ERG SES H 12, Assessment in Education
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.
This study focuses on the prospective middle school mathematics teacher productive noticing through lesson planning within the case of misconceptions. In this regard, qualitative research design was used to investigate prospective teachers’ planning abilities centering on their selected misconceptions. They made lesson plans in order to overcome the misconceptions. Patton (1985) defined qualitative research as “an effort to understand situations in their uniqueness as part of a particular context and the interactions there” (p. 1). In addition, qualitative research can give us detailed and rich information about the investigated cases or phenomenon (Cresswell, 2007). For this effort, this study seeks to understand how prospective middle school teachers planned their lessons centering the misconceptions. Participants were 27 prospective middle school mathematics teachers enrolled in elementary mathematics teacher education in a public university of Turkey. Since they were in the fourth grade of this training program, they took many courses related mathematics education (e.g. methods of teaching mathematics, developing materials). Data were collected in the context of this training program. The participants were asked to group 3-4 people and to design a lesson regarding any kind of potential students’ misconceptions. Thus, eight groups were asked to plan the lesson to overcome one possible misconception that students would have. The components of the lesson plans were the topic, grade level, objective(s), pre-requisite information, starting, an activity to overcome misconception (middle), and end. The lesson plans analyzed with using FOCUS Framework’s Planning the Lesson part. In using this framework, content analysis was used. A sentence or an explanation that is thought to be meaningful in itself and within determined themes related to the investigated phenomenon are transformed into codes in content analysis (Strauss & Corbin, 1990). Regarding this framework, the themes were attending to, making sense of, and deciding to respond. The sub-themes were the descriptions of the themes. The codes were extracted from written lesson plans. The initial analysis is presented in this paper and the analysis is still being analyzed.
Prospective teachers made lesson plans about algebraic expressions, equations, probability, fractions symmetry and operation with integers. Each of the lesson plans highlighted the targeted concepts by giving daily life examples or reminding previous lesson(s), using materials for asking questions. For instance, Group 4 described a daily life example using specific details of the concept (e.g. interpreting weather temperature for positive and negative numbers in terms of absolute value) and directed students’ attention to the absolute value using thermometer, number line and set models to consider possible reasons for students’ misconception. It can be seen that students could recognize what students have misconceptions about the mathematical concept. In the aspect of making sense, Group 2 focused the using modelling to link between students’ image of thinking fraction as two separate whole numbers and their misconception grasping the idea of the fraction with the larger numbers had bigger value due to the number value. This group tried to stress the using modelling in which student were more familiar might have made student’s misconception obvious for the students to see comparing two fractions. However all groups provided potential students’ misconceptions about the concepts, not all they did address the analysis why students might have those misconceptions or possible ways to address students’ misconception about the concepts. In this sense, Group 3’s strategy using apple and pear to overcome “3 (x+y)=3x+y” misceontion may not work. Lack of high level demand tasks or lack of adaptation students’ thinking may be reason not to demonstrate of appropriate instructional decisions. In deciding to respond aspect, teachers are expected to design a cognitive demand task. Seven groups were able to identify the misconception and develop more than one strategies which targeted the misconception. However, their suggested activities could not be high-level demanded task.
Amador, J. M.,, Carter, I., Hudson, R. A., & Galindo, E. (2017). Following a Teacher’s Mathematical and Scientific Noticing Across Career Progression from Field Experiences to Classroom Teaching. In Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 161-181). Springer, Cham. Ball, D. L. (2011). Foreword. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. xx–xxiv). New York: Routledge. Choy, B. H. (2015). The FOCUS framework: Snapshots of mathematics teacher noticing (Unpublished doctoral dissertation). University of Auckland, New Zealand. Choy, B. H., Thomas, M. O., & Yoon, C. (2017). The FOCUS Framework: Characterising Productive Noticing During Lesson Planning, Delivery and Review. In Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 445-466). Springer, Cham. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, California: Sage Publications. Jacobs, V. R., Philipp, R. A., & Sherin, M. G. (2011). Preface. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge. Jacobs, V. R., & Spangler, D. A. (2017). Research on core practices in K–12 mathematics teaching. In J. Cai (Ed.), Compendium for research in mathematics education. Reston, VA: National Council of Teachers of Mathematics. Mason, J. (2002). Researching your own practice: The discipline of noticing. London: RoutledgeFalmer. Males, L. M. (2017). Using Video of Peer Teaching to Examine Grades 6–12 Preservice Teachers’ Noticing. In Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 91-109). Springer, Cham. Sherin, M. G., & Van Es, E. A. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13, 475–491 Strauss, A., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Sage Publications, Inc. Patton, M. Q. (1985). Quality in qualitative research: Methodological principles and recent developments. Invited address to Division J of the American Educational Research Association, Chicago. Yang, Y., & Ricks, T. E. (2012). How crucial incidents analysis support Chinese lesson study. International Journal for Lesson and Learning Studies, 1(1), 41–48.
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