Can young students understand the mathematical concept of equality? A whole-year arithmetic teaching experiment in second grade
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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.
KeywordsArithmetic 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.
- Chesney, D. L., McNeil, N. M., Matthews, P. G., Byrd, C. E., Petersen, L. A., Wheeler, M. C., Fyfe, E. R., & Dunwiddie, A. E. (2014). Organization matters: mental organization of addition knowledge relates to understanding math equivalence in symbolic form. Cognitive Development, 30, 30–46. https://doi.org/10.1016/j.cogdev.2014.01.001.CrossRefGoogle Scholar
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York: Taylor & Francis.Google Scholar
- Dehaene, S. (2011). The number sense (2nd ed.). New York: Oxford University Press.Google Scholar
- Dussuc, M. P., Charnay, R., & Madier, D. (2009). Cap maths cycle 2, CE1: Nouveaux programmes. Paris: Hatier.Google Scholar
- Fischbein, E. (1989). Tacit models and mathematical reasoning. For the Learning of Mathematics, 9(2), 9–14.Google Scholar
- Fischer, J. P., & Tazouti, Y. (2012). Unraveling the mystery of mirror writing in typically developing children. Journal of Educational Psychology, 104(1), 193–205. https://doi.org/10.1037/a0025735.
- Fuchs, L. S., Fuchs, D., Hamlet, C. L., Powell, S. R., Capizzi, A. M., & Seethaler, P. M. (2006). The effects of computer-assisted instruction on number combination skill in at-risk first graders. Journal of Learning Disabilities, 39(5), 467–475. https://doi.org/10.1177/00222194060390050701.CrossRefGoogle Scholar
- Fuchs, L. S., Powell, S. R., Cirino, P. T., Schumacher, R. F., Marrin, S., Hamlett, C. L., Fuchs, D., Compton, D. L., & Changas, P. C. (2014). Does calculation or word-problem instruction provide a stronger route to prealgebraic knowledge? Journal of Educational Psychology, 106(4), 990–1006. https://doi.org/10.1037/a0036793.CrossRefGoogle Scholar
- Ginsburg, H. (1977). Children’s arithmetic. New York: Van Nostrand.Google Scholar
- Glass, G. V., McGaw, B., & Smith, M. L. (1981). Meta-analysis in social research. Beverly Hills: Sage.Google Scholar
- Joffredo-Le Brun, S., Morellato, M., Sensevy, G., & Quilio, S. (2018). Cooperative engineering as a joint action. European Educational Research Journal, 17(1), 187–208. https://doi.org/10.1177/1474904117690006.
- Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37, 297–312.Google Scholar
- McNeil, N. M., Rittle-Johnson, B., Hattikudur, S., & Petersen, L. A. (2010). Continuity in representation between children and adults: arithmetic knowledge hinders undergraduates’ algebraic problem solving. Journal of Cognition and Development, 11(4), 437–457. https://doi.org/10.1080/15248372.2010.516421.CrossRefGoogle Scholar
- McNeil, N. M., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Brletic-Shipley, H. (2011). Benefits of practicing 4 = 2 + 2: nontraditional problem formats facilitate children’s understanding of mathematical equivalence. Child Development, 82(5), 1620–1633. https://doi.org/10.1111/j.1467-8624.2011.01622.x.CrossRefGoogle Scholar
- Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Core Team (2017). nlme: Linear and Nonlinear Mixed Effects Models (R package version 3.1–131). Retrieved from https://cran.r-project.org/web/packages/nlme/nlme.pdf.
- R Core Team. (2015). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.Google Scholar