Noticing in Pre-service Teacher Education: Research Lessons as a Context for Reflection on Learners’ Mathematical Reasoning and Sense-Making

Abstract

Professional noticing of learners' mathematics reasoning is a crucial ingredient of a mathematics teacher's set of teaching competencies. Research lessons in the lesson study process, with its focus on learner reasoning, provide a structured environment for the building of mathematical knowledge as well as for reflection and the development of teacher professional noticing and sense-making. This paper reports on the depth and growth in noticing of three pre-service teachers during research lessons in their third and fourth years, using the Van Es noticing framework. The study showed that two of these teachers' noticing shifted to higher levels over the two years, with greater focus on learners' mathematical reasoning and sense-making than on teacher actions and teaching. Prospective teachers need well-structured and focused opportunities, individually as well as in groups, to learn to notice and make sense of learner thinking and reasoning.

Benefits, Difficulties and Conditions of Lesson Study Implementation in Basic Teacher Education: A Review

“…Regarding the conditions and procedures for the effective implementation of the lesson study in higher education, only five international studies have been examined in Mathematics (Saito et al, 2008;Molina, 2012;Wessels, 2018), Physics (Saito et al, 2008), Chemistry (Saito et al, 2008), Biology (Saito et al, 2008) and Science (McDowell, 2010;Carrier, 2011) and none in Greece. The most important prerequisites for the effective implementation of the lesson study are the reflection of the preservice teachers who develop their knowledge, skills and willingness to use it in their teaching, the participation and cooperation of teachers, the creative presence of the mentor, policy support from teacher educators who encourage teachers to develop and maintain quality teaching.…”

“…The lesson study combines theoretical and practical learning and promotes high quality learning through high quality teaching. Improving the professional knowledge and skills of teachers enables them to be distinguished as teachers by providing high quality teaching to learners, giving the latter opportunities for meaningful acquisition of knowledge (Nishimura 2016;Wessels, 2018). Also, the lesson study enhances the critical thinking of learners through team and cooperative teaching, which activates their various skills and competences and improves their learning (Darling-Hammond & Richardson, 2009).…”

“…An effective program of professional development of future teachers, which is based on constructivism and can narrow the gap between theory and practice is a lesson study (Wessels, 2018;Rekalidou et al, 2014). The review of international and Greek literature shows that several studies have explored the contribution of the lesson study to improving student learning and professional development (McDowell, 2010;Levy & Hourigan, 2016;Dania, Voutsina & Moumouri, 2013) as well as to the formation of more positive attitudes and beliefs of participating preservice teachers (Carroll, 2013;Post & Varoz, 2008;Juhler, 2018).…”

A Learning Trajectory as a Scaffold for Pre-service Teachers’ Noticing of Students’ Mathematical Understanding

“…247). This result suggests that noticing is a complex and specialized process (Mason, 2002;Sherin, Jacobs, & Philipp, 2011;Simpson & Haltiwagner, 2017) and that it can be influenced by several factors such as: mathematical pedagogical knowledge (Schoenfeld, 2011;Stürmer, Könings, & Seidel, 2013;Stürmer, & Seidel, 2017); prior experience (Erickson, 2011); context (Coles, 2013;Mitchell & Marin, 2015); or beliefs (Shoenfeld, 2011;Wessels, 2018).…”

Developing Pmri Learning Environment Through Lesson Study for Pre-Service Primary School Teacher

“…Lesson study is a learning system that uses a collaborative system (Sato, 2014a;Sato, 2014b). Lesson study is a learning system first carried out in the education system in Japan (Darra & Kanellopoulou, 2019) and shows good results on improving the quality of teaching and learning process (Kusumah & Nurhasanah, 2017;Wessel, 2018). This Lesson Study has four main steps in the form of a Plan-Do-See-Redesign cycle, namely (1) Plan, aiming to produce a design of learning tools, made collaboratively, (2) Do, aiming to carry out learning that has been designed at the Plan stage, (3) See, aiming to find the strengths and weaknesses of the implementation of learning and finally, (4) Redesign, aiming to make improvements to the learning design if there is anything needing to be improved based on the results at the see stage (Sato, 2014a).…”