Understanding statistical graphs of students attending multigrade rural schools in Chile

Matías Bustamante-Valdés; Danilo Díaz-Levicoy

doi:10.29333/iejme/14743

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Matías Bustamante-Valdés ¹ , Danilo Díaz-Levicoy ¹ ² ^*

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

Abstract

This study aims to analyze the graphical comprehension of 5^th and 6^th grade students in multigrade rural primary education in Chile. The theoretical framework considers levels of reading and semiotic levels in statistical graphs. A qualitative methodology of descriptive level is followed, using content analysis method for the responses given to a questionnaire by 22 students from five multigrade rural schools. The results show that, overall, students do not encounter difficulties in answering questions at level 1 reading (literal reading), but difficulties gradually increase as the reading level increases. Regarding semiotic levels, difficulties arise in constructing graphs using data distribution (semiotic level 3) and completing a graph with two data distributions (semiotic level 4).

Keywords

statistics
primary education
statistical graphs
rural school
multigrade classroom

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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

INT ELECT J MATH ED, Volume 19, Issue 3, August 2024, Article No: em0785

https://doi.org/10.29333/iejme/14743

Publication date: 01 Jul 2024

Online publication date: 18 Jun 2024

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References

Abós, P., & Boix, R. (2017). Evaluación de los aprendizajes en escuelas rurales multigrado [Evaluation of learning in rural multigrade schools]. Aula Abierta [Open Classroom], 45, 41-48. https://doi.org/10.17811/rifie.45.1.2017.41-48
Alsina, Á., & Vásquez, C. (2016). La probabilidad en educación primaria. De lo que debería enseñarse a lo que se enseña [Probability in primary education. From what should be taught to what is taught]. Uno, 71, 46-52.
Arteaga, P. (2008). Análisis de gráficos estadísticos elaborados en un proyecto de análisis de datos [Analysis of statistical graphs prepared in a data analysis project] [Master’s thesis, Universidad de Granada].
Arteaga, P. (2011). Evaluación de conocimientos sobre gráficos estadísticos y conocimientos didácticos de futuros profesores [Assessment of knowledge about statistical graphs and didactic knowledge of future teachers] [PhD thesis, Universidad de Granada].
Batanero, C. (2001). Didáctica de la estadística [Teaching of statistics]. GEEUG.
Batanero, C., Arteaga, P., & Ruiz, B. (2010). Análisis de la complejidad semiótica de los gráficos producidos por futuros profesores de educación primaria en una tarea de comparación de dos variables estadísticas [Analysis of the semiotic complexity of the graphs produced by future primary education teachers in a comparison task of two statistical variables]. Enseñanza de las Ciencias [Science Teaching], 28(1), 141-154. https://doi.org/10.5565/rev/ensciencias.3627
Batanero, C., Díaz-Levicoy, D., & Arteaga, P. (2018). Evaluación del nivel de lectura y la traducción de pictogramas por estudiantes chilenos [Evaluation of reading level and translation of pictograms by Chilean students]. Avances de Investigación en Educación Matemática, 14, 49-65. https://doi.org/10.35763/aiem.v0i14.231
Bustamante-Valdés, M., & Díaz-Levicoy, D. (2020). Análisis de gráficos estadísticos en módulos de matemática para la enseñanza de escuelas rurales multigrado en Chile [Analysis of statistical graphs in mathematics modules for teaching rural multigrade schools in Chile]. Espacios, 41(16), 24.
Bustamante-Valdés, M., Díaz-Levicoy, D., & Alarcón-Bustamante, E. (2024). Analysis of formative and evaluative activities on statistical graphs in textbooks for Chilean rural multigrade education. European Journal of Investigation in Health, Psychology and Education, 14(5), 1396–1412. https://doi.org/10.3390/ejihpe14050092
Bustos, A. (2014). La didáctica multigrado y las aulas rurales: Perspectivas y datos para su análisis [Multigrade teaching and rural classrooms: Perspectives and data for analysis]. Innovación Educativa [Educational Innovation], 24, 119-131. https://doi.org/10.15304/ie.24.1994
Callingham, R., & Watson, J. (2017). The development of statistical literacy at school. Statistics Education Research Journal, 16(1), 181-201. https://doi.org/10.52041/serj.v16i1.223
Cano, A. (2020). Análisis de dificultades en la enseñanza y aprendizaje del español y las matemáticas en escuelas primarias multigrado de Veracruz-México [Analysis of difficulties in the teaching and learning of Spanish and mathematics in multigrade primary schools in Veracruz-Mexico]. Tendencias Pedagógicas [Pedagogical Trends], 37, 57-74. https://doi.org/10.15366/tp2021.37.006
Cazorla, I. (2002). A relaçao entre a habilidades viso-pictóricas e o dominio de conceitos estatísticos na leitura de gráficos [The relationship between visual-pictorial skills and the mastery of statistical concepts when reading graphs] [PhD thesis, Universidad de Campinas].
Creswell, J., & Poth, C. (2018). qualitative inquiry and research design: Choosing among five approaches. SAGE.
Cruz, A. (2013). Erros e dificuldades de alunos de 1o ciclo na representação de dados estatísticos [Errors and difficulties of 1st cycle students in representing statistical data] [Master’s thesis, Universidade de Lisboa].
Cuevas, H., & Ramírez, G. (2018). Desempeño en estocástica entre profesores de educación secundaria: Un estudio exploratorio en dos regiones de Costa Rica y México [Performance in stochastics among secondary education teachers: An exploratory study in two regions of Costa Rica and Mexico]. Educación Matemática [Mathematics Education], 30(1), 93-132. https://doi.org/10.24844/EM3001.04
Curcio, F. (1989). Developing graph comprehension. NCTM.
Del Pino, G., & Estrella, S. (2012). Educación estadística: Relaciones con la matemática [Statistical education: Relations with mathematics]. Pensamiento Educativo [Educational Thinking], 49(1), 53-64. https://doi.org/10.7764/PEL.49.1.2012.5
Díaz-Levicoy, D., Arteaga, P., & Batanero, C. (2017). Lectura de pictogramas por estudiantes chilenos de Educación Primaria [Reading pictograms by Chilean Primary Education students]. In J.M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M.L. Callejo & J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 217-226). SEIEM.
Díaz-Levicoy, D., & Batanero, C. (2020). Traducción de gráficos de barras por estudiantes chilenos de 6º grado [Translation of bar graphs by Chilean 6th grade students]. Acta Latinoamericana de Matemática Educativa, 33(2), 137-146.
Díaz-Levicoy, D., Batanero, C., & Arteaga, P. (2018). Dificultades de los estudiantes chilenos de educación básica en la construcción de diagrama de barras [Difficulties of Chilean basic education students in constructing bar diagrams]. Paradigma, 39(2), 107-129.
Díaz-Levicoy, D., Batanero, C., Arteaga, P., & Gea, M. M. (2016). Gráficos estadísticos en libros de texto de Educación Primaria: un estudio comparativo entre España y Chile [Statistical graphs in Primary Education textbooks: a comparative study between Spain and Chile]. Boletim de Educação Matemática, 30(55), 713-737. https://doi.org/00.1590/1980- 4415v30n55a20
Díaz-Levicoy, D., Giacomone, B., & Arteaga, P. (2017). Caracterización de los gráficos estadísticos en libros de texto argentinos del segundo ciclo de Educación Primaria [Characterization of statistical graphs in Argentine textbooks of the second cycle of Primary Education]. Revista de Currículum y Formación del Profesorado, 21(3), 299-326.
Díaz-Levicoy, D., Giacomone, B, López-Martín, M. M., & Piñeiro, J. L. (2016). Estudio sobre los gráficos estadísticos en libros de texto digitales de educación primaria Española [Study on statistical graphs in Spanish primary education digital textbooks]. Profesorado. Revista de Currículum y Formación del Profesorado, 20(1), 133-156.
Díaz-Levicoy, D., Osorio, M., Arteaga, P., & Rodríguez-Alveal, F. (2018). Gráficos estadísticos en libros de texto de matemática de Educación Primaria en Perú [Statistical graphs in Primary Education mathematics textbooks in Peru]. Boletim de Educação Matemática, 32(61), 503-525. https://doi.org/10.1590/1980- 4415v32n61a10
English, L. D., & Watson, J. M. (2015). Statistical literacy in the elementary school: Opportunities for problem posing. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 241-256). Springer. https://doi.org/10.1007/978-1-4614-62583_11
Friel, S., Curcio, F., & Bright, G. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158. https://doi.org/10.2307/749671
Gal, I. (2002). Adult’s statistical literacy: Meaning, components, responsibilities. International Statistical Review, 70(1), 1-25. https://doi.org/10.1111/j.1751-5823.2002.tb00336.x
Guimarães, G. L., Ferreira, V. G. G., & Roazzi, A. (2001). Interpretando e construindo gráficos [Interpreting and constructing graphs]. In Proceedings of the Annual Meeting of the National Association for Graduate Studies and Research in Education (pp. 1-19). ANPED.
