Pre-service teachers’ knowledge of the unitizing process in recognizing students’ reasoning to propose teaching decisions

Abstract

The goal of this study is to characterise how pre-service teachers recognise students' reasoning, based in the unitising process, when students solve ratio comparison problems and, how they consider the unitising process as a Key Development Understanding to propose teaching decisions. Ninety-one preservice primary teachers interpreted primary school students' answers to a ratio comparison problem and proposed teaching decisions to improve students' reasoning. Findings indicate that pre-service teachers recognised features of the unitising process as a Key Development Understanding but had difficulties to propose teaching decisions addressed to improve the students' mathematical reasoning. These findings display the role played by specific mathematical content domain when pre-service teachers make teaching decisions considering the students' mathematical reasoning.

Apoyando el desarrollo de la competencia mirar profesionalmente del futuro profesorado de matemáticas: Práctica e investigación

“…Un KDU implica un avance conceptual por parte de los estudiantes, es decir, un cambio en la capacidad para pensar y/o percibir determinadas relaciones matemáticas (Simon, 2006, p. 362). En este sentido, si el futuro profesorado reconoce los KDU de un concepto matemático particular, será capaz de anticipar o interpretar cómo la comprensión de un determinado concepto se desarrolla (Buforn et al, 2020;Llinares, Fernández y Sánchez-Matamoros, 2016;Sánchez-Matamoros et al, 2015).…”

“…Las investigaciones han aportado características para el diseño de entornos de aprendizaje en estos programas que ayuden a generar oportunidades "desde y para la práctica" al futuro profesorado de matemáticas (Buforn, Llinares, Fernández, Coles y Brown, 2020;Fernández et al, 2012; Fernández, Sánchez-Matamoros, Moreno y Callejo, 2018; Ivars, Buforn y Llinares, 2017; Ivars, Fernández, Llinares y Choy, 2018b; Sánchez-En particular, la Figura 3 muestra la distribución de sesiones de un entorno de aprendizaje centrado en el significado de fracción como parte-todo (Ivars, 2018). Este entorno de aprendizaje consta de seis sesiones de 120 minutos de duración cada una.…”

Prospective Primary School Teachers’ Competence for the Cognitive Analysis of Students’ Solutions to Proportionality Tasks

“…Moreover, it is important to study to what extent prospective teachers take into account the analysis developed in this formative intervention to propose teaching decisions (Buforn et al 2020). To this end, the research instrument should be enhanced by including decision making on how to respond to the students' wrong answers.…”

“…However, and despite the importance of this content, there is much evidence that both prospective and in-service teachers have difficulties in understanding and teaching some of the proportional reasoning components (Ben-Chaim et al 2012;Berk et al 2009;Buforn et al 2018;Livy and Vale 2011;Riley 2010;Rivas et al 2012), as well as to interpret K the responses of primary education students when they solve proportionality tasks. In particular, prospective teachers struggle to interpret the responses of primary education students when they solve proportionality tasks, and to consider the way in which students seem to understand proportionality in order to take decisions (Buforn et al 2020;Fernández et al 2013;Son 2013).…”

Anticipating Primary School Students’ Answers of Hierarchical Classifications Tasks: Features of Preservice Primary Teachers’ Curricular Reasoning

“…Interpreting the instructional task involves identifying the mathematical content in the task and seeing what the task may require to the resolutor. We have identified three preservice teachers' curricular reasoning profiles that show the interaction between mathematic knowledge, knowledge of students' learning and knowledge of mathematics teaching in the same way in how preservice teaches make teaching decision considering students' mathematical reasoning (Buforn, Llinares, Fernández, Coles, and Brown, 2020) On the other hand, the results indicate differences in how preservice teachers use the specialisation process and the transitivity of hierarchical relationships between quadrilaterals and prisms. Of the three tasks about quadrilaterals that are parallelograms (rhomboid, rhombus, and square) they have been less successful in applying the specialization process.…”