Pre-service teachers’ figurative and operative graphing actions

Kevin C. Moore, Irma E. Stevens, Teo Paoletti, Natalie L.F. Hobson, Biyao Liang

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We report on semi-structured clinical interviews to describe U.S. pre-service secondary mathematics teachers’ graphing meanings. Our primary goal is to draw on Piagetian notions of figurative and operative thought to identify marked differences in the students’ meanings. Namely, we illustrate students’ meanings dominated by fragments of sensorimotor experience and compare those with students’ meanings dominated by the coordination of mental actions in the form of covarying quantities. Our findings suggest students’ meanings that foreground operative aspects of thought are more generative with respect to graphing. Our findings also indicate that students can encounter perturbations due to potential incompatibilities between figurative and operative aspects of thought.

Original languageEnglish
Article number100692
JournalJournal of Mathematical Behavior
StatePublished - Dec 2019


  • Covariational reasoning
  • Graphing
  • Operative thought
  • Quantitative reasoning
  • Shape thinking


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