European Journal of Psychology of Education

, Volume 34, Issue 2, pp 439–456 | Cite as

Can young students understand the mathematical concept of equality? A whole-year arithmetic teaching experiment in second grade

  • Jean-Paul FischerEmail author
  • Emmanuel Sander
  • Gérard Sensevy
  • Bruno Vilette
  • Jean-François Richard


Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x) as systematically meaning perform a computation? The present paper describes the implementation of an experimental arithmetic teaching program (called ACE) drawn up in conjunction with teachers and focusing on these issues. We assessed the program's impact via an experiment involving 1140 experimental group students and 1155 control group students, and using a pretest/posttest design. The experimental group students achieved higher composite arithmetic scores, combining all four subdomains (arithmetic writing, mental computation, word-problem solving, and estimation), than control group students. The effect size, computed using individuals' posttest scores adjusted for pretest scores was d = 0.559. The ACE program was effective in all four subdomains tested; however, it was particularly successful in the arithmetic writing subdomain, especially in writing equalities. The program's effect not only held one year later, it was cumulative, as the benefits produced by following the program in both first and second grade were almost double those of following the program in just one grade.


Arithmetic teaching Arithmetic writing Arithmetic comprehension Second grade Equal sign 



We thank all the children and teachers who have taken part in the experimentation. We are also grateful to the experimenters, coders, and administrative officials who have facilitated its performing.

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Copyright information

© Instituto Superior de Psicologia Aplicada, Lisboa, Portugal and Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lorraine Laboratory of Psychology and Neuroscience (2LPN)University of LorraineNancyFrance
  2. 2.Developmental Psychology and Educational Sciences, IDEA LabUniversity of GenevaGenevaSwitzerland
  3. 3.Educational Sciences, CREAD LaboratoryUniversity Bretagne OccidentaleBrestFrance
  4. 4.Developmental Psychology, PSITEC LaboratoryUniversity LilleVilleneuve-d’AscqFrance
  5. 5.Paragraphe LaboratoryUniversity Paris 8Saint-DenisFrance

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