Hernández, A., Pérez, M., Rodríguez, T., & Juárez, J. A. (2021). Un estudio acerca de la lectura de gráficos estadísticos en alumnos de sexto grado de primaria [A study about the reading of statistical graphs in sixth grade primary school students]. Números [Numbers], 107, 55-69.
Hernández-Nieto, R. (2011). Instrumentos de recolección de datos en ciencias sociales y ciencias biomédicas [Data collection instruments in social sciences and biomedical sciences]. Universidad de los Andes.
Jiménez-Castro, M., Arteaga, P., & Batanero, C. (2020). Los gráficos estadísticos en los libros de texto de educación primaria en Costa Rica [Statistical graphs in primary education textbooks in Costa Rica]. Boletim de Educação Matemática [Mathematics Education Bulletin], 34(66), 132-156. https://doi.org/10.1590/1980-4415v34n66a07
Juárez, D., & Rodríguez, C. (2016). Factores que afectan a la equidad educativa en escuelas rurales de México [Factors that affect educational equity in rural schools in Mexico]. Pensamiento Educativo [Educational Thinking], 53(2), 1-15. https://doi.org/10.7764/PEL.53.2.2016.8
Little, A. W. (2007). Education for all and multigrade teaching: Challenges and opportunities. Springer. https://doi.org/10.1007/1-4020-4591-3
Luo, X., Yuan, Y., Zhang, K., Xia, J., Zhou, Z., Chang, L., & Gu, T. (2019). Enhancing statistical charts: Toward better data visualization and analysis. Journal of Visualization, 22, 819-832. https://doi.org/10.1007/s12650-019-00569-2
McMilan, J. H., & Schumacher, S. (2005). Investigación educativa [Educational investigation]. Pearson Adisson Wesley.
MINEDUC. (2014). Guía didáctica para el profesor matemática, módulo didáctico para la enseñanza y el aprendizaje en escuelas rurales multigrado: Leyendo, interpretando y organizando datos [Teaching guide for the mathematics teacher, teaching module for teaching and learning in rural multigrade schools: Reading, interpreting and organizing data]. MINEDUC.
Mishra, S. B., & Alok, S. (2022). Handbook of research methodology: A compendium for scholars & researches. Educreation Publishing.
Molina-Portillo, E., Contreras, J. M., Godino, J. D., & Ruz, F. (2019). Statistical literacy in the information society. Boletín de Estadística e Investigación Operativa [Bulletin of Statistics and Operational Research], 35(2), 148-169.
OECD. (2023). PISA 2022 results (volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en
Piñeiro-Naval, V. (2020). The content analysis methodology. Uses and applications in communication research on Spanish-speaking countries. Communication & Society, 33(3), 1-15. https://doi.org/10.15581/003.33.3.1-15
Rodríguez, C. (2019). Comprensión de gráficas estadísticas por estudiantes de grado octavo [Comprehension of statistical graphs by eighth grade students]. In D. Castro (Ed.), Memorias versión 1 del coloquio de educación estocástica [Reports version 1 of the stochastic education colloquium] (pp. 35-41). Universidad del Tolima.
Rosales, C. (1990). Evaluar es reflexionar sobre la enseñanza [Assess is to reflect on teaching]. Narcea.
Ruiz, A. (2015). Un estudio de caso sobre errores y dificultades observadas en la elaboración de algunas gráficas estadísticas [A case study on errors and difficulties observed in the preparation of some statistical graphs]. Góndola, Enseñanza y Aprendizaje de las Ciencias [Gondola, Science Teaching and Learning], 10(1), 26-39. https://doi.org/10.14483/jour.gdla.2015.1.a02
Samuel, M., Díaz-Levicoy, D., & Rodríguez-Alveal, F. (2019). Diseño y validación de un cuestionario para evaluar la comprensión de gráficos estadísticos en futuras educadoras de párvulos [Design and validation of a questionnaire to evaluate the understanding of statistical graphs in future early childhood educators]. Espacios, 40(41), 20.
Shaughnessy, J. M., Garfield, J., & Greer, B. (1996). Data handling. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 205- 237). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-009-1465-0_8
Vásquez, C. (2021). Comprensión y uso docente de gráficos estadísticos por futuros profesores para promover competencias para la sostenibilidad [Understanding and teaching use of statistical graphs by future teachers to promote competencies for sustainability]. Paradigma, 42(Extra 1), 165-190. https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p165-190.id1022
Wild, C. (2017). Statistical literacy as the earth moves. Statistics Education Research Journal, 16(1), 31-37. https://doi.org/10.52041/serj.v16i1.211
Zapata-Cardona, L. (2018). Enseñanza de la estadística desde una perspectiva crítica [Teaching statistics from a critical perspective]. Yupana, 10, 30-41. https://doi.org/10.14409/yu.v0i10.7695

