Handbook on the History of Mathematics Education

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