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Contro L'ora Di Matematica : Un Manifesto Per La Liberazione Di Professori E Studenti (2010)

by Paul Lockhart(Favorite Author)

4.27 of 5 Votes: 2

ISBN

8817038407 (ISBN13: 9788817038409)

languge

English

genre

Nonfiction

publisher

Rizzoli

review 1: a clear, well argued, commendable cri de coeur, to be sure; 5 stars for the indictment but maybe two for the solutions. it's true that the way we teach HS math is intellectually bankrupt. Lockhart's solution is math for math's sake - an un-curricilum built around puzzles and games, designed mostly to create those moments of pure awe that grappling with abstract concepts can bring. but like most austere utopias, I'm not sure I actually sure it's the right place for most of us to reside. there's a Sinclair quote to the effect that in writing the Jungle he aimed for America's head and hit them in the stomach instead. similar thing here - I think what Lockhart wants is a more austere math classroom, one with a lot more number theory and a lot more abstraction. I want to invi... morete Dan Meyer and the computational thinking crowd into math class. more statistics, more simulations, and a lot of "why don't you write a little script and see if that helps?" more models, more sensors, more data analysis. the aesthetics of math that captivates Lockhart is gonna hook some share of any classroom, but for a lot of others it could scan a lot like art or poetry appreciation - beautiful, but only if you're buying what's being sold.
review 2: As a mathematics teacher and long-time student of mathematics, I was overjoyed to begin reading this book, finally one that attempts to explain the beauty and elegance of mathematics and to expose the way in which we are teaching it, which does not do justice to it at all. I absolutely agree with *most* of Lockhart's assessment on many points, for example, that mathematics is an art, that it should not be taught as procedures and formulas and meaningless word problems that contrive to be about "real life."I agree, most of our math teachers do not have this kind of appreciation for mathematics, which is tragic because it means our kids will grow up scared and intimidated by math ("math anxiety") instead of awed at its power of abstract interpretation. I agree our approach needs to be completely overhauled.My 2 star rating is due to the fact that Lockhart's analysis is strongly lacking in a historical understanding as well as pedagogical/curriculum knowledge. For example, he says that word problems should not be contrived to be about real life (I agree with this point), and that math is beautiful precisely BECAUSE it is irrelevant to real life.As a mathematician I cannot possibly comprehend how another mathematician could possibly believe the beauty of mathematics comes from its "irrelevance" of abstraction: in fact, the reason math is SO powerful is that these abstract representations have all been historically "discovered" or "invented" (depending on what you believe math is: inherent in the world, or a human game of abstraction)--particularly in order to try to model and explain phenomena observed in "the real world."Lockhart says math was created by humans "for their own amusement" (p. 31), but ignores that in fact all branches of mathematics in the past were created in response to actual world problems, and not only that, but now, some of the most fascinating mathematics is being created again in response to solving some of the most complex problems we have imagined, such as the mathematics behind string theory. I don't know how Lockhart could possibly consider that humans invented counting, ways to measure their plots of land and keep track of money, or ways to measure the orbits of planets (thus leading us to the current "space age") as "purely amusement"--perhaps, if LIFE is amusement in general, but really, all of these inventions had a very REAL, concrete, specific historical cultural purpose and are not "just made up" for fun!!!In fact, math is EMBODIED in our cognitive schemas and perception, and THIS IS PRECISELY what makes it so WONDERFUL: its RELEVANCE to EVERYTHING in real life and humanity's inherent capacity for thinking about the real world in this abstract way! Math is not "just" "fantasy" (as on p. 39) (see especially Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being).I teach functions (precalculus, AP calculus) and the main theme and point of math for example at this level is to teach kids how basically, in life, we track patterns of change in anything and everything--public health data, unemployment, polling, the stock market, baseball stats, etc. Functions are just the most abstract way to model these changing patterns over time (or some other variable) and thus give us the powerful tool of projecting into the future/past and otherwise analyzing trends. Yes, functions are abstract, but they are NOT "just fantasy play," irrelevant to the real world, or made up simply for the fun of it, in fact, quite the opposite of all of these.Further, my (and I believe, many) students would be aghast to learn that a math teacher is suggesting an overhaul of math education based on the idea that"kids don't really want something that is