Does fostering reasoning strategies for relatively difficult basic combinations promote transfer by K-3 students?

Arthur J. Baroody, David J. Purpura, Michael D. Eiland, Erin E. Reid, Veena Paliwal

Research output: Contribution to journalArticlepeer-review


How best to promote fluency with basic sums and differences is still not entirely clear. Some advocate a direct approach-using drill to foster memorization of basic facts by rote. Others recommend an indirect approach that first involves learning reasoning strategies. The purpose of the present study was to evaluate the efficacy of 2 computer-based interventions that embody an indirect approach by highlighting the conceptual bases for 2 relatively difficult reasoning strategies: subtraction as addition (e.g., for 8 5, think: "What plus 5 equals 8?") and use-10 (e.g., "If 10 + 5 15 and 9 is 1 less than 10, then 9 + 5 is 1 less than 15"). After pretest, 85 Grade K-3 students were randomly assigned to subtraction, use-10, or drill conditions. The subtraction and use-10 conditions served as an active control and represented regular classroom instruction for each other; the drill condition controlled for the effect of extra practice and represented the direct approach. Each intervention involved 30-min sessions, twice weekly, for 12 weeks. Using pretest scores, mathematics achievement, and age as covariates, mixed-model analyses of covariance revealed that, at posttest at least 2 weeks later, the subtraction group outperformed both comparison groups on progress toward fluency and fluency rate with unpracticed subtraction items. The use-10 group achieved analogous results with unpracticed add-with-8 or -9 combinations. This transfer suggests that the conceptually based indirect programs were efficacious and more successful than regular classroom instruction or the direct approach in promoting progress toward fluency and fluently itself.

Original languageEnglish (US)
Pages (from-to)576-591
Number of pages16
JournalJournal of Educational Psychology
Issue number4
StatePublished - May 1 2016


  • Basic addition and subtraction facts
  • Conceptual change
  • Elementary math
  • Instructional design
  • Learning theory

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology


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