Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 28 (2025): Publicación continua

La enseñanza de la inferencia estadística informal en la formación de profesores. Una revisión sistemática

DOI:
https://doi.org/10.12802/relime.2025.28.e787
Submetido
março 11, 2026
Publicado
2025-12-19

Resumo

Esta revisão sistemática examina o ensino da inferência estatística informal na formação de professores. Foram analisados estudos publicados entre 2010 e 2024 em quatro bases de dados académicas, resultando em 16 artigos. O objetivo foi identificar relatos sobre o uso de tarefas para o ensino da inferência informal e sua ligação com a aprendizagem da inferência formal. A análise foi organizada em torno de três dimensões: conhecimento do conteúdo, conhecimento tecnológico e conhecimento relacionado à prática docente. Os resultados mostram um interesse crescente neste tema. As tarefas reportadas, em geral, promovem componentes do conhecimento de conteúdo, embora tenham sido encontrados diferentes níveis de complexidade. O uso da tecnologia como ferramenta para reorganizar o pensamento inferencial ainda é limitado. Embora vários estudos relacionem a abordagem informal com métodos formais, não há evidências empíricas apresentadas sobre o seu impacto na aprendizagem da inferência estatística formal.

Referências

  1. Abu-Ghalyoun, O. (2021). Pre-service teachers’ difficulties in reasoning about sampling variability. Educational Studies in Mathematics, 108(3), 553-77. https://doi.org/10.1007/s10649-021-10067-8
  2. American Statistical Association. (2016). Guidelines for assessment and instruction in statistics education (GAISE): College report. Author.
  3. Ball, L.D., Thames, M. H., y Phelps, G. (2008). Content knowledge for teaching: What makes it so special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  4. Batanero, C. (2002). Los retos de la cultura estadística. En Jornadas Interamericanas de Enseñanza de la Estadística. https://www.ugr.es/~batanero/pages/ARTICULOS/CULTURA.pdf
  5. Ben-Zvi, D., y Garfield, J.B. (2004). Statistical Literacy, Reasoning and Thinking: Goals, Definitions and Challenges. En D. Ben-Zvi y J. Garfield (Eds), The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 3-16). https://doi.org/10.1007/1-4020-2278-6_1
  6. Biehler, R., Frischemeier, D., Reading, C., y Shaughnessy, J. (2018). Reasoning about data. En D. Ben-Zvi, K.Makar y J.Garfield (Eds.), International handbook of research in statistics education (pp. 71-104). https://doi.org/10.1007/978-3-319-66195-7_14
  7. Biggs, J. B., y Collis, K. (1991). Multimodal learning and the quality of intelligent behavior. En H. Rowe (Ed.), Intelligence, reconceptualization and measurement (pp. 57–76). Psychology Press. https://doi.org/10.4324/9780203772560
  8. Browning, C., Goss, J., y Smith, D. (2014). Statistical knowledge for teaching: Elementary preservice teachers. En K. Makar, B. de Sousa, y R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics. International Statistical Institute.
  9. Cabrera, G., Tauber, L., y Fernández, E. (2020). Educación Estocástica para pensar estadís-críticamente. Matemáticas, Educación y Sociedad, 3(2), 89-109. https://journals.uco.es/mes/article/view/12903
  10. Castro Sotos, A., Vanhoof, S., Van den Noortage, W., y Onghena, P. (2007). Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education. Educational Research Review, 2(2), 98-113. https://doi.org/10.1016/j.edurev.2007.04.001
  11. Cobb, G. W., y Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801-823.
  12. de Vetten, A., Schoonenboom, J., Keijzer, R., y van Oers, B. (2017). Informal statistical inference and pre-service primary school teachers: The development of their content knowledge and pedagogical content knowledge during a teacher college intervention. En T. Dooley y G. Gueudet, G. (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10). Institute of Education and ERME.
