id: 05629019
dt: j
an: 2010a.00425
au: Elia, Iliada; Gagatsis, Athanasios; Panaoura, Areti; Zachariades,
Theodosis; Zoulinaki, Fotini
ti: Geometric and algebraic approaches in the concept of “limit” and the
impact of the “didactic contract”.
so: Int. J. Sci. Math. Educ. 7, No. 4, 765-790 (2009).
py: 2009
pu: Springer Netherlands, Dordrecht
la: EN
cc: I24 C34
ut: didactic contract; geometric and algebraic representations; the concept of
limit; limit of a function; understanding; grade 12; upper secondary;
empirical investigations
ci:
li: doi:10.1007/s10763-009-9149-z
ab: Summary: The present study explores students’ abilities in conversions
between geometric and algebraic representations, in problem- solving
situations involving the concept of “limit” and the interrelation
of these abilities with students’ constructed understanding of this
concept. An attempt is also made to examine the impact of the
“didactic contract” on students’ performance through the
processes they employ in tackling specific tasks on the concept of
limit. Data were collected from 222 12th-grade high school students in
Greece. The results indicated that students who had constructed a
conceptual understanding of limit were the ones most probable to
accomplish the conversions of limits from the algebraic to the
geometric representations and the reverse. The findings revealed the
compartmentalized way of students’ thinking in non-routine problems
by means of their performance in simpler conversion tasks. Students who
did not perform under the conditions of the didactic contract were
found to be more consistent in their responses for various conversion
tasks and complex problems on limits, compared to students who, as a
consequence of the didactic contract, used only algorithmic processes.
rv: