
06087483
j
2012e.00696
Yerushalmy, Michal
Swidan, Osama
Signifying the accumulation graph in a dynamic and multirepresentation environment.
Educ. Stud. Math. 80, No. 3, 287306 (2012).
2012
Springer Netherlands, Dordrecht
EN
I54
C34
R24
U24
calculus
integral
accumulation function
objectification
software artifact
semiotic mediation
doi:10.1007/s1064901193568
Summary: The present study focuses on the accumulation process involved in the integration of a singlevariable function. Observing the work of two highschool calculus students who had not yet learned any other integralrelated 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 threestage 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 lowerlimit value. This evolution is marked by semiotic changes related to the pivotal role of the ``zeros" in the accumulation graph.