  13. de Vetten, A., Schoonenboom, J., Keijzer, R. y van Oers, B. (2018). The development of informal statistical inference content knowledge of pre-service primary school teachers during a teacher college intervention. Educational Studies in Mathematics, 99, 217-234. https://doi.org/10.1007/s10649-018-9823-6
  14. de Vetten, A., Schoonenboom, J., Keijzer, R. y van Oers, B. (2019). Pre-service primary school teachers’ knowledge of informal statistical inference. Journal of Mathematics Teacher Education, 22(6), 639-661. https://doi.org/10.1007/s10857-018-9403-9
  15. de Vetten, A., Keijzer, R., Schoonenboom, J., y Oers, B. V. (2023). Pre-service primary school teachers’knowledge during teaching informal statistical inference. Statistics Education Research Journal, 22(2), Article 12. https://doi.org/10.52041/serj.v22i2.424
  16. Díaz, C., Batanero,C., y Wilhemi, M. (2008). Errores frecuentes en el análisis de datos en Educación y Psicología. Publicaciones, 38, 109-126. http://revistaseug.ugr.es/index.php/publicaciones/article/view/2244/2366
  17. Dolor, J., y Noll, J. (2015). Using Guided Reinvention to Develop Teachers’ Understanding of Hypothesis Testing Concepts. Statistics Education Research Journal, 14(1), 60-89. https://doi.org/10.52041/serj.v14i1.269
  18. Fergusson, A. (2017), Informally Testing the Fit of a Probability Distribution Model [Tesis de maestría, University of Auckland] https://hdl.handle.net/2292/36909
  19. Fergusson, A., y Pfannkuch, M. (2020). Development of an Informal Test for the Fit of a Probability Distribution Model for Teaching. Journal of Statistics Education, 28(3), 344-357. https://doi.org/10.1080/10691898.2020.1837039
  20. Fielding, J., y Makar, K. (2022). Challenging conceptual understanding in a complex system: supporting young students to address extended mathematical inquiry problems. Instructional Science, 50, 35-61. https://doi.org/10.1007/s11251-021-09564-3
  21. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., y Scheaffer, R. (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A preK-12 curriculum framework. American Statistical Association. https://www.amstat.org/asa/files/pdfs/gaise/gaiseprek-12_full.pdf
  22. Garfield, J., y Ben‐Zvi, D. (2008). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72-77. https://doi.org/10.1111/J.1467-9639.2009.00363.X
  23. Garfield, J., delMas, R., y Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM Mathematics Education, 44 (7), 883-898. https://doi.org/10.1007/s11858-012-0447-5
  24. Garfield, J., Le, L., Zieffler, A., y Ben-Zvi, D. (2015). Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88(3), 327-342. https://doi.org/10.1007/s10649-014-9541-7
  25. Godino, J. D., Batanero, C., y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  26. Gravemeijer, K. (2004). Creating opportunities for students to reinvent mathematics. En Proceedings of the Tenth International Congress in Mathematics Education (pp. 4–11). https://www.mathunion.org/fileadmin/ICMI/Conferences/ICME/ICME%20proceedings/ICME_10_2004_Copenhagen.pdf
  27. Harradine A., Batanero C., y Rossman A. (2011). Students and Teachers’ Knowledge of Sampling and Inference. En C. Batanero, G. Burrill y C. Reading (Eds.), Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education (pp. 235-246). https://doi.org/10.1007/978-94-007-1131-0_24
  28. Heaton, R. M., y Mickelson, W. T. (2002). The learning and teaching of statistical investigation in teaching and teacher education. Journal of Mathematics Teacher Education, 5(1), 35-59. https://doi.org/10.1023/A:1013886730487
  29. Hiebert, J., y Wearne, D. (1997). Instructional tasks, classroom discourse, and student learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393-425. https://doi.org/10.2307/1163241
  30. Jones, G. A., Langrall, C. W., Mooney, E. S., y Thornton, C. A. (2004). Models of development in statistical reasoning. En J. Garfield y D. Ben-Zvi (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 201-226). Springer. https://doi.org/10.1007/1-4020-2278-6_5
  31. Kilpatrick, J., Swafford, J., y Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
  32. Leavy, A. (2006). Using data comparison to support a focus on distribution: Examining preservice teachers’ understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89-114. https://doi.org/10.52041/serj.v5i2
  33. Leavy, A. M. (2010). The Challenge of Preparing Preservice Teachers to Teach Informal Inferential Reasoning. Statistics Education Research Journal, 9(1), 46-67. https://doi.org/10.52041/serj.v9i1.387
  34. Lee, H., y Hollebrands, K. (2008). Preparing to teach mathematics with technology: An integrated approach to developing technological pedagogical content knowledge. Contemporary Issues in Technology and Teacher Education, 8(4), 326-341. http://www.citejournal.org/ vol8/iss4/mathematics/article1.cfm
  35. Lee, H. S., Dung Tran, Nickell, J., y Doerr, H. (2015). Simulation approaches for informal inference: Models to develop understanding. En K. Krainer y N. Vondrová, (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9). Faculty of Education and ERME.
