Comparing the Efficacy of Early Arithmetic Instruction Based on a Learning Trajectory and Teaching-to-a-Target

Douglas H. Clements, Julie Sarama, Arthur J. Baroody, Traci S. Kutaka, Pavel Chernyavskiy, Candace Joswick, Menglong Cong, Ellen Joseph

Research output: Contribution to journalArticlepeer-review


Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding a premise of a LT approach—that to be maximally meaningful, engaging, and effective, instruction is best presented 1 LT level beyond a child’s present level of thinking. We evaluated this hypothesis using an empirically validated LT for early arithmetic with 291 kindergartners from four schools in a Mountain West state. Students randomly assigned to the LT condition received one-on-one instruction 1 level above their present level of thinking. Students in the counterfactual condition received 1-on-1 target-level instruction that involved solving story problems three levels above their initial level of thinking (a skip or teach-to-target approach). At posttest, children in the LT condition exhibited significantly greater learning, including target knowledge, than children in the teach-to-target condition, particularly those with low entry knowledge of arithmetic. Child gender and dosage were not significant moderators of the effects.

Original languageEnglish (US)
Pages (from-to)1323-1337
Number of pages15
JournalJournal of Educational Psychology
Issue number7
StatePublished - 2021


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

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology


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