated warnings from myself and others going back to the mid-1990s that these anti-reform groups were deathly serious, well-funded, well-organized, and playing for keeps, NCTM stood by twiddling its thumbs (well, maybe those thumbs were elsewhere) as district after district was picked off by "parents-with-pitchfork" groups, backed by MC & NYC-HOLD, as well as by folks affiliated with right-wing think tanks and foundations such as the Hoover Institution. Visionary districts were forced to offer "choice," which set the machinery in motion for the progressive programs to be marginalized and slowly suffocated, or simply to do away completely with programs like EVERYDAY MATH, CONNECTED MATH, CORE-PLUS, and many others. Even the rare district that made long-term commitments to these programs received nothing from the very organization that had supposedly called for just such things to be the wave of the future for mathematics education in the US in the way of pro-active strategies on how to implement and support reform methods, materials, and tools effectively.
Why was NCTM so unwilling to offer any sort of direct support? Simple. The board constantly asserted its "apolitical" nature. It would not let NCTM be perceived as endorsing (or proscribing) any curriculum. That would, after all, be (horrors!) commercialism! Of course, concerns about commercialism never stopped NCTM from selling its own materials, generally at prices well out of reach of the average teacher. It never stopped it from demanding that speakers at its national and regional conferences pay full or at best mildly reduced registration fees. Or raising rates for membership every year. Talk to anyone at the management level and one hears nothing but pleas of poverty. Yet the group never listened to calls from within to reduce the $100,000+ cost of buses to take perfectly healthy members a block or two from hotels to conference venues, outlandish wastes of member dollars that could have been drastically cut by limiting such service to the infirm and elderly. While I don't want to suggest that anyone was living in the lap of luxury feeding at the trough of NCTM membership dollars (though I frankly won't rule out the likelihood of waste to make sure that the board and executive members never got less than the best), I'd say it's remarkable that NCTM has been taking a public relations beating for well over a decade from small groups who at least in theory do not have the financial resources of an organization with a huge membership. If what we are supposed to be getting with the dollars saved by not "going political" is high-quality PR, I'd say we've been collectively screwed.
Curriculum Focal Points fiasco
A glaring example of the above is the execrable handling of the roll-out of the NCTM Curriculum Focal Points in the fall of 2006. It borders on the incomprehensible that this document could have received such completely inaccurate coverage not only by THE WALL STREET JOURNAL, but by major newspapers throughout the country. If there was a major media story about this important document that got things right, I missed it in the wave of "me, too!" coverage that followed the WSJ lead, from the NEW YORK TIMES right down to the more predictably right-wing outlets. What message was given over and over to the public? NCTM has retreated on its basic position from 1989 to 2005 and gone "back to basics." Of course, nothing could have been further from the truth, but no amount of counter-claims from then president Skip Fennell or many other folks who were involved with the authorship or supported the basic purpose of the CFPs could undo the damage.
Of course, perhaps I am giving NCTM too much credit here in believing that it really didn't intend to back away from the Standards volumes. My sense is that the CFPs were a kind of preemptive strike meant to stave off the impact of what leadership correctly anticipated would be contained in the NMP's report(s). I don't mean to suggest that the authors didn't believe that the fundamental ideas in the Standards were well-founded. And I had personally help develop a similar "bare-bones" content guide for some Michigan elementary school teachers I was coaching who were trying to figure out what absolutely needed to be covered by the end of the 2004-5 school year given the state math framework, curriculum focal points, and the anticipated content of the following October's high stakes tests. The curriculum wasn't being changed (this was the first year the district was using EVERYDAY MATHEMATICS), but the game plan needed to be refined under time constraints).
Given that a "back to basics" spin was very likely to emerge from the NMP, was NCTM simply trying to head 'em off at the pass? That's the story I've heard and maybe it's even completely true. But by not keeping the tight control on how the CFP was released, NCTM made an enormous miscalculation.
