Educational Studies in Mathematics

, Volume 93, Issue 2, pp 155–173 | Cite as

Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context

  • Dov Zazkis
  • Keith Weber
  • Juan Pablo Mejía-Ramos


We examine a commonly suggested proof construction strategy from the mathematics education literature—that students first produce a graphical argument and then work to construct a verbal-symbolic proof based on that graphical argument. The work of students who produce such graphical arguments when solving proof construction tasks was analyzed to distill three activities that contribute to students’ successful translation of graphical arguments into verbal-symbolic proofs. These activities are called elaborating, syntactifying, and rewarranting. We analyze how engaging in these activities relates to students’ success in proof construction tasks. Additionally, we discuss how each individual activity contributes to the translation of a graphical argument into a verbal-symbolic proof.


Proof Graphical argumentation Toulmin scheme 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Dov Zazkis
    • 1
  • Keith Weber
    • 2
  • Juan Pablo Mejía-Ramos
    • 2
  1. 1.Arizona State UniversityTempeUSA
  2. 2.Rutgers UniversityNew BrunswickUSA

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