Conocimiento de maestros en servicio y en formación sobre resolución de problemas aritméticos
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sep 29, 2021
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Generalmente, la enseñanza de la resolución de problemas aritméticos en el aula se caracteriza por la escasa incidencia en el razonamiento. Uno de los motivos podría ser el tipo de conocimiento matemático que han desarrollado los profesores acerca del propio proceso de resolución durante su ejercicio profesional. En el presente trabajo, se analizan las diferencias en la orientación, la coherencia y la explicitud del conocimiento en resolución de problemas aritméticos de 109 maestros (60.55 % mujeres y 39.45 % hombres) en servicio y en formación (experiencia: M = 19.22, DE =10.01). Mediante una entrevista estructurada, los maestros seleccionaron un tipo de problema, un modelo de resolución y un ejemplo de interacción de entre dos opciones en cada caso (con ayudas al razonamiento o sin ayudas), según cuál considerasen más conveniente para enseñar a los alumnos a resolver problemas, argumentando su respuesta. Los resultados indicaron que los maestros en servicio mostraron una orientación a las opciones sin razonamiento, fueron más coherentes en sus elecciones en las tres tareas (problemas, modelos e interacción), y sus argumentos fueron más explícitos que los de los maestros en formación. Como conclusión, sería recomendable enriquecer el conocimiento matemático de los maestros en relación con la resolución de problemas aritméticos.
Keywords
conocimiento, resolución de problemas, problemas aritméticos, maestros en servicio, maestros en formaciónknowledge, problem solving, word problems, in-service teacher, pre-service teacher
References
An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145-172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407. https://doi.org/10.1177/0022487108324554
Berliner, D. C. (1988). The development of expertise in pedagogy. Conferencia dictada en el Annual Meeting of the American Association of Colleges for Teacher Education, New Orleans. (File number ERIC ED298122).
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194-222. https://doi.org/10.2307/749118
Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. A. (1988). Teacher´s pedagogical content knowledge of students´ problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19(5), 385-401. https://doi.org/10.2307/749173
Carrillo-Yañez, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vaco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. https://doi.org/ 10.1080/14794802.2018.1479981
Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2020). Mathematical content knowledge and knowledge for teaching: Exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 23(5), 579-613. https://doi.org/10.1007/s10857-019-09443-2
Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152. https://doi.org/10.1207/s15516709cog0502_2
Chi, M. T. H., Glaser, R., & Rees, E. (1982). Expertise in problem solving. En S. R. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 1, pp. 7-76). Erlbaum.
Clark, C. M., & Peterson, P. L. (1986). Teachers' thought processes. En M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 255-296). McMillan.
Davis, J. D. (2009). Understanding the influence of two mathematics textbooks on prospective secondary teachers´ knowledge. Journal of Mathematics Teacher Education, 12, 365-389. https://doi.org/10.1007/s10857-009-9115-2
Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (abril, 2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6. https://doi.org/10.3389/fpsyg.2015.00348
Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers´ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26, 151-160. https://doi.org/10.1016/j.tate.2009.03.016
Ding, M., Li, X., & Capraro, M. (2013). Preservice elementary teachers’ knowledge for teaching the associative property of multiplication: A preliminary analysis. The Journal of Mathematical Behavior, 32(1), 36-52. https://doi.org/ 10.1016/j.jmathb.2012.09.002
Echegaray-Bengoa, J., & Soriano-Ferrer, M. (2016). Conocimiento de los maestros acerca de la dislexia de desarrollo: implicaciones educativas. Aula Abierta, 44, 63-69. https://doi.org/10.1016/j.aula.2016.01.001
Fennema, E., & Franke, M. L. (1992). Teacher´s knowledge and its impact. En D. A. Groews (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). McMillan.
Grossman, P. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press.
