The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge

Paula Verdugo-Hernández; Sofía Caviedes Barrera

doi:10.29333/ejmste/15473

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Paula Verdugo-Hernández ¹ ^* , Sofía Caviedes Barrera ²

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¹ Escuela de Pedagogía en Ciencias Naturales y Exactas, Facultad de Ciencias de La Educación, Universidad de Talca, Linares, CHILE² Universidad Internacional de La Rioja, SPAIN^* Corresponding Author

Abstract

This article aims to identify the knowledge that enables a prospective secondary school teacher to mobilize number sense components during a pre-professional practicum. Using a qualitative case study approach, four classroom episodes focused on fractions, percentages, and algebraic language are analyzed. The study involves one prospective teacher and 23 students from a multi-grade school in central-southern Chile. The analysis integrates teacher’s specialized knowledge and mathematical working spaces to explore how these frameworks inform the teacher’s knowledge. The findings reveal that the teacher employs personal theories, real-life examples, and graphical aids to enhance students’ understanding, though there is a reliance on rules and algorithms. While specialized knowledge aids in teaching, there is less emphasis on fostering students’ conceptual understanding and judgement. The study recommends improving teacher training programs to better equip prospective teachers in grasping number sense components, highlighting the need for more focused training on its development.

Keywords

number sense
mathematics teachers´ specialized knowledge
mathematical working spaces
prospective secondary teachers

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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: em2525

https://doi.org/10.29333/ejmste/15473

Publication date: 15 Oct 2024

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Article Downloads: 20

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References

Alajmi, A., & Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65, 77-94. https://doi.org/10.1007/s10649-006-9042-4
Alex, J. K. (2019). The preparation of secondary school mathematics teachers in South Africa: Prospective teachers’ student level disciplinary content knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 15(12), Article em1791. https://doi.org/10.29333/ejmste/105782
Almeida, R., Bruno, A., & Perdomo-Díaz, J. (2016). Strategies of number sense in pre-service secondary mathematics teachers. International Journal of Science and Mathematics Education, 14, 959-978. https://doi.org/10.1007/s10763-014-9601-6
Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97-109. https://doi.org/10.1007/s10649-008-9163-z
Australian Education Council. (1990). A national statement on mathematics for Australian schools. Curriculum Corporation.
Ball, D. L., Lubienski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433-456). Macmillan.
Bikner-Ahsbahs, A. (2009). Networking of theories: Why and how. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the 6^th Congress of the European Society for Research in Mathematics Education (pp. 6-15). Institut National de Recherche Pédagogique.
Bikner-Ahsbahs, A., & Prediger, S. (2009). Networking of theories–An approach for exploiting the diversity of theoretical approaches. In B. Sriraman, & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 483-506). Springer. https://doi.org/10.1007/978-3-642-00742-2_46
Bryman, A. (2009). Social research methods. Oxford University Press.
Carrillo, J., Climent, N., Montes, M., Contreras, L., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., & Muñoz-Catalán, M. (2018). The mathematics teacher’s specialized knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. https://doi.org/10.1080/14794802.2018.1479981
Castela, C. (2021). Reflexiones sobre la multiplicidad de las teorías en didáctica de las matemáticas [Reflections on the multiplicity of theories in mathematics education]. https://hal.science/hal-03199465/document
Caviedes Barrera, S., de Gamboa Rojas, G., & Badillo Jiménez, E. (2023).. Mathematical and didactic knowledge of preservice primary teachers about the area of 2D figures. Avances de Investigación en Educación Matemática, (24), 1-20. https://doi.org/10.35763/aiem24.4076
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316. https://doi.org/10.1007/s10649-006-9036-2
Clark, C. M., & Peterson, P. L. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 255-296). Macmillan.
Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education. Routledge. https://doi.org/10.4324/9780203029053
De Gamboa, G., Caviedes, S., & Badillo, E. (2024). The role of intra-mathematical connections in learning decimal numbers. Avances de Investigación en Educación Matemática, (25), 131-149. https://doi.org/10.35763/aiem25.6399
Espinoza-Vásquez, G., Henríquez-Rivas, C., Climent, N., Ponce, R., & Verdugo-Hernández, P. (In press). Teaching Thales’s theorem: relations between suitable mathematical working spaces and specialised knowledge. Educational Studies in Mathematics.
Gaona, J. Lopez, S., & Montoya-Delgadillo, E. (2022). Prospective mathematics teachers learning complex numbers using. International Journal of Mathematical Education in Science and Technology, 55(9), 2219-2248. https://doi.org/10.1080/0020739X.2022.2133021
Gay, A. S., & Aichele, D. B. (1997). Middle school students understanding of number sense related to percent. School Science and Mathematics, 97(1), 27-36. https://doi.org/10.1111/j.1949-8594.1997.tb17337.x
Ghazali, M., Mohamed, R., & Mustafa, Z. (2021). A systematic review on the definition of children’s number sense in the primary school years. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), em1968. https://doi.org/10.29333/ejmste/10871
Gómez-Chacón, I. M., Kuzniak, A., & Vivier, L. (2016). The teacher’s role from the perspective of mathematical working spaces. Bolema-Mathematics Education Bulletin, 30(54). https://doi.org/10.1590/1980-4415v30n54a01
Haspekian, M., Artigue, M., & Rocha, K. (2023). Networking of theories: An approach to the development and use of digital resources in mathematics education. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of digital resources in mathematics education (pp. 1-29). Springer. https://doi.org/10.1007/978-3-030-95060-6_4-1
Henríquez-Rivas, C., Ponce, R., Carrillo, J., Climent, N., & Espinoza-Vásquez, G. (2021). Trabajo matemático de un profesor basado en tareas y ejemplos propuestos para la enseñanza [Mathematical work of a teacher based on tasks and examples proposed for teaching]. Enseñanza de las Ciencias, 39(2), 123-142. https://doi.org/10.5565/rev/ensciencias.3210
Henríquez-Rivas, C. & Verdugo-Hernández, P. (2023). Diseño de tareas en la formación inicial docente de matemáticas que involucran las representaciones de una función [Design of tasks in initial teacher training in mathematics that involve representations of a function]. Educación Matemática, 35(3), 178-208. https://doi.org/10.24844/EM3503.06
Kidron, I., & Bikner-Ahsbahs, A. (2015). Advancing research by means of the networking of theories. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education, advances in mathematics education (pp. 221-232). Springer. https://doi.org/10.1007/978-94-017-9181-6_9
Kuzniak, A. (2011). The mathematical work space and its genesis. Annales de Didactique et de Sciences Cognitives, 16, 9-24.
Kuzniak, A., Montoya Delgadillo, E., & Richard, P. (2022). Mathematical work in educational context: The perspective of the theory of mathematical working spaces. Springer. https://doi.org/10.1007/978-3-030-90850-8
Kuzniak, A., Tanguay, D., & Elia, I. (2016). Mathematical working spaces in schooling: An introduction. ZDM-Mathematics Education, 48, 721-737. https://doi.org/10.1007/s11858-016-0812-x
