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des Kampfes gesellschaftlicher Mächte, see Blankertz, 1969, p. 117). It is
exactly this interplay of societal, cultural forces (like parents, teachers,
economy, science, government, and other social institutions) trying to influ-
ence the definition of the intended, implemented, and attained curriculum
that is the subject of this chapter. To use the concepts of Mogens Niss in
Mathematics in society, the chapter tries to throw light on the solution of the
justification problem, the possibility problem, and the implementation prob-
CULTURAL FRAMING
OF TEACHING AND LEARNING MATHEMATICS
edited and introduced
by
Rudolf Sträßer
Bielefeld
R. Biehler, R. W. Scholz, R. Sträßer, B. Winkelmann (Eds.),
Didactics of Mathematics as a Scientific Discipline, 399-402.
© 1994 Dordrecht. Kluwer Academic Publishers. Printed in the Netherlands.
CHAPTER 8

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INTRODUCTION TO CHAPTER 8
lem of mathematics education in society. As can be seen from this descrip-
tion, the approach of this chapter is a rather broad societal perspective.
Consequently, all four papers in this chapter step back from the precise
perspectives of former chapters of this book. Teaching and learning of
mathematics are looked upon as a political and societal endeavor as a
whole. In order to have a common topic, arguments specific to mathematics
become more pertinent than in other chapters of the book. On the other
hand, with the more global approach, it is even more difficult to make these
arguments credible and cogent from the point of view of the scientific
methodology that is used. Nevertheless, the chapter tries to bring to light
factors of mathematics education that often tend to be overlooked in didac-
tics of mathematics, factors that are of major importance to the actual as
well as future teaching and learning of mathematics.
From a historical point of view, the paper on cultural influences on math-
ematics teaching in nineteenth century Germany by Hans Niels Jahnke ana-
lyzes the case of mathematics and mathematics education in Prussia and
Germany and presents an integrated picture of ideological, social, sentimen-
tal, and technological influences on the field. The case study intentionally
contradicts the prejudice that technological requirements are the major, if
not the only, influences shaping education, showing that an educational
philosophy deeply rooted in the cultural foundations of a society may well
exert a decisive influence on mathematics as a scientific endeavor as well as
on the structure and content of mathematics education at a given place and
time. What seems most surprising in this case is the extremely negative
view of everyday practical and common calculation taken by the reformers
of that Humboldtian era, which is in sharp contrast to most of the present
approaches to curricula for mathematics teaching and learning. The argu-
ment of Humboldt and Crelle, who praised the learning, appropriation, and
appreciation of pure mathematics as an indispensable condition for the di-
rect application of mathematics and as means of developing systematic
thinking, is still worth a deep reflection. The following analysis of the im-
plications of the decay of the neohumanist philosophy of education also
shows that cultural influences are working rather slowly and cannot be
identified in a short-term study.
In terms of time, the paper on mathematics and ideology by Richard Noss
is nearer to present mathematics education: Starting from a nonpejorative
concept of ideology ("body of ideas through which we see and with which
we construct our reality"), the paper looks into the relations of ideology and
(mathematics) curricula. A first result of Noss nearly paraphrases the quote
from Weniger: "it is most useful to conceive of the curriculum as a site of
struggle in which students, teachers, parents as well as voices from indus-
trial, commercial and other settings have at various times competed . . . with
varying relative strengths to assert their priorities." Consequently, the math-
ematics curriculum is seen as "only partially determined by mathematicians
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RUDOL
F STRÄSSER
or mathematics educators." Last but not least by a comparison with music
and its social role, Noss comes to a view of the mathematics curriculum as
"a tension between the structural (from mathematics) and the ideological
meanings." For school mathematics, the process of didactical transposition
(necessarily linked with teaching/learning mathematics) opens up additional
room for the immersion of ideological, if not delineated meanings of math-
ematics: "the call to delimit school maths to its apparent structural meanings
. . . represents an attempt to focus attention (albeit implicitly) on a variety of
delineations that perform an (apparently) important ideological function." A
thorough analysis of "mathematics for all" (see, also, Usiskin, in chapter 6)
may be a good place to analyze the tensions between structural, inherent,
and ideological meanings of mathematics and the politics of mathematics
curricula.
The final paper on cultural framing of mathematics teaching and learning
by Ubiratan d'Ambrosio in some sense is a step even further in time by
looking into the future of mathematics education: Starting from a rather
negative description of the present state of society in general (a somewhat
paradoxical situation of wealth for a minority and poverty for the majority)
and the important role of mathematics, d'Ambrosio criticizes present math-
ematics education as producing fundamentally harmful social outcomes:
Mathematics (and science) education emphasizes techniques, formulae, and
theories geared toward drills, toward exam-focused topics, and is not aimed
at a contextualized understanding of mathematics and science. To counter-
act this tendency, d'Ambrosio proposes four general goals for mathematics
(and science) education, namely, teaching mathematics and science to all, so
that individuals can be wiser consumers, wiser decision makers, motivated
and prepared for new careers, and prepared to take personal decisions based
on ethical considerations. Explicitly alluding to the intentions of H.-G.
Steiner, didactics of mathematics is presented as the science to reflect on
these problems and to offer ways to cope with this societal task. The ethno-
mathematics proposal (coming from the recognition that every cultural
group generates its own ways of coping with reality, organizes these ways
into techniques, develops these into true chefs d'oeuvre, improving and
transmitting them from generation to generation) is presented as a way to
answer this global challenge. Illustrations of this approach are given from
research (cf., also, Lave, 1988) as well as teacher training and curriculum
development – showing ethnomathematics as a theoretical program and as a
pedagogical practice.
In contrast to differences in the topics and approaches of the three papers
briefly sketched above, the same three papers show a certain homogeneity
in terms of methodology: All papers basically rely on a traditional type of
heuristics, trying to convince the reader by conveying meaning, by enhanc-
ing his or her understanding of phenomena he or she may already know.
The first paper of this chapter on comparative international research in
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INTRODUCTION TO CHAPTER 8