Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 21 No. 2 (2018): July

THE STRATEGIES OF CHILDREN IN THE RESOLUTION OF MULTIPLYING SITUATIONS: RECOGNITION AND USE OF UNITS

DOI
https://doi.org/10.12802/relime.18.2122
Submitted
November 4, 2022
Published
2018-06-26

Abstract

An analysis of the strategies used by children in the first and second grades of basic primary education (7-8 years old) from two educational institutions in Bogotá, Colombia, to solve multiplicative situations before receiving instruction on multiplication and division is presented. The analysis focused on identifying whether children recognize different units, simple or compound, and the use they make of these, in particular whether they form units to address given situations and whether they reinterpret these situations with them. This research was developed using the task-based interview method, from which it was possible to find evidence on the strategies used by children, in particular two emerging strategies that have not been reported in the international literature: equivalence between different types of unit and coordinated use of compound units.

References

  1. Bosch, A., Castro, E. y Segovia, I. (2007). El pensamiento multiplicativo en los primeros niveles: una investigación en curso. pna, 1(4), 170-190.
  2. Bosh, M. (2012). Apuntes teóricos sobre el pensamiento matemático y multiplicativo en los primeros niveles. Edma 0-6: Educación Matemática en la Infancia, 1 (1), 15-37.
  3. Caballero, S. (2005). Un estudio transversal y longitudinal sobre los conocimientos informales de las operaciones aritméticas básicas en niños de educación infantil (Tesis doctoral no publicada). Universidad Complutense de Madrid, Madrid, España.
  4. Carpenter, T., Ansell, E., Franke, M., Fennema, E. & Weisbeck, L. (1993). Models of Problem Solving: A Study of Kindergarten Children’s Problem-Solving Processes. Journal for Research in Mathematics Education, 24(5), 427-440.
  5. Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (2015). Children’s Mathematics Cognitively Guided Instruction. Portsmouth, uk: Heinemann.
  6. Castro, C., y Hernández, E. (2014). Problemas verbales de descomposición multiplicativa de cantidades en educación infantil. PNA, 8 (3), 99-114. Euclides (300 A.C./1991). Elementos. Madrid, España: Gredos.
  7. Goldin, G. (1998). Observing Mathematical Problem Solving Through Task–Based Interviews. In A. Treppo (Ed.), Qualitative Research Methods in Mathematics Education. Monograph 9, Journal for Research in Mathematics Education (pp. 40-62). Reston, va: National Council of Teachers of Mathematics.
  8. Lamon, S. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming. In G. Harel & J. Confrey (Eds.). The Development Multiplicative Reasoning in Learning of Mathematics (pp. 89-121). New York: State University of New York Press.
  9. Lamon, S. (1996). The development of unitizing: It’s role in children’s partitioning strategies. Journal for Research in Mathematics Education, 27 (2), 70-93. McCloskey, A. & Norton, A. (2009). Using Steffe’s Advanced Fraction Schemes. Mathematics Teaching in the Middle School, 15 (1), 44-50.
  10. Mulligan, J. & Watson, J. (1998). A Developmental Multimodal Model for Multiplication and Division. Mathematics Education Research Journal, 10 (2), 61-86. Norton, A. & McCloskey, A. (2008). Modeling students’ mathematics using steffe's fraction schemes. Teaching Children Mathematics, 15 (1), 48-54.
  11. Olive, J. (2001). Children’s Number Sequences: An Explanation of Steffe’s Cosntructs and an Extrapolation to Rational Numbers of Arithmetic. The Mathematics Educator, 11 (1), 4-9. Rojas, P., Romero, J., Mora, L., Bonilla, M., Rodríguez, J. y Castillo, E. (2011). La multiplicación como cambio de unidad: estrategias para promover su aprendizaje. Bogotá, Colombia: Universidad Distrital Francisco José de Caldas.
  12. Steffe, L. (1994). Children’s multiplying schemes In G. Harel, & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3-40). Albany, ny: suny Press.
  13. Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didáctique des Mathématiques, 10 (2-3), 133-170.
  14. Vergnaud, G. (1991). El niño, las matemáticas y la realidad. Ciudad de México, México: Trillas. Wright, J., Mulligan, J. & Gould, P. (2000). Extending the learning framework to multiplication and division. In J. Wright, J. Narlland & A. Staffod (Eds.), Assessment for teaching and intervention (pp. 154-176). Londres, Inglaterra: pcp.

Downloads

Download data is not yet available.

Similar Articles

<< < 

You may also start an advanced similarity search for this article.