Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education

Èdgar Ribot-Llobet; Sofía Caviedes; Genaro de Gamboa; Edelmira Badillo

doi:10.29333/iejme/19100

Full Text (PDF)

Èdgar Ribot-Llobet ¹ ^* , Sofía Caviedes ¹ , Genaro de Gamboa ¹ , Edelmira Badillo ¹

More Detail

¹ Universitat Autònoma de Barcelona, SPAIN^* Corresponding Author

Abstract

Mathematical connections are a key component of meaningful mathematical learning, yet little is known about how pre-service teachers analyse them in STEM modelling contexts. This study examines how pre-service primary teachers establish, identify, and interpret mathematical connections in a population modelling task, and how this analysis informs their instructional decisions. Participants engaged in a modelling sequence including structured reflection activities. Data from written productions and instructional proposals were analysed using qualitative content analysis, complemented by exploratory quantitative analysis. Results show that participants mainly establish procedural and representational connections, while argumentative connections are less frequent. During reflection, connections are identified selectively, with representational ones overrepresented. A strong relationship is found between connections established and identified, but not with instructional strategies. These findings highlight the need to better support the recognition and didactical use of less visible mathematical connections in teacher education.

Keywords

mathematical connections
mathematical modelling
mathematics teacher education
pre-service teachers
reflective practice
STEM education

