Growth in children's understanding of generalizing and representing mathematical structure and relationships

Blanton M., İŞLER BAYKAL I., Stroud R., Stephens A., Knuth E., Gardiner A. M.

EDUCATIONAL STUDIES IN MATHEMATICS, vol.102, no.2, pp.193-219, 2019 (SSCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1007/s10649-019-09894-7
  • Journal Indexes: Social Sciences Citation Index (SSCI), Scopus
  • Page Numbers: pp.193-219
  • Keywords: Algebraic thinking, Early algebra, Instructional intervention, Quantitative methods, Elementary grades, EARLY ALGEBRA INTERVENTION, EQUAL SIGN, LEARNING PROGRESSION, THINKING, INSTRUCTION, CURRICULUM, IMPACT, MATTER
  • Middle East Technical University Affiliated: Yes


We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3-5. Analyses showed that, while there were no significant differences between experimental and control students on a grade 3 pre-assessment measuring students' capacity for generalizing and representing generalizations, experimental students significantly outperformed control students on post-assessments at each of grades 3-5. Moreover, experimental students were able to more flexibly interpret variable in different roles and were better able to use variable notation in meaningful ways to represent arithmetic properties, expressions and equations, and functional relationships. This study provides important evidence that young children can learn to think algebraically in powerful ways and suggests that the earlier introduction of algebraic concepts and practices is beneficial to students.