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Identifying and solving problems: Making sense of basic mathematics through storytelling in the preschool class

  • Niklas Pramling
  • Ingrid Pramling Samuelsson
Articles

Summary

In a general sense, the research interest of this article concerns the preschool class, which is an intermediate form of schooling for six-year-olds in Sweden, between preschool and school and their two traditions of ‘play’ and ‘learning’, respectively. In a more specific sense, the issue of learning one aspect of basic mathematics in this practice is focused on, as a case study. A video-observation of a teacher and children verbally interacting is analysed. The case studied is the use of a story as presenting a mathematical task, where the children are being asked to draw their solutions in the form of an illustration. The empirical question is: What do the children make an issue of, that is, what is the problem as far as the learners are concerned? It is found that (a) the difficulty for the children does not primarily seem to be mathematical but one of co-ordinating one’s explanation to a visual illustration (i.e., a matter of representation), and that (b) making concrete the abstract mathematical principle of division may make it difficult for the learners to distinguish between the two senses of the term (i.e., division as a mathematical operation, and as a practical activity, respectively). The use of a story and the instruction to draw the solution to the task appear to have introduced additional difficulties for children in solving the problem. The implications of the findings for educational practice are discussed.

Key words

children mathematics preschool class representation story 

Résumé

Dans un sens général, l’intérêt de recherche de cet article concerne la classe préscolaire, forme intermédiaire de scolarisation des enfants de six ans en Suède, entre le niveau préscolaire et l’école et leurs deux traditions respectives de «jeu» et «d’apprentissage». Dans un sens plus spécifique, il s’agit d’une étude de cas sur l’apprentissage d’un aspect mathématique fondamental dans cette pratique. Une observation sur vidéo d’un enseignant et d’enfants en interaction verbale est analysée. Le cas étudié est celui de l’utilisation d’une histoire pour présenter une tâche mathématique qui demande aux enfants de dessiner leurs solutions sous forme d’illustration. La question empirique est: en quoi est-ce un problème pour les enfants, c’est-à-dire quel est le problème du point de vue des apprenants? Les observations indiquent que (a) pour les enfants, la difficulté ne semble pas d’abord mathématique mais plutôt celle de coordonner ses propres explications à une illustration visuelle (soit une question de représentation) et que (b) concrétiser le principe mathématique abstrait de la division peut rendre difficile pour les élèves la distinction entre les deux sens du terme (c’est-à-dire la division comme opération mathématique et comme activité pratique.) L’emploi d’une histoire et la consigne de dessiner la solution à la tâche semblent avoir ajouté pour les enfants des difficultés à résoudre le problème. La discussion porte sur les implications des résultats pour la pratique pédagogique.

Resumen

En un sentido general el interés investigativo de este articulo, dice relación con las clases de preescolares, que son una forma intermedia de escolarización para niños y niñas de 6 años, en Suecia. Entre el preescolar y la escuela, y sus dos tradiciones, “jugar” y “aprender” respectivamente, En un sentido mas específico, el artículo se focaliza en el aprendizaje de un elemento básico de las matemáticas, como un estudio de caso. Una observación videada de las interacciones verbales entre un profesor y sus niños y niñas es analizada. El caso estudiado corresponde al uso de una historia para presentar una tarea matemática, en donde los niños y niñas son interrogados para dibujar sus soluciones en formas de ilustraciones. La pregunta empírica es ¿Cuál es el problema que les precupa a los niños y niñas? La evidencia encontrada muestra que (a) para los niños y niñas la dificultad no parece ser el problema matemático, sino coordinar sus respuestas en forma de una ilustración. (es decir un asunto de representación) y (b) que hacer concreto el principio matemático de la división, puede hacer dificil para los aprendientes distinguir entre los dos sentidos del término (esto es, dividir como una operación matemática y como una acción práctica respectivamente). El uso de la historia y el solicitar a los niños y niñas la ilustración de la solución a la tarea parece haber generado mas dificultades para resolver el problema. Las implicancias de los hallazgos para la práctica educacional son discutidas.

