Efficacy of a learning trajectory approach compared to a teach-to-target approach for addition and subtraction

Douglas H. Clements, Julie Sarama, Arthur J. Baroody, Candace Joswick

Research output: Contribution to journalArticlepeer-review


Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a “LT approach”—that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child’s present level of thinking. The present report serves to address the question: Is it necessary to teach each contiguous level of a LT or can instruction be similarly or more effective when skipping levels, provided the necessary exemplars are made? In a multimethod research study that included individual teaching experiments embedded inside of a quasi-experimental research design, one group of 13 kindergartners received instruction based on an empirically-validated LT for addition and subtraction (the “LT” treatment). The counterfactual, “skip” treatment (n = 12), received instruction focused mainly on levels at least two levels above their present level for the same amount of time as the LT treatment. More children in the LT treatment exhibited greater addition and subtraction learning during sessions and from pretest to posttest than children in the skip treatment. Implications for future study are discussed.

Original languageEnglish (US)
Pages (from-to)637-648
Number of pages12
JournalZDM - Mathematics Education
Issue number4
StatePublished - Aug 1 2020


  • Achievement
  • Curriculum
  • Early childhood
  • Instructional design/development
  • Learning environments
  • Learning trajectories
  • Mathematics education

ASJC Scopus subject areas

  • General Mathematics
  • Education


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