Geometry and Trigonometry knowledge in pre-service Math Teachers: a systematized bibliographic review.
DOI:
https://doi.org/10.4151/07189729-Vol.63-Iss.3-Art.1465Keywords:
Knowledge teacher education trigonometry geometryAbstract
In this article, we present a comprehensive and updated synthesis of research on the knowledge of Mathematics teachers in initial training, both in general and in the areas of geometry and trigonometry. This synthesis is the result of a systematized bibliographic review that combines a secondary and tertiary study of the literature, including specific studies published between 1986 and mid-2020 in high-impact journals in the Americas and Europe, as well as previous reviews on this topic.
Among the descriptive results, related to the characteristics of the research products considered, the limited research reported on the knowledge of teachers in initial training around trigonometry stands out. Also noteworthy is the predominance of internal studies—conducted by teachers or training institutions within their own courses or settings—originating from English-speaking countries, qualitative and empirical in nature, and on a small scale, typically involving between 1 and 50 participants.
These characteristics regarding who, how, and where research in the field is conducted align with those reported in previous bibliographic reviews, showing that these trends have persisted for more than 15 years, regardless of the inclusion of Spanish- and Portuguese-speaking journals or the focus on specific educational levels and mathematical areas.
Among the analytical results, concerning the content of the research products included in the review, the focus on mathematical knowledge of teachers in initial training stands out, in comparison to the attention given to teaching knowledge or in relation to the teaching practice. Likewise, there is a predominant prescriptive and deficit-oriented view of teacher knowledge, focusing on what teachers should know or what they do not do, do not know, or do not understand.
In conclusion, we emphasize the need for more research on teacher knowledge in trigonometry, as well as large-scale studies conducted and published in Spanish- and Portuguese-speaking countries, with objectives that go beyond mathematical knowledge and the prescriptive and deficit-oriented view of the knowledge of teachers in initial training.
References
Adler, J., Ball, D., Krainer, K., Lin, F. L., & Novotna, J. (2005). Reflections on an emerging field: Researching mathematics teacher education. Educational studies in mathematics, 60(3), 359-381. https://doi.org/10.1007/s10649-005-5072-6
Andrade-Molina, M., Montecino, A., & Sánchez, M. (2020). Beyond quality metrics: defying journal rankings as the philosopher’s stone of mathematics education research. Educational Studies in Mathematics, 103, 359-374. https://doi.org/10.1007/s10649-020-09932-9
Cardoso R., P. F., Veiga F. S., M. A., & Reis T., E. (2022). Trigonometria: conhecimento de conteúdo e de ensino fundamentados em uma revisão sistemática de literatura. Revista de Ensino de Ciências e Matemática, 13(5), 1-23. https://doi.org/10.26843/rencima.v13n5a25
Cavey, L. O., & Berenson, S. B. (2005). Learning to teach high school mathematics: Patterns of growth in understanding right triangle trigonometry during lesson plan study. The Journal of Mathematical Behavior, 24(2), 171-190. https://doi.org/10.1016/j.jmathb.2005.03.001
Codina, L. (2018). Revisiones bibliográficas sistematizadas: Procedimientos generales y framework para ciencias humanas y sociales [Tesis de maestría, Universitat Pompeu Fabra]. Repositorio institucional. http://hdl.handle.net/10230/34497
Cruz-Márquez, G. & Montiel-Espinosa, G. (2022). Medición indirecta de distancias y el trabajo geométrico en la construcción de las nociones trigonométricas. Acta Scientiae, 24(4), 81-108. https://doi.org/10.17648/acta.scientiae.6911
Cruz, M. F., & Mantica, A. M. (2017). El uso del software de geometría dinámica en la formulación y validación de conjeturas. UNIÓN. Revista Iberoamericana de Educación Matemática, (51), 69-72. https://www.union.fespm.es/index.php/UNION/article/view/386
Etcheverry, N., Reid, M., & Gioda, R. B. (2013). Tecnologías de la Información y la Comunicación (TIC): las competencias matemáticas a partir de una estrategia didáctica en un ambiente de geometría dinámica. UNIÓN. Revista Iberoamericana de Educación Matemática, (36), 131-144. https://www.union.fespm.es/index.php/UNION/article/view/763
Freyre, M. L., & Mántica, A. M. (2019). Una nueva mirada a los poliedros regulares. Construcciones que generan sorpresas. UNIÓN. Revista Iberoamericana de Educación Matemática, (55), 144-158. https://www.union.fespm.es/index.php/UNION/article/view/298
Grant, M., & Booth, A. (2009). A typology of reviews: an analysis of 14 review types and associated methodologies. Health Information and Libraries Journal, 26(2), 91-108. https://doi.org/10.1111/j.1471-1842.2009.00848.x
Herbst, P., Fujita, T., Halverscheid, S., & Weiss, M. (2017). Teaching practice and teacher knowledge in geometry instruction. En P. Herbst, T. Fujita, S. Halverscheid, & M. Weiss (Eds.), The learning and teaching of geometry in secondary schools: A modeling perspective (pp. 114-155). Routledge. https://doi.org/10.4324/9781315267593
Hollebrands, K. F., & Lee, H. S. (2016). Characterizing questions and their focus when pre-service teachers implement dynamic geometry tasks. The Journal of Mathematical Behavior, 43, 148-164. https://doi.org/10.1016/j.jmathb.2016.07.004
Iglesias, M., & Ortiz, J. (2019). La demostración en geometría desde una perspectiva didáctica. UNIÓN. Revista Iberoamericana de Educación Matemática, (55), 159-183. https://www.union.fespm.es/index.php/UNION/article/view/297
Jones, K., & Tzekaki, M. (2016). Research on the Teaching and Learning of Geometry. En A. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The Second Handbook of Research on the Psychology of Mathematics Education (pp. 109-149). Sense Publishers. https://doi.org/10.1007/978-94-6300-561-6_4
Kitchenham, B., & Charters, S. M. (2007). Guidelines for performing systematic literature reviews in software engineering (EBSE Technical Report, ver. 2.3.). Keele University and University of Durham. https://www.elsevier.com/__data/promis_misc/525444systematicreviewsguide.pdf
Lerman, S. (2001). A Review of Research Perspectives on Mathematics Teacher Education. En F. L. Lin, & T. J. Cooney (Eds.), Making Sense of Mathematics Teacher Education (pp. 33-52). Springer. https://doi.org/10.1007/978-94-010-0828-0_2
Liljedahl, P., Durand-Guerrier, V., Winsløw, C., Bloch, I., Huckstep, P., Rowland, T., Thwaites, A., Grevholm, B., Bergsten, C., Adler, J., Davis, Z., Garcia, M., Sánchez, V., Proulx, J., Flowers, J., Rubenstein, R., Grant, T., Kline, K., … Chapman, O. (2009). Components of Mathematics Teacher Training. En R. Even, & D. L. Ball (Eds.), The Professional Education and Development of Teachers of Mathematics (pp. 25-33). Springer. https://doi.org/10.1007/978-0-387-09601-8_4
Llinares, S., & Krainer, K. (2006). Mathematics (student) teachers and teacher educators as learners. En A. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present and future (pp. 429-459). Brill. https://doi.org/10.1163/9789087901127_016
Mamolo, A. & Pali, R. (2014). Factors Influencing Prospective Teachers’ Recommendations to Students: Horizons, Hexagons, and Heed. Mathematical Thinking and Learning, 16(1), 32-50. https://doi.org/10.1080/10986065.2014.857804
Montiel, G. (2011). Construcción de conocimiento trigonométrico. Un estudio Socioepistemológico. Ediciones Díaz de Santos.
Moore, K. C., LaForest, K. R., & Kim, H. J. (2016). Putting the unit in pre-service secondary teachers’ unit circle. Educational Studies in Mathematics, 92, 221-241. https://doi.org/10.1007/s10649-015-9671-6
Morales, H. (2018). Influencia de un proceso de formación de profesores en el sistema de enseñanza del concepto de área en estudiantes de pedagogía en matemáticas, un estudio de caso. Bolema: Boletim de Educação Matemática, 32(62), 1050-1067. https://doi.org/10.1590/1980-4415v32n62a15
Navarro, P., & Villalva, M. (2009). Un estudio sobre la desarticulación entre la semejanza y la trigonometría en el bachillerato. En P. Lestón (Ed.), Acta Latinoamericana de Matemática Educativa 22 (pp. 287-296). Comité Latinoamericano de Matemática Educativa. http://funes.uniandes.edu.co/4829/1/VillalvaUnestudioAlme2009.pdf
Ponte, J. P., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. En A. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present and future (pp. 461-494). Brill. https://doi.org/10.1163/9789087901127_017
Sánchez, M. (2011). A review of research trends in mathematics teacher education. PNA, 5(4), 129-145. https://doi.org/10.30827/pna.v5i4.6151
Shriki, A. (2010). Working like real mathematicians: developing prospective teachers’ awareness of mathematical creativity through generating new concepts. Educational Studies in Mathematics, 73, 159-179. https://doi.org/10.1007/s10649-009-9212-2
Sinclair, N., Cirillo, M., & De Villiers, M. (2017). The learning and teaching of geometry. En J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 457-489). National Council of Teachers of Mathematics.
Tatto, M. T., Lerman, S., & Novotná, J. (2009). Overview of Teacher Education Systems Across the World. En R. Even, & D. L. Ball (Eds.), The Professional Education and Development of Teachers of Mathematics (pp. 15-23). Springer. https://doi.org/10.1007/978-0-387-09601-8_3
Tatto, M. T., Lerman, S., & Novotná, J. (2010). The organization of the mathematics preparation and development of teachers: A report from the ICMI Study 15. Journal of Mathematics Teacher Education, 13(4), 313-324. https://doi.org/10.1007/s10857-009-9139-7
Tsamir, P. (2007). When intuition beats logic: prospective teachers’ awareness of their same sides – same angles solutions. Educational Studies in Mathematics, 65, 255-279. https://doi.org/10.1007/s10649-006-9053-1
Weber, K., Mejía-Ramos, J. P., Fukawa-Connelly, T., & Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. The Journal of Mathematical Behavior, 57, 100752. https://doi.org/10.1016/j.jmathb.2019.100752
Williams, S. R., & Leatham, K. R. (2017). Journal Quality in Mathematics Education. Journal for Research in Mathematics Education JRME, 48(4), 369-396. https://doi.org/10.5951/jresematheduc.48.4.0369
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Gerardo Cruz-Márquez, Gisela Montiel-Espinosa
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
El/los autores/as otorgan licencia exclusiva y sin límite de temporalidad para que el manuscrito sea publicado en la revista Perspectiva Educacional, editada por la Pontificia Universidad Católica de Valparaíso (Chile), a través de la Escuela de Pedagogía.
