Noticing is described as how to act of focusing attention on and how people make sense of complex situations (Jacobs, Lamb and Philip, 2010). This term occurs either to describe general situations (e.g., noticing the colour of friends’ jacket) or, occurs specifically to distinct features of particular professionals (Amador et al., 2017; Jacobs & Spangler, 2017).
Early research on noticing suggested, there is a strong necessity to focus on improvement of prospective teachers’ noticing skills in education programs (Sherin and Van Es, 2005). Although they don't have classroom experience, the previous studies have shown that they have the ability to notice and this ability can be developed (Males, 2017). However, teacher educators not only need to understand how various contexts for noticing affect what prospective teachers can learn to notice, but also there will be necessity to analyse why they cannot notice. This study uses lesson planning to investigate how and what prospective middle school mathematics teachers notice about students’ misconception at middle school level during the planning of a lesson. Hence, this study also will help us to catch both aspect what prospective teachers notice and also with what prospective teachers fail to notice while designing lesson plan regarding potential students’ misconceptions.
Mathematics teacher noticing is about how and what teachers understand instructional events in the process of teaching mathematics in classrooms (Mason, 2002). Designing lesson is one of important productive noticing ability for supporting students’ understanding (Choy, Thomas, & Yoon, 2017). Productive noticing is about what teachers attend and how they act thinking mathematically in order to develop teaching and learning mathematics (Ball, 2011; Choy et al., 2017). This is an important and also hard work for teachers (Jacobs, Philipp, & Sherin, 2011). Lesson preparing is the beginning of this work and it could provides using prior knowledge and experiences in order to notice in the instruction (Choy et al., 2017; Mason, 2002).
To these purposes, this following research question is framed “What emerges as teachers’ productive noticing during planning of lesson for overcoming potential students’ misconceptions?”. To answer this question, FOCUS framework that was developed by Choy (2015) and consists of two components: an explicit focus and focusing. An explicit focus is about three focal points that proposed by Yang and Ricks (2012) and their alignments as a guide for teaching. Yang and Ricks (2012) proposed three focal points that teachers should know and implement: the ‘Key Point’, the ‘Difficult Point’, and the ‘Critical Point’ (p. 54). Key Point is the mathematical concept that is taught; Difficult Point is the difficulty that students have in learning concept; Critical Point is the main part of teaching and it requires relating key point and difficult point to design tasks. On the other hand, focusing is pedagogical reasoning that connects attending and responding phases (Choy et al. 2017). Presenting the planning part of the framework for this study, a teacher;
1. Identifies specifics of the mathematical concept(s) for the lesson;
2. Recognises what students may find difficult or confusing about the concept;
3. Analyses why students might find the concept difficult or confusing;
4. Analyses possible ways to address students’ confusion about the concept; and
5. Develops and implements a high-level cognitive demand task to target students’ potential confusion about a concept. (Choy, et al. 2017, p. 452).
All in all, we would like to offer the perspective that we must go even further beyond just analysing our prospective teachers to analyse the other prospective teachers’ lesson planning process from European countries for future studies.