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

INT ELECT J MATH ED, Volume 21, Issue 3, August 2026, Article No: em0894

https://doi.org/10.29333/iejme/19100

Publication date: 09 Aug 2026

Article Views: 8

Article Downloads: 4

Open Access References How to cite this article

References

Aoki, M. (2023). Mathematics in a Japanese overseas school: Connecting classroom study and curriculum. Asian Journal for Mathematics Education, 2(2), 204-219. https://doi.org/10.1177/27527263231187804
Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy. King’s College.
Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children’s understanding in multiplication. Educational Studies in Mathematics, 70, 217-241. https://doi.org/10.1007/s10649-008-9145-1
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects. Educational Studies in Mathematics, 22, 37-68. https://doi.org/10.1007/BF00302716
Bonett, D. G., & Wright, T. A. (2000). Sample size requirements for estimating Pearson, Kendall and Spearman correlations. Psychometrika, 65, 23-28. https://doi.org/10.1007/BF02294183
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Doctoral dissertation, Simon Fraser University].
Carrillo-Yañez, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., & Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. https://doi.org/10.1080/14794802.2018.1479981
Caviedes, S., de Gamboa, G., & Badillo, E. (2021). Mathematical objects that configure partial area meanings. International Journal of Mathematical Education in Science and Technology, 54(6), 1092-1111. https://doi.org/10.1080/0020739X.2021.1991019
Climent, N., Contreras, L. C., Montes, M., & Ribeiro, M. (2024). The MTSK model as a tool for designing tasks for teacher education. ZDM–Mathematics Education, 56, 1123-1135. https://doi.org/10.1007/s11858-024-01605-8
Cohen, L., Manion, L., & Morrison, K. (2017). Research methods in education (8th ed.). Routledge.
Couso, D., Mora, L., & Simarro, C. (2021). De las mates como instrumento a las mates como práctica [From math as an instrument to math as a practice]. Uno: Revista de Didáctica de las Matemáticas, 93, 8-14.
Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE.
De Gamboa, G., Badillo, E., Couso, D., & Márquez, C. (2021). Connecting mathematics and science in primary school STEM education: Modeling the population growth of species. Mathematics, 9, Article 2496. https://doi.org/10.3390/math9192496
De Gamboa, G., Badillo, E., & Font, V. (2023). Meaning and structure of mathematical connections in the classroom. Canadian Journal of Science, Mathematics and Technology Education, 23, 241-261. https://doi.org/10.1007/s42330-023-00281-2
Dreher, A., Kuntze, S., & Lerman, S. (2016). Why use multiple representations in the mathematics classroom? Views of English and German preservice teachers. International Journal of Science and Mathematics Education, 14, 363-382. https://doi.org/10.1007/s10763-015-9633-6
Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 273-280). Springer. https://doi.org/10.1007/0-306-47231-7_25
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131. https://doi.org/10.1007/s10649-006-0400-z
English, L. D. (2016). STEM education K–12: Perspectives on integration. International Journal of STEM Education, 3, Article 3. https://doi.org/10.1186/s40594-016-0036-1
Fernández, C., Ivars, P., & Llinares, S. (2023). El desarrollo de la competencia mirar profesionalmente el pensamiento matemático de los estudiantes durante los períodos de práctica. Revista Interuniversitaria de Formación del Profesorado, 98(38.2), 127-146. https://doi.org/10.47553/rifop.v98i37.2.99296
Frykholm, J. A., & Glasson, G. E. (2005). Connecting science and mathematics instruction. School Science and Mathematics, 105, 127-141. https://doi.org/10.1111/j.1949-8594.2005.tb18047.x
Fyfe, E. R., Alibali, M. W., & Nathan, M. J. (2017). The promise and pitfalls of making connections in mathematics. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 717-724). Hoosier Association of Mathematics Teacher Educators.
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
Gilbert, J. K., & Justi, R. (2016). Modelling-based teaching in science education. Springer. https://doi.org/10.1007/978-3-319-29039-3
Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39, 37-42. https://www.jstor.org/stable/26742011
Gravett, E. (2010). The rabbit problem. Macmillan Children’s Books.
Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.
Lehrer, R., & Schauble, L. (2007). Scientific thinking and science literacy. In W. Damon, R. M. Lerner, K. A. Renninger, & I. E. Siegel (Eds.), Handbook of child psychology. Wiley. https://doi.org/10.1002/9780470147658.chpsy0405
Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66, 349-371. https://doi.org/10.1007/s10649-006-9071-z
León del Carmen, A., León del Carmen, W., García-García, J., & Salgado-Beltrán, G. (2024). Mathematical connections made by preservice mathematics teachers when solving tasks about systems of linear equations. International Electronic Journal of Mathematics Education, 19(4), Article em0799. https://doi.org/10.29333/iejme/15590
Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6, Article 44. https://doi.org/10.1186/s40594-019-0197-9
Moreno, M., Valls, J., Sánchez-Matamoros, G., & Aráuz, D. F. (2025). Desarrollo profesional de futuros docentes de matemáticas de educación secundaria. Enseñanza de las Ciencias, 43(2), 61-80. https://doi.org/10.5565/rev/ensciencias.6320
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples. Journal of Educational Psychology, 101, 836-852. https://doi.org/10.1037/a0016026
Rodríguez-Nieto, C. A. (2021). Analysis of mathematical connections in the teaching and learning of the derivative [Doctoral dissertation, Universidad Autónoma de Guerrero].
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10, 251-296. https://doi.org/10.1023/A:1022193728205
Tashakkori, A., & Teddlie, C. (2010). SAGE handbook of mixed methods in social & behavioral research (2nd ed.). SAGE. https://doi.org/10.4135/9781506335193
Wilensky, U., & Reisman, K. (2006). Thinking like a wolf, a sheep, or a firefly: Learning biology through constructing and testing computational theories—An embodied modeling approach. Cognition and Instruction, 24, 171-209. https://doi.org/10.1207/s1532690xci2402_1

How to cite this article

APA

Ribot-Llobet, È., Caviedes, S., de Gamboa, G., & Badillo, E. (2026). Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education. International Electronic Journal of Mathematics Education, 21(3), em0894. https://doi.org/10.29333/iejme/19100

Vancouver

Ribot-Llobet È, Caviedes S, de Gamboa G, Badillo E. Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education. INT ELECT J MATH ED. 2026;21(3):em0894. https://doi.org/10.29333/iejme/19100

AMA

Ribot-Llobet È, Caviedes S, de Gamboa G, Badillo E. Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education. INT ELECT J MATH ED. 2026;21(3), em0894. https://doi.org/10.29333/iejme/19100

Chicago

Ribot-Llobet, Èdgar, Sofía Caviedes, Genaro de Gamboa, and Edelmira Badillo. "Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education". International Electronic Journal of Mathematics Education 2026 21 no. 3 (2026): em0894. https://doi.org/10.29333/iejme/19100

Harvard

Ribot-Llobet, È., Caviedes, S., de Gamboa, G., and Badillo, E. (2026). Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education. International Electronic Journal of Mathematics Education, 21(3), em0894. https://doi.org/10.29333/iejme/19100

MLA

Ribot-Llobet, Èdgar et al. "Mathematical connections in STEM-based modelling: From activity to reflection in pre-service teacher education". International Electronic Journal of Mathematics Education, vol. 21, no. 3, 2026, em0894. https://doi.org/10.29333/iejme/19100