Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information

Francisco Rodríguez-Alveal; Carmen Gloria Aguayo-Arriagada; Danilo Díaz-Levicoy

doi:10.29333/ejmste/17503

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Francisco Rodríguez-Alveal ¹ ^* , Carmen Gloria Aguayo-Arriagada ² , Danilo Díaz-Levicoy ³

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¹ Universidad del Bío-Bío, Chillán, CHILE² Universidad de Almería, Almería, SPAIN³ Centro de Investigación en Educación Matemática y Estadística, Universidad Católica del Maule, Talca, CHILE^* Corresponding Author

Abstract

This article describes the levels of reading and the arguments provided by future secondary mathematics teachers from two Chilean universities when decoding the information presented in a histogram and a box plot. A qualitative methodology was followed, based on content analysis. As a data collection technique, an instrument with two activities was applied. The 36 participants were selected through non-probabilistic sampling. Among the main results, it was found that participants perform basic readings of graphical representations. The arguments provided are conceptual in nature and are not related to the activity’s context. Additionally, future teachers do not refute the conclusion formulated based on the box plot, which indicates that they do not connect the representation to the context; those who do fail to provide sufficient justification. The study concludes that there is a need to strengthen argumentation skills to foster statistical literacy and statistical thinking.

Keywords

argumentation
statistical thinking
statistical literacy
pre-service teachers
histogram
box plot

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 21, Issue 12, December 2025, Article No: em2751

https://doi.org/10.29333/ejmste/17503

Publication date: 03 Dec 2025

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Article Downloads: 13

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References

Aoyama, K. (2007). Investigating a hierarchy of students’ interpretations of graphs. International Electronic Journal of Mathematics Education, 2(3), 298-318. https://doi.org/10.29333/iejme/214
Armah, G. (2025). Beyond the bars: Exploring pre-service teachers’ understanding of histograms. Asian Journal of Probability and Statistics, 27(3), 82-95. https://doi.org/10.9734/ajpas/2025/v27i3724
Bakker, A., Biehler, R., & Konold, C. (2005). Should young students learn about box plots? In G. Burrill, & M. Camden (Eds.), Curricular development in statistics education: International Association for Statistical Education 2004 roundtable (pp. 163-173). International Statistical Institute.
Bernal-Valdés, F., Díaz-Levicoy, D., & Rodríguez-Alveal, F. (2025). Alfabetización estadística en la formación universitaria de futuros profesores de matemática de Educación Secundaria chilena [Statistical literacy in the undergraduate education of future mathematics teachers in Chilean Secondary Education]. Formación Universitaria, 18(4), 13-26. https://doi.org/10.4067/s0718-50062025000400013
Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. Academic Press.
Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behavior. In H. Rowe (Eds.), Intelligence: Reconceptualization and measurement (pp. 57-76). Erlbaum.
Boels, L., Bakker, A., Van Dooren, W., & Drijvers, P. (2019). Conceptual difficulties when interpreting histograms: A review. Education Research Review, 28, Article 100291. https://doi.org/10.1016/j.edurev.2019.100291
Canavos, G. (1981). Métodos estadísticos y probabilidad [Statistical methods and probability]. McGraw-Hill.
Cervantes-Barraza, J. A., & Cabañas-Sánchez, M. G. (2022). Argumentación matemática basada en refutaciones [Mathematical argumentation based on refutations]. REDIMAT–Journal of Research in Mathematics Education, 11(2), 159-179. https://doi.org/10.17583/redimat.4015
Cobb, G., & Moore, D. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104(9), 801-823. https://doi.org/10.1080/00029890.1997.11990723
Conner, A. (2008). Expanded Toulmin diagrams: A tool for investigating complex activity in classrooms. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education (pp. 361-368). Morelia.
Curcio, F. (1989). Developing graph comprehension. NCTM.
Devore, J. (2016). Probabilidad y estadística para ingeniería y ciencias [Probability and statistics for engineering and science]. CENGAGE Learning.
Díaz-Levicoy, D., Samuel, M., & Rodríguez-Alveal, F. (2021). Conocimiento especializado sobre gráficos estadísticos de futuras maestras de Educación Infantil [Specialized knowledge on statistical graphs by future teachers of early childhood education]. Formación Universitaria, 14(5), 29-38. https://doi.org/10.4067/S0718-50062021000500029
Dodge, Y. (2008). The concise encyclopedia of statistics. Springer. https://doi.org/10.1007/978-0-387-32833-1
Estrella, S., & Olfos, R. (2012). La taxonomía de comprensión gráfica de Curcio a través del gráfico de Minard: Una clase de séptimo grado [Curcio’s taxonomy of graphic comprehension through Minard’s graph: A 7^th grade class]. Educación Matemática, 24(2), 123-133.
GAISE. (2005). Guidelines for assessment and instruction in statistics education (GAISE) report: A curriculum framework for PreK-12 statistics education. American Statistical Association.
GAISE. (2016). Guidelines for assessment and instruction in statistics education college report 2016. American Statistical Association.
Garfield, J. (2002). The challenge of developing statistical reasoning. Journal of Statistics Education, 10(3), 1-12. https://doi.org/10.1080/10691898.2002.11910676
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Springer.
Gea, M.M., Arteaga, P., & Cañadas, G.R. (2017). Interpretación de gráficos estadísticos por futuros profesores de educación secundaria [Interpretation of statistical graphs by future secondary education teachers]. Avances de Investigación en Educación Matemática, 12, 19-37. https://doi.org/10.35763/aiem.v1i12.189
Goizueta, M., Ledermann, C., & Montenegro, H. (2023). El desarrollo y la evaluación de la habilidad de argumentar en el sistema educativo Chileno: Tensiones y consecuencias percibidas por el profesorado [The development and evaluation of argumentation skills in the Chilean educational system: Tensions and consequences perceived by teachers]. Pensamiento Educativo, 60(1), 1-16. https://doi.org/10.7764/pel.60.1.2023.3
González, O. (2021). Teachers’ conceptions and professional knowledge of variability from their interpretation of histograms: The case of Venezuelan in-service secondary mathematics teachers. Statistics Education Research Journal, 20(2), 1-14. https://doi.org/10.52041/serj.v20i2.412
Izagirre, A., Anasagasti, J., & Berciano, A. (2023). Conocimiento estadístico del futuro profesorado de educación primaria en la representación de datos [Statistical knowledge of future primary education teachers in data representation]. Avances de Investigación en Educación Matemática, 24, 111-130. https://doi.org/10.35763/aiem24.4646
Krippendorff, K. (1997). Metodología de análisis de contenido: Teoría y práctica [Content analysis methodology: Theory and practice]. Paidós.
Larios, V., Arellano, C., & González, N. (2018). Análisis de argumentos producidos por alumnos de bachillerato al resolver problemas de geometría [Analysis of arguments produced by high school students when solving geometry problems]. REDIMAT–Journal of Research in Mathematics Education, 7(3), 280-310. https://doi.org/10.17583/redimat.2018.2343
Martins, M. N. P., & Carvalho, C. F. (2018). O ensino de gráficos estatísticos nos anos iniciais [Teaching statistical graphics in the early years]. Revista de Ensino de Ciências e Matemática, 9(2), 247-264. https://doi.org/10.26843/rencima.v9i2.1666
Mayring, P. (2000). Qualitative content analysis. Forum Qualitative Social Research, 1(2), 1-10. https://doi.org/10.17169/fqs-1.2.1089
McConway, K. (2016). Statistics and the media: A statistician’s view. Journalism, 17(1), 49-65. https://doi.org/10.1177/1464884915593243
McMillan, J., & Schumacher, S. (2011). Investigation educativa. Pearson-Adisson Wesley.
MINEDUC. (2012). Bases curriculares Primero a Sexto básico. Unidad de Currículum y Evaluación.
MINEDUC. (2015). Bases curriculares [Curricular bases]. Unidad de Currículum y Evaluación.
MINEDUC. (2016). Desarrollo de habilidades: Aprender a pensar matemáticamente. 7° y 8° año de educación básica [Skill development: Learning to think mathematically. 7^th and 8^th grades of elementary education]. Unidad de Currículum y Evaluación.
MINEDUC. (2019). Bases curriculares 3° y 4° medio [Curriculum bases 3^rd and 4^th year of high school]. Unidad de Currículum y Evaluación.
MINEDUC. (2021). Estándares pedagógicos y disciplinarios para carrera de pedagogía en matemática [Pedagogical and disciplinary standards for a mathematics teaching degree]. Ministerio de Educación.
Monteiro, C., & Ainley, J. (2006). Student teachers interpreting media graphs. In A. Rossman, & B. Chance (Eds.), Proceedings of the 7^th International Conference on Teaching Statistics (pp. 1-6). ISI/IASE.
Muñoz, G., Santis, M., & Del Valle, J. (2016). Texto del estudiante de matemática 1 medio [Text of the 1^st year mathematics student]. SM.
Pfannkuch, M., & Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics–Challenges for teaching and teacher education. New ICMI study series (pp. 323-333). Springer. https://doi.org/10.1007/978-94-007-1131-0_31
Rodríguez-Alveal, F. (2017). Alfabetización estadística en profesores de distintos niveles formativos [Statistical literacy in teachers from distinct training levels]. Educação & Realidad, 42(4), 1459-1477. https://doi.org/10.1590/2175-623662610
Rodríguez-Alveal, F., Díaz-Levicoy, D., & Vásquez, C. (2021). Análisis de las actividades sobre variabilidad estadística en los libros de texto de educación secundaria: Una mirada desde las propuestas internacionales [Analysis of statistical variability activities in secondary education textbooks: a study from an international proposal standpoint]. Uniciencia, 35(1), 108-123. https://doi.org/10.15359/ru.35-1.7
Rodríguez Alveal, F., & Sandoval, P. (2012). Habilidades de codificación y descodificación de tablas y gráficos estadísticos: Un estudio comparativo en profesores y alumnos de pedagogía en enseñanza básica [Statistical tables and graphs codification and decodification abilities: A comparative study with pedagogy teachers and students of basic elementary education]. Avaliação: Revista da Avaliação da Educação Superior, 17(1), 207-235. https://doi.org/10.1590/S1414-40772012000100011
Rumsey, C., & Langrall, C. (2016). Promoting mathematical argumentation. Teaching Children Mathematics, 22(7), 412-419. https://doi.org/10.5951/teacchilmath.22.7.0412
Shaughnessy, J. M., & Pfannkuch, M. (2002). How faithful is old faithful? Statistical thinking: A story of old variation. Mathematics Teacher, 95(4), 252-259. https://doi.org/10.5951/MT.95.4.0252
Toulmin, S. (2003). The uses of argument. Cambridge University Press. https://doi.org/10.1017/CBO9780511840005
Triola, M. (2006). Estadística [Statistics]. Pearson.
Tukey, J. W. (1977). Exploratory data analysis. Addison-Wesley Publications.
Watson, J., & Callingham, R. (2003). Statistical literacy: A complex hierarchical construct. Statistics Education Research Journal, 2(2), 3-46. https://doi.org/10.52041/serj.v2i2.553
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 221-248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x

