Measures of central tendency in primary education textbooks in Chile

José Hernán Parra-Fica; María del Mar López-Martín; Danilo Díaz-Levicoy

doi:10.29333/ejmste/14592

Full Text (PDF)

José Hernán Parra-Fica ¹ ^* , María del Mar López-Martín ² , Danilo Díaz-Levicoy ¹

More Detail

¹ Universidad Católica del Maule, Talca, CHILE² Universidad de Almería, Almería, SPAIN^* Corresponding Author

Abstract

This study analyzed the tasks associated with measures of central tendency proposed to Chilean students from 5^th to 8^th year of basic education. For this purpose, the activities involving mean, median, and/or mode were identified through the revision of two series of textbooks (16). The units of analysis were (1) type of measure, (2) task, (3) context, (4) support, and (5) cognitive skill. The main findings allowed us to indicate that the texts are aligned with the curricular guidelines, with tasks mostly associated with mean and mode, prioritizing calculation. Additionally, the tasks lack a context that gives meaning to the data. The support in which the data is presented is written and tabular. Finally, regarding the type of cognitive skills with the greatest presence in the textbooks, these are at a basic level.

Keywords

statistics
textbook
basic education
homework
measures of central tendency

License

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 20, Issue 6, June 2024, Article No: em2454

https://doi.org/10.29333/ejmste/14592

Publication date: 01 Jun 2024

Online publication date: 07 May 2024

Article Views: 1124

Article Downloads: 529

Open Access References How to cite this article

References

Amorim, N., & Silva, R. (2016). Apresentação e utilização de tabelas em livros didáticos de matemática do 4º e 5º anos do ensino fundamental [Presentation and use of tables in mathematics textbooks for the 4^th and 5^th years of elementary school]. Revista de Educação Matemática e Tecnológica Iberoamericana [Iberoamerican Mathematics and Technological Education Magazine], 7(1), 1-21.
Anderson, W. L., David, R., & Krathwohl, D. R. (2001). Una taxonomía para el aprendizaje, enseñanza y evaluación: Una revisión de la taxonomía de Bloom de objetivos educativos [A taxonomy for learning, teaching, and assessment: A review of Bloom’s taxonomy of educational objectives]. Longman.
Barrantes, M., & Zapata M. A. (2008). Obstáculos y errores en la enseñanza-aprendizaje de las figuras geométricas [Obstacles and errors in the teaching-learning of geometric figures]. Campo Abierto [Open Field], 27(1), 55-71.
Barrantes, M., López, M., & Fernández, M. (2015). Análisis de las representaciones geométricas en los libros de texto [Analysis of geometric representations in textbooks]. PNA, 9(2), 107-127. https://doi.org/10.30827/pna.v9i2.6105
Bloom, B. S. (1956). Taxonomy of educational objectives, handbook: The cognitive domain. David McKay.
Braga, G., & Belver, J. (2016). El análisis de libros de texto: Una estrategia metodológica en la formación de los profesionales de la educación [The analysis of textbooks: A methodological strategy in the training of education professionals]. Revista Complutense de Educación [Complutense Education Magazine], 27(1), 199-218. https://doi.org/10.5209/rev_RCED.2016.v27.n1.45688
Cantoral, R., Montiel, G., & Reyes-Gasperini, D. (2015). Análisis del discurso matemático escolar en los libros de texto, una mirada desde la teoría socio-epistemológica [Analysis of school mathematical discourse in textbooks, a view from socio-epistemological theory]. Avances de Investigación en Educación Matemática [Research Advances in Mathematics Education], 8, 9-28. https://doi.org/10.35763/aiem.v1i8.123
Chamorro M., & Vecino, F. (2003). El tratamiento y la resolución de problemas [Treatment and problem solving]. In M. Chamorro (Ed.), Didáctica de las matemáticas para primaria [Mathematics teaching for primary school] (pp. 273-299). Pearson.
Chevallard, Y. (1991). La transposición didáctica: Del saber sabio al saber enseñado [The didactic transposition: From wise knowledge to taught knowledge]. AIQUE.
Cobo, B. (2003). Significado de las medidas de posición central para los estudiantes de secundaria [Meaning of central position measures for high school students] [Doctoral thesis, Universidad de Granada].
Cobo, B., & Batanero, C. (2004). Significado de la media en los libros de texto de secundaria [Meaning of average in high school textbooks]. Enseñanza de las Ciencias [Science Teaching], 22(1), 5-18. https://doi.org/10.5565/rev/ensciencias.3899
Cockcroft, W. H. (1985). Las matemáticas sí cuentan [Mathematics does count]. Ministry of Education and Science.
Del Pino, G., & Estrella, S. (2012). Educación estadística: Relaciones con la matemática [Statistical education: Relations with mathematics]. Revista de Investigación Latinoamericana [Latin American Research Magazine], 49(1), 53-64. https://doi.org/10.7764/PEL.49.1.2012.5
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 graphics in Primary Education textbooks: A comparative study between Spain and Chile]. Bolema: Boletim de Educação Matemática, 30(55), 713-737. https://doi.org/10.1590/1980-4415v30n55a20
Díaz-Levicoy, D., Morales, R. & López-Martín, M.M. (2015). Tablas estadísticas en libros de texto chilenos de 1° y 2° año de Educación Primaria [Statistical tables in Chilean textbooks for 1st and 2nd year of Primary Education]. Revista Paranaense de Educação Matemática, 4(7), 10-39.
Díaz-Levicoy, D., Morales-Garcia, L. & Rodríguez-Alveal, F. (2020). Las medidas de tendencia central en libros de texto de educación primaria en México [Measures of central tendency in primary education textbooks in Mexico]. Paradigma, 41(1), 706-729.
