A quadratic growth learning trajectory

Nicole L. Fonger, Amy B. Ellis, Muhammed F. Dogan

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


This paper introduces a quadratic growth learning trajectory, a series of transitions in students’ ways of thinking (WoT) and ways of understanding (WoU) quadratic growth in response to instructional supports emphasizing change in linked quantities. We studied middle grade (ages 12–13) students’ conceptions during a small-scale teaching experiment aimed at fostering an understanding of quadratic growth as phenomenon of constantly-changing rate of change. We elaborate the duality, necessity, repeated reasoning framework, and methods of creating learning trajectories. We report five WoT: Variation, Early Coordinated Change, Explicitly Quantified Coordinated Change, Dependency Relations of Change, and Correspondence. We also articulate instructional supports that engendered transitions across these WoT: teacher moves, norms, and task design features. Our integration of instructional supports and transitions in students’ WoT extend current research on quadratic function. A visual metaphor is leveraged to discuss the role of learning trajectories research in unifying research on teaching and learning.

Original languageEnglish (US)
Article number100795
JournalJournal of Mathematical Behavior
StatePublished - Sep 2020


  • DNR
  • Instructional supports
  • Learning trajectory
  • Quadratic function
  • Quantitative reasoning
  • Representational fluency

ASJC Scopus subject areas

  • Education
  • Applied Mathematics
  • Mathematics (miscellaneous)


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