id: 06545329
dt: j
an: 2016b.00957
au: Park, Jungeun
ti: Communicational approach to study textbook discourse on the derivative.
so: Educ. Stud. Math. 91, No. 3, 395-421 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: U20 I40
ut: calculus; function; derivative; textbooks; communicational approach
ci:
li: doi:10.1007/s10649-015-9655-6
ab: Summary: This paper investigates how three widely used calculus textbooks
in the U.S. realize the derivative as a point-specific object and as a
function using Sfardâ€™s communicational approach. For this purpose,
the study analyzed word-use and visual mediators for the {\it limit
process} through which the derivative at a point was objectified, and
word-use and visual mediators for the {\it derivative process} through
which the derivative as a function was objectified. The analysis
highlighted inconsistency in realizations of the limit process and
object, and derivative process and object found in some instances, and
implicit discussion on relations among different visual mediators.
Specifically, the results of this study led to four observations about
issues suggested by one or more of the textbooks: a) visual mediators
of the initial and final objects, and the visual mediators of these
processes were often inconsistent; b) transformations of visual
mediators from initial object, through process, to final object were
often implicit both in one visual mediator and across multiple visual
mediators; c) visual mediators for the limit processes were sometimes
disconnected from the initial and final objects, or the connections
were not explicit; and d) realizations of both the derivative at a
point and the derivative of a function were mediated with nearly
identical symbols suggesting a possible difficulty with understanding
the difference between them.
rv: