id: 06477123
dt: j
an: 2015e.00741
au: Nitsch, Renate; Fredebohm, Anneke; Bruder, Regina; Kelava, Augustin;
Naccarella, Dominik; Leuders, Timo; Wirtz, Markus
ti: Students’ competencies in working with functions in secondary mathematics
education ‒ empirical examination of a competence structure model.
so: Int. J. Sci. Math. Educ. 13, No. 3, 657-682 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: I23 C43
ut: change of representation; competence structure model; elements of cognitive
action; item response theory; representations of functional
relationships
ci:
li: doi:10.1007/s10763-013-9496-7
ab: Summary: In the subject matter of functional relationships, a student’s
ability to translate from one form of representation to another is seen
as a central competence. In the course of the HEUREKO project
(heuristic work with representations of functional relationships and
the diagnosis of mathematical competencies of students), a theoretical
competence structure model comprising five competence dimensions was
developed. These are based on four types of representation (graph,
numerical table, algebraic equation and situational description) and
correspond to the skill to translate from one type of representation to
another. The following study was aimed to examine the facets of the
model. The 5-dimensional model was empirically tested with a sample of
$N = 645$ students of grades 9 and 10. This was accomplished by
comparing competing item response models with regard to model fit using
information criteria measures. In comparison with other possible model
structures, our postulated 5-dimensional model showed the best model
fit, suggesting that all translations are relevant for competence
assessment and development. Furthermore, in order to allow for the
identification of structural components of cognitive actions, the
employed tasks used in the empirical testing were divided into
categories with regard to the different demands of cognitive action.
Our results suggest that cognitive actions may have a specific
dimensional structure. These findings can contribute to a better
diagnostic approach concerning specific strengths and weaknesses and
can therefore foster students’ competencies.
rv: