Análisis de la interacción de maestros cuando resuelven problemas realistas conjuntamente con sus alumnos en aulas de primaria, teniendo en cuenta su experiencia docente

  1. Sánchez-Barbero, Beatriz
  2. Calatayud, María
  3. Chamoso, José Mª.
Revista:
Uni-pluriversidad

ISSN: 1657-4249

Ano de publicación: 2019

Título do exemplar: Investigación, competencias y modelos para la formación profesional de profesores de matemáticas

Volume: 19

Número: 2

Páxinas: 40-59

Tipo: Artigo

DOI: 10.17533/UDEA.UNIPLURI.19.2.03 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Outras publicacións en: Uni-pluriversidad

Obxectivos de Desenvolvemento Sustentable

Resumo

Training of Primary mathematics teachers needs to know and analyze the real practice of the classroom. This work focuses on a joint resolution of problems in the classroom. Educational research has shown that there is little reasoning and participation of students when teachers and students jointly solve routine problems in Primary math classrooms. Some studies showed that this reasoning and participation increases when they solve non-routine problems, but it does not always happen when teachers are novel. Therefore, it is intended to analyze what happens when a special type of non-routine problems such as realistic problems is used, which the literature has considered with interest, taking into account the experience of the teacher. Specifically, the objective of this work is to analyze the interaction between two teachers, an expert and a novel, when they solve realistic problems along with their students in their usual classroom, attending to the processes, degree of participation, and teaching experience of the teachers. The results showed that both reasoning and participation of the students increased, and the expert teacher promoted the reasoning more than the novel and also, she made a better realistic interpretation of the problems in the resolution. Although it is a small sample, these results allow us to take a step to open future lines of research that could have educational implications for both preservice teachers and in-service teachers.

Referencias bibliográficas

  • Aksoy, Y., Bayazit, I. y Kirnap, S. M. (2015). Prospective Primary school teachers´ proficiencies in solving real-words problems: approaches, strategies and models. Eurasia Journal of Mathematics, Science & Technology Education, 1(4), 827-839.
  • Ausubel, D., Novak, J. y Hanesian, H. (1983). Psicología Educativa: Un punto de vista cognoscitivo. México: Trillas.
  • Bakker, A., Smit, J. y Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM Mathematics Education, 47, 1047-1065.doi: 10.1007/s11858-015-0738-8.
  • Beswick, K. (2011). Putting context in context: an examination of the evidence for the benefits of “contextualized” tasks. International Journal of Science and Mathematics Education 9(2), 367-390. doi:10.1007/s10763-011-9323-y.
  • Blanton, M. L., Berenson, S. B. y Norwood, K. (2001). Using classroom discourse to understand a prospective mathematics teacher´s developing practice. Teaching and Teacher Education, 17, 227-242.
  • Boston, M. D. (2013). Connecting changes in secondary mathematics teachers´ knowledge to their experiences in a profesional development workshop. Journal of Mathematics Teacher Education, 16(1), 7-31. doi: 10.1007/s10857-012-9211-6.
  • Burgos, S., Domínguez, M., Rojas, F.J., Planas, N. y Vilella, X. (2006). La participación en el aula de Matemáticas. En J. M. Goñi (coord.), Matemáticas e Interculturalidad (49-62). Barcelona: Graó.
  • Cai, J. y Lester, F. (2010). Why is teaching with problem solving important to student learning? Reston, VA: National Council of Teachers of Mathematics.
  • Carrillo, J., Climent, N., Gorgorió, N., Prat, M. y Rojas, F. (2008). Análisis de secuencias de aprendizaje matemático desde la perspectiva de la gestión de la participación. Enseñanza de las Ciencias, 26(1), 67-76.
  • Chamoso, J. M., Vicente, S., Rosales, J. y Orrantia, J. (2007). Análisis de la interacción profesor-alumno en el aula de matemáticas: actividades, autonomía e incidentes. En E. Mancera & C. A. Pérez, Historia y Prospectiva de la Educación Matemática. Memorias de la XII CIAEM (pp. 77-97). Méjico: Edebé Internacional.
  • Chandia, E., Rojas, D., Rojas, F. y Howard, S. (2016). Creencias de formadores de profesores de matemáticas sobre resolución de problemas. Bolema, Rio Claro (SP), 30, 605 - 624. doi: 10.1590/1980-4415v30n55a15.
  • Chapman, O. (2006). Classroom practices for context of mathematics Word problems. Educational Studies in Mathematics, 62(2), 211-230. doi: 10.1007/s10649-006-7834-1.
  • Depaepe, F., De Corte, E. y Verschaffel, L. (2010). Teachers´ approaches towards Word problem solving: elaborating or restricting the problem context. Teaching and Teacher Education, 26(2), 152-160.
  • Elbers, E. (2003). Classroom interaction as reflection: learning and teaching mathematics in a community of inquiri. Educational Studies in Mathematics, 54, 77-99.
  • Escribano, M., Sánchez-Barbero, B. y Chamoso, J. M. (2019). Análisis de la interacción profesor-alumnos cuando resuelven problemas realistas en el aula. Memorias de la XIII CIAEM.
  • Flavell, J.H. (1985). Cognitive Development. New York: Prentice-Hall
  • Flavell, J.H. (1987). Speculations about the nature and development of metacognition. En: F. E. Weinert& R. H. Kluwe (Eds). Metacognition, Motivation and Understanding. Hillsdale, NJ: Erlbaum.
  • Gerofsky, S. (1997). A linguistic and narrative view of word problems in mathematics education. For the Learning of Mathematics, 16(2), 36-45.
  • González, G. y DeJarnette, A.F. (2015). Teachers’ and students’ negotiation moves when teachers scaffold group work. Cognition and Instruction, 33(1), 1-45.
  • Jiménez, L. y Verschaffel, L. (2014). Development of Children´s solutions of non-standard arithmetic word problem solving. Revista de Psicodidáctica, 19(1), 93-123.
  • Kiliç, Ç. (2017). The Realistic Reasons for Unrealistic Solutions of Pre-Service Primary School Mathematics Teachers in Non-Standard Word Problems: The Example from Turkey. Mustafa Kemal University Journal of Social Sciences Institute, 14(37), 285-298.
  • Koichu, B. (2014) (with contributions by G. Goldin, I. Weinzweig, S. Vinner and R. Leikin). Reflections on problem solving. En M. N. Fried & T. Dreyfus (Eds.), Mathematics & Mathematics Education: Searching for Common Ground. Advances in Mathematics Education (pp. 113–135). Dordrecht, The Netherlands: Springer.
  • Kolovou, A., van den Heuvel-Panhuizen, M. y Bakker, A. (2009). Non-routine problem solving tasks in Primary School Mathematics textbooks-a needle in a Haystack. Mediterranean Journal for Research in Mathematics Education, 8(2), 31-68.
  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29-63.
  • Lave, J. (1992). Word problems: A microcosm of theories of learning. Context and Cognition: Ways of Learning and Knowing, 74-92. New York, NY: Harvester Wheatsheaf.