Gvozdic, K., & Sander, E. (2018). When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies. Educational Studies in Mathematics, 98, 157-175. https://doi.org/10.1007/s10649-018-9806-7
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problem: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18-32. https://doi.org/10.1037/0022-0663.87.1.18
Hiebert, J., Gallimore, R., Givvin, K. B., Hollingsworth, H., Jacobs, J., Chui, A. M., Wearne, D., Smith, M., Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P., & Stigler, J. (2003). Teaching mathematics in seven countries. Results from the TIMSS 1999 video study. National Center for Education Statistics (NCES).
Hill, H. C., Blunk, M., Charalambous, C., Lewis, J., Phelps, G., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
Hogan, T., & Rabinowitz, M. (2009). Teacher expertise and the development of a problem representation. Educational Psychology, 29(2), 153-169. https://doi.org/10.1080/01443410802613301
Hogan, T., Rabinowitz, M., & Craven, J. A. (2003). Representation in teaching: Inferences from research of expert and novice teachers. Educational Psychologist, 38(4), 235-247. https://doi.org/10.1207/S15326985EP3804_3
Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. The Journal of Mathematical Behavior, 31(4), 417-430. https://doi.org/10.1016/j.jmathb.2012.06.001
International Association for the Evaluation of Educational Achievement. (2019). PISA 2018. Programa para la evaluación internacional de los alumnos (Informe español). Ministerio de Educación y Formación Profesional/Ministerio de Cultura y Deporte. https://sede.educacion.gob.es/publiventa/pisa-2018-programa-para-la-evaluacion-internacional-de-los-estudiantes-informe-espanol/evaluacion-examenes/23505
International Association for the Evaluation of Educational Achievement. (2016). TIMSS 2015. Estudio internacional de tendencias en Matemáticas y Ciencias. (Informe español: resultados y contexto). Ministerio de Educación, Cultura y Deporte. http://www.educacionyfp.gob.es/inee/dam/jcr:4fc1ecde-6414-4255-aa98-2a6acb8a09dd/timss2015final.pdf
Izsàk, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/07370000701798529
Jaime, A., & Gutiérrez, A. (1990). Una propuesta de fundamentación para la enseñanza de la geometría: el modelo Van Hiele. En S. Llinares & M. V. Sánchez (Eds.), Teoría y práctica en educación matemática (pp. 295-384). Alfar.
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2012). Teacher´s content knowledge and pedagogical content knowledge: The role of structural differences in teacher education. Journal of Teacher Education, 20(10), 1-17. https://doi.org/10.1177/0022487112460398
Leinhardt, G., & Greeno, J. G. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78(2), 75-95. https://doi.org/10.1037/0022-0663.78.2.75
Li, X. (2011). Mathematical knowledge for teaching algebraic routines: A case study of solving quadratic equations. Journal of Mathematics Education, 4(2), 1-16. http://educationforatoz.com/images/Xuhui_Li.pdf
Lo, J., & Luo, F. (2012). Prospective elementary teacher´s knowledge of fraction division. Journal of Mathematics Teacher Education, 15, 481-500. https://doi.org/10.1007/s10857-012-9221-4
Meyer, D. K., & Turner, J. C. (2002). Using instructional discourse analysis to study the scaffolding of student self-regulation. Educational Psychologist, 37, 5-13. https://doi.org/10.1207/S15326985EP3701_3
Mullins, I., & Martin, M. O. (2018). TIMSS 2019. Marcos de la evaluación. Instituto Nacional de Evaluación Educativa.
Nesher, P., & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem solving. Educational Studies in Mathematics, 6, 41-51. https://doi.org/10.1007/BF00590023
Newton, K. J. (2008). An extensive analysis of preservice elementary teacher´s knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851
Organización para la Cooperación y el Desarrollo Económicos. (1999). Measuring student knowledge and skills. A new framework for assessment. Autor. http://www.oecd.org/education/school/programmeforinternationalstudentassessmentpisa/33693997.pdf
Orrantia, J., Tarín, J., & Vicente, S. (2011). El uso de la información situacional en la resolución de problemas aritméticos. Infancia y Aprendizaje, 34(1), 81-94. https://doi.org/10.1174/021037011794390094
Piñeiro, J. L., Castro-Rodríguez, E., & Castro, E. (2019). Componentes de conocimiento del profesor para la enseñanza de la resolución de problemas en educación primaria. PNA 13(2), 104-129. https://revistaseug.ugr.es/index.php/pna/article/view/v13i2.7876
Rosales, J., Vicente, S., Chamoso, J. M., Muñez, D., & Orrantia, J. (2012). Teacher-student interaction in joint word problem solving. The role of situational and mathematical knowledge in mainstream classrooms. Teaching and Teacher Education, 28(8), 1185-1195. https://doi.org/10.1016/j.tate.2012.07.007
Sánchez, M. R., & Vicente, S. (2015). Modelos y procesos de resolución de problemas aritméticos verbales propuestos por los libros de texto de matemáticas españoles. Cultura y Educación, 27(4), 695-725. https://doi.org/10.1080/11356405.2015.1089389
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets y Zeitlinger Publishers.
Vicente, S., & Manchado, E. (2017). Dominios de contenido y autenticidad: un análisis de los problemas aritméticos verbales incluidos en los libros de texto españoles. PNA, 11(4), 253-279. https://revistaseug.ugr.es/index.php/pna/article/view/6242
Vicente, S., Manchado, E., & Verschaffel, L. (2018). Solving arithmetic word problems. An analysis of Spanish textbooks. Cultura y Educación, 30(1), 71-104. https://doi.org/10.1080/11356405.2017.1421606
Vicente, S., Orrantia, J., & Verschaffel, L. (2007). Influence of situational and conceptual rewording on word problem solving. British Journal of Educational Psychology, 77, 829-840. https://doi.org/ 10.1348/000709907X178200
Vicente, S., Rosales, J., Chamoso, J. M., & Múñez, D. (2013). Análisis de la práctica educativa en clases de matemáticas españolas de Educación Primaria: una posible explicación para el nivel de competencia de los alumnos. Cultura y Educación, 25(4), 535-548. https://doi.org/10.1174/113564013808906799
Vicente, S. Sánchez, R., & Verschaffel, L. (2020). Word problem solving approaches in mathematics textbooks: A comparison between Singapore and Spain. European Journal of Psychology of Education, 35(3), 567-587. https://doi.org/ 10.1007/s10212-019-00447-3
Webb, N. (2009). The teacher’s role in promoting collaborative dialogue in the classroom. British Journal of Educational Psychology, 79, 1-28. https://doi.org/https://doi.org/10.1348/000709908X380772
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407. https://doi.org/10.1177/0022487108324554
Berliner, D. C. (1988). The development of expertise in pedagogy. Conferencia dictada en el Annual Meeting of the American Association of Colleges for Teacher Education, New Orleans. (File number ERIC ED298122).
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194-222. https://doi.org/10.2307/749118
Carpenter, T. P., Fennema, E., Peterson, P. L., & Carey, D. A. (1988). Teacher´s pedagogical content knowledge of students´ problem solving in elementary arithmetic. Journal for Research in Mathematics Education, 19(5), 385-401. https://doi.org/10.2307/749173
Carrillo-Yañez, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vaco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. https://doi.org/ 10.1080/14794802.2018.1479981
Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2020). Mathematical content knowledge and knowledge for teaching: Exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 23(5), 579-613. https://doi.org/10.1007/s10857-019-09443-2
Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152. https://doi.org/10.1207/s15516709cog0502_2
Chi, M. T. H., Glaser, R., & Rees, E. (1982). Expertise in problem solving. En S. R. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 1, pp. 7-76). Erlbaum.
Clark, C. M., & Peterson, P. L. (1986). Teachers' thought processes. En M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 255-296). McMillan.
