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Rethinking Mathematics Paperback – March, 2005
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Nowhere in this book do I see the Math concepts that I (as a high school math teacher) am required to teach my students in Algebra 2 or PreCalculus. (Solving quadratics, polynomials, conic sections, trigonometry, logarithms, etc.) I challenge anyone to find a multicultural way to approach the concept of dividing polynomials or simplifying rational expressions. This is what the "experts" tell us that high school teachers should do but I have yet to have anyone show me how. The only state standards that are met by the examples in this book are those that encourage critical thinking skills. What about the other 95% of the standards that require us to teach higher level math concepts that can't easily be turned into a "real world" application. Just because a skill (i.e. simplifying a rational expression) may not have a "real world self-discovery application) does not mean that students won't need to know how to simply expressions in Calculus (which does have real-life applications for engineers, and scientists).
It's a fine book, but it is a Social Science book, not a Math book. This is why the reviews are so polarized with the mathematics people on one side and the social science people on the other side.
This book contains no algebra, geometry, calculus, number theory, trigonometry, or any other actual math topic. It is overwhelmingly just tables and graphs of statistics, hand picked for their political agenda. There was one suggestion of using the Pythagorean Theorem to calculate the length of a wheelchair ramp. This was an exercise to highlight injustices to the handicapped. But the Pythagorean theorem was not itself a topic, only its application to this. A similar mention of integration (as in calculus) was applied to wealth distribution. Neither article had actual math content. I just mention these in case someone says "hey, the book talked about integration". Most of the book requires nothing more than ordinary arithmetic.
This book is Marxist style "re-education camp" brainwashing. It consists of various "exercises" or "lessons" to lead kids to find " injustice". Che Guevara is quoted in one place. One "lesson" for the class was to make a table of all U.S. presidents who had slaves, for how many years, how many slaves, etc. Another "lesson", "Deconstructing Barbie", is to measure various bodily dimensions and ratios of a Barbie doll and comparing them to an average person. The goal is to illustrate injustice to girls, i.e., promoting insecurities, eating disorders, etc. (is serious math going on here ?? ). Then there is another "lesson", where the Mercator map is condemned as being unfair to persons of color, since they largely inhabit southern or equitorial regions. The idea is that northern areas are expanded on the Mercator map, thus magnifying the apparent size of Europe and North America, relative to South America and Africa. Of course it also magnifies the uninhabited regions of Greenland and Siberia more than any other. So I suppose the understanding should be that the uninhabited regions are the most important of all ! To correct this "injustice", the book touts another map (the Peters projection) which shrinks the Northern regions. (One would have to stay up at night trying to think up things this silly). Then another lesson complains about land gained by the USA in the 1848 war with Mexico. It invites the student to compute the price per acre from the amount paid, $15 million. Clearly no grievance is sufficiently out of date to not be used to foster resentments among kids. Again, there is no actual mathematics anywhere in all this, just pictorials and tabulated statistics.
Everyone is depicted a hyphenated-American, as a victim, or with a grievance. Each hyphenated group is to be viewed as in a zero sum game against another hyphenated group (usually white European males). I can illustrate one fallacy of this: Suppose I present the statistic that 90% of the prison population is male. Well, that's actually true. But isn't that a blatant social injustice, requiring remedial action ? Well actually not, if you recognize gender differences are real and not just a social construct. In fact, males are actually more prone to violence than females. In that light, there is no injustice, but merely a reflection of reality. But if you are to insist on being politically correct, and claim that both genders are entirely equal, except for social conditioning, then there is an injustice. Then what about that? Then you must insist on remedial action. Such as finding injustice to males in the court system (as is done for blacks who also have disproportionate incarceration rates). Or something. Otherwise, you must acknowledge that the claim (that gender differences are merely a social construct) is false. You can't have it both ways. But this book never offers, in a similar vein, a fair discussion of why certain statistics are what they are, if they represent a truth vs an injustice, or offer differing viewpoints. The explanation is always the evils of capitalism, male dominance, Euro-centrism, corporate evil, the rich, etc.
Of course the book ignores the overarching fact that capitalism has lifted more people from poverty than any other system yet devised. Here is a question: Why don't people, with the views represented by this book, organize corporations that embody their ideas? i.e., equal pay for everyone. What is stopping them ? Couldn't they organize a "cooperative" or "collective" along these lines ? But the simple answer is that it doesn't work. Equal pay for everyone = no motivation. That is one reason it doesn't work. If it worked, wouldn't it be happening ? Another "exercise": List non-capitalist countries with high living standards of economics, political freedom, and medical care.
