Main Article Content
Abstract
This article describes the didactic analysis carried out by an expert teacher and a novice teacher, based on the didactic suitability criteria (DSC) of the Onto Semiotic Approach (OSA) when analyzing episodes of a high school mathematics class in Costa Rica. This is a qualitative investigation with an interpretive hermeneutic approach. First, a questionnaire was applied to the two participants, to classify them as novice and expert, based on certain defined characteristics. Both teachers then analyzed three video segments using a guide for didactic analysis and, finally, an interview was conducted to elaborate on the reflections previously obtained. The data analysis focused on identification, classification, and comparison of elements in each of the video segments with reference to the OSA’s DSC indicators. The results show that there are differences and similarities between the didactic analysis carried out by these teachers. It is concluded that the novice teacher provides a more descriptive analysis, in which errors are not specified, and focuses on the activities carried out by his students, while the expert teacher, who provides a thoughtful evaluative analysis of, identifying errors in the concepts and focusing his analysis on the teacher’s actions and performance in the video segments.
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References
- Auerbach, A. J., Higgins, M., Brickman, P., & Andrews, T. C. (2018). Teacher Knowledge for Active-Learning Instruction: Expert–Novice Comparison Reveals Differences. CBE—Life Sciences Education, 17(1), s.p. https://doi.org/10.1187/cbe.17-07-0149
- Bardin, L. (1996). Análisis de contenido (2da Edición). Aka
- Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teacher noticing and its growth toward expertise: An expert–novice comparison with pre-service and in-service secondary mathematics teachers. Educational Studies in Mathematics, 110(2), 205-232. http://dx.doi.org/10.1007/s10649-021-10128-y
- Berliner, D. C. (1988). The development of expertise in pedagogy. American Association of Colleges for Teacher Education.
- Berliner, D. C. (2001). Learning about and learning from expert teachers. International journal of educational research, 35(5), 463-482. https://doi.org/10.1016/S0883-0355(02)00004-6
- Berliner, D. C. (2004). Describing the behavior and documenting the accomplishments of expert teachers. Bulletin of Science, Technology and Society, 24(3), 200-212. https://doi.org/10.1177/0270467604265535
- Borko, H., & Livingston, C. (1989). Cognition and improvisation: Differences in mathematics instruction by expert and novice teachers. American educational research journal, 26(4), 473-498. https://doi.org/10.3102/00028312026004473
- Borko, H., Koellner, K., Jacobs, J., & Seago, N. (2011). Using video representations of teaching in practice-based professional development programs. ZDM, 43(1), 175-187. https://doi.org/10.1007/s11858-010-0302-5
- Bozu, Z. (2010). El profesorado universitario novel: Estudio teórico de su proceso de inducción o socialización profesional [New university professors: Theoretical study of their professional induction or socialization process]. Revista Electrónica de Investigación y Docencia, (3), 55-72. https://revistaselectronicas.ujaen.es/index.php/reid/article/view/1161
- Breda, A., Font, V., & Pino-Fan, L. R., (2018). Criterios valorativos y normativos en la didáctica de las matemáticas: El caso del constructo idoneidad didáctica [Evaluative and normative criteria in the didactics of mathematics: The case of the didactic suitability construct], Bolema, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13
- Breda, A., Pino-Fan, L., & Font, V. (2017). Meta didactic-mathematical knowledge of teachers: criteria for the reflection and assessment on teaching practice. EURASIA Journal of Mathematics Science and Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a
- Brown, R. E. (2022). Using Written Teaching Replays to Learn What Early Career Secondary Mathematics Teachers Notice. International Journal of Science and Mathematics Education, 20(8), 1635-1657. https://doi.org/10.1007/s10763-021-10220-y
- Cai, J., LaRochelle, R., Hwang, S., & Kaiser, G. (2022). Expert and preservice secondary teachers’ competencies for noticing student thinking about modelling. Educational Studies in Mathematics, 109(2), 431-453. http://dx.doi.org/10.1007/s10649-021-10071-y
- Chi, M. T. H. (2011). Theoretical Perspectives, Methodological Approaches, and Trends in the Study of Expertise. In Y. Li and G. Kaiser (Eds.), Expertise in Mathematics Instruction (pp. 17-39). Springer. https://doi.org/10.1007/978-1-4419-7707-6_2
- Climent, N., & Carrillo, J. (2007). El uso del vídeo para el análisis de la práctica en entornos colaborativos [The use of videos for the analysis of practice in collaborative environments]. Revista Investigación en la Escuela, (61), 23-35. https://idus.us.es/xmlui/handle/11441/60915
- Climent, N., Romero-Cortés, J. M., Carrillo, J., Muñoz-Catalán, M., & Contreras, L. C. (2013). ¿Qué conocimientos y concepciones movilizan futuros maestros analizando un vídeo de aula? [What knowledge and conceptions mobilize future teachers analyzing a classroom video?] Revista latinoamericana de investigación en matemática educativa, 16(1), 13-36. http://www.scielo.org.mx/scielo.php?pid=S1665-24362013000100002&script=sci_arttext
- Coles, A. (2014). Mathematics teachers learning with video: the role, for the didactician, of a heightened listening. ZDM, 46(2), 267-278. https://doi.org/10.1007/s11858-013-0541-3
- Céspedes, M. J. C., Navarro, M. B., & Godino, J. D. (2022). Guidelines for the analysis of mathematics textbooks lessons on the subject of proportionality. Uniciencia, 36(1), 1-19. https://doi.org/10.15359/ru.36-1.14
- Dewey, J. (1989). How we think. (M.A. Galmarini, Trans.). Paidós.
- Esqué, D., & Breda, A. (2021). Valoración y rediseño de una unidad sobre proporcionalidad utilizando la herramienta idoneidad didáctica [Assessment and redesign of a unit on proportionality using the didactic suitability tool]. Uniciencia, 35(1), 38-54. https://doi.org/10.15359/ru.35-1.3
- Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas [Indicators of the didactic suitability of mathematics teaching and learning processes]. Cuadernos de Investigación y Formación en Educación Matemática, 8(11), 111-132. https://revistas.ucr.ac.cr/index.php/cifem/article/view/14720/13965
- Godino, J. D. (2014). Síntesis del enfoque ontosemiótico del conocimiento y la instrucción matemáticos: Motivación, supuestos y herramientas teóricas [Synthesis of the ontosemiotic approach to mathematical knowledge and instruction: Motivation, assumptions and theoretical tools]. Universidad de Granada. http://enfoqueontosemitico.ugr.es/documentos/sintesis_EOS_2abril2016.pdf
- Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39 (1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
- Godino, J. D., Batanero, C., & Font, V. (2008). Un enfoque ontosemiótico del conocimiento y la instrucción matemática [An ontosemiotic approach to mathematical knowledge and instruction]. Revista de Ensino de Ciências e Matemática, (10), 7-37. https://www.ugr.es/~jgodino/funciones-semioticas/sintesis_eos_10marzo08.pdf
- Godino, J. D., Bencomo, D., Font, V., and Wilhelmi, M. R. (2006). Análisis y valoración de la idoneidad didáctica de procesos de estudio de las matemáticas [Analysis and assessment of the didactic suitability of mathematics study processes]. Paradigma, 27(2), 221-252. https://www.ugr.es/~jgodino/funciones-semioticas/idoneidad-didactica.pdf
- Godino, J. D., Contreras, A., and Font, V. (2006). Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática [Analysis of instructional processes based on the ontological-semiotic approach to mathematical cognition]. Recherches en Didactiques des Mathematiques, 26(1), 39-88. https://dialnet.unirioja.es/servlet/articulo?codigo=2200862
- Godino, J. D., Giacomone, B., Batanero, C., and Font, V. (2017). Onto-Semiotic Approach to Mathematics Teacher's Knowledge and Competences. Bolema, 31(57), 90-113. http://dx.doi.org/10.1590/1980-4415v31n57a05
- Haggarty, L. (1996). What is content analysis?. Medical Teacher, 18(2), 99-101. https://www.tandfonline.com/doi/abs/10.3109/01421599609034141
- Kaiser, G., Busse, A., Hoth, J., König, J., and Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13(2), 369-387. https://doi.org/10.1007/s10763-015-9616-7
- Li Y., & Kaiser, G. (2011). Expertise in Mathematics Instruction: Advancing Research and Practice from an International Perspective. In Y. Li and G. Kaiser (Eds.), Expertise in Mathematics Instruction (pp. 3-15). MA, Boston: Springer. https://doi.org/10.1007/978-1-4419-7707-6_1
- Moodliar, J., & Abdulhamid, L. (2021). Novice and expert grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra. Pythagoras, 42(1), 1-13. http://dx.doi.org/10.4102/PYTHAGORAS.V42I1.624
- Morales-López, Y., & Araya-Román, D. (2020). Helping Preservice Teachers to Reflect. Acta Scientiae, 22(1), 88–111. http://doi.org/10.17648/acta.scientiae.5641
- Morales-López, Y., & Font, V. (2019). Evaluation by a teacher of the suitability of her mathematics class. Educação e Pesquisa, 45, 1-19. https://doi.org/10.1590/S1678-4634201945189468
- Posadas, P., & Godino, J. D. (2013). Reflexión sobre la práctica docente como estrategia formativa para desarrollar el conocimiento didáctico-matemático [Reflection on teaching practice as a training strategy to develop didactic-mathematical knowledge]. Didacticae: Revista de Investigación en Didácticas Específicas, (1), 77-96. http://revistes.ub.edu/index.php/didacticae/article/view/18092
- Rojas, N. (2014). Caracterización del conocimiento especializado del profesor de matemáticas: un estudio de casos [Characterization of specialized knowledge of the mathematics teacher: a case study] Doctoral Thesis. Universidad de Granada. http://funes.uniandes.edu.co/6428/
- Rojas, N., Carrillo, J., & Flores, P. (2012). Características para identificar a profesores de matemáticas expertos [Characteristics to identify expert mathematics teachers]. In A. Estepa, Á. Contreras, J. Deulofeu, M. Penalva, F. García and L. Ordoñez (Eds.), Investigación en educación matemática XVII (pp. 479-485). SEIEM. https://core.ac.uk/download/pdf/12342342.pdf
- Rojas, N., Carrillo, J., & Flores, P. (2015). Conocimiento especializado de un profesor de matemáticas de educación primaria al enseñar los números racionales [Specialized knowledge of a primary school mathematics teacher when teaching rational numbers]. Bolema: Boletim de Educação Matemática, 29(51), 143-166. https://dx.doi.org/10.1590/1980-4415v29n51a08
- Russ, R. S., Sherin, B., & Sherin, M. G. (2011). Images of Expertise in Mathematics Teaching. In Y. Li and G. Kaiser (Eds.), Expertise in Mathematics Instruction (pp. 41-60). MA, Boston: Springer. https://doi.org/10.1007/978-1-4419-7707-6_3
- Schempp, P., Tan, S., Manross, D., & Fincher, M. (1998). Differences in Novice and Competent Teachers’ Knowledge. Teachers and Teaching, 4(1), 9–20. https://doi.org/10.1080/1354060980040102
- Schön, D. (1983). The reflective practitioner: How professionals think in action. Basic Books.
- Seckel, M., & Font, V. (2020). Competencia reflexiva en formadores del profesorado de matemática [Reflective competence in mathematics teacher educators]. Magis, Revista Internacional De Investigación En Educación, 12(25), 127-144. https://doi.org/10.11144//Javeriana.m12-25.crfp
- Shulman, L. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
- Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4 -14. https://doi.org/10.3102/0013189x015002004
- Strutchens, M. E., Huang, R., Losano, L., Potari, D., Cyrino, M. C. D. C. T., Da Ponte, J. P., & Zbiek, R. M. (2017). The mathematics education of prospective secondary teachers around the world (p. 58). Springer Nature.Suárez, N. (2018). Análisis didáctico de clases de matemáticas en el nivel superior [Didactic analysis of mathematics classes at the higher level]. In L. Serna and D. Pagés (Eds.), Acta Latinoamericana de Matemática Educativa (pp. 1686-1693). México, DF: Colegio Mexicano de Matemática Educativa A. C. y Comité Latinoamericano de Matemática Educativa A.C.
- Wittmann, E.C. (2021). The Mathematical Training of Teachers from the Point of View of Education. In: Connecting Mathematics and Mathematics Education. Springer, Cham. https://doi-org.sire.ub.edu/10.1007/978-3-030-61570-3_4
- Wolff, C., Van den Bogert, N., Jarodzka, H., and Boshuizen, H. (2015). Keeping an Eye on Learning: Differences between expert and novice teachers' representations of classroom management events. Journal of Teacher Education. 66(1), 68-85. https://doi.org/10.1177/0022487114549810
References
Auerbach, A. J., Higgins, M., Brickman, P., & Andrews, T. C. (2018). Teacher Knowledge for Active-Learning Instruction: Expert–Novice Comparison Reveals Differences. CBE—Life Sciences Education, 17(1), s.p. https://doi.org/10.1187/cbe.17-07-0149
Bardin, L. (1996). Análisis de contenido (2da Edición). Aka
Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teacher noticing and its growth toward expertise: An expert–novice comparison with pre-service and in-service secondary mathematics teachers. Educational Studies in Mathematics, 110(2), 205-232. http://dx.doi.org/10.1007/s10649-021-10128-y
Berliner, D. C. (1988). The development of expertise in pedagogy. American Association of Colleges for Teacher Education.
Berliner, D. C. (2001). Learning about and learning from expert teachers. International journal of educational research, 35(5), 463-482. https://doi.org/10.1016/S0883-0355(02)00004-6
Berliner, D. C. (2004). Describing the behavior and documenting the accomplishments of expert teachers. Bulletin of Science, Technology and Society, 24(3), 200-212. https://doi.org/10.1177/0270467604265535
Borko, H., & Livingston, C. (1989). Cognition and improvisation: Differences in mathematics instruction by expert and novice teachers. American educational research journal, 26(4), 473-498. https://doi.org/10.3102/00028312026004473
Borko, H., Koellner, K., Jacobs, J., & Seago, N. (2011). Using video representations of teaching in practice-based professional development programs. ZDM, 43(1), 175-187. https://doi.org/10.1007/s11858-010-0302-5
Bozu, Z. (2010). El profesorado universitario novel: Estudio teórico de su proceso de inducción o socialización profesional [New university professors: Theoretical study of their professional induction or socialization process]. Revista Electrónica de Investigación y Docencia, (3), 55-72. https://revistaselectronicas.ujaen.es/index.php/reid/article/view/1161
Breda, A., Font, V., & Pino-Fan, L. R., (2018). Criterios valorativos y normativos en la didáctica de las matemáticas: El caso del constructo idoneidad didáctica [Evaluative and normative criteria in the didactics of mathematics: The case of the didactic suitability construct], Bolema, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13
Breda, A., Pino-Fan, L., & Font, V. (2017). Meta didactic-mathematical knowledge of teachers: criteria for the reflection and assessment on teaching practice. EURASIA Journal of Mathematics Science and Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a
Brown, R. E. (2022). Using Written Teaching Replays to Learn What Early Career Secondary Mathematics Teachers Notice. International Journal of Science and Mathematics Education, 20(8), 1635-1657. https://doi.org/10.1007/s10763-021-10220-y
Cai, J., LaRochelle, R., Hwang, S., & Kaiser, G. (2022). Expert and preservice secondary teachers’ competencies for noticing student thinking about modelling. Educational Studies in Mathematics, 109(2), 431-453. http://dx.doi.org/10.1007/s10649-021-10071-y
Chi, M. T. H. (2011). Theoretical Perspectives, Methodological Approaches, and Trends in the Study of Expertise. In Y. Li and G. Kaiser (Eds.), Expertise in Mathematics Instruction (pp. 17-39). Springer. https://doi.org/10.1007/978-1-4419-7707-6_2
Climent, N., & Carrillo, J. (2007). El uso del vídeo para el análisis de la práctica en entornos colaborativos [The use of videos for the analysis of practice in collaborative environments]. Revista Investigación en la Escuela, (61), 23-35. https://idus.us.es/xmlui/handle/11441/60915
Climent, N., Romero-Cortés, J. M., Carrillo, J., Muñoz-Catalán, M., & Contreras, L. C. (2013). ¿Qué conocimientos y concepciones movilizan futuros maestros analizando un vídeo de aula? [What knowledge and conceptions mobilize future teachers analyzing a classroom video?] Revista latinoamericana de investigación en matemática educativa, 16(1), 13-36. http://www.scielo.org.mx/scielo.php?pid=S1665-24362013000100002&script=sci_arttext
Coles, A. (2014). Mathematics teachers learning with video: the role, for the didactician, of a heightened listening. ZDM, 46(2), 267-278. https://doi.org/10.1007/s11858-013-0541-3
Céspedes, M. J. C., Navarro, M. B., & Godino, J. D. (2022). Guidelines for the analysis of mathematics textbooks lessons on the subject of proportionality. Uniciencia, 36(1), 1-19. https://doi.org/10.15359/ru.36-1.14
Dewey, J. (1989). How we think. (M.A. Galmarini, Trans.). Paidós.
