id: 05977661
dt: j
an: 2011f.00582
au: García, Mercedes; Llinares, Salvador; Sánchez-Matamoros, Gloria
ti: Characterizing thematized derivative schema by the underlying emergent
structures.
so: Int. J. Sci. Math. Educ. 9, No. 5, 1023-1045 (2011).
py: 2011
pu: Springer Netherlands, Dordrecht
la: EN
cc: I45 D65 D35
ut: derivatives; derivative schema; relationship between a function and its
first derivative; consciousness; reflective abstraction; thematization;
first year students; empirical investigations; educational research
ci:
li: doi:10.1007/s10763-010-9227-2
ab: Summary: This paper reports on different underlying structures of the
derivative schema of three undergraduate students that were considered
to be at the trans level of development of the derivative schema
(action-process-object-schema). The derivative schema is characterized
in terms of the students’ ability to explicitly transfer the
relationship between a function and its first derivative to the
derivative function and the second derivative. This conscious shift of
properties of derivatives is differently manifested by the students in
the trans level of development of the derivative schema and can be
considered evidence of the different characteristics of the
thematization of derivative schema. From here we suggest that there are
different underlying structures in the constructed schema due to the
consciousness in which students use the relations between a function
and its derivative.
rv: