Main Article Content

Axel Dircio-Vargas
Javier García-García
Gerardo Salgado-Beltrán
Aloisius Loka Son

Abstract

To improve children's arithmetic learning, it is important to understand the strategies they use when solving arithmetic problems and the obstacles they find in this process. So, the objective of this research is to identify the strategies used by a group of Mexican fourth grade elementary school students in solving additive verbal arithmetic problems. We used a framework where the main theoretical elements that guided the study were characterized: strategies, types of strategies, verbal arithmetic problems, and the semantic and syntactic structures of the additive problems. This qualitative research, with a descriptive scope, uses case study as a method. The study cases were seven students from an Elementary School Located in ​​Zumpango de Neri, Guerrero, Mexico. To collect data, Task-Based Interviews were used, that were applied to the case studies in November 2024. The results allowed the identification of four reflective strategies: identifies a relevant keyword; selects the appropriate operation; performs mental calculation; and decomposes a numerical factor. Additionally, three non-reflective strategies were identified: uses an inappropriate keyword; operates with given data; and answers without performing operations. Some of the case studies used more than one strategy when solving some of the proposed tasks. These results allow suggesting that in the classroom the personal strategies used by students must be assessed in order to identify those that are thoughtless to help students travel towards the use of reflexive strategies. This will be possible through designs that incorporate problems resolving such as a central activity in the classroom.

Article Details

How to Cite
Dircio-Vargas, A. ., García-García, J., Salgado-Beltrán, G. ., & Son, A. L. (2025). Strategies Used by Mexican Fourth-Grade Elementary Students in Solving Additive Word Problems. Indonesian Educational Research Journal, 2(3), 126–141. https://doi.org/10.56773/ierj.v2i3.72
Section
Original Research

References

Altun, M., Bintaş, J., Yazgan, Y.& Arslan C. (2004). İlköğretim Çağındaki Çocuklarda Problem Çözme Gelişiminin İncelenmesi [Investigation of Problem-Solving Development in Primary School Children]. Bursa: Uludağ Üniversitesi, Bilimsel Araştırma Projeleri Birimi. https://10.13140/RG.2.1.2611.9927.

Ariza, K. (2020). Modelos y enfoques de la compresión en la solución de problemas aritméticos verbales [Models and Approaches to Comprehension in Solving Arithmetic Word Problems]. Didasc@lia: Didáctica y Educación, 11(4), 1-13.

Arnal-Palacián, M., de Nava-Tapia, S. & Begué, N. (2023). Análisis de problemas aditivos en libros de texto de educación primaria en México [Analysis of Additive Problems in Elementary School Textbooks in Mexico]. Revista de Investigación en Educación, 21(2), 192-207. https://doi.org/10.35869/reined.v21i2.4599.

Bal, A. P. & Artut, P. D. (2022). Investigation of primary school students solving arithmetic verbal problems. Journal of Education and Learning, 16(1), 76~84. https://doi.org/10.11591/edulearn.v16i1.20336.

Baroody, A. J. (1990). Children's Mathematical Learning: A Cognitive View. Journal for Research in Mathematics Education, 4, 51-64. https://doi.org/10.2307/749912.

Bingham, A. J. (2023). From Data Management to Actionable Findings: A Five-Phase Process of Qualitativa Data Analysis. International Journal of Qualitative Methods, 22. https://doi.org/10.1177/16094069231183620.

Blanco, L., Caballero, A., & Cárdenas, J. (2015). Los problemas aritméticos escolares [School arithmetic problems]. In L. J. Blanco, J. A. Cárdenas, & A. Caballero (Eds.), La resolución de problemas de Matemáticas en la formación inicial de profesores de primaria (pp. 123-138). Spain: Universidad de Extremadura.

Bonilla, M., Sánchez, N., & Guerrero, F. (1999). Estructura aditiva y formación de profesores para la educación básica [Additive structure and teacher training for basic education]. In M. Bonilla, N. Sánchez, M. Vidal, F. Guerrero, J. Lurduy, J. Romero, P. Rojas, L. Mora, & C. Barón (Eds.), La enseñanza de la aritmética escolar y la formación del profesor (pp. 1-150). Bogotá, Colombia: Grupo Editorial Gaia.

Butto, C., & Martínez, C. (2012). Abordaje basado en competencias: la resolución de problemas aditivos en el nivel básico [Competency-based approach: Solving additive problems at the basic level]. Revista Horizontes Pedagógicos, 14(1), 30-42.

Carpenter, T. P., & Moser, J. M. (1982). The Development of Addition and Subtraction Problem-Solving Skills. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and Subtraction: A Cognitive Perspective (pp. 9-24). Hillsdale, NJ: Lawrence Erlbaurn Associates.

Castillo, M., & Ramírez, A. (2013). Difficulties associated with the statement of additives verbal arithmetic problems of the students of the first three grades primary. Revista de Investigación, 37(79), 145-168.

Castro, A., Gorgorió, N., & Prat, M. (2014). Indicios verbales en los PAEV aditivos planteados por estudiantes para maestro [Verbal cues in additive word problems posed by pre-service teachers]. In M. T. González, M. Codes, D. Arnau, & T. Ortega (Eds.), Investigación en Educación Matemática XVIII (pp. 217-226). Salamanca: SEIEM.

Chamoso, J. M., Vicente, S., Manchado, E., & Múñez, D. (2014). Los Problemas de Matemáticas Escolares de Primaria, ¿Son solo Problemas para el aula? [Are elementary school math problems only for the classroom?]. Cuadernos de Investigación y Formación en Matemática, 9, 261–279.

de Oliveira, J. M., & Marques, R. (2022). Investigando estratégias de resolução de situações-problema do campo aditivo [Investigating strategies for solving additive word problems]. Revemop, 4, 1-26. https://doi.org/10.33532/revemop.e202228.

Fan, L. & Zhu, Y. (2000). Problem solving in Singaporean secondary mathematics textbooks. The Mathematics Educator, 5(1),117-141

García-García, J. (2014). Los problemas aritméticos en primaria: un estudio sobre las concepciones de profesores bilingües [Arithmetic problems in primary school: a study on the conceptions of bilingual teachers]. Números, 87, 37-58.

García-García, J. (2019). Estrategias en la resolución de problemas algebraicos en un contexto intercultural en el nivel superior [Strategies for solving algebraic problems in an intercultural context at the higher level]. Bolema, 33(63), 205-225. http://dx.doi.org/10.1590/1980-4415v33n63a10.

García-García, J., Rodríguez, F. M., & Navarro, C. (2015). Las estrategias utilizadas por los niños Tee Savi en la resolución de problemas aritméticos [Strategies used by Tee Savi children in solving arithmetic problems]. Revista latinoamericana de investigación en matemática educativa, 18(2), 213-244.

Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517–545). Lawrence Erlbaum Associates.

Haser, Ç., Doğan, O. & Erhan, G. K. (2022). Tracing students’ mathematics learning loss during school closures in teachers’ self-reported practices. International Journal of Educational Development, 88, (102536). https://doi.org/10.1016/j.ijedudev.2021.102536.

Heller, J. I., & Greeno, J. G. (1978). Semantic processing in arithmetic word problem solving. Paper presented at the Midwestern Psychological Association. Chicago.

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18-32.

Hickendorff, M., Torbeyns J. & Verschaffel L. (2019), Multi-digit Addition, Subtraction, Multiplication, and Division Strategies. In A. Fritz, V. G. Haase and P. Räsänen (Eds.), International Handbook of Mathematical Learning Difficulties (pp. 543-560). Springer. https://doi.org/10.1007/978-3-319-97148-3_32.

Hinault, T. & Lemaire, P. (2016). What does EEG tell us about arithmetic strategies? A review. International Journal of Psychophysiology, 106, 115-126. https://doi.org/10.1016/j.ijpsycho.2016.05.006.

LeBlanc, M. D. & Weber-Russell, S. (1996). Text Integration and Mathematical Connections: A Computer Model of Arithmetic Word Problem Solving. Cognitive Science, 20, 357-407

Martins, L. G. & Martinho, M. H. (2021). Strategies, Difficulties, and Written Communication in Solving a Mathematical Problem. Bolema, 35(70), 903-936. https://doi.org/10.1590/1980-4415v35n70a16.

Mateus-Nieves, E. & Devia, H. (2020). Development of mathematical thinking skill from the formulation and resolution of verbal arithmetic problems. Acta Scientiae, 23(1), 30-52. https://doi.org/10.17648/acta.scientiae.5845.

Meneses-Patiño, Y. P. & Ardila, L. (2019). The Singapore Method as a didactic strategy for the strengthening of the competence of solving additive problems in elementary school students. Eco Matemático, 10(1), 28–41. https://doi.org/10.22463/17948231.2540.

Moreno-Pantoja, L. M., Banguera-Ortíz, J. A. & Martínez-Patiño, L. F. (2023). Difficulties and errors in solving simple additive type problems. Revista Perspectiva, 8(1), 64-76. https://doi.org/10.22463/25909215.4114.

Önal, H. (2023). A Comparison of Problem-Solving strategies of Primary School 3rd and 4th-Graders. Mimbar Sekolah Dasar, 10(1), 80-91. https://doi.org/10.53400/mimbar-sd.v10i1.46242.

Orrantia, J., González, L. B., & Vicente, S. (2005). Un análisis de los problemas aritméticos en los libros de texto de Educación Primaria [An analysis of arithmetic problems in elementary school textbooks]. Infancia y Aprendizaje: Journal for the Study of Education and Development, 28(4), 429-451.

Polotskaia, E., Savard, A. & Freiman, V. (2016). Investigating a case of hidden misinterpretations of an additive word problem: structural substitution. European Journal of Psychology of Education, 31(2), 135-153.

Powell, S. R. (2011). Solving Word Problems Using Schemas: A Review of the Literature. Learning Disabilities Research & Practice, 26(2), 94-108.

Powell, S., Berry, K. & Benz, S. (2020). Analyzing the Word-problem performance and strategies of students experiencing mathematics difficulty. The Journal of Mathematical Behavior, 58(191). 1-16. https://doi.org/10.1016/j.jmathb.2020.100759.

Puig, L., & Cerdán, M. (1988). Problemas aritméticos [Arithmetic problems]. Síntesis.

Puspitasari, L., In’am, A. & Syaifuddin, M. (2019). Analysis of Students’ Creative Thinking in Solving Arithmetic Problems. International Electronic Journal of Mathematics Education, 14(1), 49-60. https://doi.org/10.12973/iejme/3962.

Rizo, C. & Campistrous, L. (1999). Problem-solving strategies in school. Revista Latinoamericana de Investigación en Matemática Educativa, 2(2), 31-46.

Rodríguez-Nieto, C. A., Navarro-Sandoval, C., Castro-Inostroza, A. N., & García-González, M. S. (2019). Estructuras semánticas de problemas aditivos de enunciado verbal en libros de texto mexicanos [Semantic structures of additive word problems in Mexican textbooks]. Educación Matemática, 31(2), 75-104.

Sánchez, M. & Vicente, S. (2015). Models and processes for solving arithmetic word problems proposed by Spanish mathematics textbooks. Culture and education, 27(4), 695-725.

Siswono, T. Y. (2004). Identifying creative thinking process of students through mathematics problem posing. In M. Nita (Ed.), Proceeding of the International Conference on Statistics and Mathematics and Its Application in the Development of Science and Technology (pp. 85-80). Bandung Islamic University.

Stake, R. E. (1978). The Case Study Method in Social Inquiry. Educational Researcher, 7(2), 5-8. https://doi.org/10.3102/0013189X007002005.

Tárraga-Mínguez, R., & Tarín-Ibáñez, J. (2022). Problemas aritméticos verbales en Educación Primaria. Un análisis de guías didácticas [Arithmetic word problems in elementary education. An analysis of teaching guides]. Revista De Educación, 396-536. https://doi.org/10.4438/1988-592X-RE-2022-396-536.

Tárraga-Mínguez, R., Tarín-Ibáñez, J., & Lacruz-Pérez, I. (2021). Analysis of word problems in primary education mathematics textbooks in Spain. Mathematics, 9(17), 2123.

Verschaffel, L. & De Corte, E. (1993). A decade of Research on world problem solving in Leuven: theoretical, methodological, and practical outcomes. Educational Psychology Review, 5(3), 239-256.

Verschaffel, L., Greer, B., & De Corte, E. (2000). Making Sense of Word Problems. Educational Studies in Mathematics 42(2), 211-213.

Vicente, S., Verschaffel, L., Sánchez, R. & Múñez, D. (2022). Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks. Educational Studies in Mathematics, 111, 375–397. https://doi.org/10.1007/s10649-022-10169-x.

Wee, T. M. & Yeo, K. K. J. (2024). An analysis of semantic structures of addition and subtraction word problems used in primary two mathematics textbooks. Contemporary Mathematics and Science Education, 5(2), ep24011. https://doi.org/10.30935/conmaths/14690.