Mathematical Teacher Noticing: The Key to Learning from Lesson Study
Mi Yeon Lee and Ban Heng Choy
Abstract Lesson Study has been adapted by many countries in support of teachers’ learning from their practice. However, learning from Lesson Study does not come naturally and it is unclear how teachers can be supported in such learning. Moreover, lesson preparation, a critical component of mathematics teaching, is still largely under-explored in the study of teacher noticing. This chapter presents an analysis of what and how teachers notice when they make instructional decisions during the planning and reviewing stages of Lesson Study. It compares and contrasts two groups of elementary school teachers: one group of pre-service teachers (PSTs) from the United States, and the other group of in-service teachers (ISTs) from Singapore, in terms of what they see and think about their students’ mathematical reasoning during Lesson Study. Using a notion of productive noticing, we provide snapshots of mathematics teacher noticing, which highlights the key role noticing plays in learning from Lesson Study, and offer insights as to how teacher noticing can be supported in the context of lesson planning and reflection.
Keywords Noticing • Lesson Study • Lesson planning • Lesson reflection • Teacher education
To teach mathematics effectively, teachers should notice and build on student thinking, adjusting their instruction to support their students’ learning (National Council of Teachers of Mathematics [NCTM], 2014). Teaching in this manner is
M.Y. Lee (H)
National Institute of Education, Nanyang Technological University,
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E.O. Schack et al. (eds.), Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks, Research in Mathematics Education,
both ambitious and challenging, and requires knowledgeable teachers to enact these productive teaching practices (National Research Council, 2005; Smith & Stein, 2011). In light of this, teacher education researchers suggest that meaningful teacher learning occurs when teachers have opportunities to reflect upon their teaching practice and work in professional communities in order to solve instructional problems related to their teaching practice (Ball & Cohen, 1999; Hiebert, Morris, & Glass, 2003). However, participation in these learning communities alone, while deemed necessary, would be insufficient. Instead, it is crucial that teachers develop a common language to discuss issues with regard to teaching and learning (Bryk, 2009; Loughran, 2009).
Mathematics teacher noticing is one such means to improve teaching expertise because how teachers pay attention to and make sense of what happens in their classroom can influence the quality of mathematics teaching (Jacobs, Lamb, & Philipp, 2010; Sherin, Jacobs, & Philipp, 2011). Despite the growing number of research studies on teacher noticing, many of these studies centred on exploring teacher noticing skills displayed when reviewing their teaching videos (Sherin & van Es, 2009; Star & Strickland, 2008; Stockero, 2008), and only a few studies examined teacher noticing during the lesson preparation (Choy, 2014; Santagata, 2011). For example, some researchers provided teachers with another teacher’s instruction video and asked them to describe what they notice in the teaching video (Colestock & Sherin, 2009; Kersting, 2008; Star, Lynch, & Perova, 2011), and others asked teachers to retrospectively recall what they were noticing during their own teaching by watching a video from their own classroom (Ainley & Luntley, 2007). In some cases, researchers asked teachers to watch and discuss excerpts of their teaching video with other teachers as a peer group (Sherin & van Es, 2009). As part of a larger study, Choy (2014) explores what teachers notice during the lesson preparation stage of Lesson Study and extends the realm of the study of noticing to lesson planning.
Lesson Study is a collaborative teacher-inquiry professional development approach that emphasizes reflection on practice and students’ thinking (Fernandez & Yoshida, 2004; Stigler & Hiebert, 1999), and can be used to effectively develop teachers’ expertise and foster meaningful teacher learning. However, learning from Lesson Study does not come naturally (Takahashi & McDougal, 2016). In this regard, Fernandez, Cannon, and Chokshi (2003) highlight three critical lenses, that of researcher, curriculum developer, and student, needed to learn from the processes of Lesson Study. Adopting these lenses requires teachers to use varying perspectives to focus their attention on mathematically worthwhile aspects (Schifter, 2001) and interpret students’ mathematical ideas in order to make instructional decisions productive for enhancing students’ reasoning (Jacobs et al., 2010). Thus, we hypothesize that teacher noticing, which consists of observing, analyzing and responding (Sherin et al., 2011), plays a critical role in teachers adopting these lenses. Furthermore, even though it is important to prepare oneself to notice (Mason, 2002), the role of noticing during lesson preparation has been relatively unexplored.
In this chapter, we will examine mathematics teacher noticing during the planning as well as the review stages of Lesson Study by applying these three critical lenses. The key questions that guided our inquiry are as follows:
- 1. What do teachers notice when they plan and review lessons during Lesson Study?
- 2. How do teachers notice what they observe during Lesson Study?
- 3. How can we support teachers to learn from Lesson Study through a focus on noticing?