This wasn't just a case of Mathematically Correct & Company spreading a few silly lies: this was every paper that carried the story getting it wrong. How could that possibly have been allowed to happen? Why is that false viewpoint still the one most people believe and will continue to believe? At best, it's due to simple incompetence on the part of NCTM's management and public relations personnel. At worst, it reflects the inertia and conservatism that lies at the heart of NCTM and its board. Again, despite the claim by its enemies that NCTM is too radical for what American mathematics education needs, the truth is far more likely that it is too conservative, too cautious, and too incompetent. It either accidentally or purposefully shot its own foot off with the CFP release, and there's no sign of correction on the horizon.
Wimpy non-response to NMP report
Another abject failure on the part of NCTM's leadership is its tepid response to the recent release of the report by the National Mathematics Panel (NMP). This clearly politically-skewed group essentially has attempted to roll back the clock to the 1950s or perhaps the last big period of "back-to-basics," the 1970s. With its emphasis on skills and a narrow view of what school mathematics should be (basically NOT what real mathematics IS), the NMP has clearly intended to codify and enshrine a national mathematics policy that is completely in synch with the phony interpretation of NCTM's CFP. And this is not a coincidence. The same forces that tried to attack every reform effort over the past 15 years were well-represented on the NMP, and they were the same voices that were quick to spread and second the WSJ lies about the intent and content of the CFP.
Yes, you really can fool some of the people all of the time. But should that include the very organization that purports to lead America towards a more enlightened approach to math teaching and learning? Wouldn't you expect a fiery response to the NMP's attempt to turn back the clock and do in the NCTM Standards (1989 through 2000)? Here is what we were given instead:
NCTM appreciates the focus the work of the National Math Panel has brought to mathematics education. In addition to these six Principal Messages, the Panel’s final report includes numerous findings and more than 40 recommendations. More extensive reports of the panel’s task groups on Conceptual Knowledge and Skills; Learning Processes; Instructional Practices; Teachers; and Assessment are also available online.I'm not sure what to say in response to this remarkably passive reply except to ask what brand of lubricant NCTM's leadership asked for prior to publishing that surrender. I'm struck in particular by the sell-out to the right-wing notion that what mathematics education in this country is about is "ensuring America's stature as a world leader." Really? I always thought it was about educating students to give them the ability to achieve life, liberty, and the pursuit of happiness. Could we see a more naked expression of NCTM's willingness to play along to get along? To kowtow to capitalist, anti-democratic values? To swallow whole a hegemonic view of the role of education in the United States? I know I didn't go into mathematics education, commit to teaching at-risk students, and deepen individual and collective teacher understanding of mathematics and its pedagogy, in order to serve the cause of keeping America ahead in some idiotic, jingoistic competition with people and governments and corporations from other countries. That wasn't what I signed on for when I decided to become any sort of teacher 35 years or so ago.
The report highlights the differences between the American public’s view of the importance and utility of learning mathematics and those of other countries. Ensuring America’s stature as a world leader hinges on its ability to educate all students as we move into an era with increased technical demands.
The Panel’s recommendations are a next step in preparing America’s students not only to excel in mathematics, but to become leaders in the fields of science, engineering, and research. NCTM urges the administration to provide the funding to put the Panel’s recommendations into action and to identify and develop expanded, rigorous research needed to guide future actions.
Does this mean I don't want to see Americans succeed? Of course not. On the contrary, I'd like to see us succeed individually and as a people. As long as its part of a HUMAN striving for improving the lives of everyone on the planet, rather than some absurd nationalistic xenophobia that informs the anti-NCTM, anti-progressive, anti-reform rhetoric that spews forth from Mathematically Correct, et al. These folks have been trying to scare us with bogie men from China, Singapore, India, Japan, and other "inscrutable" Asian countries that are ostensibly beating our tails through superior mathematics education. Maybe we'll be hearing the likes of Wayne Bishop and other MC ideologues joining with Lou Dobbs to call for an "intellectual" wall to be built around our borders to keep out the invaders.
