Stimulus Equivalence and Difficulties in Solving Addition and Subtraction Problems

Authors

  • Marcelo Henrique Oliveira Henklain Universidade Federal de São Carlos
  • João dos Santos Carmo Universidade Federal de São Carlos

Keywords:

Problem solving, Addition and subtraction, Stimulos equivalence, Teaching of algorithms

Abstract

This study investigated whether the formation of equivalence classes among four types of addition problems increases the percentage of correct responses in problems with different forms of presentation, unknown positions and semantic structures. Eight 2nd to 5th grade Elementary School students with low percentages of correct responses in solving addition and subtraction problems participated in this study. After the formation of equivalence classes, an increase of correct responses in all problem types was observed. Then, the effect of teaching algorithms on solving addition and subtraction problems was investigated. No homogeneous pattern of improvement was observed after teaching these algorithms. Participants committed no errors on the generalization test. The results indicate that the adopted procedures contributed to improve the effectiveness of problem solving behavior.

Downloads

Download data is not yet available.

References

Bryant, P. (2011). Children`s understanding and use of inversion in arithmetic. In Comité Interamericano de Educación Matemática (Ed.), Anais da XIII Conferencia Interamericana de Educación Matemática (pp. 1-7), Recife: CIAEM.
Costa, A. L. M., Galvão, O. F., & Ferreira, B. P. (2008). ARIT ”“ um software baseado em equivalência de estímulos dirigido a crianças com histórico de fracasso na aprendizagem de conceitos aritméticos. In: Sociedade Brasileira de Computação (Ed.), Anais do XIX Simpósio Brasileiro de Informática na Educação [CD], (pp. 125-134) Fortaleza: SBC.
Fayol, M. (1992). From number to numbers in use: Solving arithmetic problems. In J. Bideaud, C. Meljac, & J. P. Fischer (Eds.), Pathways to number: Children’s developing numerical abilities (pp. 283-306). New Jersey: Lawrence Erlbaum Associates.
Fossa, J. A., & Sá, P. F. (2008). Uma distinção entre problemas aritméticos e algébricos. Revista Educação em Questão, 33(19), 253-278.
Haydu, V. B., Paranzini, A. C. S., Isquierdo, G. R., Ausec, H. O., Mazzo, I. M. B., Pires, I. T. M., ... & Pimentel, N. S. (2001). Dificuldades e facilidades produzidas pela forma de apresentação de problemas aritméticos com a incógnita em diferentes posições. In M. C. Marquezine, M. A. Almeida & E. D. O. Tanaka (Eds.), Perspectivas multidisciplinares em Educação Especial II (pp. 593-601). Londrina, PR: Eduel.
Haydu, V. B., Costa, L. P., & Pullin, E. M. M. P. (2006). Resolução de problemas aritméticos: efeito de relações de equivalência entre três diferentes formas de apresentação dos problemas. Psicologia: Reflexão & Crítica, 19, 44-52.
Hiebert, J. (1982). The position of the unknown set and children’s solutions of verbal arithmetic. Journal for Research in Mathematics Education, 13, 341-349.
Iégas, A. L. F. (2003). Software para a resolução de problemas aritméticos: o modelo da balança. (Dissertação de Mestrado não publicada). Universidade Estadual de Londrina, Paraná.
Magina, S. P. M., Santana, E. R. S., Cazorla, I. M., & Campos, T. M. M. (2010). As estratégias de resolução de problemas das estruturas aditivas nas quatro primeiras séries do Ensino Fundamental. Zetetiké, 18(34), 15-50.
Marcicano, D. C., Carmo, J. S., & Prado, P. S. T. (2011). Software ProgMTS: possibilidades de delineamento e condução de programas de ensino em Análise Experimental do Comportamento [Computer software ]. Anais da 41ª Reunião Anual da Sociedade Brasileira de Psicologia: formação e produção do conhecimento em psicologia, Belém.
Neef, N. A., Nelles, D. E., Iwata, B. A., & Page, T. J. (2003). Analysis of precurrent skills in solving mathematics story problems. Journal of Applied Behavior Analysis, 36, 21-33.
Nesher, P., Greeno, J. G., & Riley, M. S. (1982). The development of semantic categories for addition and subtraction. Educational Studies in Mathematics, 13(4), 373-394.
Nunes, T., & Bryant, P. (1996). Giving meaning to addition and subtraction. In T. Nunes, & P. Bryant (Eds.), Children doing mathematics (pp. 114-141). Oxford: Blackwell.
Resnick, L. B., & Rosenthal, D. J. A. (1974). Children’s solution processes in arithmetic word problems. Journal of Educational Psychology, 66, 817-825.
Sidman, M., & Tailby, W. (1982). Conditional discrimination vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37(1), 5-22.
Sophian, C. (1996). The sum of the parts. In C. Sophian (Ed.), Children’s numbers (pp. 73-88). Colorado: Westview Press.
Verschaffel, L., & De Corte, E. (1997). Word problems: A vehicle for promoting authentic mathematical understanding and problem solving in the primary school? In T. Nunes, & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 69-97). Hove, England: Psychology Press.

Published

2013-10-16

How to Cite

Henklain, M. H. O., & Carmo, J. dos S. (2013). Stimulus Equivalence and Difficulties in Solving Addition and Subtraction Problems. Psicologia: Teoria E Pesquisa, 29(3), 341–350. Retrieved from https://periodicos.unb.br/index.php/revistaptp/article/view/17619

Most read articles by the same author(s)