  • Lepage, P., Darling-Hammond, L. Akar, H. Gutierrez, C. Jenkins-Gunn, E., y Rosebrock, K. (2005). Classroom Management. En L. Darling-Hammond y J. Bransford (Eds.), Preparing teachers for a changing world, what teachers should learn and able to do (pp.327-357). San Francisco: Jossey-Bass.
  • Mellone, M., Verschaffel, L. y Van Dooren, W. (2017). The effect of rewording and dyadic interaction on realistic reasoning in solving Word problems. The Journal of Mathematical Behavior, 46, 1-12.
  • Mullins, I., Martin, M., Ruddock, G., O´Sullivan, C. y Preuschoff, C. (2012). TIMSS 2011. Marcos de la Evaluación. Madrid: Ministerio de Educación, Cultura y Deporte.
  • Nathan, M.J. y Knuth, E.J. (2003). A study of who classroom mathematical discourse and teacher change. Cognition and Instruction, 21(2), 175-207.
  • Planas, N. y Morera, L. (2011). Educación Matemática e interacción en el aula de secundaria. Uno. Revista de Didáctica de las Matemáticas, 58, 77-83.
  • Praetorius, A. K., Pauli, C., Reusser, K., Rakoczy, K. y Klieme, E. (2014). One lesson is all you need? Stability of instructional quality across lessons. Learning and Instruction, 31, 2-12.
  • Riveros, M., Zanocco, P., Cnudde, V., Espinoza, F., Rojas, X. y Baeza, P. (2010). Habilidades de pensamiento metacognitivo y resolución de problemas matemáticos. Boletín de Investigación Educacional, 15(1), 89-107. Facultad de Educación, Pontificia Universidad Católica de Chile, Santiago, Chile.
  • Rosales, J., Orrantia, J., Vicente, S. y Chamoso, J. M. (2008a). La resolución de problemas aritméticos en el aula. ¿Qué hacen los profesores cuando trabajan conjuntamente con sus alumnos? Cultura y Educación, 20(4), 423-439.
  • Rosales, J., Orrantia, J., Vicente, S. y Chamoso, J. M. (2008b). Studying mathematics problem-solving classrooms. A comparision between the discourse of in-service teachers and student teachers. European Journal of Psychology of Education, 23(3), 275-294.
  • Rosales, J., Vicente, S., Chamoso, J. M., Muñez, D. y 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.
  • Sánchez, B., Carrillo, J., Vicente, S. y Juárez, J. A. (2015). Análisis de la interacción alumnos-profesor al resolver problemas no rutinarios en aulas de Primaria. En XIV Conferencia interamericana de Educación Matemática (XIV CIAEM). Chiapas (México).
  • Sánchez-Barbero, B., Chamoso, J. M., Vicente, S. y Rosales, J. (2018). Análisis de la metacognición en la interacción profesor-alumnos al resolver problemas de matemáticas en aulas de Primaria. En L. J. Rodríguez-Muñiz, L. Muñiz-Rodríguez, A. Aguilar-González, P. Alonso, F. J. García García y A. Bruno (Eds.), Investigación en Educación Matemática XXII (pp. 544-553). Gijón: SEIEM.
  • Sánchez-Barbero, B., Ciudad, J. C., Galán, E., Chamoso, J. M., Vicente, S., Rodríguez, M. M., Cáceres, M. J. y Salomón, M. S. (2019). Análisis de la interacción profesor-alumnos cuando resuelven conjuntamente problemas realistas en aulas de Secundaria. En J. M. Marbán, M. Arce, A. Maroto, J. M. Muñoz-Escolano y Á. Alsina (Eds.), Investigación en Educación Matemática XXIII (p. 650). Valladolid: SEIEM.
  • Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A. y Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 123-140.
  • Smart, J. B. y Marshall, J. C. (2013). Interactions between classroom discourse, teacher questioning, and student cognitive engagement in middle school science. Journal of Science Teacher Education, 24(2), 249-267.
  • Staub, F. C. y Reusser, K. (1995). The role of presentational structures in understanding and solving mathematical word problems. En C. A. Weaver III, S. Mannes & C. R. Fletcher (Eds.), Discourse Comprehension: Essays in honor of Walter Kintsch (pp. 285-305). Hillsdale, NJ: Lawrence Erlbaum.
  • Turner, J. C., Midgley, C., Meyer, D. K., Gheen, M., Anderman, E. M., Kang, Y. y Patrick, H. (2002). The classroom environment and students' reports of avoidance strategies in mathematics: A multimethod study. Journal of Educational Psychology, 94(1), 88.
  • Van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54, 9–35.
  • Verschaffel, L., De Corte, E. y Borghart, I. (1997). Pre-service teachers´ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7, 339-359.
  • Verschaffel, L., De Corte, E. y Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4, 273–294.
  • Verschaffel, L. Greer, B. y De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.
  • Vicente, S. y Orrantia, J. (2007). Resolución de problemas y comprensión situacional. Cultura y Educación, 19(1), 61-85.
  • Vicente, S., Rosales, J., Chamoso, J. M. y 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.
  • Wells, G. (1999). Dialogic inquiry: Toward a sociocultural practice and theory of education. Cambridge: CUP.
  • Zaslavsky, O. (2007). Mathematics-related task, teacher education, and teacher educator. Journal of Mathematics Teacher Education, Londres, 10(4-6), 433-440. doi: 10.1590/1980-4415v30n55a15.
Fonte de datos: Dialnet