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Schipper, Goei, de Vries, and van Veen (2017) reviewed the literature, claiming that for teachers to have professional growth through the lesson study approach, adaptive teaching competence is crucial. This competence includes four dimensions: (1) in-depth subject content knowledge and knowledge about differentiation; (2) knowledge of student conceptions to diagnose individual student learning, needs, and characteristics; (3) “teaching methods as part of the repertoire of teaching approaches; and (4) classroom management in order to create conditions which facilitate student learning” (Brühwiler & Blatchford, 2011, as cited in Schipper et al., 2017). The National Council of Teacher of Mathematics (NCTM) regarded eight areas to consider for an effective mathematics teaching practice. Firstly, teachers should establish clear goals for student learning to guide instructional decisions. Secondly, teachers should implement tasks that promote reasoning and problem solving for students to discuss the tasks with appreciation of varied solutions strategies.
Thirdly, the mathematical tasks should engage students to use and connect mathematical representations to deepen their understanding in both mathematical procedure and concepts. Fourthly, teachers should facilitate students with meaningful mathematical discourse by analyzing and comparing students’ ideas to share a common understanding of mathematical ideas. Fifthly, teachers should pose purposeful questions relating to the task implementation. The questions are very important to stimulate students’ thinking, reasoning, and relating mathematical ideas. The sixth area involves building students’ procedural fluency from conceptual understanding so that they will have a strong foundation to solve contextual mathematical problems. The seventh area supports productive struggle in learning mathematics. By providing them an opportunity to struggle with mathematical problems, they will be individually and collectively engaged and learn from the tasks. Finally, teachers elicit and use evidence of student thinking to adapt instruction for students’ further learning (NTCM, 2014).
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teaching competence,” or the ability to adjust teachers’ planning and teaching to students’ individual learning processes, determine teachers’ professional growth, and become more conscious about students’ different educational needs. Teachers learned a great deal about students’ characteristics and how students learn, differentiating their subject matter to meet students’ learning preferences.
Additionally, Moss, Hawes, Naqvi, and Caswell (2015) modified the Japanese lesson study cycle with four adaptations to enhance teaching and learning geometry. These four adaptations include teachers engaging in mathematics, conducting co-designed task-based clinical interviews, collaborating with researchers to design and teach exploratory lessons, and creating resources for other teachers. The study found the approach successful as it helps members gain “deep content knowledge and broaden conceptualization of geometry and spatial reasoning.” Da Ponte, Quaresma, Mata-Pereira, and Baptista (2018) also adapted lesson study in the Portuguese context through the project using 12 sessions. The study presented interesting findings; although teachers initially had difficulty choosing the teacher to conduct the research lesson, they realized the values of lesson study for their professional learning experiences. These values included various beneficial tasks, consideration for students’ prior knowledge, students’ strategies for solving problems, generalizations, and justifications as well as fostering students’ learning through class discussions. The study also argued that employing lesson study was not ideal if teachers’ major concerns involve covering a wide range of topics and curriculum aims. However, it would be best suited if teachers value in-depth work. Some of the aforementioned studies have shown that non-Japanese lesson study adaptations greatly affect teachers’ professional learning to improve teaching and student learning. The following are some insights into how some countries adapted lesson study.
2.6.1 Lesson study in the United States of America
Lesson study was brought to the United States by four publications. These include Yoshida’s (1999) dissertation, entitled “Lesson Study: A case study of a Japanese approach to improving instruction through school-based teacher development”; Lewis’s (2002) lesson study handbook, entitled “Lesson Study: A handbook of teacher-led instructional change” (see Figure 5); the Mill College Lesson Study Group (2000); and Stigler and Hiebert’s (1999) book, entitled “The Teaching Gap: Best ideas from the world’s teachers for improving education in the classroom.” After these publications, lesson study rapidly spread across the United States. Within four years, lesson study was adapted in 32 states and, approximately, over 225 schools (Lewis, Perry, & Murata, 2006).
28 Figure 5. Lesson study model (Lewis, 2002)
Watanabe (2018) also summarized that lesson study in the US was initiated by the studies of Yoshida (1999), Stigler and Hiebert (1999), and Lewis and Tsuchida (1998). Yoshida’s study was later published as Fernandez and Yoshida’s (2004) book of the same name. The book conceptualized a six-step lesson study practice: (1) collaboratively plan a research the lesson, (2) observe the employed study lesson, (3) discuss the study lesson, (4) revise the lesson plan (optional), (5) reteach the lesson with a different group of students (optional), and (6) share reflections on the observation (Fernandez
& Yoshida, 2004). Stigler and Hiebert (1999, pp.112-116) defined eight steps of lesson study practice:
(1) defining the problem, (2) lesson planning, (3) teaching the lesson, (4) evaluating the lesson and reflecting on its effect, (5) revising the lesson, (6) teaching the revised lesson, (7) evaluating and reflecting, (8) and sharing the new results. The US’s version of the lesson study involves classroom research to develop teacher knowledge. This is consistent with the Japanese educators’ perspectives that teaching is recognized as research. Lesson study is embedded in Japanese daily teaching, therefore,
“classroom teachers often talk about their own ‘research agendas’, and mathematics teacher educators will say that the main objective of student teaching is for teacher candidates to identify and sharpen their agenda of research” (Watanabe, 2018). Lewis, Perry, and Hurd (2005) conducted lesson study with 26 volunteer teachers of K-8 in 2000. They found changes in teachers’ knowledge of subject matter, instruction, student thinking, and the capacity to capture it, as well as their motivation to improve the lesson, capacity to work with colleagues, and accountability to value practice community.
For example, teachers increased their understanding that if the arrangement of the triangles is modified, the mathematical pattern would change. Teachers also alter their conceptions about student learning
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because how students count is a representation of their mathematical thinking. The change in pedagogy is that correctly completing the chart does not guarantee students’ understanding of a mathematical pattern. Students’ understanding of mathematical patterns will be deepened when they manipulate the triangles themselves (Lewis et al., 2009). Gonzalez and Deal (2017) revealed that teachers change their understanding of subject content knowledge about “perpendicular bisector in relation to other concepts in curriculum.” They explain the definitions of perpendicular bisectors while discussing the lesson plan. Their knowledge of students’ conceptions also changes because they anticipate students’
mathematical thinking in tasks related to perpendicular bisectors. There is also a change regarding content knowledge of teaching because the teachers set a criterion to select the tasks “that would best enable student discovery of specific properties of perpendicular bisectors.”
2.6.2 Lesson study in Singapore
During an international conference in Singapore in 2004, Catherine Lewis and her academic team from Japan introduced the concept of lesson study to Singaporean researchers and teacher educators (Lee & Lim-Ratnam, 2015, p. 42). It “has been adopted by some schools as a school-based professional development program or as cluster-initiated program” (Cheng & Yee, 2012). In 2006, after being acquainted with lesson study for two years, the teacher educators and researchers of the National Institute of Education (NIE) started implementing lesson study practice within primary schools. Catherine Lewis, Patsy Wang Iverson, and Akihiko Takahashi perhaps influenced the lesson study process in Singapore, as they guided several workshops from 2006 to 2009. Consequently, it started booming, and the numbers of Singapore schools practicing lesson study dramatically increased from eight schools in 2007 and 112 schools in 2010 to 170 schools in 2012 (Lee & Lim-Ratnam, 2015, p. 42). Apparently, to gain more from lesson study’s effectiveness, Singaporean researchers did not limit their opportunity by adopting a singular lesson study model, even combining Lewis’ model based on the handbook (2002). They also utilized the learning studies of Hong Kong’s lesson study model by adopting “pre-and post-tests for diagnosis of students’ prior knowledge and assessment of learning outcomes and variation theory to analyze the research lessons” (Fang & Lee, 2015).
