Anticipating primary school students’ answers of hierarchical classifications tasks: features of preservice primary teachers’ curricular reasoning
Tipo de documento
Autores
Lista de autores
Bernabeu, Melania, Moreno, Mar y Llinares, Salvador
Resumen
Background: anticipating students’ answers involves reasoning with knowledge from scientific domains supporting the practice of teaching mathematics and it is an evidence of preservice teachers’ reasoning curricular. A key aspect in the geometrical thinking development is to understand the relationship between definition and classification of geometric objects. Thus, the way in which preservice teachers relate the definition and classification can provide information about their curricular reasoning. Objective: the aim of this study is to characterise how preservice teacher anticipate students’ answers to hierarchical classification tasks of quadrilaterals and prisms. Design: the data collection instrument was a hierarchical classification task with four versions in which preservice teacher had to define geometric objects take into account some inclusion conditions. Setting and participants: twenty-eight preservice teacher from a university of Spain participated in this study. Data collection and analysis: the data was collected in two moments, firstly preservice teachers answered to the task with 2d figures and then to the 3d shapes. We carried out an inductive analysis through two phases take into account the specialization of definitions and transitivity of inclusion relationships. Results: we identified three profiles of the preservice teachers' curricular reasoning considering how they define the geometrical object considering the inclusion relations. Furthermore, some variability between the quadrilaterals and prisms was displayed considering curricular reasoning. Conclusions: the results under light the relationship between geometry knowledge and preservice teachers’ curricular reasoning.
Fecha
2021
Tipo de fecha
Estado publicación
Términos clave
Inicial | Noción | Otro (geometría) | Razonamiento | Tareas
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Volumen
23
Número
6
Rango páginas (artículo)
121-146
ISSN
21787727
Referencias
Amador, J., Males, L., Earnest, D., & Dietiker, L. (2017). Curricular Noticing: Theory on and Practice of Teachers’ Curricular Use. In E. Schak; M. Fisher & J. Wilhelm, (Eds.), Teacher Noticing: Bridging and Broadening Perspectives, Contexts and Frameworks (pp. 427443). Springer. Bernabeu, M., Llinares, S. (2017). Comprensión figuras geométricas en niños de 6-9 años. Educación Matemática, 29(2), 9-35. http://doi.org/10.24844/EM2902.01 Breyfogle, M. L., Roth McDuffie, A., & Wohlhuter, K. A. (2010). Developing curricular reasoning for grades pre-K-12 mathematics instruction. In B. Reys, R. E. Reys, & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 307–320). National Council of Teachers of Mathematics. Brunheira, L. & da Ponte, P. (2019). From the classification of quadrilaterals to the classification of prisms: An experiment with prospective teachers. Journal of Mathematical Behavior, 53, 65-80. https://doi.org/10.1016/j.jmathb.2018.06.004 Buforn, A., Llinares, S., Fernández, C., Coles, A., Brown, L. (2020). Preservice teachers’ knowledge of the unitizing process in recognizing students’ reasoning to propose teaching decisions. International Journal of Mathematical Education in Science and Technology, https://doi.org/10.1080/0020739X.2020.1777333 De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11–18. Dietiker, L., Males, J., Amador, J., & Earnest, D. (2018). Research Commentary: Curricular Noticing: A Framework to Describe Teachers’ Interactions with Curriculum Materials. Journal for Research in Mathematics Education, 49 (5), 521-532. https://doi.org/10.5951/jresematheduc.49.5.0521 Fernandez, C., Sánchez-matamoros. G., Valls, J., Callejor, M.L. (2018). Noticing students’ mathematical thinking: characterizatrion, development and contexts. AIEM. Avances de Investigación en Educación Matemática, 13, 39-61. Fischbein, E. (1993). The theory of figural concepts. Educational studies in mathematics, 24(2), 139–162. https://doi.org/10.1007/BF01273689 Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60-72. http://doi.org/10.1016/j.jmathb.2011.08.003 Fujita, T. & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3–20. https://doi.org/10.1080/14794800008520167 Gueudet, G. (2019). Studying Teachers’ Documentation Work: Emergence of a Theoretical Approach. In L. Trouche, G. Gueudet, & B. Pepin (Eds.), The ‘Resource’ Approach to Mathematics Education (pp. 1742). Springer. Hershkowitz, R. (1990). Psychological aspects of learning geometry. In Nesher & Kilpatrick (Eds.), Mathematics and cognition (pp. 70-95). Cambridge University Press. Jones, K. & Tzekaki, M. (2016). Research on teaching and learning geometry. In A. Gutierrez, G. Leader, & P. Boero (Eds.), The second Handbook of research on the psychology of mathematics education (pp. 109149). Sense. Lehrer, R., Slovin, H., & Dougherty, B. (2014). Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Grades 3-5. NCTM. Llinares, S., Fernández, C., Sánchez-Matamoros, G. (2016). Changes in how prospective teachers anticipate secondary students’ answers. Eurasia Journal of Mathematics, Science & Technology Education, 12(8), 2155-2170. http://doi.org/10.12973/eurasia.2016.1295a Markopoulos, C. (2003). Teaching and learning of solids with the use of technological tools. Unpublished Doctoral Dissertation, University of Patra, Greece. Pittalis, M. & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in mathematics, 75(2), 191-212. https://doi.org/10.1007/s10649-0109251-8 Sinclair, N., Bussi, M. G. B., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM, 48(5), 691-719. https://doi.org/10.1007/s11858-016-0796-6 Usiskin, Z. & Griffin, G. (2008). The classification of Quadrilaterals. A Study of definition. IAP. Remillard, J, (2019). Teacher’Use of mathematics Resources: A Look Across Cultural Boundaries. In L. Trouche, G. Gueudet, & B. Pepin (Eds.), The ‘Resource’ Approach to Mathematics Education, (pp. 173-194). Springer. Wilson, S., M., Shulman, L. & Richert, A. E. (1987). ‘150 different ways of knowing: Representations of knowledge in teaching. In J. Calderhead (ed.), Exploring Teachers’ Thinking, (104-124). Casssell van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.