Abstract:

Noticing mathematics teaching-learning situations has been shown as an important competence to be developed in teacher education programs and has generated an important research agenda in mathematics education. This competence is linked to teachers’ professional practices for mathematics teaching, such as:
(i) analysing and interpreting students’ mathematical thinking;
(ii) analysing, selecting and designing mathematical activities; or
(iii) managing mathematical discussions in the classroom.

In this study, we focus on the latter practice, which involves different teachers’ actions: anticipating students’ answers, obtaining information about students’ strategies when they are working in pairs or small groups, selecting which students could present their strategies in the whole class discussion, sequencing, and connecting them during the whole discussion. This study focuses on designing a professional task to enhance pre-service primary school teachers’ noticing competence of managing mathematical discussions in the classroom.

Noticing mathematics teaching-learning situations involves identifying important details in the mathematics classroom and interpreting them using mathematical and pedagogical content knowledge to decide next steps. This competence has been conceptualized from different perspectives, but with a focus on managing mathematical discussions in the classroom, this competence is conceptualized in our study as:
(i) identifying relevant teacher actions during a lesson related to the management of the mathematical discussion in the classroom;
(ii) interpreting which teacher’s actions do (not) support the management of the mathematical discussion; and
(iii) deciding which other teacher’s actions can enhance the management of the mathematical discussion in the classroom.

The design approach followed is based on research that shows that representations of practice, also called vignettes (e.g., student responses, interactions between teachers and students in the classroom), theoretical lenses, understood as the theoretical information from research in mathematics education, and guiding questions support the development of noticing competence in initial teacher education programs. Therefore, our design is based on these principles: the use of representations of practice, the use of guiding questions and the use of a theoretical lens to analyse the management of the mathematical discussion in the classroom.

The representation of practice consists of a classroom situation in a comic format in which the teacher is managing a lesson on solving a problem through the phases of presentation, exploration, and discussion that involves a fraction operation. Some of the teacher’s actions support effective management of the whole-group discussion, while others could be modified to improve it. The guiding questions focus on the analysis of pre-service teachers on identifying teacher actions and interpreting their appropriateness for managing the mathematical discussion in the classroom (identifying and interpreting) and on proposing other actions to improve the management of the mathematical discussion in the classroom (deciding). The theoretical document presents the results of research in mathematics education on the management of a problem-solving lesson (the actions a teacher should consider in each phase of a problem-solving lesson) and on aspects of student learning related to fractions.

Keywords:

Vignette learning, pre-service primary school teachers, managing mathematical discussion, noticing.