# CHARACTERISTICS OF PRE-SERVICE MATHEMATICS TEACHERS' NOTICING OF STUDENTS' MATHEMATICAL THINKING

Noticing what is happening in a classroom is an important skill for teachers. However, noticing effectively is both complex and challenging (Jacobs, Lamb, & Philipp, 2010; Mason, 2002). Noticing has been defined in a multitude of ways but the common theme is how teachers process complex classroom events. In initial teacher education contexts, the interest on the development of the skill of noticing should be seen as a way to understand how prospective teachers learn to make sense the mathematics teaching and learning. A particular focus for mathematics teacher’s noticing is the students’ mathematical thinking. Recent studies have shown that the noticing skill could be developed and have identified aspects that support its development (Fernández, Llinares, & Valls; 2011, 2012). In this study, we focused on the development of prospective mathematics teachers’ noticing of student’s understanding of the derivative designing a learning environment based on a e-learning methodology.

For the designing of the learning environment we adapted Wells (2002)’s socio-cultural perspective considering that individuals encounter different opportunities for making sense of students’ mathematical thinking: experience, information, knowledge building and understanding. Eight prospective mathematics teachers (PTs) participated in the learning environment of seven sessions of two hours each (one session per week). In the first session, PTs answered a questionnaire in order to identify in which extent PTs identified and interpreted students’ understanding of the derivative concept (“Experience”). During the next five sessions PTs read and discussed theoretical papers (“Information”) about the learning of derivative concept. These sessions used a virtual platform to enhance the interaction among pre-service students. PTs worked individually or in pairs in activities that required describing and interpreting students’ answers using the theoretical information. Next, there was a discussion to share their interpretations (‘‘Knowledge building’’). In the last session, PTs answered another questionnaire that provided us information about the changes on PTs noticing of students’ mathematical thinking (“Understanding”).

Results show that the learning environment helped to develop prospective teachers’ skill of noticing of students’ mathematical thinking but this development was not simple and was related to the ability to describe students’ answers to the problems using noteworthy mathematical elements.

References:

Fernández, C., Llinares, S., & Valls, J. (2011). Development of prospective Mathematics Teachers’ Professional noticing in a specific domain: Proportional Reasoning. In Ubuz, B. (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 329-236). Ankara, Turkey: PME.

Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM Mathematics Education, 44, 747-759.

Jacobs, V.R., Lamb, L.C., & Philipp, R.A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169-202.

Mason, J. (2002). Researching your own practice. The discipline of noticing. London: Routledge Falmer.

Wells, G. (2002). Dialogic Inquiry. Towards a sociocultural practice and theory of education (second edition). Cambridge: Cambridge University Press.