Influence of In-Depth Teacher Knowledge of Fractions in 4th Grade Students
DOI:
https://doi.org/10.24320/redie.2020.22.e10.2285Keywords:
Teacher knowledge, fractions, mathematics education.Supporting Agencies:
Doctorado Nacional 2015-21151548, Proyecto DIULS INICIACIÓN PI14151 Universidad de la SerenaAbstract
The aim of this study is to establish to what extent the teacher’s deep knowledge about fractions and knowledge for the teaching of fractions, adjusted by the socioeconomic level and the school mathematical knowledge (SIMCE), influences the learning of the students in the conceptualization of fractions in fourth grade. Information was obtained from 378 4th grade students of 9 schools and their respective mathematics teachers. The results of the regression analysis show that effect of teacher’s deep knowledge is significant in the learning per student (p = 0.001), beyond what is explained by the SIMCE score of the school, which is also significant (p = 0.02).Downloads
References
Ball, D., Thames, M. y Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T. , Jordan A., Klusmann, U., Krauss, S., Neubrand, M. y Tsai, Y.-M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133-180. https://doi.org/10.3102/0002831209345157
Behr, M., Harel, G., Post, T. y Lesh, R. (1993). Rational numbers: toward a semantic analysis-emphasis on the operator construct. En T. Carpenter, E. Fennema y T. Romberg (Eds.), Rational numbers: an integration of research (pp. 13-47). Lawrence Erlbaum.
Butto, Z. C. (2013). El aprendizaje de fracciones en educación primaria: una propuesta de enseñanza en dos ambientes. Revista Horizontes Pedagogicos, 15(1), 33-45.
Byrnes, J. P. y Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27(5), 777. https://doi.org/10.1037/0012-1649.27.5.777
Carrillo, J., Climent, N., Contreras, L. y Muñoz-Catalán, M. (2013). Determining specialized knowledge for mathematics teaching. Actas, VIII Congress of the European Society for Research in Mathematics Education [CERME] (pp. 2985-2994). Turquía: Middle East Technical University.
Chaparro, A., González, C. y Caso, J. (2016). Familia y rendimiento académico: configuración de perfiles estudiantiles en secundaria. Revista Electrónica de Investigación Educativa, 18(1), 53-68. http://redie.uabc.mx/redie/article/view/774
Charalambous, C. Y. y Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293-316. https://doi.org/10.1007/s10649-006-9036-2
Cortina, J., Cardoso, E. y Zúñiga, C. (2012). El significado cuantitativo que tienen las fracciones para estudiantes mexicanos de 6o. de primaria. Revista Electrónica de Investigación Educativa, 14(1), 70-85. https://redie.uabc.mx/redie/article/view/297/460
Cueto, S., León, J., Sorto, M. A. y Miranda, A. (2017). Teachers’ pedagogical content knowledge and mathematics achievement of students in Peru. Educational Studies in Mathematics, 94(3), 329-345.
Davis, B. y Simmt, E. (2006). Mathematics-for-teaching: an ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293-319. https://doi.org/10.1007/s10649-006-2372-4
Escolano, R. y Gairín, J. M. (2005). Modelos de medida para la enseñanza de números racionales en educación primaria. UNIÓN Revista Latinoamericana de Educación Matemática,1, 17-35.
Fandiño, M. I. (2009). Las fracciones. Aspectos conceptuales y didácticos. Magisterio.
Fazio, L. y Siegler, R. (2011). Enseñanza de las fracciones. UNESCO. https://unesdoc.unesco.org/ark:/48223/pf0000212781_spa
Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R., Gersten, R. y Changas, P. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683-700. https://doi.org/10.1037/a0032446
Fuchs, L. S., Schumacher, R. F., Sterba, S. K., Long, J., Namkung, J., Malone, A., Hamlett, C. L., Jordan, N. C., Gersten, R., Siegler, R. S. y Changas, P. (2014) (2014). Does working memory moderate the effects of fraction intervention? An aptitude-treatment interaction. Journal of Educational Psychology, 106(2), 499-514. https://doi.org/10.1037/a0034341
Gallardo, J., González, J. y Quispe, W. (2008). Interpretando la comprensión matemática en escenarios básicos de valoración. Un estudio sobre las interferencias en el uso de los significados de la fracción. Revista Latinoamericana de Investigación en Matemática Educativa, 11(3), 355-382.
Godino, J. (2004). Didáctica de las matemáticas para maestros. Proyecto Edumat-Maestros. http://www.ugr.es/~jgodino/edumat-maestros/manual/9_didactica_maestros.pdf
Grossman, P., Wilson, S. y Shulman, L. (2005). Profesores de sustancia: el conocimiento de la materia para la enseñanza. Profesorado. Revista de currículum y formación del profesorado, 9(2), 1-24.
Hansen, N., Jordan, N. C. y Rodrigues, J. (2015). Identifying learning difficulties with fractions: a longitudinal study of student growth from third through sixth grade. Contemporary Educational Psychology, 50, 45-59 https://doi.org/10.1016/j.cedpsych.2015.11.002
Harbison, R. W. y Hanushek, E. A. (1992). Educational performance for the poor: lessons from rural northeast Brazil. Oxford University Press.
Hill, H., Ball, D. y Schilling, S. (2008). Unpacking pedagogical content knowledge: conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
Hill, H., Rowan, B., y Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
Jakobsen, A., Ribeiro, C. M. y Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3-4), 135-150.
Kieren, T. (1993). Rational and fractional numbers: from quotient fields to recursive understanding. En T. Carpenter, E. Fennema y T. Romberg (Eds.), Rational numbers: an integration of research (pp. 49-84). Lawrence Erlbaum.
Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum.
Ma, L. (2010). Conocimiento y enseñanza de las matemáticas elementales. La comprensión de las matemáticas fundamentales que tienen los profesores en China y los EE.UU. Academia Chilena de Ciencias.
Ministerio de Educacion. (2012) Matemática. Programa de Estudio Cuarto Año Básico. Autor. http://www.curriculumenlineamineduc.cl/605/articles-18979_programa.pdf
Ministerio de Educacion. (2017). Revisión de las políticas educativas en Chile desde 2004 a 2016. Reporte Nacional de Chile. Autor.
https://centroestudios.mineduc.cl/wp-content/uploads/sites/100/2017/06/CBR_Mineduc-WEB.pdf
Mullens, J., Murnane, R. y Willett, J. (1996). The contribution of training and subject matter knowledge to teaching effectiveness: a multilevel analysis of longitudinal evidence from Belize. Comparative Education Review, 40(2), 139-57. https://doi.org/10.1086/447369
Murillo, F. J. y Román, M. (2008). Resultados de aprendizaje en América Latina a partir de las evaluaciones nacionales. Revista Iberoamericana de Evaluación Educativa, 1(1), 6-35.
National Mathematics Advisory Panel. (2008). Foundations for success: report of the task group on teachers and teacher education. U.S. Department of Education.
OCDE (2016). Estudiantes de bajo rendimiento: por qué se quedan atrás y cómo ayudarles a tener éxito. Autor. http://www.oecd.org/pisa/keyfindings/PISA-2012-Estudiantes-de-bajo-rendimiento.pdf
OCDE (2018). Evaluaciones de políticas nacionales de educación. Educación en Chile. Autor. http://www.oecd-ilibrary.org/education/educacion-en-chile_9789264288720-es
Pino-Fan, L., Godino, J. D. y Font, V. (2018). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education, 21(1), 63-94.
Pinto, H. y Ribeiro, C. M. (2013). Conhecimento e formação de futuros professores dos primeiros anos - o sentido de número racional [Conocimiento y formación de futuros profesores de los dos primeros anos – el sentido del número racional]. Da Investigação às Práticas, 3(1), 85-105.
Rittle-Johnson, B. y Schneider, M. (2014). Developing conceptual and procedural knowledge of mathematics. En R. Kadosh y A. Dowker (Eds.), Oxford Handbook of Numerical Cognition. Oxford University Press.
Rittle-Johnson, B., Schneider, M. y Star, J. R. (2015). Not a one-way street: bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587-597. https://doi.org/10.1007/s10648-015-9302-x
Rodríguez, P. de la C. y Olfos, R. (2018). Instrumentos consistentes para la enseñanza de fracciones en 4o. grado. Revista Electrónica de Investigación Educativa, 20(1), 48-58. https://doi.org/10.24320/redie.2018.20.1.1358
Rowland, T., Huckstep, P. y Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281. https://doi.org/10.1007/s10857-005-0853-5
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. http://www.fisica.uniud.it/URDF/masterDidSciUD/materiali/pdf/Shulman_1986.pdf
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I. y Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691-697. https://doi.org/10.1177/0956797612440101
Stylianides, A. y Stylianides, G. (2014). Viewing “mathematics for teaching” as a form of applied mathematics: implications for the mathematical preparation of teachers. Notices of the AMS, 61(3), 266-276.
Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76(2), 141-164. https://doi.org/10.1007/s10649-010-9269-y
Tchoshanov, M., Cruz, M. D., Huereca, K., Shakirova, K., Shakirova, L. e Ibragimova, E. N. (2017). Examination of lower secondary mathematics teachers’ content knowledge and its connection to students’ performance. International Journal of Science and Mathematics Education, 15(4), 683-702. https://doi.org/10.1007/s10763-015-9703-9
Torbeyns, J., Schneider, M., Xin, Z. y Siegler, R. (2015). Bridging the gap: fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13. https://doi.org/10.1016/j.learninstruc.2014.03.002
Tuñón, I. y Poy, S. (2016). Factores asociados a las calificaciones escolares como proxy del rendimiento educativo. Revista Electrónica de Investigación Educativa, 18(1), 98-111. http://redie.uabc.mx/redie/article/view/615
Downloads
-
HTML
-
PDF
-
XMLSPANISH 99
Article abstract page views: 1826
Published
2020-04-07License
Copyright (c) 2020 Revista Electrónica de Investigación Educativa
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.