Archives
Current issue
About
About us
Aims and Scope
Abstracting and Indexing
Editorial Office
Open Access Policy
Publication Ethics
Journal History
Publisher
Follow us: Twitter
Contact
For Authors
Editorial Policy
Peer Review Policy
Manuscript Preparation Guidelines
Copyright & Licencing
Publication Fees
Fee Waiver Policy for Doctoral Students
EJMSTE Language Editing Service
More
Statistics
Special Issues
Special Issue Announcements
Published Special Issues
RESEARCH PAPER
Mathematical processes for the development of algebraic reasoning in geometrical situations with in-service secondary school teachers
1
Research Institute on the Teaching of Mathematics, Pontifical Catholic University of Peru, PERU
2
Public University of Navarre, Pamplona-Iruña, SPAIN
Publication date: 2024-12-11
EURASIA J. Math., Sci Tech. Ed 2024;20(12):em2553
KEYWORDS
ABSTRACT
This paper starts from the hypothesis that algebraic reasoning can be used as an axis between
different mathematical domains at school. This is relevant given the importance attributed to
mathematical connections for curriculum development and the algebraic reasoning makes it
possible to articulate it in a coherent manner. A definition of generalized algebraic reasoning is
proposed, based on the notion of elementary algebraic reasoning of the onto-semiotic approach,
and it is used to highlight the presence of typical algebraic processes in problem solving in
geometrical contexts. To develop these ideas, a training course is designed and implemented with
in-service secondary school teachers. Based on design-based research, the results obtained are
contrasted with the expected answers. In this way, relevant information is obtained on how
teachers mobilize different typically algebraic processes, that is, particularization-generalization,
representation-signification, decomposition-reification and modelling. Actually, it is clear to affirm
that teachers need specific training to improve their skills about how algebraic reasoning can help
them to develop mathematical connections with their students.
REFERENCES (38)
1.
Aké, L. P. (2021). El carácter algebraico en el conocimiento matemático de maestros en formación [The algebraic character of the mathematical knowledge of teachers in training]. Tecné, Episteme y Didaxis: TED, 49, 15-34. https://doi.org/10.17227/ted.n....
2.
Barana, A. (2021). From formulas to functions through geometry: A path to understanding algebraic computations. European Journal of Investigation in Health, Psychology and Education, 11(4), 1485-1502. https://doi.org/10.3390/ejihpe....
3.
Boester, T., & Lehrer, R. (2008). Visualizing algebraic reasoning. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 211-234). Routledge. https://doi.org/10.4324/978131....
5.
Bueno, S., Burgos, M., Godino, J. D., & Pérez, O. (2022). Intuitive and formal meanings of the definite integral in engineering education. Revista Latinoamericana de Investigación en Matemática Educativa, 25(2), 135-168. https://doi.org/10.12802/relim....
6.
Burgos, M., Batanero, C., & Godino, J. D. (2022). Algebraization levels in the study of probability. Mathematics, 10(1), Article 91. https://doi.org/10.3390/math10....
7.
Burgos, M., Tizón-Escamilla, N., & Godino, J. D. (2024). Expanded model for elementary algebraic reasoning levels. Eurasia Journal of Mathematics, Science and Technology Education, 20(7), Article em2475. https://doi.org/10.29333/ejmst....
8.
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections [Unpublished PhD dissertation]. Simon Fraser University.
9.
Carraher, D. W., Martínez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM Mathematics Education, 40, 3-22. https://doi.org/10.1007/s11858....
10.
Castro, E. (2012). Dificultades en el aprendizaje del álgebra escolar [Difficulties in learning school algebra]. In A. E. Castro, A. C. de la Fuente, J. D. Piquet, M. C. P. Martinez, F. J. Garcia, & L. O. Canada (Eds.), Investigación en educación matemática XVI (pp. 75-94). SEIEM.
11.
Castro, W. F., & Pino-Fan, L. (2021). Comparing the didactic-mathematical knowledge of derivative of in-service and pre-service teachers. Acta Scientiae, 23(3), 34-99. https://doi.org/10.17648/acta.....
12.
Castro, W. F., Pino-Fan, L., & Velásquez-Echavarría, H. (2018). A proposal to enhance pre-service teachers noticing. Eurasia Journal of Mathematics, Science & Technology Education, 14(11), Article em1569. https://doi.org/10.29333/ejmst....
13.
Cooper, T. J., & Warren, E. (2008). The effect of different representations on years 3 to 5 students’ ability to generalize. ZDM Mathematics Education, 40, 23-37. https://doi.org/10.1007/s11858....
14.
Font, V., & Contreras, A. (2008). The problem of the particular and its relation to the general in mathematics education. Educational Studies in Mathematics, 69, 33-52. https://doi.org/10.1007/s10649....
15.
Font, V., Godino, J. D., & Contreras, A. (2008). From representations to onto-semiotic configurations in analysing the mathematics teaching and learning processes. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, historicity, and culture (pp. 157-173). Sense. https://doi.org/10.1163/978908....
16.
Gaita, C., Wilhelmi, M. R., Ugarte, F., & Gonzales, C. (2022). General core curriculum for the development of elementary algebraic reasoning. In A. L. Manrique, & C. L. Oliveira (Eds.), Anais IX CIBEM Congreso Iberoamericano de Educação Matemática (pp. 3662-3673). University of Sao Paulo.
