Strategies of students with autism when solving a permutation problem without repetition

Authors

DOI:

https://doi.org/10.35763/aiem24.4861

Keywords:

Combinatorics, Strategies Issues, Permutations, Problems, Autism Spectrum Disorder

Abstract

In this research, we identify the strategies of students with autism when solving a problem of permutations without repetition. Eight students associated with different educational levels and schooling modalities participated. On the one hand, three of them answered the question of the problem correctly, relying on strategies such as the use of representations or the systematic enumeration of possible triples. In both cases, the use of graphic schemes and tables facilitated a good organization of the information, both to determine the number of possible triples and the configuration of each one. On the other hand, the participants who resorted to alternative strategies or simply did not adopt a clear one, gave incorrect answers. In this article we conjecture the possible causes why this could happen, understanding that they could be related to the characteristic cognitive traits of people with neurodiversity.

Downloads

Download data is not yet available.

References

American Psychiatric Association, APA. (2013). Diagnostic and Statistical Manual of Mental Disorders (DSM-5). American Psychiatric Association.

Chen, L., Abrams, D. A., Rosenberg-Lee, M., Iuculano, T., Wakeman, H. N., Prathap, S., Chen, T., & Menon, V. (2019). Quantitative analysis of heterogeneity in academic achievement of children with autism. Clinical Psychological Science, 7(2), 362-380. https://doi.org/10.1177%2F2167702618809353

Delisio, L., Bukaty, C., & Taylor, M. (2018). Effects of a Graphic Organizer Intervention Package on the Mathematics Word Problem Solving Abilities of Students with Autism Spectrum Disorders. The Journal of Special Education Apprenticeship, 7(2), 1-21.

García de Tomás, J. (2016). Razonamiento combinatorio en alumnos de educación secundaria obligatoria. Trabajo Fin de Máster sin publicar, Universidad de Granada.

García-Moya, M. (2018). Resolución de problemas con niños con Trastorno del Espectro Autista (TEA). En A, Carmeiro-Barrera & A, Díaz-Román (Coords.), Avances en Ciencias de la Educación y del Desarrollo (pp. 419-426). Asociación Española de Psicología Conductual (AEPC).

García-Moya, M. (2022). Enseñanza de las matemáticas a alumnado con trastorno del espectro autista. Tesis Doctoral sin publicar, Universidad de Castilla la Mancha.

García-Moya, M., González-Ruiz, I., & Polo-Blanco, I. (2023). Argumentos del estudiantado con trastorno del espectro autista al comparar probabilidades simples: un estudio de casos. Bolema: Boletim de Educação Matemática, 37(75), 91-109.

Gea, M. M., Batanero, C., & Venegas, A. (2019). Lenguaje y estrategias utilizados por futuros profesores de educación primaria en la resolución de problemas combinatorios. Práxis Educacional, 15(33), 208-232. https://doi.org/10.22481/praxisedu.v15i33.5283

Happé, F. G. (1993). Communicative competence and theory of mind in autism: a test of relevance theory. Cognition, 48(2), 101-119. https://doi.org/10.1016/0010-0277(93)90026-R

Ingelin, B. L., Intepe-Tingir, S., & Hammons, N. C. (2021). Increasing the Number Sense Understanding of Prechool Student With ASD. Topics in Early Childhood Special Education, 43(2), 116-128. https://doi.org/10.1177/02711214211006190

Lamanna, L., Gea, M. M., & Batanero, C. (2022). Do Secondary School Students’ Strategies in Solving Permutation and Combination Problems Change with Instruction? Canadian Journal of Science, Mathematics and Technology Education, 22, 602-616. https://doi.org/10.1007/s42330-022-00228-z

Ley Orgánica 3/2020, de 29 de diciembre, por la que se modifica la Ley Orgánica 2/2006, de 3 de mayo, de Educación. Boletín Oficial del Estado, 340, de 30 de diciembre de 2020. https://www.boe.es/boe/dias/2020/12/30/pdfs/BOE-A-2020-17264.pdf

Lockwood, E. (2022). Leveraging prediction and reflection in a computational setting to enrich undergraduate students’ combinatorial thinking. Cognition and Instruction, 40(3), 413-455. https://doi.org/10.1080/07370008.2021.2020793

Lockwood, E., & Purdy, B. (2020). An unexpected outcome: Students’ focus on order in the multiplication principle. International Journal of Research in Undergraduate Mathematics Education, 6, 213-244. https://doi.org/10.1007/s40753-019-00107-3

Matitaputty, C., Nusantara, T., & Hidayanto, E. (2022). Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes. Journal on Mathematics Education, 13(3), 393-414. https://doi.org/10.22342/jme.v13i3.pp393-414

Navarro-Pelayo, V., Batanero, C., & Godino, J. D. (1997). Razonamiento combinatorio en alumnos de Secundaria. Educación matemática, 8(1), 26-39.

Ozonoff, S., & Schetter, P. L. (2007). Executive dysfunction in Autism Spectrum Disorders: From research to practice. En L. Meltzer (Ed.), Executive function in education: From theory to practice (pp. 287-308). Guilford.

Peltenburg, M. C., Van den Heuvel-Panhuizen, M. H. A. M., & Robitzsch, A. (2012). “Yes, I got them all”–Special education students’ ability to solve ICT-based combinatorics problems. En 12th International Congress on Mathematical Education (pp. abcde-fghij). ICME-12.

Polo-Blanco, I., Suárez-Pinilla, P., Goñi-Cervera, J., Suárez-Pinilla, M., & Payá, B. (2022). Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: The Influence of Cognitive Profile. Journal of Autism and Developmental Disorders, 1-13. https://doi.org/10.1007/s10803-022-05802-w

Ricart, M., & Estrada, A. (2022). Combinatorial and Proportional Task: Looking for Intuitive Strategies in Primary Education. Mathematics, 10(8), 1340. https://doi.org/10.3390/math10081340

Roa, R., Batanero, C., Godino, J. D., & Cañizares, M. J. (1997). Estrategias en la resolución de problemas combinatorios por estudiantes con preparación matemática avanzada. Epsilon, 36, 433-446.

Root, J. R., Ingelin, B., & Cox, S. K. (2021). Teaching Mathematical Word Problem Solving to Students with Autism Spectrum Disorder: A Best-Evidence Synthesis. Education and Training in Autism and Developmental Disabilities, 56(4), 420-436.

Sabariego, P., Polo-Blanco, I., García-Moya, M., & Goñi-Cervera, J. (2021). Diseño, construcción y validación de un cuestionario para evaluar el pensamiento probabilístico en alumnado con Trastorno del Espectro Autista. En A. Vico Bosch, L. Vega Caro & O. Buzón García (Eds.), Entornos virtuales para la educación en tiempos de pandemia: perspectivas metodológicas (pp. 438-468). Dykinson S. L.

Yin, R.K. (2009). Case Study Research: Design and Methods (6. ed.). Sage.

Zapata-Cardona L. (2018) Supporting young children to develop combinatorial reasoning. En A. Leavy, M. Meletiou-Mavrotheris & E. Paparistodemou (Eds.), Statistics in early childhood and primary education. (pp. 257-272). Springer. https://doi.org/10.1007/978-981-13-1044-7_15

Published

2023-11-03

How to Cite

González-Ruiz, I., & García-Moya, M. (2023). Strategies of students with autism when solving a permutation problem without repetition. Advances of Research in Mathematics Education, (24), 131–150. https://doi.org/10.35763/aiem24.4861

Issue

Section

Artículos