Research Article

Teachers’ mathematical work on quadrilaterals area with digital technology

Jesus Victoria Flores Salazar 1 * , Daysi Julissa García-Cuéllar 1 , Carolina Henríquez-Rivas 2 , Alain Kuzniak 3
More Detail
1 Pontificia Universidad Católica del Perú, Lima, PERU2 Universidad Católica del Maule, Talca, CHILE3 Université Paris Cité, Paris, FRANCE* Corresponding Author
European Journal of Science and Mathematics Education, 14(3), July 2026, 306-321, https://doi.org/10.30935/scimath/18435
Published: 17 April 2026
OPEN ACCESS   120 Views   62 Downloads
Download Full Text (PDF)

ABSTRACT

The aim of this paper is to analyze the mathematical work done by teachers when interacting with a GeoGebra application in a task on the area of quadrilaterals. The theoretical framework is focused on the mathematical working space (MWS) theory. The research approach is qualitative, based on a case study. The research subjects are two high school mathematics teachers. Results show that, in the personal MWS of both subjects, iconic visualization and pragmatic proof prevail, and the activation of the semiotic and discursive genesis is largely highlighted. Also, the type of device used has been proven to generate different MWS.

CITATION (APA)

Salazar, J. V. F., García-Cuéllar, D. J., Henríquez-Rivas, C., & Kuzniak, A. (2026). Teachers’ mathematical work on quadrilaterals area with digital technology. European Journal of Science and Mathematics Education, 14(3), 306-321. https://doi.org/10.30935/scimath/18435