Estrella, S. (2008). Medidas de tendencia central en la enseñanza básica en Chile [Measures of central tendency in basic education in Chile]. Revista Chilena de Educación Matemática [Chilean Magazine of Mathematics Education], 4(1), 20-32.
Fernández-Mosquera, E., & Mejía, M.F. (2010). Análisis de textos escolares para el diseño de situaciones de enseñanza [Analysis of school texts for the design of teaching situations]. In G. García (Ed.), Proceedings of the 11^th Colombian Meeting of Educational Mathematics (pp. 61-68). Colombian Association of Educational Mathematics.
García-García, J., Díaz-Levicoy, D., Vidal-Henry, S. & Arredondo, E. H. (2019). Las tablas estadísticas en libros de texto de educación primaria en México [Statistical tables in primary education textbooks in Mexico]. Paradigma, 40(2), 153-175.
García-García, J. I., Imilpán, I., Díaz-Levicoy, D., & Arredondo, E. H. (2021). Las medidas de tendencia central en libros de texto de séptimo básico de Chile [Measurements of central tendency in seventh grade textbooks in Chile]. Conrado, 17(81), 261-268.
Gómez, B. (2011). El análisis de manuales y la identificación de problemas de investigación en didáctica de las matemáticas [The analysis of manuals and the identification of research problems in mathematics didactics]. PNA, 5(2), 49-65. https://doi.org/10.30827/pna.v5i2.6157
Gómez-Torres, E., Ortiz, J., & Gea, M.M. (2014). Conceptos y propiedades de probabilidad en los libros de texto españoles de educación primaria [Concepts and properties of probability in Spanish primary education textbooks]. Avances de Investigación en Educación Matemática [Research Advances in Mathematics Education], 5, 49-71. https://doi.org/10.35763/aiem.v1i5.63
González-Astudillo, M., & Sierra, M. (2004). Metodología de análisis de libros de texto de matemáticas: Los puntos críticos en la enseñanza secundaria en España durante el siglo XX [Mathematics textbook analysis methodology: The critical points in secondary education in Spain during the 20^th century]. Enseñanza de las Ciencias [Science Teaching], 22(3), 389-408. https://doi.org/10.5565/rev/ensciencias.3872
Herbel, B. A. (2007). From intended curriculum to written curriculum: Examining the “voice” of a mathematics textbook. Journal for Research in Mathematics Education, 38(4), 344-369.
Hernández, R., Fernández, C., & Baptista, P. (2010). Metodología de la investigación [Investigation methodology]. McGraw Hill.
Jurečková, M., & Csachová, L. (2020). Statistical literacy of Slovak lower secondary school students. Technium Social Sciences Journal, 9(1), 163-173. https://doi.org/10.47577/tssj.v9i1.966
Krippendorff, K. (2013). Content analysis: An introduction to its methodology. SAGE.
Kus, M. (2022). A comparative textbook analysis on measures of center in selected school mathematics textbooks of Australia and Turkey. International Journal for Mathematics Teaching and Learning, 23(2), 144-173. https://doi.org/10.4256/ijmtl.v23i2.381
Latorres, D., & Vásquez, C. (2022). Las tablas estadísticas en libros de texto Chilenos de ciencias naturales [Statistical tables in Chilean natural science textbooks]. Revista de Ensino de Ciências e Matemática [Science and Mathematics Teaching Magazine], 13(6), 1-20. https://doi.org/10.26843/rencima.v13n6a12
Mayén, S. (2009). Comprensión de las medidas de tendencia central en estudiantes mexicanos de educación secundaria y bachillerato [Understanding measures of central tendency in Mexican secondary and high school students] [Doctoral thesis, Universidad de Granada].
McConway, K. (2016). Statistics and the media: A statistician’s view. Journalism, 17(1), 49-65. https://doi.org/10.1177/1464884915593243
MINEDUC. (2012). Matemática educación básica: Bases curriculares [Basic education mathematics: Curricular bases]. Curriculum and Assessment Unit, Ministry of Education.
MINEDUC. (2015). Bases curriculares 7°básico a 2° medio [Curriculum bases 7^th grade to 2^nd grade]. Curriculum and Assessment Unit, Ministry of Education.
Monterrubio, M. C., & Ortega, T. (2011). Diseño y aplicación de instrumentos de análisis y valoración de textos escolares de matemáticas [Design and application of instruments for analysis and assessment of school mathematics texts]. PNA, 5(3), 105-127. https://doi.org/10.30827/pna.v5i3.6152
Moore, D., & Cobb, G. (2000). Statistics and mathematics: Tension and cooperation. The American Mathematical Monthly, 107(7), 615-630. https://doi.org/10.1080/00029890.2000.12005247
Occeli, M., & Valeiras, N. (2013). Los libros de texto de ciencias como objeto de investigación: Una revisión bibliográfica [Science textbooks as an object of research: A bibliographic review]. Enseñanza de las Ciencias [Science Teaching], 31(2), 133- 152. https://doi.org/10.5565/rev/ec/v31n2.761
OECD. (2003). Marcos teóricos de PISA 2003: Conocimientos y destrezas en matemática, lectura, ciencias y solución de problemas [PISA 2003 theoretical frameworks: Knowledge and skills in mathematics, reading, science and problem-solving]. OECD Publishing.
Ortiz, J. J. (1999). Significado de los conceptos probabilísticos elementales en los libros de texto de bachillerato [Meaning of elementary probabilistic concepts in high school textbooks] [Doctoral thesis, Universidad de Granada].
Ortiz, J. J. (2002). La probabilidad en los libros de texto [Probability in textbooks]. Universidad de Granada.
Pallauta, J. D., Gea, M. M., & Arteaga, P. (2021). Caracterización de las tareas propuestas sobre tablas estadísticas en libros de texto chilenos de educación básica [Characterization of the proposed tasks on statistical tables in Chilean basic education textbooks]. Paradigma, 42, 32-60. https://doi.org/