Esqué, D., & Breda, A. (2021). Valoración y rediseño de una unidad sobre proporcionalidad utilizando la herramienta idoneidad didáctica [Assessment and redesign of a unit on proportionality using the didactic suitability tool]. Uniciencia, 35(1), 38-54. https://doi.org/10.15359/ru.35-1.3
Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas [Indicators of the didactic suitability of mathematics teaching and learning processes]. Cuadernos de Investigación y Formación en Educación Matemática, 8(11), 111-132. https://revistas.ucr.ac.cr/index.php/cifem/article/view/14720/13965
Godino, J. D. (2014). Síntesis del enfoque ontosemiótico del conocimiento y la instrucción matemáticos: Motivación, supuestos y herramientas teóricas [Synthesis of the ontosemiotic approach to mathematical knowledge and instruction: Motivation, assumptions and theoretical tools]. Universidad de Granada. http://enfoqueontosemitico.ugr.es/documentos/sintesis_EOS_2abril2016.pdf
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39 (1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
Godino, J. D., Batanero, C., & Font, V. (2008). Un enfoque ontosemiótico del conocimiento y la instrucción matemática [An ontosemiotic approach to mathematical knowledge and instruction]. Revista de Ensino de Ciências e Matemática, (10), 7-37. https://www.ugr.es/~jgodino/funciones-semioticas/sintesis_eos_10marzo08.pdf
Godino, J. D., Bencomo, D., Font, V., and Wilhelmi, M. R. (2006). Análisis y valoración de la idoneidad didáctica de procesos de estudio de las matemáticas [Analysis and assessment of the didactic suitability of mathematics study processes]. Paradigma, 27(2), 221-252. https://www.ugr.es/~jgodino/funciones-semioticas/idoneidad-didactica.pdf
Godino, J. D., Contreras, A., and Font, V. (2006). Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática [Analysis of instructional processes based on the ontological-semiotic approach to mathematical cognition]. Recherches en Didactiques des Mathematiques, 26(1), 39-88. https://dialnet.unirioja.es/servlet/articulo?codigo=2200862
Godino, J. D., Giacomone, B., Batanero, C., and Font, V. (2017). Onto-Semiotic Approach to Mathematics Teacher's Knowledge and Competences. Bolema, 31(57), 90-113. http://dx.doi.org/10.1590/1980-4415v31n57a05
Haggarty, L. (1996). What is content analysis?. Medical Teacher, 18(2), 99-101. https://www.tandfonline.com/doi/abs/10.3109/01421599609034141
Kaiser, G., Busse, A., Hoth, J., König, J., and Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13(2), 369-387. https://doi.org/10.1007/s10763-015-9616-7
Li Y., & Kaiser, G. (2011). Expertise in Mathematics Instruction: Advancing Research and Practice from an International Perspective. In Y. Li and G. Kaiser (Eds.), Expertise in Mathematics Instruction (pp. 3-15). MA, Boston: Springer. https://doi.org/10.1007/978-1-4419-7707-6_1
Moodliar, J., & Abdulhamid, L. (2021). Novice and expert grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra. Pythagoras, 42(1), 1-13. http://dx.doi.org/10.4102/PYTHAGORAS.V42I1.624
Morales-López, Y., & Araya-Román, D. (2020). Helping Preservice Teachers to Reflect. Acta Scientiae, 22(1), 88–111. http://doi.org/10.17648/acta.scientiae.5641
Morales-López, Y., & Font, V. (2019). Evaluation by a teacher of the suitability of her mathematics class. Educação e Pesquisa, 45, 1-19. https://doi.org/10.1590/S1678-4634201945189468
