Mathematical Deceptions

Peter Wood

                 Eric is a math teacher who teaches --or taught--Mexican kids in an elementary school in Chicago. His classroom name—his nom de guerre—is Mr. Rico. He’s studied Paulo Freire and knows all about “critical mathematical agency” and stuff like that. He uses “hope” as a code word for socialism and sees teachers as revolutionaries. He tests his pedagogical theories in his math classroom at Rivera, a Chicago public school where most of the students are low-income Latinos, mostly from Mexico.

                One of “Mr. Rico’s” projects for eighth graders is to have them analyze different map projections so that they can discover how the powerful privilege their worldview. After showing his students that Mercator map projections make the southern hemisphere look smaller and were invented to aid colonial exploitation, he turns Mexico’s area into the standard unit of measurement. The students are upset that Mexico’s size is diminished on Mercator’s projection. Lively discussion follows. Lupe says “We should make our analysis public and let it be known.” Paulina asks, “Why don’t people stand up and fight to change the map?” Ricardo says this revelation makes him “feel insecure of what other wrong things we have been taught.” Alejandra adds that she feels she had been “tricked [into] thinking some countries were bigger than others.” She wonders, “What else are they lying to us about?” And says her eyes have been opened: “I’m learning how small details have a lot to do with racism.” 

                There is indeed some trickery here. Have these children never seen a globe? Globes have virtually no distortion of relative land mass. And Mercator projections, of course, are but one of a variety of techniques for depicting curved surfaces on flat pages. Were Lupe, Paula, Ricardo, and Alejandra really lied to or tricked? Did Eric really undeceive them? 

                Eric himself seems engaged in a kind of trickery in which ordinary facts are colored with sinister meanings. I think we can be reasonably assured that no one teaching Social Studies in Chicago elementary schools is seeking to propagandize on behalf of colonial empires. Getting students to feel “tricked” by their previous teachers wasn’t so hard, but it was manipulative. Eric’s avowed aim was to use a math class to instill ethnic pride, and he seems to have achieved his end:   

               Finally, Armando summed up the feelings of many students and implicitly linked the project to other ideas we had studied over the two years: “The new [Peters] map is like the rebellious Chicanos and African Americans. It is showing the world a reflection of its true perception.”

               The Peters projection, of course, has its own distortions, though it seeks to conserve the relative area of land masses. And the Peters projection is itself only one of many equal area projections, some of which were produced at the height of Western colonialism. 

                Eric wanted to wise up his Mexican-American students, but only to a point. He seems to have left them in the dark that numerous cartographers regard the claims made by Arno Peters on behalf of his map as overblown and misleading. The Peters projection is, however, a favorite of leftist ideologues who can use it with a standard narrative debunking the Mercator projection as an attempt to aggrandize the West and cloud the minds of school children. 

                Eric’s venture in kiddie-agitprop is told by Eric himself, whose real name is Eric Gutstein, in “‘And that Just How It Starts’: Teaching Mathematics and Developing Student Agency,” in Teachers College Record. Last week in Bias Isn’t Bias If It’s Ours, I took a look at another Teachers College Record article, one by Barbara Applebaum that argued that “teaching for social justice” isn’t biased because its ideological emphases just off-set the biases of our systematically unjust society.   It is nice to have a detailed picture in the same journal just a few days later of how “social justice education” actually plays out in the classroom. 

                NAS has previously noted Gutstein’s math textbook, Rethinking Mathematics: Teaching Social Justice by the Numbers (2005), which is required reading at numerous ed schools , including Stanford, Iowa State University, the University of Alabama, the University of Arizona, and the Harvard Graduate School of Education. A Freire wanna-be, Gutstein relies heavily on the Freirian concept of emancipatory literacy, in which students are taught to “read the world” (change their perception so they realize that the world is against them) and “write the world” (rise up and overthrow the oppressors). Gutstein advises teachers to find “solidarity” with their students, and that instead of seeing them as unruly kids lacking discipline and in want of authority, teachers “need to partner in a common struggle against oppression and for liberation.”

                In a section of his essay subtitled “The Work of Paulo Friere,” Gutstein acknowledges his debt and labels his own work: “My pedagogical practice is shaped by major currents within liberatory education. The first is the practice of Paulo Freire (1970/1998).”

                Liberatory education? It sounds a bit like “liberal education,” but the aim is profoundly different. Liberal education is grounded in the idea that individuals can free themselves from ignorance and prejudice by embracing free inquiry and civilizing ideals. It presents education as a path that is, in principle, open to all and that leads us, no matter the starting point, to a shared destination.   Ideally liberally educated people share a respect for reasoned debate, the rule of law, and human dignity. They may disagree heartily about a lot of things, but they don’t, for example, think that you win an argument with brute force, or that you should deny your opponent the right to speak, or that you may treat those with whom you differ as contemptible. Liberally educated people, being human, sometimes fail to live up to their ideals, but the ideals themselves are robust and continue to shape our public culture even when they are frequently betrayed. 

                Shouting down a speaker at a university, or charging the stage; impeding the publication of scholarship that runs against a favored view; blocking the appointment of a faculty member because his work bolsters a heterodox theory—all these actions run counter to the ideals of liberal education. And nothing speaks louder about the continuing power of those ideals than the efforts of many of those complicit in these violations to cover them up. 

·                   Columbia University may have dodged its responsibility to hold seriously to account the students who took over the stage to end a lecture by an invited speaker. But Columbia doesn’t celebrate this debacle. 

                     When Harvard University Press deep-sixed The Case for Marriage by Linda Waite and Maggie Gallagher because the book ran against the feminist biases of some members of its Board of Syndics, Harvard didn’t correct its error, but it also didn’t announce a great victory for academic feminism. Censors may privately gloat, but they tend to be publicly circumspect—for good reason.

· When the University of Iowa History Department kept Professor Mark Moyer off the short list of candidates for a position, despite his outstanding credentials, because he had written a book defending the United States’ intervention in Vietnam the University concocted an elaborate cover story. It wants to indulge its biases in private but pretend to objectivity and fairness in public. 

Those who care about liberal education ought to be deeply disappointed in Columbia, Harvard, and the University of Iowa, but each betrayal of liberal principle was accompanied by gestures and declarations that asserted that the university believes in and upholds those principles. “Hypocrisy is a tribute which vice pays to virtue,” La Rochefoucauld tells us. 

                 If so, what Paulo Freire offers his followers is an intellectual tea party. No tribute is to be paid at all to the liberal virtues. Rather, he advises, let us directly overthrow those virtues, since all they do is keep the oppressed humbled in their oppression. This is what liberatory education offers—just the debunking of liberal ideals and their replacement by group resentment and power politics.   The rest is just the tired history of Marxist revolution and the various forms of dictatorship that it inevitably entails.

                Liberal education requires that “Mr. Rico” be granted his opportunity to speak, and he has spoken. We should be glad I suppose that there are journals such as Teachers College Record with intellectual standards low enough to provide him the opportunity.   And it is indeed helpful to know what sorts of theories are being taught in the school of education at the University of Illinois-Chicago, where he currently teaches mathematics education. 

                But my guess is that the sort of practices that Gutstein extols and that are central to “liberatory education” cannot really stand the light of day. Are the Mexican-American children at Rivera Public School better off today for having had their mathematics instruction filtered through a pedagogy that attempted to imbue them with revolutionary consciousness? Are the Chicago public schools better off for this effort? Is the nation?   

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