Does any of this sound at all familiar? It should if you recall not only the tenor of the post-Sputnik panic that informed the New Math fiasco, but a host of similar documents that appeared from various conservative reform groups going back at least to the early decades of the last century. But when one wades through the naked classism of many of those documents, it is clear that the goal wasn't anything vaguely akin to "math for all." It was always about real mathematics for the few, the elect, the elite. For everyone else, maybe how to use a checkbook. If they were lucky. To steal from CADDY SHACK, "The world needs ditch-diggers, too, you know."
Let's not forget, too, that a mathematically literate populace is more difficult to mislead. Its one that is capable of reading and understanding statistics, of making informed judgments about huge public expenditures (and wastes), of the probability that some idiotic claim is true (be it from corporations, scam artists, or governments). It's one that can weigh more intelligently the real costs of "holy wars" in Iraq and Iran, the plausibility of global warming, the reasonableness of pseudo-scientific claims about medicine, diet, and much, much more. Is that what conservatives generally fight for? Is it what the National Math Panel is calling for? Or is it just business as usual? And is the above the best response we should expect from NCTM's leadership?
Technology is a lot more that calculators and calculating
Finally, I want to address NTCM's most recent failure: its position paper on the role of technology in mathematics education. For quite some time, I've been aware of what might be fairly called "criticism from the left" of NCTM's apparent focus on calculators as the main issue when it comes to technology and mathematics teaching and learning. At times, for a group that is "apolitical," NCTM seems overly-cosy with Texas Instruments, the company that has managed to dominate quite thoroughly the use of calculators and related software and hardware that is supported in reform and many traditional textbooks from elementary school through calculus. It's just about impossible to find evidence that any company except for TI even makes calculators for K-16 mathematics. Of course, we all are impacted by technological competition (competing operating systems in computing make a lot of software available only to those who use a given platform; most of us recall the VHS-Beta war, and we've recently seen Blu-Ray win the high-capacity DVD war). Some of us are aware of what's been lost because TI took the easier route of eschewing reverse Polish notation. Perhaps others recognize the advantages color graphing gives students, an existing technology long offered by Casio, one of the lesser players in the US calculator market, but which the giant, TI, has eschewed, to the detriment of countless students. One might argue that if color were so vital, Casio would have a bigger market share, but that's assuming level playing fields. In education, once one company dominates a market, it's nearly impossible for competitors to draw even: everyone wants to be using what is already the norm, especially at the high school level, where college use has a definite impact on what teachers are prone to employ, especially in higher-level courses. TI rules college campuses and is likely to corner this market much as Microsoft has with Windows.
Which takes us to a much more serious issue: while NCTM pays lip-service to technology other than calculators, it's only in terms of specific software such as dynamic geometry and statistics packages. And it is here, in part, where NCTM most horribly fails to take advantage of something truly innovative and important when it comes to American mathematics education. As Kirby Urner, among others, has been pointing out for at least a decade, calculators are far too limited to be what is needed to help push students forward in mathematics. I don't fully concur with him about their limitations, but I agree that the way they're being implemented, even programmable graphing calculators are not being used nearly as effectively as they could be. In many ways, they're already an "old" technology, but they have a lot more power than most teachers or students have any idea of. Urner is only one fellow touting a mathematics curriculum grounded in programming (particularly with the language Python), but with a major focus on both applied and abstract mathematics - from sphere packing to polyhedra to abstract algebras to the work of Buckminster Fuller, and much more.
