Didactics of mathematics: more than mathematics and school! - CIMM

166 R. Straesser
the human parts of its discipline by concentrating on
the subject matter side via the focus on the curriculum.
The focus on subject matter, the focus on mathematics
had different faces in different countries. In France for
instance, the IREM movement clearly defined itself as
coming from an epistemological fundament. Some
French colleagues even suggested to define the
fundamental ‘‘Didactique des Mathématiques’’ as
‘‘experimental epistemology’’ (according to Brousseau
(1986, p. 103): ‘‘épistémologie expérimentale’’). For
Germany, we can exemplify the focus on subject matter
with the then widely accepted definition ‘‘didactics
of mathematics is the scientific development of courses
to be effectively used to learn in the area of mathematics.
It is also made up of the practical teaching of
such courses and their empirical evaluation. This includes
reflections on the aims and subject matter
selection of such courses’’ (‘‘Didaktik der Mathematik
ist die Wissenschaft von der Entwicklung praktikabler
Kurse für das Lernen im Bereich Mathematik sowie
der praktischen Durchführung und empirischen
Überprüfung der Kurse einschliesslich der Überlegungen
zur Zielsetzung der Kurse und der Stoffauswahl’’,
see Griesel (1971, p. 296), nearly identical in
Griesel (1974); a more recent, internationally read text
is Wittmann (1992, English version 1995). In the
beginning of the 1970s, Hans-Georg Steiner also took
didactics of mathematics as fundamentally defined by
the knowledge to be taught, by mathematics—as can
be seen from his publication on ‘‘Bildung’’ (see Steiner
1972). He described didactics of mathematics as
‘‘thinking through mathematics under the perspective
of the elementary and the motivation for the learner’’
(loc. cit., free translation from p. 326; ‘‘Das Durchdenken
des Gebäudes der Mathematik unter dem
Gesichtspunkt des Elementaren und im Hinblick auf
die Motivation des Lernenden gibt dieser Wissenschaft
ein lebensnahes Fundament ...’’). Until around the end
of the 1970s, the so-called Stoffdidaktik was the predominant
approach to didactics of mathematics in
Germany, sometimes even reducing didactics of
mathematics to a mere ‘‘elementarisation’’ of mathematics
for the purpose of its teaching.
At the end of the 1970s, Steiner had a broader definition
of didactics of mathematics. He stated that the
constraints and factors, which determine the classroom
of mathematics and its changeability, belong to didactics
of mathematics. This includes the complex processes of
social interaction related to the teaching and learning of
content matter and ways of behaviour (free translation
by RS of ‘‘Mathematikdidaktik wird dabei in einem
erweiterten Sinne verstanden -als vorwiegend materialorientierte
Entwicklungsarbeit, Einfügung RS, wonach
sowohl die den mathematischen Unterricht und
seine Veränderbarkeit bestimmenden Bedingungen
und Faktoren als auch die komplexen sozialen Interaktionsprozesse
im Unterricht in ihrem Zusammenhang
mit der Vermittlung und dem Erwerb von Inhalten und
Verhaltensweisen wesentliche Bestandteile bzw. Dimensionen
der Untersuchungsgegenstände sind’’; see
Steiner 1978, p. XL). Obviously, and probably in relation
with the creation of the national research institute
for didactics of mathematics (Institut für Didaktik der
Mathematik—IDM) in Bielefeld, Steiner looked further
than the curriculum and course developers abundant
at that time—at least in Germany. Nevertheless,
this perspective was still concentrating on the process of
teaching and learning in schools, institutions to offer (an
understanding of) mathematics to everybody.
2 An opening: mathematics in technical
and vocational education
About 10 years later and in France, we find a slightly
broader definition: didactics of mathematics (is) the
science of the specific conditions of the diffusion of
mathematical knowledge useful for the functioning of
the human institutions (‘‘La didactique des mathématiques
se place ... dans le cadre des sciences cognitives
comme la science des conditions spécifiques de la diffusion
des connaissances mathématiques utiles au
fonctionnement des institutions humaines’’, see
Brousseau 1994, p. 52). Here, didactics of mathematics
has left the narrow area of schools and looks into the
diffusion of mathematics in society at large.
Even if nearly invisible in his list of publications,
Steiner too had crossed this borderline of schools in his
activities: Because of his interest in the pedagogical
concept of ‘‘Bildung’’ (see the text entitled ‘‘Mathematik
und Bildung’’; Steiner 1972) and an ongoing
German debate on a reform of upper secondary
teaching in general, Steiner had taken the job of a
scientific counsellor of a major German reform project—the
‘‘Kollegstufe’’ piloted by Herwig Blankertz.
Kollegstufe aimed at offering upper secondary education
for virtually everybody in need of this—from the
future unskilled worker to the young adult planning an
academic career. This reform project especially fitted
with the intentions of the Bielefeld institute IDM and
Hans-Georg Steiner, because Blankertz wanted to
build his project on the joint efforts of the different
subject matter didactics (‘‘Fachdidaktiken’’) available
at that time. Steiner integrated a mathematics teacher
from the ‘‘Kollegstufe’’-project in his working group
in Bielefeld after having made upper secondary
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