Lougrhan, J., Mulhall, P., & Berry, A. (2008). Exploring pedagogical content knowledge in science teacher education. International Journal of Science Education, 30(10), 1301-1320. https://doi.org/10.1080/09500690802187009
Maghfirah, M., & Mahmudi, A. (2018). Number sense: The result of mathematical experience. Journal of Physics: Conference Series, 1097(1), Article 012141. https://doi.org/10.1088/1742-6596/1097/1/012141
Maier, H., & Beck, C. (2001). Zur theoriebildung in der interpretativen mathematikdidaktischen forschung [On theory formation in interpretive mathematics education research]. Journal für Mathematik-Didaktik, 22(1), 29-50. https://doi.org/10.1007/BF03339314
Mapolelo, D. C., & Akinsola, M. K. (2015). Preparation of mathematics teachers: Lessons from review of literature on teachers’ knowledge, beliefs, and teacher education. American Journal of Educational Research, 3(4), Article 505513. https://doi.org/10.12691/education-3-4-18
Markovits, Z., & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25, 4-29. https://doi.org/10.5951/jresematheduc.25.1.0004
Mawaddah, S., Noorbaiti, R., & Ulfah, A. (2021). Analysis of number sense capabilities of prospective mathematics teachers. Journal of Physics: Conference Series, 1760(1), Article 012042. https://doi.org/10.1088/1742-6596/1760/1/012042
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-44. https://doi.org/10.4324/9780203990247
MEFP. (2022). Real Decreto 217/2022, de 29 de marzo, por el que se establece la ordenación y las enseñanzas mínimas de la educación secundaria obligatoria [Royal Decree 217/2022, of March 29, establishing the organization and minimum teachings of compulsory secondary education]. Ministerio de Educación y Formación Profesional.
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Pournara, C., Hodgen, J., Adler, J., & Pillay, V. (2015). Can improving teachers’ knowledge of mathematics lead to gains in learners’ attainment in mathematics? South African Journal of Education, 35(3), 1-10. https://doi.org/10.15700/saje.v35n3a1083
Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (Eds.). (2008a). Comparing, combining, coordinating–Networking strategies for connecting theoretical approaches. ZDM-The International Journal on Mathematics Education, 40(2), 163-327. https://doi.org/10.1007/s11858-008-0093-0
Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008b). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM-The International Journal on Mathematics Education, 40(2), 165-178. https://doi.org/10.1007/s11858-008-0086-z
Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM-The International Journal on Mathematics Education, 40(2), 317-327. https://doi.org/10.1007/s11858-008-0090-3
Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education, 20(1), 8-27. https://doi.org/10.2307/749095
Reys, B. J. (1994). Promoting number sense in the middle grades. Mathematics Teaching in the Middle School, 1(2), 114-120. https://doi.org/10.5951/MTMS.1.2.0114
Reys, B. J., & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth and eighth grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. https://doi.org/10.5951/jresematheduc.29.2.0225
Roberts-Hull, K., Jensen, B., & Cooper, S. (2015). A new approach: Teacher education reform. Learning First.
Şengül, S., & Gülbağcı, H. (2012). An investigation of 5th grade Turkish students’ performance in number sense on the topic of decimal numbers. Procedia-Social and Behavioral Sciences, 46, 2289-2293. https://doi.org/10.1016/j.sbspro.2012.05.472
Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
Strutchens, M. E., Huang, R., Losano, L., Potari, D., da Ponte, J. P., Cyrino, M. D. C. T., & Zbiek, R. M. (2017). The mathematics education of prospective secondary teachers around the world. Springer. https://doi.org/10.1007/978-3-319-38965-3
Verdugo-Hernández, P., Espinoza-Vásquez, G. & Carrillo Yáñez, J. (2022). Análisis de una tarea sobre sucesiones desde el uso de las herramientas y el conocimiento matemático del profesor [Analysis of a task on sequences from the use of tools and the teacher's mathematical knowledge]. Enseñanza de las Ciencias, 40(2), 1-21. https://doi.org/10.5565/rev/ensciencias.3457
Watson, A., & Mason, J. (2005). Mathematics as a constructive activity. Learners generating examples. Lawrence Erlbaum Associates.
Wulandari, N. P., Hidayati, V. R., Novitasari, D., Triutami, T. W., & Lu’luilmaknun, U. (2020). Investigating the number sense ability of pre-service mathematics teachers. MaPan: Jurnal Matematika dan Pembelajaran, 8(1), 76-86. https://doi.org/10.24252/mapan.2020v8n1a6
Yang, D. C., & Li, M. F. (2008). An investigation of 3rd grade Taiwanese students performance in number sense. Educational Studies in Mathematics, 34(5), 443-455. https://doi.org/10.1080/03055690802288494
Yang, D. C., Hsu, C. J., & Huang, M. C. (2004). A study of teaching and learning number sense for sixth grade students in Taiwan. International Journal of Science and Mathematics Education, 2, 407-430. https://doi.org/10.1007/s10763-004-6486-9

How to cite this article

APA

Verdugo-Hernández, P., & Caviedes Barrera, S. (2024). The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2525. https://doi.org/10.29333/ejmste/15473

Vancouver

Verdugo-Hernández P, Caviedes Barrera S. The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge. EURASIA J Math Sci Tech Ed. 2024;20(10):em2525. https://doi.org/10.29333/ejmste/15473

AMA

Verdugo-Hernández P, Caviedes Barrera S. The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge. EURASIA J Math Sci Tech Ed. 2024;20(10), em2525. https://doi.org/10.29333/ejmste/15473

Chicago

Verdugo-Hernández, Paula, and Sofía Caviedes Barrera. "The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 10 (2024): em2525. https://doi.org/10.29333/ejmste/15473

Harvard

Verdugo-Hernández, P., and Caviedes Barrera, S. (2024). The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2525. https://doi.org/10.29333/ejmste/15473

MLA

Verdugo-Hernández, Paula et al. "The work of a prospective high school teacher in pre-professional training in highlighting mathematical knowledge". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 10, 2024, em2525. https://doi.org/10.29333/ejmste/15473