Another group that has been looking at computer science mathematics, discrete math, and other powerful, modern mathematical ideas is the group in Australia and New Zealand that produced COMPUTER SCIENCE UNPLUGGED. It's a wonderful collection of materials that can be used even with lower elementary students, yet gets into important mathematical ideas that will engage high school students. As I've been (all-too-slowly) documenting elsewhere in this blog, I'm mentoring a colleague in Saginaw who is getting inspiring results using these materials with very low-achieving, at-risk students in grades 7 to 10 in an alternative school located in Saginaw, MI. For those who don't know this economically-ravaged city, suffice it to say that the program where she teaches is in the worst part of town and that Saginaw is considered by many folks here to make Flint, Pontiac, and even Detroit look idyllic. Yet she's got kids who never previously earned a credit in mathematics really engaged with a host of important and challenging mathematical ideas. As the title suggests, no computers are required (Kirby Urner finds this ominous, but I think he's wrong in that regard, and given the situation in which my colleague teaches, she has no option to use computers right now). But perhaps the most amazing part of CSU is that it is now entirely free: every module is available as a pdf that can be downloaded at no charge from the above-linked web site.
Michael Fellows, one of the developers of CSU, has another more broad-based curriculum package, also available for free download (THIS IS MEGAMATHEMATICS: The Los Alamos Workbook) that covers such areas as graph coloring, transfinite arithmetic, knot theory, etc. My colleague and I are looking into working some of the modules from that material into what she's offering her students.
The above is, of course, just the tip of the internet iceberg when it comes to powerful use of not only technology hardware, but the underlying mathematics of computer science, discrete mathematics, etc. NCTM and many states continue to pay scant attention, if any, to the importance of discrete, finite, and related mathematics (one notable exception is New Jersey, where the contributions of Joe Rosenstein, Fred Roberts, and others affiliated with DIMACS at Rutgers University have gotten discrete math firmly embedded in the state standards). My own state, Michigan, makes some small reference to discrete mathematics in its curriculum framework, then fails to have a single mention of it in the Grade Level Content Expectations (GLCEs), the document that most teachers and districts use as a guide to what will actually be tested by the state. Guess what doesn't get taught?
So where is NCTM in all of this? Where is any mention of computer science, discrete mathematics, and a host of alternative branches on the tree of mathematics (kudos to Dan Kennedy) that might make both a motivational and meaningful career-path difference to countless students who have not been reached by the same old math content and teaching on the road to Holy Calculus Mountain? Yes, discrete math gets mentioned in various Standards volumes, but it's really the red-headed step-child of traditional curricula, lucky to get a mention, rarely taken seriously. I would suggest that a real commitment to technology as a partner in mathematics education demands a very close look at discrete and computer science mathematics as one step on students' mathematical journeys. NCTM could take a meaningful leadership role in this regard by being more critical of the "calculus uber alles" mentality that we've been sold for over a century by various folks. But once again, NCTM fails to rise to an important occasion: another opportunity to do something radical yet utterly sensible goes by the boards (and, of course The Board).
I don't claim to be an expert on computer science, discrete mathematics, or much else. I've got more questions than answers, and I'm well aware that even the most successful things I've seen relating to computer science, discrete math, and other topics mentioned above, including my own practice and that of those I've been privileged to observe and, on occasion, influence in small ways, have limitations. Something that seems great one day may go down poorly the next. No content, method, tool, or model is flawless and sure-fire. But one thing I do know for certain: some people can and do make a difference. And many of the most exciting, innovative, inspiring people out there don't seem to be making much of an impact on NCTM or in some cases bothering to try. Kirby Urner has written NCTM off as stuck in the past, and from where he sits, I'm sure he's right. The problem is that from where *I* sit, I'm increasingly convinced that he's right, and I've been in NCTM for 16 years. As I said back at the beginning, NCTM looks more and more like the proverbial dead shark. And quite a toothless one at that.
In this election year in which the question of what comprises authentic change is central, I feel compelled to ask the same thing about mathematics education. Has the time come for those of us who have had our fill of frustration and failure, of timorousness, of the politics of "non-politics," of conservatism and inertia, and of the avoidance of risk-taking, vision, and commitment to making a difference for those who need meaningful alternatives, to leave NCTM behind? I'm sure this will annoy both friends and critics alike, but perhaps it will move them to to think, and to do something without waiting for the NCTM board's imprimatur. Our kids have waited far too long already.
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