  36. Lesh, R. A., y Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching. Routledge.
  37. Lugo-Armenta, J., y Pino-Fan, L. (2021). Inferential Reasoning of Secondary School Mathematics Teachers on the Chi-Square Statistic. Mathematics, 9(19), 1-20. https://doi.org/10.3390/math9192416
  38. Lugo-Armenta, J., y Pino-Fan, L. (2022). Razonamiento inferencial de docentes de matemáticas de enseñanza media sobre el estadístico t-Student. Uniciencia, 36(1), 1-29. http://dx.doi.org/10.15359/ru.36-1.25
  39. Madden, S. R. (2011). Statistically, Technologically, and Contextually Provocative Tasks: Supporting Teachers’ Informal Inferential Reasoning. Mathematical Thinking and Learning, 13, 109-131. https://doi.org/10.1080/10986065.2011.539078
  40. Makar, K., y Fielding-Wells, J. (2011). Teaching teachers to teach statistical investigations. En C. Batanero, G. Burrill, y C. Reading (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education (pp. 347-358). https://doi.org/10.1007/978-94-007-1131-0_33
  41. Makar, K., y Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82-105. https://doi.org/10.52041/serj.v8i1.457
  42. Makar, K., y Rubin, A. (2018). Learning about statistical inference. En D. Ben-Zvi, K.Makar y J.Garfield (Eds.), International handbook of research in statistics education (pp. 261-294). https://doi.org/10.52041/serj.v8i1.457
  43. Mcclain, K. (2008). The evolution of teachers’ understandings of distribution. En C. Batanero, G. Burrill, C. Reading y A. Rossman (Eds.), Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18. IASE. https://www.stat.auckland.ac.nz/~iase/publications/rt08/T2P8_McClain.pdf
  44. Meletiou-Mavrotheris, M., Paparistodemou, E., y Stylianou, D. (2009). Enhancing statistics instruction in elementary schools: Integrating technology in professional development. The Montana Mathematics Enthusiast, 6(1-2), 57-78. https://doi.org/10.54870/1551-3440.1134
  45. Meletiou-Mavrotheris, M., y Serradó-Bayés, A. (2012). Distance training of mathematics teachers: The Early Statistics experience. Revista de Universidad y Sociedad del Conocimiento, 9(1), 340-353. https://doi.org/10.7238/rusc.v9i1.1275
  46. Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D., Shamseer, L., Tetzlaff, J. M., Akl, E. A., Brennan, S. E., Chou, R., Glanville, J., Grimshaw, J. M., Hróbjartsson, A., Lalu, M. M., Li, T., Loder, E. W., Mayo-Wilson, E., McDonald, S., … Moher, D. (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372 (71). https://doi.org/10.1136/bmj.n71
  47. Park, J. (2013). Designing an Assessment to Measure Students’ Inferential Reasoning in Statistics:The First Study, Development of a Test Blueprint. Research in Mathematical Education, 17(4), 243-266. http://dx.doi.org/10.7468/jksmed.2013.17.4.243
  48. Pea, R. D. (1987). Cognitive technologies for mathematics education. En A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 89-122). Erlbaum.