REFERENCES

  1. Balacheff, N. (1987). Processus de preuve et situations de validation [Proof processes and validation situations]. Educational Studies in Mathematics, 18(2), 147-176. https://doi.org/10.1007/BF00314724
  2. Castillo, M. (2018). Reconfiguration of polygons to determine the measure of their area with students of second grade of secondary education [Master’s thesis, Pontificia Universidad Católica del Perú].
  3. Duval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie: Développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements [The cognitive conditions for learning geometry: Development of visualization, differentiation of reasoning, and coordination of their functions.]. Annales de Didactique et de Sciences Cognitives, 10, 5-53.
  4. Henríquez-Rivas, C., Ponce, R., Carrillo Yáñez, J., Climent, N., & Espinoza-Vásquez, G. (2021). Trabajo matemático de un profesor basado en tareas y ejemplos propuestos para la enseñanza [A teacher’s mathematical work based on proposed teaching tasks and examples]. Enseñanza de las Ciencias, 39(2), 123-142. https://doi.org/10.5565/rev/ensciencias.3210
  5. Henríquez-Rivas, C., & Kuzniak, A. (2021). Profundización en el trabajo geométrico de futuros profesores en entornos tecnológicos y de lápiz y papel [Deepening the geometric work of future teachers in technological environments and pencil and paper]. Bolema: Boletim de Educação Matemática, 35(71), 1550-1572. https://doi.org/10.1590/1980-4415v35n71a15
  6. Henríquez-Rivas, C., & Montoya-Delgadillo, E. (2016). The mathematical work of teachers in the transit from synthetic to analytic geometry in high school. Bolema: Boletim de Educação Matemática, 30(54), 45-66. https://doi.org/10.1590/1980-4415v30n54a03
  7. Henríquez-Rivas, C., & Verdugo-Hernández, P. (2023). Design of tasks in initial mathematics teacher education involving representations of a function. Educación Matemática, 35(3), 178-208. https://doi.org/10.24844/EM3503.06
  8. Herendiné, E. (2016). The level of understanding geometric measurement. In Proceedings of the 9th Congress of the European Society of Research in Mathematics Education: CERME 9 (pp. 536-542).
  9. Hernández-Sampieri R., Fernández C., & Baptista P. (2014). Metodología de la investigación [Research methodology]. McGraw-Hill.
  10. Kuzniak, A., & Nechache, A. (2019). Une méthodologie pour analyser le travail personal d’étudiants dans la théorie des espaces de travail mathématique [A methodology for analyzing students’ personal work in mathematical workspace theory]. In Proceedings of the 6th Symposium on Mathematical Work Valparaíso (pp. 61-80).
  11. Kuzniak, A., & Nechache, A. (2021). On forms of geometric work: A study with pre-service teachers based on the theory of mathematical working spaces. Educational Studies in Mathematics, 106, 271-289. https://doi.org/10.1007/s10649-020-10011-2
  12. Kuzniak, A., & Rauscher J. C. (2011). How do teachers’ approach to geometric work relate to geometry students’ learning difficulties? Educational Studies in Mathematics, 77(1), 129-147.
  13. Kuzniak, A., & Richard, P. (2014). Mathematical workspaces. Viewpoints and perspectives. Relime, 17(4-I), 5-15. https://doi.org/10.12802/relime.13.1741a
  14. Kuzniak, A., Montoya, E., & Vivier, L. (2015). The mathematical workspace and its genesis. In Proceedings of the 14th Inter-American Conference on Mathematics Education.
  15. Kuzniak, A., Nechache, A., & Drouhard, J.P. (2016). Understanding the development mathematical work in the context of the classroom. ZDM Mathematics-Education, 48, 861-874. https://doi.org/10.1007/s11858-016-0773-0
  16. Kuzniak, A., Nechache, A., & Flores Salazar, J. V. (2020). Student teachers’ geometric work and flexible use of digital tools. European Society for Research in Mathematics Education. https://hal.archives-ouvertes.fr/hal-02932218/document
  17. MINEDU. (2015). Análisis de las pruebas aplicadas en la evaluación nacional de ingreso 2014 y egreso de los estudiantes 2013 y 2014 de los institutos de educación superior pedagógicos [Analysis of the tests applied in the 2014 national entrance and 2013 and 2014 student exit assessments of higher education teacher training institutes]. Ministry of Education, Peru.
  18. MINEDU. (2017). Evaluación censal de estudiantes 2016 [2016 student census evaluation]. Ministry of Education. http://umc.minedu.gob.pe/wp-content/uploads/2017/04/Informe-para-Docentes-Matem%C3%A1tica-ECE-2016-2.%C2%B0-grado-de-secundaria.pdf
  19. MINEDU. (2018). Census and mapping of pestos of the staff of public institutions of initial teacher training at the national level 2018. Ministry of Education, Peru.
  20. Montoya-Delgadillo, E. Mena-Lorca, A., & Mena-Lorca, J. (2014). Circulations and genesis in the mathematical workspace. Relime, 17(4-I), 181-197. https://doi.org/10.12802/relime.13.1749
  21. Navarro, J. (2002). Who are the teachers? Teaching careers and incentives in Latin America. IDB.
  22. Ng, O., & Sinclair, N. (2015). Area without numbers: Using touchscreen dynamic geometry to reason about shape. Canadian Journal of Science, Mathematics and Technology Education, 15(1), 84-101. https://doi.org/10.1080/14926156.2014.993048
  23. Panqueban, D., Henriquez-Rivas, C., & Kuzniak, A. (2024). Advances and trends in research on mathematical working spaces: A systematic review. Eurasia Journal of Mathematics, Science and Technology Education, 20(6), Article em2450. https://doi.org/10.29333/ejmste/14588
  24. Richard, P. R. (2004). L’inférence figurale: Un pas de raisonnement discursive-graphique [Figural inference: A step in discursive-graphic reasoning]. Educational Studies in Mathematics, 57(2), 229-263. https://doi.org/10.1023/B:EDUC.0000049272.75852.c4
  25. Flores Salazar, J. V., Gaona, J., & Richard, P. (2022). Mathematical work in the digital age. Variety of tools and the role of geneses. In A. Kuzniak, E. Montoya-Delgadillo, & P. Richard (Eds.), Mathematical work in educational context (pp. 165-210). Springer. https://doi.org/10.1007/978-3-030-90850-8_8
  26. Tan-Sisman, G., & Aksu, M. (2009). Seventh grade students’ success on the topics of area and perimeter. Elementary Education Online, 8(1), 243-253. https://ilkogretim-online.org/index.php/pub/article/view/2402
  27. Vaillant, D. (2013). Formación inicial del profesorado en América Latina: Dilemas centrales y perspectivas [Initial teacher training in Latin America: Central and personal dilemmas]. Revista Española de Educación Comparada, (22), 185-206. https://doi.org/10.5944/reec.22.2013.9329
  28. Yin, R. K. (2018). Case study research and applications: Design and methods. SAGE.