How the Mind Works
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
check the online catalog to see if the book is available.
from the book...
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
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.
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.
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.