  49. Petocz, P., Reid, A., y Gal, I. (2018). Statistics Education Research. En D. Ben-Zvi, K.Makar y J.Garfield (Eds.), International handbook of research in statistics education (pp. 71-104). https://doi.org/10.1007/978-3-319-66195-7_14
  50. Pfannkuch, M. (2005). Thinking tools and variation. Statistics Education Research Journal, 4(1), 83-91. https://doi.org/10.52041/serj.v4i1.526
  51. Pfannkuch, M. (2007). Year 11 Students’ informal inferential reasoning: A case study about the interpretation of box plots. International Electronic Journal of Mathematics Education, 2(3), 149-167. https://doi.org/10.29333/iejme/181
  52. Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1-2), 27-46. https://doi.org/10.1080/10986065.2011.538302
  53. Podworny, S., y Biehler, R. (2014). A learning trajectory on hypothesis testing with TinkerPlots – Design and exploratory evaluation. En K. Makar, B. de Sousa, y R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9). International Statistical Institute.
  54. Ponte, J. y Noll, J. (2018). Building Capacity in Statistics Teacher Education. En D. Ben-Zvi, K.Makar y J.Garfield (Eds.), International handbook of research in statistics education (pp. 433-456). https://doi.org/10.1007/978-3-319-66195-7_14
  55. Ponte, J. P. (2011). Preparing teachers to meet the challenges of statistics education. En C. Batanero, G. Burrill, y C. Reading (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education (pp. 299-309). https://doi.org/10.1007/978-94-007-1131-0_29
  56. Rodríguez-Alveal, F., y Aguerrea, M. (2024). Inferencia estadística en los textos escolares: Una aproximación al pensamiento estadístico. Uniciencia, 38(1), 341-356. https://doi.org/10.15359/ru.38-1.19
  57. Rowland, T., Huckstep, P., y Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281. https://doi.org/10.1007/s10857-005-0853-5
  58. Ruiz, B., Batanero, C. y Arteaga, P. (2011). Vinculación de la Variable Aleatoria y Estadística en la Realización de Inferencias Informales por parte de Futuros Profesores. Boletim de Educação Matemática, 24(39), 431-449. https://www.redalyc.org/pdf/2912/291222099006.pdf
  59. Santos, R., y Ponte, J. P. (2014). Learning and teaching statistical investigations: A case study of a prospective teacher. En K. Makar, B. de Sousa, y R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9). International Statistical Institute.
  60. Stein, M. K., y Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80. https://doi.org/10.1080/1380361960020103
  61. Tauber, L. (2021). Facetas de la Estadística Cívica implícitas en una experiencia de enseñanza centrada en el estudio de indicadores sociales. Paradigma, 42(Extra N.º 1), 89-117. https://doi.org/10.37618/paradigma.1011-2251.2021.p89-117.id1019
  62. Wassong, T., y Biehler, R. (2014). The use of technology in a mentor teacher course in statistics education. En K. Makar, B. de Sousa y R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics, (ICOTS9). International Statistical Institute.
  63. Zaslavsky, O. y Sullivan, P. (2011). Setting the Stage: A Conceptual Framework for Examining and Developing Tasks for Mathematics Teacher Education. En O. Zaslavsky y P. Sullivan (Eds.), Constructing Knowledge for Teaching Secondary Mathematics, Mathematics Teacher Education (pp. 1-22). https://doi.org/10.1007/978-0-387-09812-8
  64. Zieffler, A., Garfield, J., Alt, S., Dupuis, D., Holleque, K., y Chang, B. (2008). What does research suggest about the teaching and learning of introductory statistics at the college level? A review of the literature. Journal of Statistics Education, 16(2), 1-24. https://doi.org/10.1080/10691898.2008.11889566