id: 06087483
dt: j
an: 2012e.00696
au: Yerushalmy, Michal; Swidan, Osama
ti: Signifying the accumulation graph in a dynamic and multi-representation
environment.
so: Educ. Stud. Math. 80, No. 3, 287-306 (2012).
py: 2012
pu: Springer Netherlands, Dordrecht
la: EN
cc: I54 C34 R24 U24
ut: calculus; integral; accumulation function; objectification; software
artifact; semiotic mediation
ci:
li: doi:10.1007/s10649-011-9356-8
ab: Summary: The present study focuses on the accumulation process involved in
the integration of a single-variable function. Observing the work of
two high-school calculus students who had not yet learned any other
integral-related ideas, we analyze the emergence of the semiotic
relationship between personal and mathematical meanings, as expressed
through the understanding of mathematical signs in integration tasks.
Adopting Radford’s educational perspective whereby learning is
defined as a process of objectification, we identify a three-stage
evolution of the double semiotic meaning of the lower boundary and of
its role in the definition of the accumulation graph: (1) objectifying
a zero accumulation in relation to the lower limit, (2) objectifying
zero as marking the zero sum of accumulated areas, and (3) objectifying
the accumulation graph as dependent on the lower-limit value. This
evolution is marked by semiotic changes related to the pivotal role of
the “zeros" in the accumulation graph.
rv: