id: 06439920
dt: a
an: 2015c.00756
au: Schueler, Sven; Roesken-Winter, Bettina
ti: Exploring students’ mental models in linear algebra and analytic
geometry: obstacles for understanding basic concepts.
so: Nicol, Cynthia (ed.) et al., Proceedings of the 38th conference of the
International Group for the Psychology of Mathematics Education
“Mathematics education at the edge", PME 38 held jointly with the
36th conference of PME-NA, Vancouver, Canada, July 15‒20, 2014, Vol.
5. [s. l.]: International Group for the Psychology of Mathematics
Education (ISBN 978-0-86491-360-9/set; 978-0-86491-365-4/v.5). 121-128
(2014).
py: 2014
pu: [s. l.]: International Group for the Psychology of Mathematics Education
la: EN
cc: H64 G74 C34
ut: mental models; linear algebra; analytic geometry; mathematical concepts;
obstacles; difficulties
ci:
li:
ab: Summary: We discuss the relevance of ‘Grundvorstellungen’ (GVs), a
didactical category to analyze students’ mental models in comparison
to the intended mathematical meanings in the context of linear algebra
and analytic geometry. Diagnostic tasks were used to reveal students’
conceptual understanding in this field of expertise. In particular, an
open item format was chosen to elicit students’ individual GVs and to
explore how they use them while working on mathematical tasks. 30
students from upper secondary school participated in our study; data
was collected by a paper-and-pencil test. The results show that
elaborated representations of GVs foster students’ understanding of
mathematics and facilitate the process of finding problem solving
strategies.
rv: