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Abstract

This work aims to identify the criteria to design activities based on problem-solving tasks that emerge when future early childhood education teachers jointly plan their activities and reflect on them. The participants were 76 students from the Didactics of mathematics subject that was carried out in the 2nd year of the Early Childhood Education Degree of a Catalan public university. This is qualitative research in which the phases of the thematic analysis have been adapted: familiarizing with the data; systematically applying the categories to identify the student criteria emerged; triangulating the analysis with experts; reviewing and discussing the results. The Didactic Suitability Criteria (DSC), from the Ontosemiotic approach (OSA) framework to design tasks and their indicators, were used to categorise and analyse the tasks performed by future teachers. As a result, it was identified that when the future teachers adopt consensually design their activities, they are implicitly based on the Didactic Suitability Criteria (DSC). Still, not all their indicators emerge since their reflection is spontaneous and is not guided by an explicit guideline that serves them to show their didactic analysis in detail. The study concludes that it would be convenient to offer future teachers a tool, such as DSC, to have explicit criteria to guide the designs of their mathematical tasks. In this sense, a future line of research opens, much needed, to adapt the DSC to the singularities of this educational stage.

Keywords

Didactic Suitability Criteria Early Childhood Education Ontosemiotic Approach Problem-solving Task Design Teacher Training

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Sala-Sebastià, G., Breda, A., & Farsani, D. (2022). Future early childhood teachers designing problem-solving activities. Journal on Mathematics Education, 13(2), 239–256. https://doi.org/10.22342/jme.v13i2.pp239-256
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References

  1. Alsina, A. (2016). Diseño, gestión y evaluación de actividades matemáticas competenciales en el aula. Épsilon, 33(92), 7-29. https://thales.cica.es/epsilon/sites/thales.cica.es.epsilon/files/epsilon92_0.pdf
  2. Arcavi, A., & Friedlander, A. (2007). Curriculum developers and problem solving: the case of Israeli elementary school projects. ZDM Ma¬thematics Education, 39(5-6), 355-364. https://doi.org/10.1007/s11858-007-0050-3
  3. Ball, D.L, Hoover Thames M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  4. Baroody, A. J., & Coslick, R. T. (1998). Fostering Children's Mathematical Power: An Investigative Approach to K-8 Mathematics Instruction. Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410602084
  5. Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories—an approach for exploiting the diversity of theoretical approaches. In Theories of mathematics education (pp. 483-506). Springer. https://doi.org/10.1007/978-3-642-00742-2_46
  6. Blömeke, S, Hsieh, F.J., Kaiser, G., & Schmidt, W.H. (2014). International perspectives on teacher knowledge, beliefs and opportunities to learn. TEDS-M Results. Springer. https://doi.org/10.1007/978-94-007-6437-8
  7. Borasi, R. (1986). On the nature of problems. Educa¬tional Studies in Mathematics, 17(2), 125-141. https://doi.org/10.1007/BF00311517
  8. Braun, V., & Clarke, V. (2012). Thematic analysis. In H. Cooper, P. M. Camic, D. L. Long, A. T. Panter, D. Rindskopf, & K. J. Sher (Eds.), APA handbook of research methods in psychology, Vol. 2. Research designs: Quantitative, qualitative, neuropsychological, and biological (pp. 57–71). American Psychological Association. https://doi.org/10.1037/13620-004
  9. Breda, A. (2020). Características del análisis didáctico realizado por profesores para justificar la mejora en la enseñanza de las matemáticas. Bolema, 34(66), 69-88. https://doi.org/10.1590/1980-4415v34n66a04
  10. Breda, A., Font, V., & Pino-Fan, L. R. (2018). Criterios valorativos y normativos en la Didáctica de las Matemáticas: el caso del constructo idoneidad didáctica. Bolema, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13
  11. Breda, A., Pino-Fan, L. R., & Font, V. (2017). Meta Didactic-Mathematical Knowledge of Teachers: Criteria for The Reflection and Assessment on Teaching Practice. EURASIA Journal of Mathematics, Science and Technology Education, 13, 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a
  12. Breda, A., Pino-Fan, L. R., Font, V., & do Rosário Lima, V. M. (2017). Didactic assessment over a final work of a master for mathematics teachers in service. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education, p. 3272-3279. DCU Institute of Education and ERME. https://hal.archives-ouvertes.fr/hal-01949157/document
  13. Calle, E. C., Breda, A., & Font, V. (2021). Reflection on the complexity of mathematical items in initial teacher education. Journal of Higher Education Theory and Practice, 21, 197-214. https://doi.org/10.33423/jhetp.v21i13.4801
  14. Carpenter, T. P., Ansell, E., Franke, M. L., 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, 428-441. https://doi.org/10.2307/749152
  15. De Castro, C., & Escorial, B. (2007). Resolución de problemas aritméticos verbales en la Educación Infantil: Una experiencia de enfoque investigativo. Indivisa, Boletín de Estudios e Investigación, Monografía IX, 23-47. https://eprints.ucm.es/id/eprint/12643/1/De_Castro_&_Escorial_PNA_2007.pdf
  16. Even, R., & Ball, D. L. (2009). The professional education and development of teachers of mathematics. Springer. https://doi.org/10.1007/978-0-387-09601-8
  17. Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1), 97–124. http://www.jstor.org/stable/23434841
  18. Gascón, J., & Nicolás, P. (2017). Can didactics say how to teach? The beginning of a dialogue between the anthropological theory of the didactic and other approaches. For the Learning of Mathematics, 37(3), 9-13. https://www.jstor.org/stable/26548462
  19. Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. Cuadernos de Investigación y Formación en Educación Matemática, 11, 111-132. https://www.ugr.es/~jgodino/eos/jdgodino_indicadores_idoneidad.pdf
  20. Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, 39(1), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  21. Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 37- 42. https://www.jstor.org/stable/26742011
  22. Godino, J. D., Giacomone, B., Font, V., & Pino-Fan (2018). Conocimientos profesionales en el diseño y gestión de una clase sobre semejanza de triángulos. Análisis con herramientas del modelo CCDM. Avances de Investigación en Educación Matemática (AIEM), 13, 63–83. https://doi.org/10.35763/aiem.v0i13.224
  23. Gusmão, T. C. R. S. (2019). Do desenho à gestão de tarefas no ensino e na aprendizagem da Matemática. En Anais do XVIII Encontro Baiano de Educação Matemática. https://casilhero.com.br/ebem/mini/uploads/periodico/files/2019/PA2.pdf
  24. Gusmão, T. C. R. S., & Font, V. (2020). Ciclo de estudo e desenho de tarefas. Educação Matemática Pesquisa, 22(3), 666-697. https://doi.org/10.23925/1983-3156.2020v22i3p666-697
  25. Gutiérrez, A., & Boero, P. (2006). Handbook of research on the psychology of mathematics education: Past, present and future. BRILL. https://doi.org/10.1163/9789087901127
  26. Halmos, P. R. (1980). The heart of mathematics. The American Mathematical Monthly, 87(7), 519- 524. https://doi.org/10.1080/00029890.1980.11995081
  27. Hill, H.C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American educational research journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
  28. Kaiser, G., Blömeke, S., König, J., Busse, A. Dohrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—cognitive versus situated approaches. Educational Studies in Mathematics, 94, (2), 161-182. https://doi.org/10.1007/s10649-016-9713-8
  29. Kilpatrick, J. (1985). A Retrospective Account of the Twenty-five Years of Research on Teaching Mathematical Problem Solving. In E. A. Sil¬ver (Ed.), Teaching and learning mathemati¬cal problem solving: Multiple research pers¬pective (pp.1-15). Lawrence Erlbaum. https://doi-org.sire.ub.edu/10.4324/9780203063545
  30. König, J., Blömeke, S. Klein, P., Suhl, U., Busse, A., & Kaiser, G. (2014). Is teachers' general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach. Teaching and Teacher Education, 38, 76-88. https://doi.org/10.1016/j.tate.2013.11.004
  31. Malaspina, U. (2017). La creación de problemas como medio para potenciar la articulación de competencias y conocimientos del profesor de matemáticas. En J. M. Contreras, P. Artea-ga, G. R. Cañadas, M. M. Gea, B. Giacomone y M. M. López-Martín (Eds.), Actas del Se-gundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos. Pontificia Uni¬versidad Católica del Perú. http://enfoqueontosemiotico.ugr.es/ civeos/malaspina.pdf
  32. Monje, Y., Seckel, M.J., & Breda, A. (2018). Tratamiento de la Inecuación en el Currículum y Textos Escolares Chilenos. Bolema, 32(61), 480-502. https://doi.org/10.1590/1980-4415v32n61a09
  33. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics NCTM. Reston, VA. https://www-nctm-org.sire.ub.edu/standards/
  34. National Council of Teachers of Mathematics [NCTM] (2003). Principios y estándares para la educación matemática. Servicio de Publicaciones de la SAEM Thales.
  35. Niss, M. (2002). Mathematical competencies and the learning of mathematics: the Danish Kom Project. Roskilde University. https://aausmed.files.wordpress.com/2011/01/mathematical_competencies_and_the_learning_of_mathematics1.pdf
  36. Pino-Fan, L. R., Assis, A., & Castro, W.F. (2015). Towards a methodology for the characterization of teachers' didactic-mathematical knowledge. Eurasia Journal of Mathematics, Science & Technology Education,11(6), 1429-1456. https://doi.org/10.12973/eurasia.2015.1403a
  37. Pino-Fan, L. R., Báez-Huaiquián, D. I., Molina-Cabero, J. G., & Hernández-Arredondo, E. (2020). Criterios utilizados por profesores de matemáticas para el planteamiento de problemas en el aula. Uniciencia, 34(2), 114-137. http://dx.doi.org/10.15359/ru.34-2.7
  38. Pino-Fan, L., Castro, W. F., Godino, J. D., & Font, V. (2013). Idoneidad epistémica del significado de la derivada en el currículo de bachillerato. Paradigma, 34(2), 123-150. https:// doi.org/10.37618/PARADIGMA.1011-2251.2013.p123-150.id522
  39. Pochulu, M., Font, V., & Rodríguez, M. (2016). Desarrollo de la competencia en análisis didáctico de formadores de futuros profesores de matemática a través del diseño de tareas. Revista latinoamericana de investigación en matemática educativa, 19(1), 71-98. https://doi.org/10.12802/relime.13.1913
  40. Polya, G. (1986). How to Solve it. Prin¬ceton University Press.
  41. Ponte, J. P. (2005). Gestão curricular em Matemática. En GTI (Ed.) O professor e o desenvolvimento curricular. APM.
  42. Ponte, J. P. (2014). Tarefas no ensino e na aprendizagem da Matemática. En Ponte, J. P. (Org.). Práticas Profissionais dos Professores de Matemática (pp. 13-27). Instituto de Educação da Universidade de Lisboa. http://hdl.handle.net/10451/3008
  43. Putman, R., & Borko, H. (2000). What do new views of knowledge and thinking have to say? Qualitative Health Research, 9(1), 112-121. https://eric.ed.gov/?id=EJ602721
  44. Rafiepour, A., & Farsani, D. (2021). Cultural-historical analysis of Iranian school mathematics curriculum: The role of computational thinking. Research on Mathematics Education, 12(3), 411-426. https://doi.org/10.22342/jme.12.3.14296.411-426
  45. Rondero, C., & Font, V. (2015). Articulación de la complejidad matemática de la media aritmética. Enseñanza de las Ciencias, 33(2), 29-49. https://doi.org/10.5565/rev/ensciencias.1386
  46. Sánchez, A., Font, V., & Breda, A. (2021). Significance of creativity and its development in mathematics classes for preservice teachers who are not trained to develop students’ creativity. Mathematics Education Research Journal, 1-23. https:// doi.org/10.1007/s13394-021-00367-w
  47. Sapti, M., Purwanto, Irawan, E.B., As’ari, A.R., Sa’dijah, C., Susiswo, & Wijaya, A. (2019). Comparing Model-Building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking. Journal on Mathematics Education, 10(2), 171-184. https://doi.org/10.22342/jme.10.2.7351.171-184
  48. Schoenfeld, A. H. (1985). Mathematical problem sol¬ving. Academic Press. https:// doi.org/10.1016/C2013-0-05012-8
  49. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  50. Silverman, J., & Thompson, P.W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499-511. https://doi.org/10.1007/s10857-008-9089-5
  51. Singer, F.M., Ellerton, N., & Cai, J. (2015). Mathe¬matical Problem Posing. Sprin¬ger. https:// doi.org/10.1007/978-1-4614-6258-3
  52. Stahnke, R, Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research. ZDM. The International Journal on Mathematics Education, 48(1), 1-27. https://doi.org/10.1007/s11858-016-0775-y