A study about mental calculation strategies with natural numbers in elementary school students using the broken calculator

Year 2024, , 1 - 12, 30.06.2024

Angel De Jesus Pacio-quiterio , José Antonıo Juárez López

https://doi.org/10.5281/zenodo.12612518

Abstract

This article reports a study about mental calculation in a group of elementary school students. Mental arithmetic, nowadays, is recognized as a subject of interest by several authors and educational systems. The latter have tried to design programs to develop it according to the flexibility of strategies, mathematical concepts, properties of the number system, and number sense. Several authors point out that tasks or activities should be incorporated with the intention of attending to this priority and not under a memoristic or strict teaching. In this sense, this qualitative research aimed to explore and describe the processes, strategies, operations, and skills (Rathgeb-Schnierer and Green 2019) used by six students studding sixth grade primary school in Puebla, Mexico. These students were 11 years old at the time they used the Broken Calculator application as a milieu to solve tasks; and it is shown that different strategies are developed when faced with the same tasks: some are predominant, others with a simple level of complexity, and how different calculation trains are elaborated according to the mastery of the strategies.

Keywords

Mental calculation, Broken calculator, Flexibility, Strategy

Ethical Statement

The article has not been published previously. It has not been sent to any other media for evaluation and publication. The publication is authorized by all authors as expressly or tacitly by the responsible authorities of the institution in which it was carried out get the job done.

Supporting Institution

Meritorious Autonomous University of Puebla

Project Number

1

Thanks

To CONAHCYT. To the principal of the "Gral. Lázaro Cárdenas" primary school. To the "Gral. Lázaro Cárdenas" primary school.

References

• Abd Algani, Y. M., Abo Al-Haija, Y., & Hibi, W. (2021). The impact of the use of mathematical problem solving on the development of creative thinking skills for prep school students in Arab schools in Israel. Journal for the Mathematics Education and Teaching Practices, 2(1), 9-27.
• Alsina, A. (2007). ¿Por qué algunos niños tienen dificultades para calcular? Una aproximación desde el estudio de la memoria humana (Why do some children have difficulties in calculating? An approach from the study of human memory). Revista Latinoamericana de Investigación en Matemática Educativa, 10(3), 315-333.
• Barrera-Mora, F., Reyes-Rodríguez, A. & Mendoza-Hernández, J. G. (2018). Estrategias de cálculo mental para sumas y restas desarrolladas por estudiantes de secundaria (Mental calculation strategies for addition and subtraction developed by high school students). Educación Matemática, 30(3), 122-150. DOI/10.24844/EM3003.06
• Carvalho, R., & Rodrigues, M. (2021). Day number routine: An opportunity to understand students’ uses of numbers and operations. Journal of Mathematics Education, 14(1), 28-46. DOI:10.26711/007577152790062.
• Cortés, J., Backhoff, E., & Organista, J. (2004). Estrategias de cálculo mental utilizadas por estudiantes del nivel secundaria de Baja California (Mental calculation strategies used by high school students in Baja California). Educación Matemática, 16(1), 149-168.
• D’Amore, B., & Fandiño-Pinilla, M. I. (2002). Un acercamiento analítico al “triángulo de la didáctica” (An analytical approach to the "triangle of didactics"). Educación Matemática. 14(1), 48-61.
• D’Amore, B. (2021). El contrato didáctico (The didactic contract). En B. D’Amore (2ª ed), Educación Matemática (pp. 113-135). Magisterio.
• Eleftheriadi, A., Lavidas, K., & Komis, V. (2021). Teaching Mathematics in Early Childhood Education with ICT: The Views of Two Contrasting Teachers' Groups. Journal of Digital Educational Technology, 1(1), ep2103. https://doi.org/10.21601/jdet/11117
• Flores, A., Reys, B. & Reys, R. (1990). Desempeño y estrategias en la estimación en operaciones aritméticas (Performance and estimation strategies in arithmetic operations). Educación Matemática, 2(1), 30 -44.
• Gómez, B. (2005). La enseñanza del cálculo mental (Teaching mental calculation). Unión. Revista Iberoamericana de Educación Matemática, 1(4), 17-29.
• Goupil J. F. (2012). L’utilisation de la calculatrice dans l’apprentissage des mathématiques au secondaire (The use of calculators in learning secondary mathematics). En Dorier J.-L., Coutat S. (Eds.) Enseignement des mathématiques et contrat social: enjeux et défis pour le 21e siècle – Actes du colloque EMF2012 (SPE1, pp. 1583–1603).
• Hickendorff, M. (2022). Flexibility and Adaptivity in Arithmetic Strategy Use: What Children Know and What They Show. Journal of Numerical Cognition, 8(3), 367-381. DOI:10.5964/jnc.7277
• Hope, J. (1987). A case study of a Highly Skilled Mental Calculator. Journal for Research in Mathematics Education, 18(5), 331-342.
• Jurić J., & Pjanić K. (2023). An Overview of Mental Calculation Strategies and the Frequency of Their Application. Journal of Elementary Education, 16(3), 277-294. DOI:10.18690/rei.16.3.3087
• Lemonidis, C. (2016). Mental Computation and Estimation: Implications for mathematics education research teaching and learning. Routledge.
• Lemonidis, C., & Kaiafa, I. (2014). Fifth and sixth grade students’ number sense in rational numbers and its relation with problem solving ability. Journal of Educational Research, 1, 61-74.
• López, M. (2014). Desarrollo de la Memoria de Trabajo y Desempeño en Cálculo Aritmético: un Estudio Longitudinal en Niños (Development of Working Memory and Arithmetic Calculation Performance: A Longitudinal Study in Children). Electronic Journal of Research in Educational Psychology, 12(1), 171-190. DOI:10.14204/ejrep.32.13103
• Ministerio de Educación de la Ciudad de Buenos Aires. (2010). Matemática: Cálculo mental con números racionales (Mathematics: Mental calculation with rational numbers). Argentina.
• Mochón, S. & Vázquez, R. (1995). Cálculo mental y estimación: Métodos, resultados de una investigación y sugerencias para su enseñanza (Mental calculation and estimation: methods, results of an investigation, and suggestions for their teaching). Educación Matemática, 7(3), 93-105.
• Rathgeb-Schnierer, E. & Green, M. G. (2017). Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students. Journal of Mathematics Education, 10(1), 1-16. DOI:10.26711/007577152790009
• Rathgeb-Schnierer, E. & Green, M. G. (2019). Developing Flexibility in Mental Calculation. Educação & Realidade, 44(2), 1-17. DOI:10.1590/2175-623687078 1
• Rodríguez, T. & Juárez, J. A. (2019). Estrategias de cálculo mental empleadas por una alumna de segundo grado de primaria: El caso de Luisa (Mental calculation strategies used by a second grade student: The case of Louis). Números. Revista de Didáctica de las Matemáticas, 102, 67-81.
• Sánchez. J. (2013). Paradigmas de investigación educativa: de las leyes subyacentes a la modernidad reflexiva (Paradigms of educational research: from underlying laws to reflexive modernity). Entelequia: Revista Interdisciplinar, 16, 91-102.
• Sánchez, L., Butrón, P. O. & Juárez, J. A. (2020). Estrategias de cálculo mental mediante el uso de la calculadora descompuesta en estudiantes de secundaria (Mental calculation strategies using the decomposed calculator in high school students). Unión. Revista Iberoamericana de Educación Matemática, 16(59), 121-139.
• Schettini, P. & Cortazzo, I. (2016). Técnicas y estrategias en la investigación cualitativa (Techniques and strategies in qualitative research). Editorial de la Universidad de la Plata.
• Secretaría de Educación Pública. (2017). Plan y programas de Estudio de Educación Básica Secundaria (Plan and Programs of Study for Secondary Basic Education). México. Comisión Nacional de los Libros de Texto Gratuitos.
• Threlfall, J. (2002). Flexible Mental Calculation. Educational Studies in Mathematics, 50, 29–47. DOI:10.1023/A:1020572803437
• Threlfall, J. (2009) Strategies and flexibility in mental calculation. ZDM: The international journal on Mathematics Education, 41, 541–555 . DOI:10.1007/s11858-009-0195-
• Valencia, E. (2013). Desarrollo del cálculo mental a partir de entrenamiento en combinaciones numéricas y estrategias de cálculo (Development of mental calculation through training in numerical combinations and calculation strategies). Números. Revista de Didáctica de las Matemáticas, 84, 5-23.
• Weiss, E., Block, D., Civera, A., Dávalos, A. & Naranjo, G. (2019). La enseñanza de distintas asignaturas en escuelas primarias: Una mirada a la práctica docente (Teaching different subjects in elementary schools: A look at teaching practice). Revista Mexicana de Investigación Educativa, 24(81), 349-374.
• Yang, D., Li, M. & Lin, C. (2008). A Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics. International Journal of Science and Mathematics Education 6, 789–807. DOI:10.1007/s10763-007-9100-0