References

  1. Ahlberg, A. (1995).Barn och matematik [Children and mathematics]. Lund, Sweden: Studentlitteratur.Google Scholar
  2. Bruner, J. S. (1986).Actual minds, possible worlds. Cambridge, MA: Harvard University Press.Google Scholar
  3. Bruner, J. S. (1990).Acts of meaning. Cambridge, MA: Harvard University Press.Google Scholar
  4. Burton, L. (2003). Children’s mathematical narratives as learning stories. In B. van Oers (Ed.),Narratives of childhood: Theoretical and practical explorations for the innovation of early childhood education (pp. 51–67). Amsterdam, The Netherlands: VU University Press.Google Scholar
  5. Carruthers, E., & Worthington, M. (2005). Making sense of mathematical graphics: The development of understanding abstract symbolism.European Earth Childhood Education Research Journal, 13(1), 57–79.CrossRefGoogle Scholar
  6. Doverborg, E., & Pramling Samuelsson, I. (2004). Varför skall barn inte märka att de lär sig matematik? [Why should children not notice that they learn mathematics?]Nämnaren, 31(3), 2–5.Google Scholar
  7. Fijma, N. (2003). Mathematics learning in a play-based curriculum: How to deal with heterogeneity? In B. van Oers (Ed.),Narratives of childhood: Theoretical and practical explorations for the innovation of early childhood education (pp. 146–162). Amsterdam, The Netherlands: VU University Press.Google Scholar
  8. Johansson, E., & Pramling Samuelsson, I. (2006).Lek och läroplan: Möten mellan barn och lärare i förskola och skola [Play and curriculum: Encounters between children and teachers in preschool and school] (Göteborg Studies in Educational Sciences, 249). Göteborg, Sweden: Acta Universitatis Gothoburgensis.Google Scholar
  9. Johansson, E., & Pramling Samuelsson, I. (Eds.). (2003). Barns perspektiv och barnperspektiv [Children’s perspective and child perspective] [Special issue],Pedagogisk Forskning i Sverige,8(1–2).Google Scholar
  10. Kress, G., & Van Leeuwen, T. (2001).Multimodal discourse: The modes and media of contemporary communication London: Arnold.Google Scholar
  11. Merriam, S. B. (1998).Qualitative research and case study applications in education. San Francisco, CA: Jossey-Bass.Google Scholar
  12. Ministry of Education and Science. (1994/98).Curriculum for the compulsory school system, the preschool classes, and the leisure-time centre. Stockholm, Sweden: Fritzes.Google Scholar
  13. van Oers, B. (1996). Are you sure? Stimulating mathematical thinking during young children’s play.European Early Childhood Education Research Journal, 4(1), 71–87.CrossRefGoogle Scholar
  14. Peters, S. (1998). Playing games and learning mathematics: The results of two intervention studies.International Journal of Early Years Education, 6(1), 49–58.CrossRefGoogle Scholar
  15. Pramling, I. (1983).The child’s conception of learning (Göteborg Studies in Educational Sciences, 46), Göteborg, Sweden: Acta Universitatis Gothoburgensis.Google Scholar
  16. Pramling Samuelsson, I., & Asplund Carlsson, M. (2003).Det lekande lärande barnet — i en utrecklingspedagogisk teori [The playing learning child: In a developmental pedagogical theory]. Stockholm: Liber.Google Scholar
  17. Reddy, M. J. (1993). The conduit metaphor: A case of frame conflict in our language about language. In A. Ortony (Ed.),Metaphor and thought (2nd ed., pp. 164–201). New York: Cambridge University Press.Google Scholar
  18. Säljö, R. (1994). Qualitative research on learning and instruction in Scandinavia.Qualitative Studies in Education, 7(3), 257–267.CrossRefGoogle Scholar
  19. Säljö, R., & Wyndhamn, J. (1993). Solving everyday problems in the formal setting: An empirical study of the school as context for thought. In S. Chaiklin & J. Lave (Eds.),Understanding practice: Perspectives on activity and context (pp. 327–342). New York: Cambridge University Press.Google Scholar
  20. Schratz, M., & Mehan, H. (1993). Gulliver travels into a math class: In search of alternative discourse in teaching and learning.International Journal of Educational Research, 19(3), 247–264.Google Scholar
  21. Schwartz, S. L. (2005).Teaching young children mathematics. Westport, CT: Praeger.Google Scholar
  22. SOU (2004:97).Att lyfta matematiken: intresse, kunskap, kompetens. Mathematikdelegationens betänkande [Lifting mathematics: interest, knowledge, competence. The report of the mathematics delegation]. Stockholm, Sweden: Fritzes.Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Department of EducationUniversity of GotenburgGöteborgSweden

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