The book is intended primarily for graduates and senior undergraduates
in psychology, education, and cognitive science. It has implications for edu-
cation, especially in mathematics and science, but the orientation is to defin-
ing the underlying psychological processes, rather than to specifying teaching
techniques. Further work is therefore required before application in the
classroom.

Much of the argument has a mathematical basis, but I have tried to present
the math in a way that requires a minimum of specialized mathematical
knowledge. The details of the mathematical treatments are provided in ap-
pendices, footnotes, or in other published works that are cited where rele-
vant. Empirical work is presented in summary form, and the full details can
be obtained from published works.

One of the most pleasant aspects of writing a book is to recall those peo-
ple who have contributed so generously to the development of ideas through
their extremely competent criticisms and suggestions as well as their sup-
port and encouragement. In this respect I have been particularly fortunate
to have had a long association with John Bain, whose knowledge of cogni-
tion is unusual in its depth and profundity, and who has been so selfless and
supportive as a research collaborator. He deserves great credit for sharpen-
ing and developing my understanding of many concepts of cognition that
have come to take a central role in my theory of cognitive development.
There have been many other people also with whom I have been very for-
tunate to collaborate, and who have contributed in a similar way. These in-
clude Murray Maybery, Bill Wilson, Julie Stewart, Sue Smith, Janet Wiles,
Michael Humphreys, Matthew McDonald, Barbara Hodkin, Cathy Brown,
Mark Bahr, Elizabeth Leitch, Campbell Dickson, Jian Guo, Ross Gayler, Ma-
vis Kelly, Rosemary Baker, Craig Shaw, Susan Robinson, and Susan Buntine.

Another major debt is to the people whose contributions to the literature
have provided inspiration for, as well as the building blocks of, this work,
and who are acknowledged of course in the citations. However there are
some with whom I have been fortunate to enjoy a special relationship from
which I have derived great intellectual stimulation, as well as support and
encouragement. These are too numerous to mention exhaustively, but I would
like to express my special appreciation to John Flavell, Bob Siegler, Dedre
Gentner, Robbie Case, Pat Cheng, Keith Holyoak, Rochel Gelman, Donald
Broadbent, Alan Baddeley, Lyn Reder, John Anderson, David Klahr, and Jac-
queline Goodnow. The deficiencies that remain despite the best efforts of my
friends and collaborators will be recognizably mine.

My most special acknowledgement of all goes to my wife, Lyn English,
whose support, love, and enthusiasm gave me the resources I needed to do
this work.

-- Graeme S. Halford

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