id: 06545284
dt: j
an: 2016b.00178
au: Scheiner, Thorsten
ti: New light on old horizon: constructing mathematical concepts, underlying
abstraction processes, and sense making strategies.
so: Educ. Stud. Math. 91, No. 2, 165-183 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: C30
ut: cognition; learner types; reflective abstraction; reflectural abstraction;
sense-making strategies; structural abstraction; theory development
ci:
li: doi:10.1007/s10649-015-9665-4
ab: Summary: The initial assumption of this article is that there is an
overemphasis on abstraction-from-actions theoretical approaches in
research on knowing and learning mathematics. This article uses a
critical reflection on research on studentsâ€™ ways of constructing
mathematical concepts to distinguish between abstraction-from-actions
theoretical approaches and abstraction-from-objects theoretical
approaches. Acknowledging and building on research on knowing and
learning processes in mathematics, this article presents a theoretical
framework that provides a new perspective on the underlying abstraction
processes and a new approach for interpreting individualsâ€™ ways of
constructing concepts on the background of their strategies to make
sense of a mathematical concept. The view taken here is that the
abstraction-from-actions and abstraction-from-objects approaches
(although different) are complementary (rather than opposing)
frameworks. The article is concerned with the theoretical description
of the framework rather than with its use in empirical investigations.
This article addresses the need for more advanced theoretical work in
research on mathematical learning and knowledge construction.
rv: