Mathematical connections promoted in telebachillerato textbooks about slope concept
DOI:
https://doi.org/10.33010/ie_rie_rediech.v14i0.1825Keywords:
Content analysis, mathematical connections, textbooks, slope, telebachilleratoAbstract
The aim of this research was to identify the mathematical connections promoted in four Mexican telebachillerato school textbooks when exploring different conceptualizations of slope. To achieve this, a conceptual framework was adapted to define the concept of mathematical connections and the different conceptualizations of slope. Content analysis was employed to analyze the textbooks. Based on the lesson presentations in these materials, the mathematical connections were categorized as either implicit or explicit. The findings revealed a total of 160 explicit and 202 implicit mathematical connections, underscoring the vital role that teachers must play in instructing students on how to utilize these connections in the Mexican telebachillerato classroom, since mathematical connections are promoted wihin the textbooks but they are implicit in some instances. The results indicated that the four textbooks analyzed promote the following mathematical connections: procedural, different representations, meaning, feature, part-whole, inter-conceptual, modeling, and implication.
References
Bardin, L. (1997). Análise de conteúdo. Edições 70. https://ia802902.us.archive.org/8/items/bardin-laurenceanalise-
Beswick, K., y Muir, T. (2013). Making connections: Lessons on the use of video in pre-service teacher education. Mathematics Teacher Education and Development, 15(2), 27-51. https://eric.ed.gov/?id=EJ1018707
Bingölbali, E., y Coşkun, M. (2016). A proposed conceptual framework for enhancing the use of making connections skill in Mathematics teaching. Education and Science, 41(183), 233-249. https://doi.org/10.15390/EB.2016.4764
Businskas, A. (2008). Conversations about connections: How secondary Mathematics teachers conceptualize and contend with mathematical connections [Tesis de Doctorado no publicada]. Simon Fraser University, Canadá.
Byerley, C., y Thompson, P. (2017). Secondary mathematics teachers’ meanings for measure, slope, and rate of change. The Journal of Mathematical Behavior, 48, 168-193. https://doi.org/10.1016/j.jmathb.2017.09.003
Campo-Meneses, K., y García-García, J. (2020). Explorando las conexiones matemáticas asociadas a la función exponencial y logarítmica en estudiantes universitarios colombianos. Educación Matemática, 32(3), 209-240. https://doi.org/10.24844/EM3203.08
Campo-Meneses, K., y García-García, J. (2021). La comprensión de las funciones exponencial y logarítmica: una mirada desde las conexiones matemáticas y el enfoque ontosemiótico. PNA. Revista de Investigación en Didáctica de la Matemática, 16(1), 25-56. https://doi.org/10.30827/pna.v16i1.15817
Caviedes-Barrera, S., De Gamboa-Rojas, G., y Badillo-Jiménez, E. (2019). Conexiones matemáticas que establecen maestros en formación al resolver tareas de medida y comparación de áreas. Praxis, 15(1), 69-87. https://doi.org/10.21676/23897856.2984
Cho, P., y Nagle, C. (2017). Procedural and conceptual difficulties with slope: An analysis of students’ mistakes on routine tasks. International Journal of Research in Education and Science, 3(1), 135-150. https://eric.ed.gov/?id=EJ1126738
Conaliteg [Comisión Nacional de Libros de Texto Gratuitos] (s.f.). Libros Conaliteg. https://librosconaliteg.com.mx/telebachillerato/
De Gamboa, G., y Figueiras, L. (2014). Conexiones en el conocimiento matemático del profesor: propuesta de un modelo de análisis. En M. González, M. Codes, D. Arnau y T. Ortega (eds.), Investigación en educación matemática XVIII (pp. 337-344). SEIEM. http://funes.uniandes.edu.co/6005/
Dolores, C., García-García, J., y Gálvez-Pacheco, A. (2017). Estabilidad y cambio conceptual acerca de las razones de cambio en situación escolar. Educación Matemática, 29(2), 125-158. https://doi.org/10.24844/EM2902.05
Dolores, C., e Ibáñez, G. (2020). Conceptualizaciones de la pendiente en libros de texto de Matemáticas. Bolema: Boletim de Educação Matemática, 34(67), 825-846. https://doi.org/10.1590/1980-4415v34n67a22
Dolores, 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: Boletim de Educação Matemática, 31(57), 158-180. https://doi.org/10.1590/1980-4415v31n57a08
Dolores-Flores, C., Rivera-López, M., y 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. https://doi.org/10.1080/0020739X.2018.1507050
Eli, J., Mohr-Schroeder, M., y Lee, C. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula [Tesis de Doctorado no publicada]. Pennsylvania State University College of Education, Estados Unidos de Norteamérica.
Garbín, S. (2005). ¿Cómo piensan los alumnos entre 16 y 20 años el infinito? La influencia de los modelos, las representaciones y los lenguajes matemáticos. Revista Latinoamericana de Investigación en Matemática Educativa, 8(2), 169-193. https://www.redalyc.org/pdf/335/33580205.pdf
García-García, J. (2023, en prensa). Mexican High School students’ mathematical understanding about linear equations and functions. The Mathematics Enthusiast.
García-García, J., Hernández-Yañez, M., 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.v13i0.1485
García-García, J., y 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
García-García, J., y Dolores-Flores, C. (2021a). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1-22. https://doi.org/10.1007/s13394-019-00286-x
García-García, J., y 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
Garrido-Méndez, M. (2015a). Telebachillerato Comunitario. Segundo Semestre, Matemáticas II. Secretaría de Educación Pública. https://librosconaliteg.com.mx/telebachillerato/segundo-semestre/matematicas-ii-segundo-semestre-telebachillerato/
Garrido-Méndez, M. (2015b). Telebachillerato Comunitario. Cuarto Semestre, Matemáticas IV. Secretaría de Educación Pública. https://librosconaliteg.com.mx/telebachillerato/tercer-semestre/matematicas-iii-tercer-semestre-telebachillerato/
Garrido-Méndez, M., Llamas-Casoluengo, L., y Sánchez-Linares, I. (2015). Telebachillerato Comunitario. Primer Semestre, Matemáticas I. Secretaría de Educación Pública. https://librosconaliteg.com.mx/telebachillerato/primer-semestre/matematicas-i-primer-semestre-telebachillerato/
Kenedi, A., Ramadhani, D., Sukirno, Fransyaigu, R., Asnawi, y Mulyahati, B. (2021). Mathematical connection ability of elementary school students during the Covid-19 pandemic. En 2nd International Conference on Science, Technology, and Modern Society (ICSTMS 2020) (pp. 269-271). Atlantis Press. https://doi.org/10.2991/assehr.k.210909.060
Lehmann, C. (2008). Geometría analítica. Limusa.
Maulyda, M., Rosyidah, A., y Hidayati, V. (2022). Elementary school students’ mathematical connection in problem-posing activities. Jurnal Elemen, 8(1), 99-116. https://doi.org/10.29408/jel.v8i1.4364
Moore-Russo, D., Conner, A., y Rugg, K. (2011). Can slope be negative in 3-space? Studying concept image of slope through collective definition construction. Educational Studies in Mathematics, 76(1), 3-21. https://doi.org/10.1007/s10649-010-9277-y
Nagle, C., y Moore-Russo, D. (2013). The concept of slope: Comparing teachers’ concept images and instructional content. Investigations in Mathematics Learning, 6(2), 1-18. https://doi.org/10.1080/24727466.2013.11790330
NCTM [National Council of Teachers of Matematics] (2014). Principles to action: Ensuring mathematical success for all. NCTM.
Okeeffe, L. (2013). A framework for textbook analysis. International Review of Contemporary Learning Research, 2(1), 1-13. https://doi.org/10.12785/irclr/020101
Pambudi, D., Budayasa, I., y Lukito, A. (2018). Mathematical connection profile of junior high School students in solving mathematical problems based on gender difference. International Journal of Scientific Research and Management, 6(8), 1-6. https://doi.org/10.18535/ijsrm/v6i8.m01
Putri, E., Budiyono, B., e Indriati, D. (2020). Pogil model on mathematical connection ability viewed from self-regulated learning. International Journal of Evaluation and Research in Education (IJERE), 9(2), 394. https://doi.org/10.11591/ijere.v9i2.20321
Rivera-López, M., Salgado-Beltrán, G., y Dolores-Flores, C. (2019). Explorando las conceptualizaciones de la pendiente en estudiantes universitarios. Bolema: Boletim de Educação Matemática, 33(65), 1027-1046. https://doi.org/10.1590/1980-4415v33n65a03
Rodríguez-Nieto, C., García-García, J., y Rodríguez, F. (2021). Pre-service Math teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education (Turcomat). https://doi.org/10.16949/turkbilmat.797182
Rodríguez-Nieto, C., Rodríguez-Vásquez, F., y Moll, V. (2022). A new view about connections: The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 53(6), 1231-1256. https://doi.org/10.1080/0020739X.2020.1799254
Salazar-Puente, R. (2015). Telebachillerato Comunitario. Tercer Semestre, Matemáticas III. Secretaría de Educación Pública. https://librosconaliteg.com.mx/telebachillerato/tercer-semestre/matematicas-iii-tercer-semestre-telebachillerato/
Salgado-Beltrán, G., Rivera-López, M., y Dolores-Flores, C. (2019). Conceptualizaciones de pendiente: contenido que enseñan los profesores del bachillerato. Unión, (57), 41-56. http://revistaunion.org/index.php/UNION/article/view/87
Samo, D. (2021). Analysis of mathematical connections ability on junior high school students. International Journal of Educational Management and Innovation, 2(3), 261. https://doi.org/10.12928/ijemi.v2i3.3785
SEMS [Subsecretaría de Educación Media Superior] (2015). Documento Base. Telebachillerato Comunitario. Subsecretaría de Educación Media Superior. http://www.dgb.sep.gob.mx/servicioseducativos/telebachillerato/normatividad/DOCUMENTO_BASE_TBC_2015.pdf
SEP [Secretaría de Educación Pública] (2017). Programas de estudio del telebachillerato mexicano. SEP. https://dgb.sep.gob.mx/oferta-educativa/telebachillerato-comunitario/
Stump, S. (1999). Secondary mathematics teachers’ knowledge of slope. Mathematics Education Research Journal, 11(2), 124-144.
Stump, S. (2001). Developing preservice teachers’ pedagogical content knowledge of slope. The Journal of Mathematical Behavior, 20(2), 207-227.
Suárez, M. (2019). Libro de texto, práctica educativa y competencia comunicativa. Revista de Educación, 3, 26-45. http://revista.celei.cl/index.php/PREI/article/view/267
Suastika, I., y Suwanti, V. (2019). College student’s error analysis based on their mathematical connections on graph representation. Jurnal Pendidikan Matematika Indonesia, 4(1), 18-23.
Wagino, W., y Andriani, A. (2021). Analysis of mathematical connection skills using realistic mathematical education. Indo-MathEdu Intellectuals Journal, 2(2), 83-91.
Weiss, E., Antonio, L., Bernal, E., Guzmán, C., y Pedroza, P. (2017). El telebachillerato comunitario. Una innovación curricular a discusión. Revista Latinoamericana de Estudios Educativos, 47(3-4), 7-26. https://doi.org/10.48102/rlee.2017.47.3-4.134
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Alan Andrés Cruz Acevedo, Javier García-García
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