relevant to their daily lives." This is the most absurd statement I have ever heard, so I am guessing Lockhart knows nothing about adolescent/child development, interest, and pedagogical literature. Learning in general is based on making connections to prior knowledge, and I have never heard any question asked more often in math class when I didn't explain the relevance in advance than "Why do I need to know this? How is this relevant to my life?" This is probably the MOST pressing question for adolescents in general..Other examples of pedagogical tragedies in this book include Lockhart's admonitions that "you can't teach teaching," that "schools of education are a complete crock" and that teachers shouldn't lesson plan because this is somehow "not real" or authentic (p. 46-47). While I agree schools of education are not preparing our teachers well and what we need is much more systemic training in content knowledge (for example, math teachers should all have to double major in math/pedagogy or education), IT IS absolutely not true or supported by any research (except perhaps by the current corporate brand of the reform movement) that teaching is something you "have" that you don't need to "learn" and, further, that you shouldn't plan because this is inauthentic.A plan should of course never prevent a teacher from moving in new directions as suggested by the course of the class, but coming in without a plan is certainly not considered sound practice in any theory of learning and from any angle, and in general is not a sound principle of life (i.e., just doing everything by the seat of your pants and counting on your "genius" to lead you through whatever you should have planned usually doesn't work, unless you are in a feel-good movie). Only in Lockhart's fantasy "lala land" of irrelevancy is planning a vice and not a virtue. Plus, there's so much more to "planning" than thinking about the flow of the lesson, how you will help students make connections, etc. I assess and plan hand in hand for example, so I will grade the last night's HW and that day's Exit Slip and plan the next days's and week's lessons all the while incorporating items my students did not fully understand the first time, and also while addressing specifically the mistakes they made (and each class/year of students tends to have different problems and make different mistakes so it is important to constantly plan and reflect as a teacher on what is best for your particular students NOW).POSTSCRIPT, after received comments:Some comment I have received on this review first made me realize that I somehow implied math is not art: I could not agree with that more, math is NOT and should not be taught as something which is only "useful" for real life. I love math because its beauty in expressing such ideas as infinity (and different kinds of infinity at that!) is truly unique to this language.My initial post was born out of my own research in grad school, which has centered around the notion of embodiment, and "embodied" mathematics; it's hard to describe "in a nutshell" but basically embodiment is referred to by phenomenologist philosophers when they describe how human ideals/concepts are born in experience, and our experiential perceptions are in turn shaped by our ideas, creating the cyclical process of learning and expanding our horizons. If one believes in "embodied" education, in which experience/perception are perpetually interconnected to our cognitive schemas in a cycle of expansion, then to say as Lockheart does, that math, or that ANYTHING, for that matter, is purely "of the mind", is falsely dualistic and basically cuts experience and our perceptions out of the equation. I did not mean teach students "math for engineering" courses where they only learn applied mathematics. I meant, teach the history of mathematics, and experiment with the ideas IN CONTEXT, for example, have students imagine WHY our ancestors might have "invented" zero, why this "invention" took many generations more than inventing other numbers, teach them to consider why human experiences may have given rise to this beautiful and abstract language and why it has become so powerful at describing certain HUMAN ideas BORN of human Experience/perception.Nothing is "born in our mind" alone; nothing exists in our "mind" alone; and for anything to make sense, the very idea of something having a sense, comes from our experiential perception: * the ideas of positive/negative parallels our perceptive ability to set dualistic reference points in/with our bodies, i.e. east west, up down, side to side, etc which is further related to our bipedal structure* the idea of 0 being was hard to conceive b/c the human mind cannot by definition, conceive of nothing, the minute it tries to grasp this nothing it turns into something, so 0 took a while to come around, * The ideas of Euclidean geometry vs. non; Euclidean, though it incorrectly describes the ACTUAL universe, actually DOES describe our PERCEIVED universe quite accuratelyBasically, Mathematical structures/ideas is BORN in Perception/Experience!!! Don't just trust me, read the experts: :) Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being less

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