30 2.6.3 Lesson study in the United Kingdom
Peter Dudley introduced lesson study to the United Kingdom (UK) in 2001. Generally, this model was taught with three research or study lessons (see Figure 6). Dudley’s perspective on lesson study was “a specified form of classroom action research focusing on the development of teacher practice knowledge” (Dudley, 2014, p. 1). This practice knowledge is tacit knowledge, and it “tends to stay with the teacher who discovered it and who is usually unconscious of its existence.” Dudley conceptualized lesson study into three cycles. First, lesson study group members jointly planned the first lesson. They then taught and observed the lesson, interviewed students, and held a post-lesson discussion.
Figure 6. Lesson study in the UK (Dudley, 2014) 2.6.4 Lesson study in Thailand
Thailand has eight educational universities and 36 Teacher Colleges that are responsible for training primary and secondary school teachers (Inprasitha, 2006). Dr. Maitree Inprasitha of Khone Kaen University first introduced lesson study in Thai mathematics teacher education in 2002. He incorporated the lesson study concept with Open Approach using open-ended problems to run the mathematics class activities. Initially, he piloted with 15 pre-service teachers in seven secondary schools in Khon Kaen city. This project has positively influenced mathematics teacher education in Thailand, expanding to other schools and provinces. For example, in 2004 and 2005, over 800 teachers participated to “train using open-ended problems to create rich mathematical activities in their classrooms” (WALS, 2015). This innovative integrated approach continued gaining attention from schools and universities. Consequently, in 2010, 22 project schools that train pre-service teachers from Chiang Mai University were implementing this approach. There were “60 project schools implementing lesson study and Open Approach across Thailand” (WALS, 2015). This innovative
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approach of the 2010 model has three simple steps for mathematics teachers to perform collaboratively:
(1) design a lesson (“PLAN”), observe the research lesson (“DO”), and reflect on the teaching practice (“SEE”). The second step, “DO,” has four specific steps of teaching—posing open-ended problems, students’ self-learning, whole class discussion and comparison, and summarizing through connecting students’ mathematical ideas that emerge in the classroom (Inprasitha, 2010). Nonetheless, the “SEE”
step the 2015 model has slightly changed from “collaboratively reflection on teaching practice” to
“collaboratively discuss and reflect on the research lesson” (see Figure 7) (Inprasitha, 2015; WALS, 2015).
Figure 7. Lesson study with Open Approach (Inprasitha, 2015, p. 220)
Lesson study practice in Thailand is a weekly cycle. It perhaps is aiming to closely relate to everyday teaching practices by demanding to cover all content stipulated by the curriculum.
Subsequently, a step is eliminated in the revised and re-taught version of the lesson plan. If the teachers want to utilize this version, they must wait a year to implement it. Utilizing the Thai lesson study method, previous research—entitled “Professional development of mathematics teachers with lesson study and Open Approach: The process for changing teachers values about teaching mathematics”—
determined some changes to teachers’ perspectives on how to teach mathematics. They have altered their view and classroom evaluation, changing from teacher-centered to “directing and stimulating students’ ideas,” valuing student-centered instruction, changing from one-way teacher speaking to listening to students, and have gained confidence (Kadroon & Inprasitha, 2013). The lesson study incorporated with structured problem solving has changed teachers’ value of teaching mathematics for all steps, including modifying lesson planning, research lessons, observation focus, assessment, and post-lesson discussions (Inprasith, 2010, as cited in Kadroon & Inprasitha, 2013). It also influenced
Collaborativel y design research lesson (Plan)
Collaborativel y observe
research lesson (Do) Collaborativel
y reflect research lesson
(See)
Posing
open-ended problem Students’
self-learning
Whole class discussion Summarize through
connecting students’
mathematical ideas emerged in the
classroom
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pre-service teachers to increase collaborative work, consider multiple solutions for problems, and increase their reasonability. Nevertheless, prospective teachers faced some issues associated with tension, anxiety, and confidence especially when their ideas are rejected by the group participants (Inprasitha, 2006). Therefore, there is a need for the teachers and teacher educators to be knowledgeable in lesson study and possess a strong mathematical background “to grasp student solution methods in real time and to recognize whether and how they relate to the key mathematical points that need to be learned” (Silver et al., 2005, as cited in Takahashi et al., 2013). Moreover, they must be skillful in the problem-solving method to utilize this integrated approach effectively.