Main Article Content
Abstract
Research in mathematics education has shown that individuals' beliefs play a fundamental role in their responses to and interest in mathematics and their application of these beliefs in real-life situations. Although the literature related to the affective domain in general, and beliefs in particular, has explored the relationship between beliefs and student educational level, there still needs to be a research gap regarding the empirical testing of this variable in the context of secondary mathematics education in Chile. Therefore, the present study, with a quantitative and exploratory methodology, aims to fill this gap by adapting the Mathematics-Related Beliefs Questionnaire MRBQ to describe and analyze students' beliefs in mathematics at two levels of secondary education. The main results of the study indicate that mostly positive beliefs are observed in the three types of beliefs studied: Beliefs about the social context, about self-concept, and mathematics education, highlighting the dimension of beliefs about the social context or classroom environment, in which students showed a highly positive perception of the role of the mathematics teacher.
Keywords
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
- Alastre, V., & Borjas, H. (2017). Creencias de los estudiantes sobre el aprendizaje
- de la matemática. ARJÉ. Revista de Postgrado FaCE-UC, 11(20), 325-332. http://www.arje.bc.uc.edu.ve/arj20/art31.pdf
- Attard, C., Ingram, N., Forgasz, H., Leder, G., & Grootenboer, P. (2016). Mathematics education and the affective domain. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison and K. Fry (Eds.). Research in Mathematics Education in Australasia: 2012-2015 (pp. 73-96). https://doi.org/10.1007/978-981-10-1419-2_5
- Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers' professional competence. In M. Kunter, J. Baumert, U. Klusmann, W. Blum, S. Krauss and M. Neubrand (Eds). Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers: Results from the COACTIV (pp.25-48). Boston, MA: Springer. https://doi.org/10.1007/978-1-4614-5149-5_2
- Carvajal, A., Centeno, C., Watson, R., & Bruera, E. (2011). A comprehensive study of psychometric properties of the Edmonton Symptom Assessment System (ESAS) in Spanish advanced cancer patients. European Journal of Cancer, 47(12), 1863-1872. https://doi.org/10.1016/j.ejca.2011.03.027
- Castro-Velásquez, M. & Rivadeneira-Loor, F. (2022). Posibles causas del bajo rendimiento en las matemáticas: una revisión a la literatura. Polo del Conocimiento, 7(2), 1089-1098.DOI: https://doi.org/10.23857/pc.v7i1.3635
- De Corte, E., Op’t Eynde, P., & Verschaffel, L. (2002). Knowing what to believe: The relevance of students’ mathematics beliefs for mathematics education. In B.K. Hofer and P.R. Pintrich (Eds.). Personal Epistemology: The Psychology of Be¬liefs about Knowledge and Knowing (pp. 297-320). Mahwah, NJ. Lawrence Erlbaum Associates. https://psycnet.apa.org/record/2001-18187-014
- Diego-Mantecón, J., Andrews, P., & Op’t Eynde, P. (2008). Mejora y evaluación de un cuestionario de creencias de matemáticas en función de nacionalidad, edad y sexo. Investigación en Educación Matemática, 1(1), 325-334. http://funes.uniandes.edu.co/1265/1/Diego2008Mejora_SEIEM_325.pdf
- Erazo-Hurtado, J. D., & Aldana-Bermúdez, E. (2015). Sistema de creencias sobre las matemáticas en los estudiantes de educación básica. Praxis, 11, 163-169. https://doi.org/10.21676/23897856.1562
- Erdogan, F., & Sengul, S. (2014). A study on the elementary school students’ mathematics self- concept. Procedia - Social and Behavioral Sciences, 152(7), 596-601. https://doi.org/10.1016/j.sbspro.2014.09.249
- Gamboa, R., & Moreira, T. (2017). Actitudes y creencias hacia las matemáticas: un estudio comparativo entre estudiantes y profesores. Actualidades Investigativas en Educación, 17(1), 514-559. http://dx.doi.org/10.15517/aie.v17i1.27473
- Grootenboer, P. J., & Marshman, M. (2016). Mathematics Affect and Learning: Middle School Students’ Beliefs and Attitudes about Mathematics Education. 1st ed. Springer.
- Guay, F., Marsh, H. W., & Boivin, M. (2003). Akademic self-concept and academic achievement: Developmental perspectives on their causal ordering. Journal of Educational Psychology, 95(1), 124-136. http://dx.doi.org/10.1037//0022-0663.95.1.124
- Hannelotte, L. T., Sylke, W. M., & Johannes, E. H. (2017). The relation between mathematics self-concept, test and mathematics anxiety, achievement motivation and mathematics achievement in 12 to 14-year-old typically developing adolescents. Psychology, Society, & Education, 9(1), 89-103. https://doi.org/10.25115/psye.v9i1.465
- Hernández, R, Fernández, C. & Baptista, P. (2014). Metodología de la Investigación (6.a Edición). México DF: Mc Graw Hill. https://www.uca.ac.cr/wp-content/uploads/2017/10/Investigacion.pdf
- Hidalgo, S., Maroto, A., Ortega, T., & Palacios, A. (2014). Influencia del dominio afectivo en el aprendizaje de las matemáticas. En V. Mellado, L. Blanco, A. Borrachero y J. Cárdenas (Eds.). Las emociones en la enseñanza y el aprendizaje de las ciencias y las matemáticas (pp. 218-238). Extremadura: Grupo de Investigación DEPROFE. https://dialnet.unirioja.es/servlet/libro?codigo=533150
- Hidalgo, A., Maroto, A., & Palacios, A., (2015). Una aproximación al sistema de creencias matemáticas en futuros maestros. Educacion Matemática, 27(1), 65-90. https://www.redalyc.org/pdf/405/40540690004.pdf
- Hyrkäs, K., Appelqvist-Schmidlechner, K., & Oksa, L. (2003). Validating an instrument for clinical supervision using an expert panel. International Journal of Nursing Studies, 40(6), 619-625. http://dx.doi.org/10.1016/s0020-7489(03)00036-1
- Hoffman, B. (2010). I think I can, but I’m afraid to try: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and Individual Differences, 3(20), 276-283. http://dx.doi.org/10.1016/j.lindif.2010.02.001
- Li, Y., & Schoenfeld, A.H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6(1), 44. https://doi.org/10.1186/s40594-019-0197-9
- Liljedahl, P., Oesterle, S., & Bernèche, C. (2012). Stability of beliefs in mathematics education: A critical analysis. Nordic Studies in Mathematics Education, 17(3-4), 101-118. https://www.researchgate.net/publication/294263765_Stability_of_Beliefs_in_Mathematics_Education_A_Critical_Analysis
- Marsh, H.W., Trautwein, U., Ludtke, O., Koller, O., & Baumert, J. (2005). Academic self-concept, interest, grades and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76, 397-416. https://doi.org/10.1111/j.1467-8624.2005.00853.x
- Mineduc (2019). Bases Curriculares 3° y 4° Medio. (1ª edición). Santiago de Chile: Ministerio de Educación. https://hdl.handle.net/20.500.12365/14364
- Montero, Y., Pedroza, M., Astiz, M., & Vilanova, S. (2015). Caracterización de las
- actitudes de estudiantes universitarios de Matemática hacia los métodos numéricos. Revista
- Electronica de Investigacion Educativa, 17(1), 88–99. https://www.scielo.org.mx/pdf/redie/v17n1/v17n1a6.pdf
- Nagy, G., Watt, H., Eccles, J., & Trautwein, U. (2010). The development of students’ mathematics self-concept in relation to gender: Different countries, different trajectories? Journal of Research on Adolescence, 20(2), 482-506. https://doi.org/10.1111/j.1532-7795.2010.00644.x
- OECD (2018). PISA 2021 Mathematics Framework (Second Draft). OECD:Paris. https://www.oecd.org/pisa/pisaproducts/pisa-2021-mathematics-framework-draft.pdf
- Op’t Eynde, P., & De Corte, E. (2003). Students’ mathematics-related belief systems: design and analysis of a questionnaire. Proceedings of the Annual Meeting of the American Educational Research Association. Chicago. https://files.eric.ed.gov/fulltext/ED475708.pdf
- Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs: a quest for conceptual clarity and a comprehensive categorization. In G. Leder, E. Pehkonen and G. Törner (Eds.). Beliefs: A Hidden Variable in Mathematics Education? (pp. 13-37). Dordrecht: Kluwer Academic Publishers.
- Paternina, A., & Quessep, D. (2017). Creencias y concepciones: una mirada a la evaluación matemática en la educación superior. Boletín Redipe, 6(4), 150-159. file:///C:/DESCARGAS/Dialnet-CreenciasYConcepciones-6119353%20(1).pdf
- Patton, M. (2002). Qualitative Evaluation and Research Methods (3rd ed.). CA Sage Publication. Retrieved from:https://www.academia.edu/28766598/Qualitative_evaluation_and_research_methods
- Rojo, V., Madariaga, J.M., & Villarroel, J.D. (2020). Secondary education students’ beliefs about mathematics and their repercussions on motivation. Mathematics, 8(3), 368. https://doi.org/10.3390/math8030368
- Rojo, V., Villarroel, J.D., & Madariaga, J.M. (2018).The affective domain in learning mathematics according to students' gender. Revista Latinoamericana de Investigación en Matemática Educativa, 21(2), 182-198. https://doi.org/10.12802/relime.18.2123
- Segarra, J., & Julià, C. (2022). Mathematics teaching efficacy belief and attitude of pre-service teachers and academic achievement. European Journal of Science and Mathematics Education, 10(1), 1-14. https://doi.org/10.30935/scimath/11381
- Schoenfeld, A. H. (2016). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics (Reprint). Journal of Education, 196(2), 1-38. https://doi.org/10.1177/002205741619600202
- Staub, F., & Stern, E. (2002). The nature of teachers’ pedagogical content beliefs matters for students’ achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344-355. https://doi.org/10.1037//0022-0663.94.2.344
- Tuohilampi, L., Hannula, M., Varas, L., & Giaconi, V. (2014). Challenging western approach to cultural comparisons: young pupils’ affective structures regarding mathematics in Finland and in Chile. International Journal of Science and Mathematics Education, 13(6). https://doi.org/10.1007/s10763-014-9562-9
- Turşucu, S., Spandaw, J., Flipse, S., Jongbloed, G., & De Vries, M.J. (2018). Teachers’ beliefs systems about improving transfer of algebraic skills from mathematics into physics in senior pre-university education. International Journal of Science Education, 40(12), 1493-1519. https://doi.org/ 10.1080/09500693.2018.1486520
- Vásquez, C., Seckel, M., & Alsina, Á. (2020). Belief system of future teachers on education for sustainable development in math classes. Uniciencia, 34(2), 1-30. https://doi.org/10.15359/ru.34-2.1
- Vesga-Bravo, G., & De Losada, M. (2018). Creencias epistemológicas de docentes de matemáticas en formación y en ejercicio sobre las matemáticas, su enseñanza y aprendizaje. Revista Colombiana de Educación, 74, 243-267. https://doi.org/10.17227/rce.num74-6909
- Videla, M.V., Rojas, F., Ulloa, R., Chandía, E., Ortíz, E., & Perdomo, J. (2019). Creencias y conocimiento matemático escolar al comienzo de la formación inicial docente en estudiantes de Pedagogía General Básica. Pensamiento Educativo. Revista de Investigación Educacional Latinoamericana, 56(2), 1-19. https://doi.org/ 10.7764/PEL.56.2.2019.9
- Wong, N. Y., Ding, R., & Zhang, Q. P. (2016). From classroom environment to conception of mathematics. In R. B. King and A. B. I. Bernardo (Eds.). The Psychology of Asian Learners (pp. 541–557). Singapore: Springer. https://doi.org/10.1007/978-981-287-576-1_33
- Xie, S., & Cai, J. (2020). Teachers’ beliefs about mathematics, learning, teaching, students, and teachers: Perspectives from Chinese high school in-service mathematics teachers. International Journal of Sciences and Mathematics Education, 13(2), 265-287. https://doi.org/10.1007/s10763-020-10074-w
- Zakaria, E., & Musiran, N. (2010). Beliefs about the nature of mathematics, mathematics teaching and learning among trainee teachers. The Social Sciences, 5, 346-351. https://doi.org/10.3923/sscience.2010.346.351
References
Alastre, V., & Borjas, H. (2017). Creencias de los estudiantes sobre el aprendizaje
de la matemática. ARJÉ. Revista de Postgrado FaCE-UC, 11(20), 325-332. http://www.arje.bc.uc.edu.ve/arj20/art31.pdf
Attard, C., Ingram, N., Forgasz, H., Leder, G., & Grootenboer, P. (2016). Mathematics education and the affective domain. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison and K. Fry (Eds.). Research in Mathematics Education in Australasia: 2012-2015 (pp. 73-96). https://doi.org/10.1007/978-981-10-1419-2_5
Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers' professional competence. In M. Kunter, J. Baumert, U. Klusmann, W. Blum, S. Krauss and M. Neubrand (Eds). Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers: Results from the COACTIV (pp.25-48). Boston, MA: Springer. https://doi.org/10.1007/978-1-4614-5149-5_2
Carvajal, A., Centeno, C., Watson, R., & Bruera, E. (2011). A comprehensive study of psychometric properties of the Edmonton Symptom Assessment System (ESAS) in Spanish advanced cancer patients. European Journal of Cancer, 47(12), 1863-1872. https://doi.org/10.1016/j.ejca.2011.03.027
Castro-Velásquez, M. & Rivadeneira-Loor, F. (2022). Posibles causas del bajo rendimiento en las matemáticas: una revisión a la literatura. Polo del Conocimiento, 7(2), 1089-1098.DOI: https://doi.org/10.23857/pc.v7i1.3635
De Corte, E., Op’t Eynde, P., & Verschaffel, L. (2002). Knowing what to believe: The relevance of students’ mathematics beliefs for mathematics education. In B.K. Hofer and P.R. Pintrich (Eds.). Personal Epistemology: The Psychology of Be¬liefs about Knowledge and Knowing (pp. 297-320). Mahwah, NJ. Lawrence Erlbaum Associates. https://psycnet.apa.org/record/2001-18187-014
Diego-Mantecón, J., Andrews, P., & Op’t Eynde, P. (2008). Mejora y evaluación de un cuestionario de creencias de matemáticas en función de nacionalidad, edad y sexo. Investigación en Educación Matemática, 1(1), 325-334. http://funes.uniandes.edu.co/1265/1/Diego2008Mejora_SEIEM_325.pdf
Erazo-Hurtado, J. D., & Aldana-Bermúdez, E. (2015). Sistema de creencias sobre las matemáticas en los estudiantes de educación básica. Praxis, 11, 163-169. https://doi.org/10.21676/23897856.1562
Erdogan, F., & Sengul, S. (2014). A study on the elementary school students’ mathematics self- concept. Procedia - Social and Behavioral Sciences, 152(7), 596-601. https://doi.org/10.1016/j.sbspro.2014.09.249
Gamboa, R., & Moreira, T. (2017). Actitudes y creencias hacia las matemáticas: un estudio comparativo entre estudiantes y profesores. Actualidades Investigativas en Educación, 17(1), 514-559. http://dx.doi.org/10.15517/aie.v17i1.27473
Grootenboer, P. J., & Marshman, M. (2016). Mathematics Affect and Learning: Middle School Students’ Beliefs and Attitudes about Mathematics Education. 1st ed. Springer.
Guay, F., Marsh, H. W., & Boivin, M. (2003). Akademic self-concept and academic achievement: Developmental perspectives on their causal ordering. Journal of Educational Psychology, 95(1), 124-136. http://dx.doi.org/10.1037//0022-0663.95.1.124
Hannelotte, L. T., Sylke, W. M., & Johannes, E. H. (2017). The relation between mathematics self-concept, test and mathematics anxiety, achievement motivation and mathematics achievement in 12 to 14-year-old typically developing adolescents. Psychology, Society, & Education, 9(1), 89-103. https://doi.org/10.25115/psye.v9i1.465
Hernández, R, Fernández, C. & Baptista, P. (2014). Metodología de la Investigación (6.a Edición). México DF: Mc Graw Hill. https://www.uca.ac.cr/wp-content/uploads/2017/10/Investigacion.pdf
Hidalgo, S., Maroto, A., Ortega, T., & Palacios, A. (2014). Influencia del dominio afectivo en el aprendizaje de las matemáticas. En V. Mellado, L. Blanco, A. Borrachero y J. Cárdenas (Eds.). Las emociones en la enseñanza y el aprendizaje de las ciencias y las matemáticas (pp. 218-238). Extremadura: Grupo de Investigación DEPROFE. https://dialnet.unirioja.es/servlet/libro?codigo=533150
Hidalgo, A., Maroto, A., & Palacios, A., (2015). Una aproximación al sistema de creencias matemáticas en futuros maestros. Educacion Matemática, 27(1), 65-90. https://www.redalyc.org/pdf/405/40540690004.pdf
Hyrkäs, K., Appelqvist-Schmidlechner, K., & Oksa, L. (2003). Validating an instrument for clinical supervision using an expert panel. International Journal of Nursing Studies, 40(6), 619-625. http://dx.doi.org/10.1016/s0020-7489(03)00036-1
Hoffman, B. (2010). I think I can, but I’m afraid to try: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and Individual Differences, 3(20), 276-283. http://dx.doi.org/10.1016/j.lindif.2010.02.001
Li, Y., & Schoenfeld, A.H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6(1), 44. https://doi.org/10.1186/s40594-019-0197-9
Liljedahl, P., Oesterle, S., & Bernèche, C. (2012). Stability of beliefs in mathematics education: A critical analysis. Nordic Studies in Mathematics Education, 17(3-4), 101-118. https://www.researchgate.net/publication/294263765_Stability_of_Beliefs_in_Mathematics_Education_A_Critical_Analysis
Marsh, H.W., Trautwein, U., Ludtke, O., Koller, O., & Baumert, J. (2005). Academic self-concept, interest, grades and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76, 397-416. https://doi.org/10.1111/j.1467-8624.2005.00853.x
Mineduc (2019). Bases Curriculares 3° y 4° Medio. (1ª edición). Santiago de Chile: Ministerio de Educación. https://hdl.handle.net/20.500.12365/14364
Montero, Y., Pedroza, M., Astiz, M., & Vilanova, S. (2015). Caracterización de las
actitudes de estudiantes universitarios de Matemática hacia los métodos numéricos. Revista
Electronica de Investigacion Educativa, 17(1), 88–99. https://www.scielo.org.mx/pdf/redie/v17n1/v17n1a6.pdf
Nagy, G., Watt, H., Eccles, J., & Trautwein, U. (2010). The development of students’ mathematics self-concept in relation to gender: Different countries, different trajectories? Journal of Research on Adolescence, 20(2), 482-506. https://doi.org/10.1111/j.1532-7795.2010.00644.x
OECD (2018). PISA 2021 Mathematics Framework (Second Draft). OECD:Paris. https://www.oecd.org/pisa/pisaproducts/pisa-2021-mathematics-framework-draft.pdf
Op’t Eynde, P., & De Corte, E. (2003). Students’ mathematics-related belief systems: design and analysis of a questionnaire. Proceedings of the Annual Meeting of the American Educational Research Association. Chicago. https://files.eric.ed.gov/fulltext/ED475708.pdf
Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs: a quest for conceptual clarity and a comprehensive categorization. In G. Leder, E. Pehkonen and G. Törner (Eds.). Beliefs: A Hidden Variable in Mathematics Education? (pp. 13-37). Dordrecht: Kluwer Academic Publishers.
Paternina, A., & Quessep, D. (2017). Creencias y concepciones: una mirada a la evaluación matemática en la educación superior. Boletín Redipe, 6(4), 150-159. file:///C:/DESCARGAS/Dialnet-CreenciasYConcepciones-6119353%20(1).pdf
Patton, M. (2002). Qualitative Evaluation and Research Methods (3rd ed.). CA Sage Publication. Retrieved from:https://www.academia.edu/28766598/Qualitative_evaluation_and_research_methods
Rojo, V., Madariaga, J.M., & Villarroel, J.D. (2020). Secondary education students’ beliefs about mathematics and their repercussions on motivation. Mathematics, 8(3), 368. https://doi.org/10.3390/math8030368
Rojo, V., Villarroel, J.D., & Madariaga, J.M. (2018).The affective domain in learning mathematics according to students' gender. Revista Latinoamericana de Investigación en Matemática Educativa, 21(2), 182-198. https://doi.org/10.12802/relime.18.2123
Segarra, J., & Julià, C. (2022). Mathematics teaching efficacy belief and attitude of pre-service teachers and academic achievement. European Journal of Science and Mathematics Education, 10(1), 1-14. https://doi.org/10.30935/scimath/11381
Schoenfeld, A. H. (2016). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics (Reprint). Journal of Education, 196(2), 1-38. https://doi.org/10.1177/002205741619600202
Staub, F., & Stern, E. (2002). The nature of teachers’ pedagogical content beliefs matters for students’ achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344-355. https://doi.org/10.1037//0022-0663.94.2.344
Tuohilampi, L., Hannula, M., Varas, L., & Giaconi, V. (2014). Challenging western approach to cultural comparisons: young pupils’ affective structures regarding mathematics in Finland and in Chile. International Journal of Science and Mathematics Education, 13(6). https://doi.org/10.1007/s10763-014-9562-9
Turşucu, S., Spandaw, J., Flipse, S., Jongbloed, G., & De Vries, M.J. (2018). Teachers’ beliefs systems about improving transfer of algebraic skills from mathematics into physics in senior pre-university education. International Journal of Science Education, 40(12), 1493-1519. https://doi.org/ 10.1080/09500693.2018.1486520
Vásquez, C., Seckel, M., & Alsina, Á. (2020). Belief system of future teachers on education for sustainable development in math classes. Uniciencia, 34(2), 1-30. https://doi.org/10.15359/ru.34-2.1
Vesga-Bravo, G., & De Losada, M. (2018). Creencias epistemológicas de docentes de matemáticas en formación y en ejercicio sobre las matemáticas, su enseñanza y aprendizaje. Revista Colombiana de Educación, 74, 243-267. https://doi.org/10.17227/rce.num74-6909
Videla, M.V., Rojas, F., Ulloa, R., Chandía, E., Ortíz, E., & Perdomo, J. (2019). Creencias y conocimiento matemático escolar al comienzo de la formación inicial docente en estudiantes de Pedagogía General Básica. Pensamiento Educativo. Revista de Investigación Educacional Latinoamericana, 56(2), 1-19. https://doi.org/ 10.7764/PEL.56.2.2019.9
Wong, N. Y., Ding, R., & Zhang, Q. P. (2016). From classroom environment to conception of mathematics. In R. B. King and A. B. I. Bernardo (Eds.). The Psychology of Asian Learners (pp. 541–557). Singapore: Springer. https://doi.org/10.1007/978-981-287-576-1_33
Xie, S., & Cai, J. (2020). Teachers’ beliefs about mathematics, learning, teaching, students, and teachers: Perspectives from Chinese high school in-service mathematics teachers. International Journal of Sciences and Mathematics Education, 13(2), 265-287. https://doi.org/10.1007/s10763-020-10074-w
Zakaria, E., & Musiran, N. (2010). Beliefs about the nature of mathematics, mathematics teaching and learning among trainee teachers. The Social Sciences, 5, 346-351. https://doi.org/10.3923/sscience.2010.346.351