Ir al contenido

Documat

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

  • Autores: Jean-Paul Fischer, Emmanuel Sander, Gérard Sensevy, Bruno Vilette, Jean François Richard
  • Localización: European journal of psychology of education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 34, Nº 2, 2019, págs. 439-456
  • Idioma: inglés
  • DOI: 10.1007/s10212-018-0384-y
  • Texto completo no disponible (Saber más ...)
  • Resumen

    • 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.

  • Referencias bibliográficas
    • Alibali, M. W., Phillips, K. M. O., & Fischer, A. D. (2009). Learning new problem-solving strategies leads to changes in problem representation....
    • Bailey, D. H., Nguyen, T., Jenkin, J. M., Domina, T., Clements, D. H., & Sarama, J. S. (2016). Fadeout in an early mathematics intervention:...
    • Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children’s understanding and reasoning...
    • Baroody, A. J. (1999). Children’s relational knowledge of addition and subtraction. Cognition and Instruction, 17(2), 137–175. https://doi.org/10.1207/S1532690XCI170201.
    • Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the “equals” sign. The Elementary...
    • Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software,...
    • Brissiaud, R. (1994). Teaching and development: solving “missing addend” problems using subtraction. European Journal of Psychology of Education,...
    • Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to...
    • Byrd-Hornburg, C., Rieber, M. L., & McNeil, N. M. (2017). An integrative data analysis of gender differences in children’s understanding...
    • 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)....
    • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York: Taylor & Francis.
    • Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344–377....
    • DeCaro, M. S. (2016). Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics. Memory & Cognition,...
    • Dehaene, S. (2011). The number sense (2nd ed.). New York: Oxford University Press.
    • Dussuc, M. P., Charnay, R., & Madier, D. (2009). Cap maths cycle 2, CE1: Nouveaux programmes. Paris: Hatier.
    • Fischbein, E. (1989). Tacit models and mathematical reasoning. For the Learning of Mathematics, 9(2), 9–14.
    • Fischer, J. P., & Tazouti, Y. (2012). Unraveling the mystery of mirror writing in typically developing children. Journal of Educational...
    • Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: current use, calculations, and interpretation. Journal of...
    • Fuchs, L. S., Fuchs, D., Hamlet, C. L., Powell, S. R., Capizzi, A. M., & Seethaler, P. M. (2006). The effects of computer-assisted instruction...
    • 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....
    • Ginsburg, H. (1977). Children’s arithmetic. New York: Van Nostrand.
    • Glass, G. V., McGaw, B., & Smith, M. L. (1981). Meta-analysis in social research. Beverly Hills: Sage.
    • Hattikudur, S., & Alibali, M. W. (2010). Learning about the equal sign: does comparing with inequality symbols help? Journal of Experimental...
    • Jara-Ettinger, J., Piantadosi, S., Spelke, E. S., Levy, R., & Gibson, E. (2017). Mastery of the logic of natural numbers is not the result...
    • Joffredo-Le Brun, S., Morellato, M., Sensevy, G., & Quilio, S. (2018). Cooperative engineering as a joint action. European Educational...
    • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
    • Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving...
    • Kreft, I., & De Leeuw, J. (1998). Introducing multilevel modeling. London: Sage Publications.
    • McNeil, N. M. (2007). U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology,...
    • McNeil, N. M., Rittle-Johnson, B., Hattikudur, S., & Petersen, L. A. (2010). Continuity in representation between children and adults:...
    • McNeil, N. M., Fyfe, E. R., Petersen, L. A., Dunwiddie, A. E., & Brletic-Shipley, H. (2011). Benefits of practicing 4 = 2 + 2:...
    • McNeil, N. M., Fyfe, E. R., & Dunwiddie, A. E. (2015). Arithmetic practice can be modified to promote understanding of mathematical equivalence....
    • Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Core Team (2017). nlme: Linear and Nonlinear Mixed Effects Models (R package version...
    • Powell, S. R. (2012). Equations and the equal sign in elementary mathematics textbooks. The Elementary School Journal, 112(4), 627–648.
    • R Core Team. (2015). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
    • Verschaffel, L., Bryant, P., & Torbeyns, J. (2012). Introduction. Educational Studies in Mathematics, 79(3), 327–334. https://doi.org/10.1007/s10649-012-9381-2.
    • Zieffler, A. S., Harring, J. R., & Long, J. D. (2011). Comparing groups: randomization and bootstrap methods using R. Hoboken: Wiley.
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno