id: 06356543
dt: j
an: 2014f.00748
au: Swidan, Osama; Yerushalmy, Michal
ti: Learning the indefinite integral in a dynamic and interactive technological
environment.
so: ZDM, Int. J. Math. Educ. 46, No. 4, 517-531 (2014).
py: 2014
pu: Springer, Berlin/Heidelberg
la: EN
cc: I54 U74 I24
ut: indefinite integral; objectification; mediation; dynamic artifact; graphs
ci:
li: doi:10.1007/s11858-014-0583-1
ab: Summary: The present study was designed to identify the objectification
processes involved in making sense of the concept of an indefinite
integral when studied graphically in a dynamic technological
environment. The study focuses on 11 pairs of 17-year-old students
familiar with the concept of differentiation but not of integration.
The students were asked to explain the possible connection between two
linked dynamic graphs: the function and the primitive function graphs.
The present study was guided by objectification theory, which considers
artifacts to be fundamental to cognition and which views learning as
the process of becoming aware of the knowledge that exists within a
cultural context. In the course of two rounds of data analysis we
identified six elements in the processes of objectification:
objectifying the relationships between segments based on the location,
inclination, and concavity of the function graph; and on the
relationships between the zero, the extreme, and the inflection points
in the function graph and the corresponding points in the primitive
function graph.
rv: