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Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 10 No. 3 (2007): Noviembre

LEVEL OF ABSTRACTION OF ARITHMETIC PROBLEMS IN URBAN AND RURAL STUDENTS

Submitted
July 10, 2024
Published
2007-08-13

Abstract

This study analyzes the incidence of the level of abstraction in the resolution of problems of addition and subtraction in urban and rural students. The sample was made up of 192 students from first to fourth grade of primary education; 50% came from a Mexican rural environment and the remaining 50% from a Mexican urban environment. Empirical tasks consisted in resolving arithmetical problems with objects, drawings, algorithms and verbally. The results show that the presence of objects or drawings improves performance in first and second grade students, and lowers performance in third grade students. It should also be pointed out that rural students obtained their best results in verbal problems. Modeling strategies are used in similar ways in all the courses in the rural environment, while in an urban setting they are primarily used in first and second grades. Rural students make use of counting strategies, and urban students lean more toward using numerical facts. Finally, some educative applications will be suggested from the results of the study.

References

  1. Bagni, G. (2000). "Simple" rules and general rules in some high school students' mistakes. Journal für Mathematik Didaktik 21(2), 124-138.
  2. Abreu, G. de (1995). Understanding how children experience the relationship between home and school mathematics. Mind, Culture and Activity 2(2), 119-142.
  3. Abreu, G. de (1998). The mathematics learning in sociocultural contexts: the mediating role of social valorisation. Learning and Instruction 8(6), 567-572.
  4. Alanís, J., Cantoral, R., Cordero, F., Farfán, R., Garza, A. y Rodríguez, R. (2000). Desarrollo del pensamiento matemático. México: Trillas.
  5. Baroody, A. J. (1987). The development of counting strategy for single-digit addition. Journal for Research in Mathematics Education 18(2), 141-157.
  6. Bermejo, V. (1990). El niño y la aritmética. Madrid, España: Paidós.
  7. Bermejo, V. (2004). Como enseñar matemáticas para aprender mejor. Madrid, España: CCS.
  8. Bermejo, V. y Rodriguez, P. (1987). Estructura semántica y estrategias infantiles en la solución de problemas verbales de adición. Infancia y Aprendizaje, 39-40, 71-81.
  9. Bermejo, V. y Rodríguez, P. (1993). La operación de sumar. competencia conceptual vs. competencia de procedimiento. En J. A. Beltrán, L. Pérez, E. González, R. González y D. Vence. (Eds.), Líneas actuales en la intervención psicopedagógica I: Aprendizaje y contenidos del currículum (pp. 711-726). Madrid, España: Universidad Complutense.
  10. Bermejo, V., Lago, M . O. y Rodríguez, P. (1998). Aprendizaje de la adición y sustracción. Secuenciación de los problemas verbales según su dificultad. Revista de Psicología General y Aplicada 51(3-4), 533-552.
  11. Bermejo, V., Lago, M. O., Rodriguez, P., Dopico, C. y Lozano, J. M. (2002) PEI. Un programa de intervención para la mejora del rendimiento matemático. Madrid, España: Editorial Complutense.
  12. Brown, J. S., Collins, A. y Duguid, P. (1989). Situated cognition and the culture of learning Educational Researcher 18, 32-42.
  13. Carpenter, T. P. (1985). Learning to add and subtract: An exercise in problem solving. In E. A Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 17-40). Hillsdale, NJ: Erlbaum.
  14. Carpenter, T. P. (1986). Conceptual knowledge as a foundation for procedural knowledge: implications from research on the initial learning of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 113-132). Hillsdale, NJ: Erlbaum.
  15. Carpenter, T. P. y Moser, J. M. (1982). The development of addition and subtraction problem- solving skills. En T. P. Carpenter, J. M. Moser y T. A. Romberg (Eds.), Addition and subtraction: a cognitive perspective (pp. 9-24). Hillsdale, NJ: Erlbaum.
  16. Carpenter, T. P., Hiebert, J. y Moser, J. M. (1981). Problem structure and first-grade children's initial solution processes for simple addition and subtraction problems. Journal for Research in Mathematics Education 12, 27-29.
  17. Carraher, T. N., Carraher, D. W. y Schliemann, A. D. (1985). Mathematics in the streets and in schools. British Journal of Development Psychology 3, 21-29.
  18. Carraher, T. N., Carraher, D. W. y Schliemann, A. D. (1987). Written and oral mathematics. Journal for Research in Mathematics Education 18(2), 83-97.
  19. De Corte, E. y Verschaffel, L. (1987). The effect of semantic structure on first grader's strategies for solving addition and subtraction word problems. Journal for Research in Mathematics Education 18(5), 363-381
  20. Fuson, K. C. y Willis, G. B. (1989). Second grader's use of shematic drawings in solving addition and subtracion word problems. Journal of Educational Psychology 81, 514-520.
  21. Kamii, C., Kirkland, L. y Lewis, B. A. (2001). Representation and abstraction in young children's numerical reasoning. In NCTM (Ed.), The roles of representation in school mathematics (pp.24-34). Reston, VA: NCTM.
  22. Kamii, C., Lewis, B. A. y Kirkland, L. D. (2001).Manipulatives: when are they useful? Journal of Mathematical Behavior 20(1), 21-31.
  23. Kato, Y., Kamii, C., Ozaki, K. y Nagahiro, M. (2002). Young children's representations of groups of objects: The relationship between abstraction and representation. Journal for Research in Mathematics Education 33(1), 30-45
  24. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  25. Nunes, T. N., Schliemann, A. D. y Carraher, D. W. (1993). Street mathematics and school mathematics. New Cork, USA: Cambridge University Press.
  26. OCDE (2002). Conocimientos y aptitudes para la vida. Resultados de Pisa 2000. México: Santillana Aula XXI
  27. OCDE (2005). Informe Pisa 2003. Aprender para el mundo del mañana, Madrid, España: OCDE- Santillana.
  28. Putnam, R. T., deBettencourt, L. U. y Leinhardt, G. (1990). Understanding of derived-fact strategies in addition and subtraction. Cognition and Instruction 7, 245-285.
  29. Resnick, L. (1987). Learning in school and out. Educational Researcher, 16, 13-20.
  30. Rico, L. (1997). Consideraciones sobre el currículo de matemáticas para educación secundaria. En L. Rico (Coord.), La educación matemática en la enseñanza secundaria (pp. 15-38). Barcelona, España: Horsori.
  31. Riley, M. S., Greeno, J. G. y Heller, J. 1. (1983). Development of children's problem solving ability in arithmetic, En H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153-196 ). New York, USA: Academic Press.
  32. Rogoff, B. (1990). Apprenticeship in thinking. Cognitive development in social context. New York, USA: Oxford University Press.
  33. Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale, NJ: Erlbaum.
  34. Saxe, G. B. (2002), Children's developing mathematics in collective practices. A framework for analysis. Journal of the Learning Science 11(2-3), 275-300.
  35. Saxe, G. B. y Gearhart, M. (1990). The development of topological concepts in unschooled straw weavers. British Journal of Developmental Psychology 8, 251-258.
  36. Schliemann, A. D. (1995). Some concerns about bringing everyday mathematics to mathematics education. En L. Meira y D. Carraher (Eds.), Proceedings of the XIX International onference for the Psychology of Mathematics Education (pp. 45-60). Recife, Brazil.
  37. Schliemann, A. D. y Carraher, D. W. (2002). The evolution of mathematical reasoning: Everyday versus idealized understandings. Development Review 22(2), 242-266.
  38. Willis, G. B. y Fuson, K. C. (1988). Teaching children to use schematic drawings drawings to solve addition and subtraction word problems. Journal of Educational Psychology 80(2), 192-201.
  39. Wolters, M. A. D. (1983). The part-whole schema and arithmetical problems. Educational Studies in Mathematics 14(2), 127-138.

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