Inferential reasoning of high school mathematics teachers about t-Student statistic

Keywords: Inferential reasoning, Student’s t, statistical inference, mathematical practice, statistical education


One of the topics that have been deeply studied in Statistical Education is that of how to promote formal inferential reasoning (FIR) based on the results of informal inferential reasoning (IIR). However, it is still necessary to have proposals to explore and progressively develop the inferential reasoning of students and teachers from IIR to FIR. In this context, this article seeks to characterize the inferential reasoning displayed by high school mathematics teachers in the practices they developed for solving problems about Student’s t statistic. To do this, we use theoretical and methodological notions introduced by the Onto-Semiotic Approach (OSA) to mathematical knowledge and instruction, among which are the notion of mathematical practice, mathematical object and the theoretical proposal of progressive levels of inferential reasoning about the Student’s t statistic. The subjects who participated in this qualitative study were 59 teachers in training from Costa Rica and 22 practicing teachers from Chile. The practices developed by the pre-service teachers and the practicing teachers were found to have similar elements (representations, concepts/definitions, properties, procedures, arguments). The principal conclusion of this investigation was that the proposal of inferential reasoning levels about Student’s t statistic proved to be a useful predictor of the practices developed by the teachers, making it possible to distinguish characteristic elements of each level of inferential reasoning.


