Mathematical connections skills associated with the concept of quadratic equation established by prospective Mexican mathematics teachers
DOI:
https://doi.org/10.15359/ru.37-1.13Keywords:
Mathematical connections, prospective mathematics teachers, quadratic equationAbstract
[Objective] This investigation seeks to identify the mathematical connections established by prospective mathematics teachers related to the concept of the quadratic equation. [Methodology] A focal group interview was used to collect information. It consisted of assigning five tasks to eight prospective mathematics teachers who are pursuing a Licentiate’s degree in Mathematics in the area of Educational Mathematics. The participants are from the city of Chilpancingo in the state of Guerrero in Mexico, and were from 21 to 23 years old. Due to the COVID-19 pandemic, the four group sessions were held virtually, each lasting 80 minutes. Data were analyzed using a thematic approach. [Results] The written and verbal responses of prospective mathematics teachers indicated that each of them used mathematical connections skills in a different way. In general, the most frequent skills were related to procedures, characteristics, and meaning, and less frequently to part-whole, modeling, and implication. These connections correspond to those specified in the theoretical framework; therefore, it can be argued that this framework is valid and relevant for exploring the mathematical connections among prospective mathematics teachers when solving mathematical tasks. [Conclusions] The participants assigned meaning to the concept of quadratic equation in terms of what it represents in real contexts, and were able to present the quadratic function in different forms in the algebraic and graphical terms. However, most of them did not make the intended mathematical connections.
References
Aguilar, S. y Barroso, O. (2015). La triangulación de datos como estrategia en investigación educativa. Pixel-bit. Revista de medios y educación, (47), 73-88.
Braun, V. and Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa
Braun, V. and Clarke, V. (2012). Thematic analysis. In H. Cooper (ed.), Handbook of research methods in psychology (pp. 57-71), Washington (DC): American Psychological Association. https://doi.org/10.1037/13620-004
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. [Unpublished PhD thesis]. Faculty of Education-Simon Fraser University, Canada.
Didis, M. (2018). Secondary School Students’ Conception of Quadratic Equations with One Unknown. International Journal for Mathematics Teaching and Learning, 19(1), 112-129.
Didis, M. G. and Erbas, A. K. (2015). Performance and difficulties of students in formulating and solving quadratic equations with one unknown. Educational Sciences: Theory & Practice, 15(4), 1137-1150.
Dolores-Flores, C. y García-García, J. (2017). Conexiones intramatemáticas y extramatemáticas que se producen al resolver problemas de cálculo en contexto: un estudio de casos en el nivel superior. Bolema - Mathematics Education Bulletin, 31(57), 158-180. https://doi.org/10.1590/1980-4415v31n57a08
Dolores-Flores, C., Rivera-López, M. I., and García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematical Education in Science and Technology, 50(3), 369-389. http://doi.org/10.1080/0020739X.2018.1507050
Dörnyei, Z. (2007). Research Methods in Applied Linguistics: quantitative, qualitative, and mixed methodologies. Oxford University Press.
Eli, J. A., Mohr-Schroeder, M. J., and Lee, C. W. (2011). Mathematical connections and their relationship to mathematics knowledge for teaching geometry. School Science and Mathematics, 113(3), 120-134. https://doi.org/10.1111/ssm.12009
Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula. [Unpublished dissertation]. Pennsylvania State University College of Education, United States of America.
García-García, J. (2019). Escenarios de exploración de conexiones matemáticas. Números: Revista de Didáctica de las Matemáticas, 4 (100), 129-133.
García-García, J. and Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus task. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. DOI: 10.1080/0020739X.2017.1355994
García-García, J. and Dolores-Flores, C. (2021a). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/s13394-019-00286-x
García-García, J. and Dolores-Flores, C. (2021b). Exploring pre-university students’ mathematical connections when solving calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
García-García, J., Hernández-Yañez, M. E. y Rivera López, M. I. (2022). Conexiones matemáticas promovidas en los planes y programas de estudio mexicanos de nivel secundaria y media superior sobre el concepto de ecuación cuadrática. IE Revista de Investigación Educativa de la REDIECH, 13, e1485. https://doi.org/10.33010/ie_rie_rediech
Garza, B. (2014). Álgebra. Pearson.
Gibson, F. (2007). Conducting focus groups with children and young people: strategies for success. Journal of research in nursing, 12(5), 473-483. https://doi.org/10.1177/1744987107079791
Guner, P. (2017). High school students’ achievement of solving quadratic equations. Bartin University Journal of Faculty Education, 6(2), 447-467.
Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher y M. Blanton (eds.), Algebra in the early grades (pp. 5-18). Mahwah, NJ: Lawrence Erlbaum/Taylor & Francis Group & National Council of Teachers of Mathematics. https://doi.org/10.4324/9781315097435-2
Kotsopoulos, D. (2007). Unravelling student challenges with quadratics: A cognitive approach. Australian Mathematics Teacher, 63(2), 19-24.
Krueger, R. (2006). Is it a focus group? Tips on how to tell. Journal of Wound Ostomy & Continence Nursing, 33(4), 363-366. https://doi.org/10.1097/00152192-200607000-00003
Lau, W. W. (2019). Pre-service mathematics teachers’ professional learning in a pedagogy course: Examining changes in beliefs and confidence in teaching algebra. Mathematics Education Research Journal, 1-17. https://doi.org/10.1007/s13394-019-00285-y
López, J., Robles, I., and Martínez-Planell, R. (2016). Students’ understanding of quadratic equations. International Journal of Mathematical Education in Science and Technology, 47(4), 552-572. https://doi.org/10.1080/0020739X.2015.1119895
Martínez, R. N. R. (2012). Reseña metodológica sobre los grupos focales. Diá-Logos, (9), 47-53. https://doi.org/10.5377/dialogos.v1i9.1565
McCarthy, J. (2020). Solving quadratic equations activity & revisions. Ohio Journal of School Mathematics, 84(1), 71-90.
McDermott, M. J. (2013). Take your pick, ANA Magazine, 32-42.
Moon, K., Brenner, M. E., Jacob, B., and Okamoto, Y. (2013). Prospective secondary mathematics teachers understanding and cognitive difficulties in making connections among representations. Mathematical Thinking and Learning, 15(3), 201-227. https://doi.org/10.1080/10986065.2013.794322
National Council of Teachers of Mathematics (NCTM). (2014). Principles to action: Ensuring mathematical success for all. United State of America.
Polit, D. and Beck C. (2006). Essentials of nursing research: methods, appraisal and utilization. Philadelphia, USA: Lippincott Williams and Wilkins.
Rodas, F. y Pacheco, V. (2020). Grupos focales: marco de referencia para su implementación. INNOVA Research Journal, 5(3), 182-195. I: https://doi.org/10.33890/innova.v5.n3.2020.1401
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., and García-García, J. (2021). Pre-service mathematics teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education, 12(1), 202-220. https://doi.org/10.16949/turkbilmat.797182
Steketee, S. and Scher, D. (2016). Connecting functions in Geometry and Algebra. Mathematics Teacher, 109(6), 448-455. https://doi.org/10.5951/mathteacher.109.6.0448
Stewart, D. and Shamdasani, P. (2015). Focus groups: Theory and practice. Sage publications.
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