This Handbook strives to present the history of teaching and
learning mathematics over the various
epochs and civilizations, cultures, and countries. This
comprehensive approach became possible only
now because of the recent development of research. The aim of this
Handbook is, on the one hand, to
refl ect the current state of the history of mathematics education
and to make more accessible the
results of existing research, and on the other hand, thereby to
facilitate the further development of this
fi eld, drawing attention to that which has not yet been studied.
Our conviction is that concern about the future of mathematics
education is impossible without an
understanding of what is going on in the present, which in turn is
impossible without an understanding
(and consequently the study) of the past. We would like to instill
this conviction in our readers as well,
and not limit ourselves merely to providing them with a reference
book that contains needed information
(although this aim is important for us, too).
The manner in which mathematics education developed is important
for today’s mathematics
educators, but it is likewise important for researchers of the
history of education, of which mathematics
education is a part. Our view is that, even more broadly, for
researchers of cultural history and even
of social history as a whole, an appreciation of the historical
development of mathematics education
will be useful also.
It should be emphasized that at present our knowledge (and hence
our understanding) is limited.
In certain cases, the spread of knowledge is hampered by
linguistic barriers – important and substantive
studies remain unread even by those who would be receptive to them
and fi nd them interesting.
In other cases, there have simply been no studies – it would be no
mistake to say that educational
documents lying in archives practically in any country have not
been suffi ciently researched.
We should say at once that, in discussing the history of
mathematics teaching and learning, we are
mainly concentrating on that which in recent centuries has been
called pre-university education. This
terminology is naturally not applicable, say, to Antiquity, or
even to later periods, but nonetheless it
may be said that education which in one way or another corresponds
to “higher level education” is
usually discussed in this Handbook only in order to gain a better
general picture of education at preceding
levels (for example, when the discussion concerns mathematics
teacher education). Being even
more specifi c, we can say that typically Handbook chapters focus
mainly on secondary education
(or its equivalents) rather than on primary.
Mathematics education is a complex phenomenon, and therefore an
attempt has been made in this
Handbook to investigate it from different angles. Consequently,
the Handbook is divided into parts.
Part I is devoted to the history of mathematics education as a
scientifi c fi eld, with a discussion of its
scholarly literature and methodologies. Parts II, III and IV are
organized along chronological and
geographical lines, containing analysis of mathematics education
during different periods and in different
regions. Part V is devoted to the study of
various mathematical subjects and teaching practices.
Finally, Part VI examines processes that are common to different
countries – the emergence of
international cooperation, the introduction of technology, and the
spread of teacher preparation.
Different chapters in the Handbook are written from different
viewpoints and refl ect different
existing approaches to historical research in mathematics
education. Nor did the editors strive to
achieve complete uniformity in more technical aspects of the text
– in particular, in the spelling of
non-English words, as different systems of transliteration have
developed for historical reasons, and
not infrequently even the same name in different cases is
pronounced in English in different ways.
Attempts to achieve a uniform approach might have rendered the
text incomprehensible.
It should be noted that certain chapters consist of subchapters
that were written separately from one
another. In such cases, the authors of these subchapters are
indicated in the text. All of the authors of
such subchapters are also listed at the beginning of the chapter
and in the table of contents in alphabetical
order. Other chapters were worked on jointly by their authors, in
such cases the authors of
chapters’ parts are not indicated.
In conclusion, it should be reiterated that this book does not and
cannot claim to be absolutely
complete. Readers (as well as editors) may justifi ably express
regret that for one or another reason not
enough has been said about one or another country or one or
another phenomenon. If the recognition
of such insuffi ciencies leads to new research, however, the
editors will consider this an important
achievement of the present volume.
New York, NY, USA Alexander Karp
Bielefeld, Germany Gert Schubring