Davis, J. D. (2009). Understanding the influence of two mathematics textbooks on prospective secondary teachers´ knowledge. Journal of Mathematics Teacher Education, 12, 365-389. https://doi.org/10.1007/s10857-009-9115-2
Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (abril, 2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6. https://doi.org/10.3389/fpsyg.2015.00348
Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers´ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26, 151-160. https://doi.org/10.1016/j.tate.2009.03.016
Ding, M., Li, X., & Capraro, M. (2013). Preservice elementary teachers’ knowledge for teaching the associative property of multiplication: A preliminary analysis. The Journal of Mathematical Behavior, 32(1), 36-52. https://doi.org/ 10.1016/j.jmathb.2012.09.002
Echegaray-Bengoa, J., & Soriano-Ferrer, M. (2016). Conocimiento de los maestros acerca de la dislexia de desarrollo: implicaciones educativas. Aula Abierta, 44, 63-69. https://doi.org/10.1016/j.aula.2016.01.001
Fennema, E., & Franke, M. L. (1992). Teacher´s knowledge and its impact. En D. A. Groews (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). McMillan.
Grossman, P. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press.
Gvozdic, K., & Sander, E. (2018). When intuitive conceptions overshadow pedagogical content knowledge: Teachers’ conceptions of students’ arithmetic word problem solving strategies. Educational Studies in Mathematics, 98, 157-175. https://doi.org/10.1007/s10649-018-9806-7
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problem: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18-32. https://doi.org/10.1037/0022-0663.87.1.18
Hiebert, J., Gallimore, R., Givvin, K. B., Hollingsworth, H., Jacobs, J., Chui, A. M., Wearne, D., Smith, M., Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P., & Stigler, J. (2003). Teaching mathematics in seven countries. Results from the TIMSS 1999 video study. National Center for Education Statistics (NCES).
Hill, H. C., Blunk, M., Charalambous, C., Lewis, J., Phelps, G., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
Hogan, T., & Rabinowitz, M. (2009). Teacher expertise and the development of a problem representation. Educational Psychology, 29(2), 153-169. https://doi.org/10.1080/01443410802613301
Hogan, T., Rabinowitz, M., & Craven, J. A. (2003). Representation in teaching: Inferences from research of expert and novice teachers. Educational Psychologist, 38(4), 235-247. https://doi.org/10.1207/S15326985EP3804_3
Huang, R., & Kulm, G. (2012). Prospective middle grade mathematics teachers’ knowledge of algebra for teaching. The Journal of Mathematical Behavior, 31(4), 417-430. https://doi.org/10.1016/j.jmathb.2012.06.001
International Association for the Evaluation of Educational Achievement. (2019). PISA 2018. Programa para la evaluación internacional de los alumnos (Informe español). Ministerio de Educación y Formación Profesional/Ministerio de Cultura y Deporte. https://sede.educacion.gob.es/publiventa/pisa-2018-programa-para-la-evaluacion-internacional-de-los-estudiantes-informe-espanol/evaluacion-examenes/23505
International Association for the Evaluation of Educational Achievement. (2016). TIMSS 2015. Estudio internacional de tendencias en Matemáticas y Ciencias. (Informe español: resultados y contexto). Ministerio de Educación, Cultura y Deporte. http://www.educacionyfp.gob.es/inee/dam/jcr:4fc1ecde-6414-4255-aa98-2a6acb8a09dd/timss2015final.pdf
Izsàk, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/07370000701798529
Jaime, A., & Gutiérrez, A. (1990). Una propuesta de fundamentación para la enseñanza de la geometría: el modelo Van Hiele. En S. Llinares & M. V. Sánchez (Eds.), Teoría y práctica en educación matemática (pp. 295-384). Alfar.
Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2012). Teacher´s content knowledge and pedagogical content knowledge: The role of structural differences in teacher education. Journal of Teacher Education, 20(10), 1-17. https://doi.org/10.1177/0022487112460398
Leinhardt, G., & Greeno, J. G. (1986). The cognitive skill of teaching. Journal of Educational Psychology, 78(2), 75-95. https://doi.org/10.1037/0022-0663.78.2.75
Li, X. (2011). Mathematical knowledge for teaching algebraic routines: A case study of solving quadratic equations. Journal of Mathematics Education, 4(2), 1-16. http://educationforatoz.com/images/Xuhui_Li.pdf
Lo, J., & Luo, F. (2012). Prospective elementary teacher´s knowledge of fraction division. Journal of Mathematics Teacher Education, 15, 481-500. https://doi.org/10.1007/s10857-012-9221-4
Meyer, D. K., & Turner, J. C. (2002). Using instructional discourse analysis to study the scaffolding of student self-regulation. Educational Psychologist, 37, 5-13. https://doi.org/10.1207/S15326985EP3701_3
Mullins, I., & Martin, M. O. (2018). TIMSS 2019. Marcos de la evaluación. Instituto Nacional de Evaluación Educativa.