17.
Godino, J. D., Aké, L., Gonzato, M., & Wilhelmi, M. R. (2014b). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros [Levels of algebraization of school mathematics activity. Implications for teacher training]. Enseñanza de las Ciencias, 32(1), 199-219. https://doi.org/10.5565/rev/en....
18.
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, 39, 127-135. https://doi.org/10.1007/s11858....
19.
Godino, J. D., Bencomo, D., Font, V., & Wilhelmi, M. R. (2006a). Análisis y valoración de la idoneidad didáctica de procesos de estudio de las matemáticas [Analysis and assessment of the didactic suitability of mathematics study processes]. Paradigma, 27(2), 221-252.
20.
Godino, J. D., Castro, W. F., Aké, L., & Wilhelmi, M. R. (2012). Naturaleza del razonamiento algebraico elemental [Nature of elementary algebraic reasoning]. Bolema, 26(42B), 483-511. https://doi.org/10.1590/S0103-....
21.
Godino, J. D., Font, V., & Wilhelmi, M. R. (2006b). Análisis ontosemiótico de una lección sobre la suma y la resta [Ontosemiotic analysis of a lesson on addition and subtraction]. Relime, 9(Extra 1), 131-156.
22.
Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas [Ontosemiotic approach to the knowledge and skills of mathematics teachers]. Bolema, 31(57), 90-113. https://doi.org/10.1590/1980-4....
23.
Godino, J. D., Neto, T., Wilhelmi, M. R., Aké, L. P., Etchegaray, S., & Lasa, A. (2015). Niveles de algebrización de las prácticas matemáticas escolares. Articulación de las perspectivas ontosemiótica y antropológica [Levels of algebraization of school mathematical practices. Articulation of ontosemiotic and anthropological perspectives]. Avances de Investigación en Educación Matemática, (8), 117-142. https://doi.org/10.35763/aiem.....
24.
Godino, J. D., Rivas, H., Arteaga, P., Lasa, A., & Wilhelmi, M. R. (2014a). Ingeniería didáctica basada en el enfoque ontologico Semiótico del conocimento y de la intrucción matemáticos [Didactic engineering based on the ontological-semiotic approach to mathematical knowledge and instruction]. Recherches en Didactique des Mathématiques, 34(2-3), 167-200.
25.
Godino, J. D., Wilhelmi, M. R., Blanco, T. F., de la Fuente, Á. C., & Giacomone, M. B. (2016). Análisis de la actividad matemática mediante dos herramientas teóricas [Analysis of mathematical activity using two theoretical tools: Semiotic representation registers and ontosemiotic configuration]. Avances de Investigación en Educación Matemática, (10), 91-110. https://doi.org/10.35763/aiem.....
26.
Gras, R., Suzuki, E., Guillet, F., & Spagnolo, F. (2008). Statistical implicative analysis. Theory and applications. Springer. https://doi.org/10.1007/978-3-....
27.
Hatisaru, V., Stacey, K., & Star, J. (2024). Mathematical connections in preservice secondary mathematics teachers’ solution strategies to algebra problems. Avances de Investigación en Educación Matemática, (25), 33-55. https://doi.org/10.35763/aiem2....
28.
Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Routledge. https://doi.org/10.4324/978131....
29.
Ledezma, C., Rodríguez-Nieto, C. A., & Font, V. (2024). The role played by extra-mathematical connections in the modelling process. Avances de Investigación en Educación Matemática, 25, 81-103. https://doi.org/10.35763/aiem2....
30.
Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277-289. https://doi.org/10.1007/BF0031....
31.
MINEDU. (2016). Currículo nacional de la educación básica [National curriculum for basic education]. Ministry of Education of Peru. https://repositorio.minedu.gob....
32.
Montiel, M., Wilhelmi, M. R., Vidakovic, D., & Elstak, I. (2009). Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. Educational Studies in Mathematics, 72, 139-160. https://doi.org/10.1007/s10649....
33.
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
34.
Pallauta, J., Gea, M., Batanero, C., & Arteaga, P. (2023). Algebraization levels of activities linked to statistical tables in Spanish secondary textbooks. In G. F. Burrill, L. de Oliveria Souza, & E. Reston (Eds.), Research on reasoning with data and statistical thinking: International perspectives (pp. 317-339). Springer. https://doi.org/10.1007/978-3-....
35.
Pino-Fan, L., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers’ didactic-mathematical knowledge. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/euras....
36.
Pino-Fan, L., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21(1), 63-94. https://doi.org/10.1007/s10857....
37.
Silva, M. J. F. (2021). A construção de fórmulas: Uma articulação entre geometría e álgebra [The construction of formulas: An articulation between geometry and algebra]. Quintaesencia, 12(1), 103-114. https://doi.org/10.54943/rq.v1....
38.
Strømskag, H., & Chevallard, Y. (2022). Elementary algebra as a modelling tool: A plea for a new curriculum. Recherches en Didactique des Mathématiques, 42(3), 371-409.
Share
RELATED ARTICLE
| eISSN: | 1305-8223 |
| ISSN: | 1305-8215 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
