A didactic proposal for teaching factorization cases of expressions of the form ax2+by+cx+ay+exy+f through Mathigon

Paola Alejandra Balda Álvaréz; Marcos Chacón-Castro; Romina Soledad Busain; Janio Jadán-Guerrero

doi:10.29333/ejmste/15198

A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon

Full Text (PDF)

Paola Alejandra Balda Álvaréz ¹ , Marcos Chacón-Castro ² ^* , Romina Soledad Busain ³ , Janio Jadán-Guerrero ⁴

More Detail

¹ Secretaría de Educación de Soacha, Institución Educativa General Santander, Soacha, COLOMBIA² Grupo de Investigación GIECI, Fundación Universitaria Internacional de La Rioja, Bogotá, COLOMBIA³ Instituto de Educación Mercedes Pacheco, Escuela de Educación Secundaria n°61, La Plata, Buenos Aires, ARGENTINA⁴ Mechatronics and Interactive Systems (MIST), Universidad Indoamérica, Quito, ECUADOR^* Corresponding Author

Abstract

This paper presents the results of research conducted in a classroom setting with eighth-grade students in a public school in Argentina. The experience aimed, within the framework of an algebra course, to introduce the design and results of the implementation of a didactic proposal designed to establish relationships between expressions of the form ax²+by+cx+ay+exy+f, with a, b ∈ N and c, d, e, f ∈ Z, as a product of factors through the virtual manipulative Mathigon. The evidence collected leads to the identification that algebraic work using virtual manipulatives allows students to give a different meaning to mathematics, explore various forms of representation, and construct their own knowledge.

Keywords

Mathigon
mathematics education
factoring
algebra
didactic engineering

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 10, October 2024, Article No: em2514

https://doi.org/10.29333/ejmste/15198

Publication date: 01 Oct 2024

Online publication date: 25 Sep 2024

Article Views: 104

Article Downloads: 96

Open Access References How to cite this article

References

Armando, M., Régner, I., & Ochs, M. (2023). Toward a tool against stereotype threat in math: Children’s perceptions of virtual role models. In Proceedings of the International Conference on Multimodal Interaction (pp. 306-310). ACM. https://doi.org/10.1145/3610661.3616179
Babo, L., Pinto, C. M. A., Mendonça, J., Rasteiro, D. M. L. D., Caridade, C. M. R., Lavicza, Z., Ulbrich, E., Rahmadi, I. F., Anđić, B., Abrori, F. M., Kocadere, S. A., Petridis, K., Nikolopoulos, C. D., Kokkinos, E. A., & Vardiambasis, I. O. (2023). MATHematics DIGital escape rooms–Empowering students. In A. Mesquita, A. Abreu, J. V. Carvalho, & C. H. P. de Mello (Eds.), Perspectives and trends in education and technology. Smart innovation, systems and technologies (pp. 375-385). Springer. https://doi.org/10.1007/978-981-19-6585-2_34
Brousseau, G. (1986). Fondements et méthodes de la didactiques des mathématiques [Foundations and methods of mathematics teaching]. Recherches en Didactique des Mathématiques, 7(2), 4-10.
Cabero, J., & Marín, V. (2014). Posibilidades educativas de las redes sociales y el trabajo en grupo. Percepciones de los alumnos universitarios [Educational possibilities of social networks and group work. University students’ perceptions]. Comunicar [Communicate], 42.
Caro, M. (2015). Los beneficios del aprendizaje adaptativo [The benefits of adaptive learning]. http://ideasqueinspiran.com/2015/12/14/los-beneficios-del-aprendizaje-adaptativo/
Chacón-Castro, M., Aimacaña-Espinosa, L., & Jadán-Guerrero, J. (2021). Escape rooms: Mathematical challenges available to educators. In A. Mesquita, A. Abreu, J. V. Carvalho, & C. H. P. de Mello (Eds.), Perspectives and trends in education and technology. Smart innovation, systems and technologies (pp. 195-205). Springer. https://doi.org/10.1007/978-981-16-5063-5_16
Chiappe, A. (2016). Tendencias sobre contenidos educativos digitales en América Latina [Trends in digital educational content in Latin America]. UNESCO. http://unesdoc.unesco.org/images/0024/002456/245673s.pdf
da Silva, R., & Duarte, V. (2019). Didactic situations: The application of oval tangram in the education of angles in the 6^th year of fundamental education. International Journal of Emerging Technologies in Learning, 2(1), 32-46. https://doi.org/10.31692/2595-2498.V2I1.71
Ferreira, J. F., & Mendes, A. (2020). Open and interactive learning resources for algorithmic problem solving. In Formal Methods. FM 2019 International Workshops (pp. 200-208). Springer. https://doi.org/10.1007/978-3-030-54997-8_13
García, M. D., Prieto, F. J. G., & Hurtado, I. G. (2017). Moodle y Facebook como herramientas virtuales didácticas de mediación de aprendizajes: Opinión de profesores y alumnos universitarios [Moodle and Facebook as virtual didactic tools for learning mediation: Opinion of university professors and students]. Revista Complutense de Educación [Complutense Education Magazine], 29(3), 807-827. https://doi.org/10.5209/rced.53968
Guizado, J. V., & Ortiz, J. Á. R. (2022). Retos digitales del profesorado en gestión de la enseñanza virtual de matemáticas [Digital challenges for teachers in managing virtual mathematics teaching]. Revista Venezolana de Gerencia [Venezuelan Management Magazine], 27, 390-408. https://doi.org/10.52080/rvgluz.27.7.26
Hodovaniuk, T., Makhometa, T., Tiahai, I., Medivedieva, M., & Pryshchepa, S. (2020). The use of ICT in the flip teaching of future mathematics teachers. In Proceedings of the 16^th International Conference on ICT in Education (pp. 709-720). https://doi.org/10.31812/123456789/4457
Huda, M. E. (2019). The problematic: Teachers’ pedagogical ability in using technology on mathematics learning of junior high school. Journal of Physics, 1200, 012009. https://doi.org/10.1088/ 1742-6596/1200/1/012009
Kechil, R., Mohd, A., & Mohammad, A. (2022). Geogram: Digital game-based learning tool for improving basic geometric knowledge. https://ir.uitm.edu.my/id/eprint/60342/1/60342.pdf
Keldgord, F., & Ching, Y.-H. (2022). Teachers’ experiences with and perceptions of virtual manipulatives following the COVID-19 pandemic. TechTrends, 66, 957-967. https://doi.org/10.1007/s11528-022-00796-9
Klizienė, I., Taujanskienė, G., Augustiniene, A., Simonaitienė, B., & Cibulskas, G. (2021). The impact of the virtual learning platform EDUKA on the academic performance of primary school children. Sustainability, 13(4), 2268. https://doi.org/10.3390/su13042268
Lee, J. Y., Pyon, C. U., & Woo, J. (2023a). Digital twin for math education: A study on the utilization of games and gamification for university mathematics education. Electronics, 12(15), 3207. https://doi.org/10.3390/electronics12153207
López-García, A. (2023). Effectiveness of a teaching methodology based on the theory of historical thinking through active methods and digital resources in Spanish adolescents. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1175123
Martín Díaz, A., Alario-Hoyos, C., Estévez-Ayres, I., Delgado Kloos, C., & Fernández-Panadero, C. (2023). ABENEARIO: A system for learning early maths with ABN. Education and Information Technologies, 28, 12859-12881. https://doi.org/10.1007/s10639-023-11692-x
Martin, C. S., Harbour, K., & Polly, D. (2022). Examining how emergency remote teaching influenced mathematics teaching. TechTrends, 66(2), 338-350. https://doi.org/10.1007/s11528-022-00711-2
Martín-Gutiérrez, J., Mora, C. E., Añorbe-Díaz, B., & González-Marrero, A. (2017). Virtual technologies trends in education. EURASIA Journal of Mathematics, Science and Technology Education, 13(2), 469-486. https://doi.org/10.12973/eurasia.2017.00626a
Mato-Vázquez. D., Castro-Rodríguez M., & Pereiro-González, C. (2018). Análisis de materiales didácticos digitales para guiar y/o apoyar el proceso de enseñanza-aprendizaje de las matemáticas [Analysis of digital teaching materials to guide and/or support the teaching-learning process of mathematics]. Revista d’Innovació Educativa [Educational Innovation Magazine], 20, 80-88. https://doi.org/10.7203/attic.20.12117
Mayasari, N., Hasanudin, C., & Fitrianingsih, A. (2020). The use of wingeom software in geometry subject, how is the learning outcomes of junior high school students? Journal of Physics: Conference Series, 1477, 042042. https://doi.org/10.1088/1742-6596/1477/4/042042
Moral-Sánchez, S. N., Sánchez-Compaña, M. ª. T., & Romero, I. (2022). Geometry with a STEM and gamification approach: A didactic experience in secondary education. Mathematics, 10(18), 3252. https://doi.org/10.3390/math10183252
Oliveira Jr, A. P., & Datori Barbosa, N. (2023). Tasks about impossible random events: A pedagogical game as a teaching tool for the early years of elementary school. Acta Scientiae [Journal of Science], 25(6), 183-208. https://doi.org/10.17648/acta.scientiae.7654
Palma, G. A., Arteaga, M. J., Hermosilla, A. S., Delgado, A., & Lee, E. (2023). Development of a web system to improve and reinforce learning in mathematics in primary and secondary students in Peru. International Journal on Recent and Innovation Trends in Computing and Communication, 11(5), 23218169. https://doi.org/10.17762/ijritcc.v11i5s.6597
Polypad – virtual manipulatives – mathigon. (2023). https://mathigon.org/polypad
Rahayu, E. G. S., Juandi, D., & Jupri, A. (2021). Didactical design for distance concept in solid geometry to develop mathematical representation ability in vocational high school. Journal of Physics: Conference Series, 1882(1), 012077. https://doi.org/10.1088/1742-6596/1882/1/012077
Rumanová, L. (2022). Reflection of problem solving task and importance of a-priori analysis in preparing teacher for the teaching process. TEM Journal, 11(2), 837-841. https://doi.org/10.18421/tem112-42
Salas, R., Ramírez, J., Eslava, A., Castañeda, R., & de la Cruz, G. (2022). Teachers’ perception of web games and mobile devices at the higher educational level during the COVID-19 pandemic. Texto Livre [Free Text], 15, e37074. https://doi.org/10.35699/1983-3652.2022.37074
Sepeng, P. (2023). Unlocking mathematical potential–The impact of dynamic symmetry activities on learning and teaching mathematics. Symmetry: Culture and Science, 34(3), 297-316. https://doi.org/10.26830/symmetry_2023_3_297
Tetchueng, J.-L., Garlatti, S., & Laube, S. (2007). A didactic-based model of scenarios for designing an adaptive and context-aware learning system. In Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence (pp. 703-726). IEEE. https://doi.org/10.1109/wi.2007.4427180
Thompson, M., Leonard, G., Mikeska, J. N., Lottero, P. S., Maltese, A., Pereira, G., Hillaire, G., Waldron, R., Slama, R., & Reich, J. (2022). Eliciting learner knowledge: Enabling focused practice through an open-source online tool. Behavioral Sciences, 12(9), 324. https://doi.org/10.3390/bs12090324
Vergara, A. (2021) ¿Se aprende matemáticas en un modelo virtual? [Do you learn mathematics in a virtual model?] https://observatorio.tec.mx/edu-bits-blog/aprendizaje-de-las-matematicas-en-un-modelo-virtual/
Zaikin, O., Malinowska, M., Bakhtadze, N., & Żyławski, A. (2017). Motivation and social aspects of competence-based learning process. Procedia Computer Science, 112, 1092-1101. https://doi.org/10.1016/j.procs.2017.08.131

