Abstract:

Noticing students' mathematical thinking is a key skill that pre-service teachers should develop. This skill implies identifying evidence of student mathematical achievement and interpreting students’ understanding. Therefore, this skill implies that pre-service teachers move from evaluative comments to interpretative comments based on evidence. During the last decades, research has provided contexts for its development: on-line contexts, face-to-face meetings and video recordings. In this study we use the narratives as a pedagogical tool to help pre-service teachers learning to notice students’ mathematical thinking during their teaching practices. A narrative is a story that tells a sequence of events that are significant for the author and has an internal logic that makes sense to him/her. As a consequence, the narratives of pre-service teachers describing what they notice about the teaching of other teachers and students’ mathematical thinking might be a relevant tool in their learning to be a teacher. Our aim is to examine how pre-service primary school teachers become engaged in meaning-making students’ mathematical thinking when writing narratives related to critical events observed during their teaching practices and sharing with others in an online discussion.

Participants were 19 pre-service primary school teachers enrolled in the last year of their degree to become primary teachers. These pre-service primary school teachers were in the period of teaching practices at primary schools (practicum). The first part of their practices was a period of observation where pre-service teachers have to identify, describe and interpret critical events in the observed lessons related to students’ mathematical thinking. During this period, pre-service teachers were asked to write a narrative related to the development of the students’ mathematical competence.

We provided pre-service teachers with specific guidelines:
(1) describe the mathematics teaching-learning situation in which you had found evidence of mathematical competence of students,
(2) interpret the situation, which should contain evidence of student understanding and
(3) modify the situation in order to help students to develop other aspects of the mathematical competence.

Pre-service teachers have to share their narratives in an online discussion. Shared narratives were analyzed by other classmates, generating a dynamic collaboration and arguing suggestions for improvement the aspects of the narrative. After participating in the online discussion, pre-service teachers have to re-write their narrative taking into account the comments of the discussion.

The initial narratives and those made after participation in the online discussion were analyzed by three researchers in order to identify the nature of the changes made. Findings suggest that online discussion helped pre-service teachers to focus on interpretative comments based on evidence of students’ understanding that can be consider a characteristic of the development of the skill of "noticing" student's mathematical thinking.

Keywords:

Pre-service teachers learning, professional noticing, sharing critical events of mathematics teaching, narratives, online discussion.