I had thought that the “math wars” were low-intensity conflicts, but I was wrong. My column about a month ago, in response to one by three NMSU experts a few days earlier, in turn, a response to one by a parent two months earlier, provoked many responses. Most of the comments following my opinion column on the Las Cruces Sun-News website and all of the half dozen or so emails from math professors, engineers, parents, and a former school board chair have supported my position. The only dissent came from the authors, first, NMSU Professor Ted Stanford (website exchanges), then, NMSU Professor Karin Wilburg (letter to the editor).
Stanford’s responses to my request for some answers to questions about his column reveal him, on this subject, to be more an ideologue than a pedagogue. He insinuates that I had misrepresented the authors’ statements in order to refute them, but he offers then or later no instance of my doing so. He claims to see no connection between their recommended methods and my example of poor math ability by a college student educated locally by their methods. And he evades my question about his interest in student “understanding” of mathematics and indifference to parent “understanding” about the effects on their children’s competence, by giving an answer which implies that it is a question about their motives about caring for children.
Wiburg’s letter offers the strange notion that “The curriculum one uses is not the major issue; what matters is how well the teachers know mathematics and how to teach mathematics.” She repeats the thesis of the original column: “This includes teaching useful procedures, mathematical fluency, and deeper conceptual understanding of the meaning of these procedures.” Her defense is that “After 30 years of my own published research, some of it based on over 500 hours of classroom observation, what matters for student achievement is the level of implementation of mathematics teaching in the classroom, including the level of student participation, regardless of the curriculum.” I have the grave doubts about teaching any subject undefined by a curriculum; I also have grave doubts about the sufficiency, not to mention the reliability, of just over two days’ worth of classroom observation per year.
Such responses reflect the political, not the educational, nature of the “math wars.” So it will help to understand that Investigations and Connected Mathematical Project are the latest of the evolving re-articulations of a view of, and an approach to, mathematics education which emerged during, and has persisted since, the Vietnam War. The hue-and-cry by the anti-war movement was “Down with the System.” That cry translated into a challenge to, and an undermining of, systems, structures, standards, and authority. In short, the “math wars” are a continuation of the “culture wars” in one field of battle.
In the field of education, the call was for the diminution or abolition of anything in history or literature which smacked of white male hegemony (down with the “canon”); grammar and principles of composition, which presumably repressed individual expression or self-identity (Black English, “ebonics,” and dual-language instruction became wedge issues); fundamentals of mathematics and science; and knowledge and skills in any subject acquired by rote and drills. Teachers became resources; approved instructional techniques became student-centered learning or group-oriented activities and projects. Even school architecture reflected reaction to order and discipline in the craze for the “open classroom.” From the onset, before there were long-term, reliable, peer-reviewed data, educational researchers offered “research” assuring the public that these reforms fostered a better education because it emphasized creativity and curiosity. Entirely consistent with the political motives of this movement was a lack of concern for demonstrable competence. Thus arose the contrast between the authentic and the elite.
A brief digression. The political values of this liberal movement affected other fields. In psychiatry, for instance, the fashion was to think that mental-health institutions were repressive and thus unhealthy. So the movement led to the discharge of many patients in the belief that, if they could be restored to non-institutionalized life, they would at least ameliorate their conditions, if not recover from them. The result of this concept of individual freedom, with its liberation from institutionalization, was the return to the public sphere of thousands and thousands of disturbed, dysfunctional people. Today, there are about 350,000 mentally ill homeless people, the victims of an ideology-, not a reality-, driven approach to mental health.
I digressed to make a point: the political—indeed, the ideological, not the pedagogical—basis of these methods of mathematics instruction. But there are other ways to see the effects of ideology in the advocacy of these methods.
Bad enough is the ideological indifference to results. The authors make a strong claim about benefits of the mathematical methods which they advocate: “Investigations and the other NSF-funded curricula provide rich and rigorous mathematical learning if implemented correctly,” which learning results in “understanding” mathematics. The authors do not support this central claim or even explain what the important terms mean or how they appraise them. I doubt that they can support this claim. Certainly, standardized proficiency test scores in New Mexico do not demonstrate “understanding.”
Worse, the authors protect their unsupported and probably unsupportable claim with a refutation-dodging “out,” the conditional clause: “if [they are] implemented correctly.” The dodge works by divorcing ivory-tower theory from results-oriented practice; the argument makes refutation impossible because it is divorced from results. The authors, on the basis of experience which they do not describe or justify as conclusive, are right; everyone else, with first-hand experience with students in the classroom, children at home, or employers at work, is wrong. According to their theory, poor test scores or complaints by parents or employers indict poor instruction or improper expectations; they do not indicate the inadequacy of the preferred methods. The claim with this condition boils down to a “heads I win, tails you lose” proposition. There is little value in methods for teaching mathematics if they care rarely be correctly implemented.
Worst of all, the authors show themselves indifferent to test results, to effects on students, and to concerns of parents and employers. They are content that their ideal methods, for which they make big promises, hold sway in the classroom, whether or not students acquire demonstrable or useful “understanding” of mathematics or competence in mathematical computations.
All of which calls into question what these NMSU professors think about research, teaching, and service—the three missions of a land-grant university. All activities in accordance with these missions depend on the facts in the field, so to speak. In lieu of evidence or argument, however, they rely on appeals to authority: the National Academy of Sciences, some mathematicians and mathematical educators, and a compendium of standards distilling those of 45 states. What is missing is one of many academic jobs: explaining data in terms of theory, not advocating theory in disregard of data.
In their service-oriented involvement with public education, these authors assume a special responsibility in mediating between theory and reality. They provide advice; districts consume it; districts rely on that advice in providing instruction for the benefit of students (and, indirectly, their parents). If a theory cannot be “implemented correctly” in one school after another, as state test results and parental and employer complaints suggest, then any academics dedicated to research, teaching, and service would return to his study or his laboratory to consider the flaws, if not the failure, of their theory. It is counter-academic to find fault with reality in order to save the theory. In their political advocacy of their theory, the authors betray the purposes of the public land-grant institution which employs them while coat-tailing on its academic reputation and their professorial status.