How to cite this article

APA

Balda Álvaréz, P. A., Chacón-Castro, M., Busain, R. S., & Jadán-Guerrero, J. (2024). A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2514. https://doi.org/10.29333/ejmste/15198

Vancouver

Balda Álvaréz PA, Chacón-Castro M, Busain RS, Jadán-Guerrero J. A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon. EURASIA J Math Sci Tech Ed. 2024;20(10):em2514. https://doi.org/10.29333/ejmste/15198

AMA

Balda Álvaréz PA, Chacón-Castro M, Busain RS, Jadán-Guerrero J. A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon. EURASIA J Math Sci Tech Ed. 2024;20(10), em2514. https://doi.org/10.29333/ejmste/15198

Chicago

Balda Álvaréz, Paola Alejandra, Marcos Chacón-Castro, Romina Soledad Busain, and Janio Jadán-Guerrero. "A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 10 (2024): em2514. https://doi.org/10.29333/ejmste/15198

Harvard

Balda Álvaréz, P. A., Chacón-Castro, M., Busain, R. S., and Jadán-Guerrero, J. (2024). A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2514. https://doi.org/10.29333/ejmste/15198

MLA

Balda Álvaréz, Paola Alejandra et al. "A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 10, 2024, em2514. https://doi.org/10.29333/ejmste/15198