id: 05912588
dt: b
an: 2011f.00254
au: Brown, Tony
ti: Mathematics education and subjectivity. Cultures and cultural renewal.
so: Mathematics Education Library 51. Berlin: Springer (ISBN
978-94-007-1738-1/hbk; 978-94-007-3744-0/pbk; 978-94-007-1739-8/ebook).
xi, 216~p. (2011).
py: 2011
pu: Berlin: Springer
la: EN
cc: C90 C60 C50 D30
ut: subjectivity; curriculum reform; Jacques Lacan
ci: Zbl 0987.00003; ME 2002f.04631
li: doi:10.1007/978-94-007-1739-8
ab: I believe that this book makes a very important contribution to the
developing dialogue concerning the nature of mathematics. It resonates
with the arguments of George Lakoff and Rafael E. Nuñez against “The
Romance of Mathematics" [{\it G. Lakoff} and {\it R. E. Núñez}, Where
mathematics comes from. How the embodied mind brings mathematics into
being. New York, NY: Basic Books (2000; ME 2002f.04631, Zbl
0987.00003), pp. 339‒340]. Lakoff and Nuñez list seven beliefs in
The Romance, the first two of which are: “1) Mathematics is an
objective feature of the universe; mathematical objects are real;
mathematical truth is universal, absolute, and certain and 2) What
human beings believe about mathematics therefore has no effect on what
mathematics really is. Mathematics would be the same even if there were
no human beings or beings of any sort. Although mathematics is abstract
and disembodied, it is real." Just as Lakoff and Nuñez argue against
the romance and show that mathematics is a product of the human mind,
this book presents a compelling argument that mathematics is in fact a
meme, i.e. “an idea, behavior or style that spreads from person to
person within a culture." A determination of whether mathematics is
subjective or objective has far-reaching consequences for how it is
learned and taught. From the Professor Brown’s Introduction: “This
book is centrally concerned with how we represent mathematical teaching
and learning with a view to changing them to suit new circumstances. It
considers teachers, students, and researchers. It explores their
mathematical thinking and the concepts that this thought produces,
concepts that shape subsequent thought. The book examines some of the
linguistic and cultural filters that influence mathematical
understanding in schools. But above all it is concerned with how we
understand ourselves in relation to the school-learning contexts that
produce mathematics\dots. The attitude of the proposed reconsideration
is to think of the purpose of school mathematics as being to provide
filters on life, a grammar through which we tell stories of life. That
is, mathematics provides a way of making sense of life, or modeling
life. It also presents frameworks, or analytical apparatus, against
which life is constructed. But, in particular, mathematics gives us
ways of seeing how we are all a part of that life, with the capacity to
change that life, and to be changed by it. The book proposes that
mathematics can provoke us to think differently about our environments,
whether they are spatial, social, cultural, educational, philosophical
or political, as successive chapters examine. This reorientation might
enable us to build our world differently. Part I of this book is a
portrayal of how learners and teachers in different cultural settings
construct mathematical knowledge according to their particular social
needs\dots. Part II focuses on renewal. There is a common propensity to
see scientific activity in general and mathematics in particular, as
being concerned with eternal entities\dots. The book argues that
mathematics needs to be centered in an attitude of experimentation and
critique, to support ever-fresh approaches to the new challenges that
we will surely face. Mathematics itself can be responsive to life and
not just serve as a stable point of reference\dots. Some examples are
offered of how re-conceptualizations of the philosophical environment
might enable us to trigger classroom mathematical activity towards more
futuristic possibilities. Here learning is understood as participation
in cultural renewal\dots. [The concluding chapter] gathers some remarks
on how we might understand the interface of mathematics with humans.
Subjectivity is depicted as embracing both our physical experience of
the world and our capacity to symbolize this experience. Ultimately
teachers, students and researchers need to be attentive to how they are
subject to restrictive encounters with mathematics and with each
other."
rv: Steven C. Althoen (Holly)