Bakker, A., Ben-Zvi, D., & Makar, K. (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference. Mathematics Education Research Journal, 29(4), 455-470.
Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147-168). Dordrecht: Kluwer Academic Publishers.
Batanero, C. (2013). Del análisis de datos a la inferencia: Reflexiones sobre la formación del razonamiento estadístico. Cuadernos de Investigación y Formación en Educación Matemática, 11, 277-291.
Batanero, C. (2018). Treinta años de investigación didáctica sobre el análisis inferencial de datos. En A. Ávila. (Ed.) Rutas de la Educación Matemática (pp. 186-199). México: Sociedad Mexicana de Investigación y Divulgación de la Educación Matemática.
Batanero, C., Vera, O. D., & Díaz, C. (2012). Dificultades de estudiantes de psicología en la comprensión del contraste de hipótesis. Números. Revista de Didáctica de las Matemáticas, 80, 91-101.
Ben-Zvi, D., & Garfield, J.B. (2004). Statistical Literacy, Reasoning, and Thinking: Goals, Definitions, and Challenges. In D. Ben-Zvi, J. Garfield (Eds). The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 3-16). Dordrecht: Springer.
Biehler, R., Frischemeier, D., & Podworny, S. (2015). Preservice teachers reasoning about uncertainty in the context of randomization tests. Reasoning about uncertainty: Learning and teaching informal inferential reasoning, 129-162.
Cohen, J. (1992). Cosas que he aprendido (hasta ahora). Anales de Psicología/Annals of Psychology, 8(1-2), 3-18.
Cohen, L., Manion, L., & Morrison, K. (2011). Research methods in education (6th Ed.). Routledge.
Edgeworth, F. Y. (1885). On Methods of Ascertaining Variations in the rate of Births, Deaths and Marriages”, Journal of the Statistical Society, 48, 628-649.
Fisher, R. A. (1925). Statistical methods for research workers. Oliver and Boyd.
Font, V., & Rubio, N.V. (2017). Procesos matemáticos en el enfoque ontosemiótico. En J. M. Contreras, P. Arteaga, G.R. Cañadas, M.M. Gea, B. Giacomone y M. M. López-Martín (Eds.), Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos.
Galton, F. (1875). IV. Statistics by intercomparison, with remarks on the law of frequency of error. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer.
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325-355.
Godino, J. D. Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127-135.
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
Godino, J. D., Font, V., Wilhelmi, M. R., & Lurduy, O. (2011). Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects. Educational Studies in Mathematics, 77, 247–265.
Harradine A., Batanero C., & Rossman A. (2011). Students and Teachers’ Knowledge of Sampling and Inference. In C. Batanero, G. Burrill, C. Reading (Eds.) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education (pp. 235-246). Dordrecht.
Inzunsa, S., & Jiménez, J. V. (2013). Caracterización del razonamiento estadístico de estudiantes universitarios acerca de las pruebas de hipótesis. Revista latinoamericana de investigación en matemática educativa, 16(2), 179-211.
Jacob, B.L., & Doerr, H. M. (2014). Statistical Reasoning with the sampling distribution. In K. Makar, B. de Sousa, R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9, July, 2014), Flagstaff, Arizona, USA.
Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., Finzer, W., Horton, N. J., & Kazak, S. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13(1-2), 68-86.
Lipsey, M. W., & Aiken, L. S. (1990). Design sensitivity: Statistical power for experimental research (Vol. 19). Newbury Park, CA: Sage.
López-Martín, M. D. M., Batanero, C., & Gea, M. M. (2019). ¿Conocen los futuros profesores los errores de sus estudiantes en la inferencia estadística? Bolema: Boletim de Educação Matemática, 33(64), 672-693.
Lugo-Armenta, J. G., & Pino-Fan L. R. (2021a). Niveles de razonamiento inferencial para el estadístico T-Student. Bolema:Boletim de Educação Matemática, 35(71). 1776-1802.
Lugo-Armenta, J. G., & Pino-Fan L. R. (2021b). Inferential Statistical Reasoning of Math Teachers: Experiences in Virtual Contexts Generated by the Covid-19 Pandemic. Education Sciences, 11(7), 363.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.
Makar, K., & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar, J. Garfield (Eds.), International handbook of research in statistics education (pp. 261-294). Springer International.
Ministerio de Educación de Chile [Mineduc]. (2019). Bases Curriculares 3º y 4º medio. Santiago de Chile: Unidad de Currículum y Evaluación.
Pfannkuch, M., Arnold, P., & Wild, C. J. (2015). What I see is not quite the way it really is: Students’ emergent reasoning about sampling variability. Educational Studies in Mathematics, 88(3), 343-360.
Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking: What can we learn from practice? Statistics Education Research Journal, 15(2).
Pfannkuch, M., & Wild, C. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 17-46). Dordrecht: Kluwer Academic Publishers.
Pino-Fan, L., Godino, J. D., & Font, V. (2016). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education.
Presmeg, N. (2014) Semiotics in Mathematics Education. En S. Lerman (Eds.), Encyclopedia of Mathematics Education. Springer.
Reading, C., & Reid, J. (2006). An emerging hierarchy of reasoning about distribution: From a variation perspective. Statistics Education Research Journal, 5(2), 46-68.
Rossman, A. J. (2008). Reasoning about Informal Statistical Inference: One Statistician’s View. Statistics Education Research Journal, 7(2), 5-19.
Sotos, A. E. C., Vanhoof, S., Van den Noortgate, W. & 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.
Stigler, S. M. (2017). Los siete pilares de la sabiduría estadística. Grano de Sal.
Stohl, H., Angotti, R. L., & Tarr, J. E. (2010). Making comparisons between observed data and expected outcomes: students' informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68-96.
Vallecillos, A. (1997). El papel de las hipótesis estadísticas en los contrastes: Concepciones y dificultades de aprendizaje. Educación Matemática, 9(2), 5-20.
Vera, O. D., & Díaz, C. (2013). Dificultades de estudiantes de psicología en relación con el contraste de hipótesis. Probabilidad condicionada: Revista de didáctica de la Estadística, (2), 197-203.
Weinberg, A., Wiesner, E., & Pfaff, T. J. (2010) Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity. Journal of Statistics Education, 18(2).
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.
Yates, F. (1951). The influence of “Statistical methods for research workers” on the development of the science of statistics. Journal of the American Statistical Association, 46, 19-34.
Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40–58.
How to Cite
Lugo-Armenta, J., & Pino-Fan, L. (2022). Inferential reasoning of high school mathematics teachers about t-Student statistic. Uniciencia, 36(1), 1-29.
Original scientific papers (evaluated by academic peers)

Comentarios (ver términos de uso)

Most read articles by the same author(s)