Signifying the accumulation graph in a dynamic and multi-representation environment

Michal Yerushalmy, Osama Swidan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)287-306
Number of pages20
JournalEducational Studies in Mathematics
Issue number3
StatePublished - Jul 2012


  • Accumulation function
  • Calculus
  • Integral
  • Objectification
  • Semiotic mediation
  • Software artifact

ASJC Scopus subject areas

  • General Mathematics
  • Education


Dive into the research topics of 'Signifying the accumulation graph in a dynamic and multi-representation environment'. Together they form a unique fingerprint.

Cite this