How to cite this article

APA

Rodríguez-Alveal, F., Aguayo-Arriagada, C. G., & Díaz-Levicoy, D. (2025). Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information. Eurasia Journal of Mathematics, Science and Technology Education, 21(12), em2751. https://doi.org/10.29333/ejmste/17503

Vancouver

Rodríguez-Alveal F, Aguayo-Arriagada CG, Díaz-Levicoy D. Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information. EURASIA J Math Sci Tech Ed. 2025;21(12):em2751. https://doi.org/10.29333/ejmste/17503

AMA

Rodríguez-Alveal F, Aguayo-Arriagada CG, Díaz-Levicoy D. Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information. EURASIA J Math Sci Tech Ed. 2025;21(12), em2751. https://doi.org/10.29333/ejmste/17503

Chicago

Rodríguez-Alveal, Francisco, Carmen Gloria Aguayo-Arriagada, and Danilo Díaz-Levicoy. "Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 12 (2025): em2751. https://doi.org/10.29333/ejmste/17503

Harvard

Rodríguez-Alveal, F., Aguayo-Arriagada, C. G., and Díaz-Levicoy, D. (2025). Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information. Eurasia Journal of Mathematics, Science and Technology Education, 21(12), em2751. https://doi.org/10.29333/ejmste/17503

MLA

Rodríguez-Alveal, Francisco et al. "Statistical knowledge of future secondary mathematics teachers in reading and arguing graphical information". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 12, 2025, em2751. https://doi.org/10.29333/ejmste/17503