
05629019
j
2010a.00425
Elia, Iliada
Gagatsis, Athanasios
Panaoura, Areti
Zachariades, Theodosis
Zoulinaki, Fotini
Geometric and algebraic approaches in the concept of ``limit'' and the impact of the ``didactic contract''.
Int. J. Sci. Math. Educ. 7, No. 4, 765790 (2009).
2009
Springer Netherlands, Dordrecht
EN
I24
C34
didactic contract
geometric and algebraic representations
the concept of limit
limit of a function
understanding
grade 12
upper secondary
empirical investigations
doi:10.1007/s107630099149z
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 12thgrade 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 nonroutine 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.