Nesher, P., & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem solving. Educational Studies in Mathematics, 6, 41-51. https://doi.org/10.1007/BF00590023
Newton, K. J. (2008). An extensive analysis of preservice elementary teacher´s knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851
Organización para la Cooperación y el Desarrollo Económicos. (1999). Measuring student knowledge and skills. A new framework for assessment. Autor. http://www.oecd.org/education/school/programmeforinternationalstudentassessmentpisa/33693997.pdf
Orrantia, J., Tarín, J., & Vicente, S. (2011). El uso de la información situacional en la resolución de problemas aritméticos. Infancia y Aprendizaje, 34(1), 81-94. https://doi.org/10.1174/021037011794390094
Piñeiro, J. L., Castro-Rodríguez, E., & Castro, E. (2019). Componentes de conocimiento del profesor para la enseñanza de la resolución de problemas en educación primaria. PNA 13(2), 104-129. https://revistaseug.ugr.es/index.php/pna/article/view/v13i2.7876
Rosales, J., Vicente, S., Chamoso, J. M., Muñez, D., & Orrantia, J. (2012). Teacher-student interaction in joint word problem solving. The role of situational and mathematical knowledge in mainstream classrooms. Teaching and Teacher Education, 28(8), 1185-1195. https://doi.org/10.1016/j.tate.2012.07.007
Sánchez, M. R., & Vicente, S. (2015). Modelos y procesos de resolución de problemas aritméticos verbales propuestos por los libros de texto de matemáticas españoles. Cultura y Educación, 27(4), 695-725. https://doi.org/10.1080/11356405.2015.1089389
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets y Zeitlinger Publishers.
Vicente, S., & Manchado, E. (2017). Dominios de contenido y autenticidad: un análisis de los problemas aritméticos verbales incluidos en los libros de texto españoles. PNA, 11(4), 253-279. https://revistaseug.ugr.es/index.php/pna/article/view/6242
Vicente, S., Manchado, E., & Verschaffel, L. (2018). Solving arithmetic word problems. An analysis of Spanish textbooks. Cultura y Educación, 30(1), 71-104. https://doi.org/10.1080/11356405.2017.1421606
Vicente, S., Orrantia, J., & Verschaffel, L. (2007). Influence of situational and conceptual rewording on word problem solving. British Journal of Educational Psychology, 77, 829-840. https://doi.org/ 10.1348/000709907X178200
Vicente, S., Rosales, J., Chamoso, J. M., & Múñez, D. (2013). Análisis de la práctica educativa en clases de matemáticas españolas de Educación Primaria: una posible explicación para el nivel de competencia de los alumnos. Cultura y Educación, 25(4), 535-548. https://doi.org/10.1174/113564013808906799
Vicente, S. Sánchez, R., & Verschaffel, L. (2020). Word problem solving approaches in mathematics textbooks: A comparison between Singapore and Spain. European Journal of Psychology of Education, 35(3), 567-587. https://doi.org/ 10.1007/s10212-019-00447-3
Webb, N. (2009). The teacher’s role in promoting collaborative dialogue in the classroom. British Journal of Educational Psychology, 79, 1-28. https://doi.org/https://doi.org/10.1348/000709908X380772
Cómo citar
Ramos, M., Rosales, J., & Vicente, S. (2021). Conocimiento de maestros en servicio y en formación sobre resolución de problemas aritméticos. Universitas Psychologica, 19, 1–15. https://doi.org/10.11144/Javeriana.upsy19.cmsf
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