One reviewer, "Inkslave", declares the book to be " rigorous math". This person apparently doesn't understand what that term means within the mathematics community. Mathematics is a deductive art & science, where propositions (about mathematics) are logically proven, starting with axioms, rules of inference and a deductive process. That is the essence of mathmatical rigor. Nowhere in this book does such a notion appear. Yet, that is the heart of REAL mathematics. There is no mention of the structure of the number system, for example, proving the uniqueness of decimal (or any other base) place system representation of a number. Nothing about a careful development of geometric theorems from axioms and postulates, as in traditional Euclidean geometry (a whole year course itself). Nothing about fundamental concepts like prime numbers. Or the beautiful, but simple, proof of the infinitude of primes (which should be easily grasped by a high school student). Or the elegant proof of the irrationality of the square root of 2 (again easily grasped by a high school student). Or unique factoring into primes. Nor the extensive drill and practice needed to master algebra. Or other topics in the fascinating subject of number theory. Nothing about trigonometric identities, analytic geometry, complex numbers, or calculus. Nothing about fascinating topics like encryption algorithms, fractals, etc. No mention of any of the greatest mathematicians like Descartes, Fermat, Euler, Gauss, Lagrange, Galois, Riemann, or any other great European mathematicians over the centuries. No, not one.
But there is a lot of emphasis on cultures that produced virtually nothing, mathematically speaking. Mathematics from Sub Saharan Africa is discussed, despite no meaningful history of mathematical output from that region. In one part of the book, titled "Chicanos Have Math in their Blood", the Mesoamerican base 20 ("vigesimal") numbering system is discussed. (Mesoamerica was a large region including the Mayan civilization). The author says it's unknown whether they knew how to do division and multiplication, but that they did do addition and subtraction. Does a system that primitive warrant study, in comparison to European mathematics? There is not enough time for all the mathematics (of first rate significance) we would like to teach, so we shouldn't waste time teaching something that is only of interest to cultural specialists. And BTW, it would be very difficult to do multiplication with base 20. You would have to memorize a much larger multiplication table with (approximately) (½)(18 x18) ~ = 162 entries. Most entries would have 2 digits, each digit being one of 20 possible characters. The notation is very cumbersome. (I don't think the author was quite correct to say only 3 symbols are used. Each number from 0 to 19 is still distinct, even if each is built up from these 3 symbols.)
Its disturbing that some people teach math and science seem to have distorted notions about their subject. The idea that Mayan astronomy is somehow on an equal footing with European astronomy, or warrants the time for kids to study it, is such a case. The motive was obviously "multicultural", not teaching the best math or physics. Mayan astronomy was like pre-Copernican astronomy, which observed cycles and projected ahead where things would be. But there was no underlying physical theory, as was Newtonian mechanics. That had precise mathematical laws of motion and gravity. That was a theory capable of broad generalization into innumerable terrestrial and astronomical applications. Even to this day Newtonian mechanics is applicable as ever. On the other hand, Mayan astronomy was a scientific dead end, more like astrology that a true science. There was in this article, by implication, that teaching only European mathematics (or not teaching Mayan mathematics) somehow insults Chicano sensibilities. Perhaps by lingering feelings connected with the actions of Cortez, events alluded to in the article. Fully granting that was horrible, it has nothing to do with the present teaching of mathematics. It's as if we are expected to teach Mayan math as a reparation for Cortez. It's Silly. Lets just teach the best math we know.
Above all, and my greatest objection to this book is, there is no sense of mathematics being an art and science worth study for its own sake. It's inherent beauty and fascination is entirely ignored in this book. Math (if we are to admit the book has any) is only a political vehicle in this book. The sense of wonder and magic that math can have is totally missing. There is the astounding claim in the book, made with considerable emphasis, that math cannot be taught without political content. According to this book, NOT having political content is still a form of political content (fascism or such they would say)! It's like saying not collecting stamps is a hobby. We might get a better idea of how terrible this is if we transplant their principles to other subjects: Suppose we can only teach music that has their political agenda. After all, according to them, not doing so is also political (fascist). So, suppose we must teach only music with socialist jingles and lyrics, for example. Obviously a hideous concept, redolent of Nazism or Stalinism. This kind of thinking smacks of fanaticism. For them, their politics must touch everything. There can be no serenity for them, or will they allow it for us or our children.
The political content of such a math class could result in an argumentative classroom atmosphere. When some parents find out, they will prime their children to argue back. That would take up a lot of time that should be dedicated to actually teaching mathematics. Even without the argumentative atmosphere, the political content is almost certain to provoke long discussions unrelated to mathematics, again diluting the actual math content. The general approach obviously promotes antagonisms between races and ethnicities. Rather than thinking of ourselves simply as Americans, we are being taught to view our particular ethnicity or race as a victime of some another. That is bound to fuel more hate and friction rather than reduce it.
I wonder if parents fully realize how their children are being politicized and being given an inferior math education (at least as evidenced by this book). And at taxpayer's expense.
Social engineering was NEVER meant to be the job of the schools. This new 'thinking' is only brainwashing government schoolchildren into accepting and celebrating homosexuality (sin), abortion (legal contract killing), and other liberal leftist vices.
It's all too evident that the government schools are no longer teaching reading, writing, arithmetic, or English grammar. They're just producing ignorant 'progressive' leftist adults who follow the liberal crowd. What a shame.