10.37618/PARADIGMA.1011-2251.2021.p32-60.id1017
Pino, J., & Blanco, L. J. (2008). Análisis de los problemas de los libros de texto de matemáticas para alumnos de 12 a 14 años de edad de España y de Chile en relación con los contenidos de proporcionalidad [Analysis of the problems of mathematics textbooks for students aged 12 to 14 in Spain and Chile in relation to proportionality contents]. Publicaciones [Publications], 38, 63-88.
Quispe, W., Gallardo, J., & González, J. L. (2010). ¿Qué comprensión de la fracción fomentan los libros de texto de matemáticas Peruanos? [What understanding of fraction do Peruvian mathematics textbooks promote?] PNA, 4(3), 111-131. https://doi.org/10.30827/pna.v4i3.6166
Rico, L. (2013). El método del análisis didáctico [The method of didactic analysis]. Revista Iberoamericana de Educación Matemática [Ibero-American Journal of Mathematics Education], 33, 11-27.
Salgado, A. (2007). Investigación cualitativa: Diseños, evaluación del rigor metodológico y retos [Qualitative research: Designs, evaluation of methodological rigor and challenges]. Liberabit, 13(13), 71-78.
Vargas, M. F., Fernández-Plaza, J. A., & Ruiz-Hidalgo, J. F. (2020). La derivada en los libros de texto de 1º de bachillerato: Un análisis a las tareas propuestas [The derivative in 1^st year baccalaureate textbooks: An analysis of the proposed tasks]. Avances de Investigación en Educación Matemática [Research Advances in Mathematics Education], 18, 87-102. https://doi.org/10.35763/aiem.v0i18.288
Vargas-Delgado, L., Yepes, D.M., & Ávila-Toscano, J.H. (2021). Significado de las medidas de tendencia central en textos de matemática para secundaria [Meaning of measures of central tendency in secondary school mathematics texts]. Praxis, 17(2), 196-212. https://doi.org/10.21676/23897856.3575
Vásquez, C., Arredondo, E., & García-García, J.I. (2022). Representaciones estadísticas a temprana edad: Una aproximación desde los libros de texto de Chile y México [Statistical representations at an early age: An approach from the textbooks of Chile and Mexico]. Bolema [Bulletin], 36(72), 116-145. https://doi.org/10.1590/1980-4415v36n72a06
Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41-65. https://doi.org/10.1007/s10649-015-9595-1