How to cite this article

APA

Bustamante-Valdés, M., & Díaz-Levicoy, D. (2024). Understanding statistical graphs of students attending multigrade rural schools in Chile. International Electronic Journal of Mathematics Education, 19(3), em0785. https://doi.org/10.29333/iejme/14743

Vancouver

Bustamante-Valdés M, Díaz-Levicoy D. Understanding statistical graphs of students attending multigrade rural schools in Chile. INT ELECT J MATH ED. 2024;19(3):em0785. https://doi.org/10.29333/iejme/14743

AMA

Bustamante-Valdés M, Díaz-Levicoy D. Understanding statistical graphs of students attending multigrade rural schools in Chile. INT ELECT J MATH ED. 2024;19(3), em0785. https://doi.org/10.29333/iejme/14743

Chicago

Bustamante-Valdés, Matías, and Danilo Díaz-Levicoy. "Understanding statistical graphs of students attending multigrade rural schools in Chile". International Electronic Journal of Mathematics Education 2024 19 no. 3 (2024): em0785. https://doi.org/10.29333/iejme/14743

Harvard

Bustamante-Valdés, M., and Díaz-Levicoy, D. (2024). Understanding statistical graphs of students attending multigrade rural schools in Chile. International Electronic Journal of Mathematics Education, 19(3), em0785. https://doi.org/10.29333/iejme/14743

MLA

Bustamante-Valdés, Matías et al. "Understanding statistical graphs of students attending multigrade rural schools in Chile". International Electronic Journal of Mathematics Education, vol. 19, no. 3, 2024, em0785. https://doi.org/10.29333/iejme/14743