Posadas, P., & Godino, J. D. (2013). Reflexión sobre la práctica docente como estrategia formativa para desarrollar el conocimiento didáctico-matemático [Reflection on teaching practice as a training strategy to develop didactic-mathematical knowledge]. Didacticae: Revista de Investigación en Didácticas Específicas, (1), 77-96. http://revistes.ub.edu/index.php/didacticae/article/view/18092
Rojas, N. (2014). Caracterización del conocimiento especializado del profesor de matemáticas: un estudio de casos [Characterization of specialized knowledge of the mathematics teacher: a case study] Doctoral Thesis. Universidad de Granada. http://funes.uniandes.edu.co/6428/
Rojas, N., Carrillo, J., & Flores, P. (2012). Características para identificar a profesores de matemáticas expertos [Characteristics to identify expert mathematics teachers]. In A. Estepa, Á. Contreras, J. Deulofeu, M. Penalva, F. García and L. Ordoñez (Eds.), Investigación en educación matemática XVII (pp. 479-485). SEIEM. https://core.ac.uk/download/pdf/12342342.pdf
Rojas, N., Carrillo, J., & Flores, P. (2015). Conocimiento especializado de un profesor de matemáticas de educación primaria al enseñar los números racionales [Specialized knowledge of a primary school mathematics teacher when teaching rational numbers]. Bolema: Boletim de Educação Matemática, 29(51), 143-166. https://dx.doi.org/10.1590/1980-4415v29n51a08
Russ, R. S., Sherin, B., & Sherin, M. G. (2011). Images of Expertise in Mathematics Teaching. In Y. Li and G. Kaiser (Eds.), Expertise in Mathematics Instruction (pp. 41-60). MA, Boston: Springer. https://doi.org/10.1007/978-1-4419-7707-6_3
Schempp, P., Tan, S., Manross, D., & Fincher, M. (1998). Differences in Novice and Competent Teachers’ Knowledge. Teachers and Teaching, 4(1), 9–20. https://doi.org/10.1080/1354060980040102
Schön, D. (1983). The reflective practitioner: How professionals think in action. Basic Books.
Seckel, M., & Font, V. (2020). Competencia reflexiva en formadores del profesorado de matemática [Reflective competence in mathematics teacher educators]. Magis, Revista Internacional De Investigación En Educación, 12(25), 127-144. https://doi.org/10.11144//Javeriana.m12-25.crfp
Shulman, L. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4 -14. https://doi.org/10.3102/0013189x015002004
Strutchens, M. E., Huang, R., Losano, L., Potari, D., Cyrino, M. C. D. C. T., Da Ponte, J. P., & Zbiek, R. M. (2017). The mathematics education of prospective secondary teachers around the world (p. 58). Springer Nature.Suárez, N. (2018). Análisis didáctico de clases de matemáticas en el nivel superior [Didactic analysis of mathematics classes at the higher level]. In L. Serna and D. Pagés (Eds.), Acta Latinoamericana de Matemática Educativa (pp. 1686-1693). México, DF: Colegio Mexicano de Matemática Educativa A. C. y Comité Latinoamericano de Matemática Educativa A.C.
Wittmann, E.C. (2021). The Mathematical Training of Teachers from the Point of View of Education. In: Connecting Mathematics and Mathematics Education. Springer, Cham. https://doi-org.sire.ub.edu/10.1007/978-3-030-61570-3_4
Wolff, C., Van den Bogert, N., Jarodzka, H., and Boshuizen, H. (2015). Keeping an Eye on Learning: Differences between expert and novice teachers' representations of classroom management events. Journal of Teacher Education. 66(1), 68-85. https://doi.org/10.1177/0022487114549810