How to cite this article

APA

Parra-Fica, J. H., López-Martín, M. D. M., & Díaz-Levicoy, D. (2024). Measures of central tendency in primary education textbooks in Chile. Eurasia Journal of Mathematics, Science and Technology Education, 20(6), em2454. https://doi.org/10.29333/ejmste/14592

Vancouver

Parra-Fica JH, López-Martín MDM, Díaz-Levicoy D. Measures of central tendency in primary education textbooks in Chile. EURASIA J Math Sci Tech Ed. 2024;20(6):em2454. https://doi.org/10.29333/ejmste/14592

AMA

Parra-Fica JH, López-Martín MDM, Díaz-Levicoy D. Measures of central tendency in primary education textbooks in Chile. EURASIA J Math Sci Tech Ed. 2024;20(6), em2454. https://doi.org/10.29333/ejmste/14592

Chicago

Parra-Fica, José Hernán, María del Mar López-Martín, and Danilo Díaz-Levicoy. "Measures of central tendency in primary education textbooks in Chile". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 6 (2024): em2454. https://doi.org/10.29333/ejmste/14592

Harvard

Parra-Fica, J. H., López-Martín, M. D. M., and Díaz-Levicoy, D. (2024). Measures of central tendency in primary education textbooks in Chile. Eurasia Journal of Mathematics, Science and Technology Education, 20(6), em2454. https://doi.org/10.29333/ejmste/14592

MLA

Parra-Fica, José Hernán et al. "Measures of central tendency in primary education textbooks in Chile". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 6, 2024, em2454. https://doi.org/10.29333/ejmste/14592