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Home > Resources > Math > Stephen Pinker

Stephen Pinker - How the Mind Works

Title: How the Mind Works Author: Stephen Pinker (a noted neuroscientist at MIT) Publisher: New York: W.W. Norton, 1999, c1997 Discription: xii, 660 p.: ill.; 25cm ISBN: 0393318486 (pbk.) Location: KCC Library - General Collection (2nd floor) Call Number: QP360.5 .P56 1999 Please check the online catalog to see if the book is available. Quote from the book... The … way to get to mathematical competence is similar to the way to get to Carnegie Hall: practice. Mathematical concepts come from snapping together old concepts in a useful new arrangement. But those old concepts are assemblies of still older concepts. Each subassembly hangs together by the mental rivets called chunking and automaticity: with copious practice, concepts adhere into larger concepts, and sequences of steps are compiled into a single step. Just as bicycles are assembled out of frames and wheels, not tubes and spokes, and recipes say how to make sauces, not how to grasp spoons and open jars, mathematics is learned by fitting together overlearned routines. Calculus teachers lament that students find the subject difficult…because you can't do calculus unless algebraic operations are second nature, and most students enter the course without having learned the algebra properly and need to concentrate every drop of mental energy on that. Mathematics is ruthlessly cumulative, all the way back to counting to ten. The ascendant philosophy of mathematical education in the United States is constructivism, a mixture of Piaget's psychology with counterculture and postmodernist ideology. Children must actively construct mathematical knowledge for themselves in a social enterprise driven by disagreements about the meanings of concepts. The teacher provides the materials and the social milieu but does not lecture or guide the discussion. Drill and practice, the routes to automaticity, are called “mechanistic” and seen as detrimental to understanding. (Constructivism) ignores the difference between our factory-installed equipment and the accessories that civilization bolts on afterward. Setting our mental modules to work on material they were not designed for is hard. Children do not spontaneously see a string of beads as elements in a set, or points on a line as numbers…and without practice that compiles a halting sequence of steps into a mental reflex, a learner will always be building mathematical structures out of the tiniest nuts and bolts, like the watchmaker who never made subassemblies and had to start from scratch every time he put down a watch to answer the phone.