Review: How to Solve It: A New Aspect of
G. Polya. Princeton, NJ: Princeton University Press, 1957, Second Edition.
by Jennifer Norton, Graduate Student Associate, TRC
to Solve It details the motives and procedures that lead to solutions
in mathematical problem solving and shows teachers how to help their students
learn how to solve problems. The interactive approach illustrated
in this text is designed to help students with their problem- solving
skills, while making sure they perform a reasonable amount of the work.
Teachers use questions to guide students effectively and unobtrusively,
and to enhance their problem-solving skills through imitation and practice.
The book is divided into four sections:
In the Classroom:
This section begins with a concise table that carries the reader through
the four phases of problem solving: 1) understanding the problem, 2) devising
a plan and recognizing the connection of parts of the problem, 3) carrying
out the plan, and 4) looking back: reexamining, discussing, and checking
the results in order to aid future problem solving. This section then
details these aspects of Polya's approach and walks the reader through
How to Solve
It: An imaginary dialogue between a student and teacher illustrates
Polya's approach with respect to a particular mathematical problem.
Heuristic: The dictionary provides references for particular aspects
of problem solving, including such topics as the following: using analogies
to aid problem solving, introducing auxiliary elements to aid problem
solving, checking the result and deriving it differently, using the results
of earlier problems to solve new problems, decomposing and recombining
problems, thinking inductively, using notation, setting up equations,
varying problems, and recognizing signs of progress.
Hints, Solutions: This section provides many sample problems to let
readers test their knowledge and understanding of the approach introduced
in this book. By encouraging the teacher/readers to participate in the
learning process from a student's perspective, Polya helps readers internalize
the approach and integrate it with their teaching skills.
first edition dates from 1945 and the author is writing to teachers of
mathematics, How to Solve It offers insights and practical solutions
for the difficult task of teaching students to solve problems in several
disciplines. If you find yourself solving problems for your students because
they can't do it themselves, or frustrated that you can't get them to
understand, try Polya's approach!