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A collaborative inquiry to promote pedagogical knowledge of mathematics in practice
Abstract
The present study attempts to report a collaborative cycle of professional development in teaching elementary school mathematics through lesson study. It explores a practice of lesson study conducted by teachers aiming to improve their knowledge of pedagogy. The study adopts an ethnographic approach to examine how collaborative teaching within an adapted lesson study framework might change the teaching-learning process. More explicitly, the present research looks at how lesson study influences teaching mathematics and how it helps the teachers learn from their peers in a discursive schoolbased setting. The study suggests that teachers need to aim high when dealing with students, and use more daily life situations in their math problems. It also particularly reveals that lesson study could have the potential to help teachers promote their teaching and boost students’ learning. Furthermore, it might also be used as an effective alternative to traditional professional development programs. © 2015, Western Australian Institute for Educational Research Inc. All rights reserved.
... As above-noted, the group adopted a four-stage classic model of lesson study, PDCA (Cheng, 2019;Moghaddam et al., 2015). Based on this model, the group identified an area of focus during our initial meetings and started planning the lesson study prior to the beginning of the semester. ...
... Challenges like this and the other ones described in this study informed our understanding of lesson study and will provide other practitioners with insights into the nature of lesson study. Concurring with Moghaddam et al. (2015), our study implies that despite the clear framework and steps lesson study provides contextual considerations are required to successfully implement lesson study in different educational settings. Another implication for lesson study practitioners in postsecondary education is that lesson study supports professional development even in a group of different backgrounds and has the potential to enhance culture of collaborative teaching and learning. ...
Purpose
The purpose of this collaborative self-study inquiry was to enhance the professional practice of faculty members through the adoption of lesson study. A seven-member faculty of education self-study group engaged in lesson study in a computer and learning resources for primary/elementary teachers’ course with teacher candidates.
Design/methodology/approach
This study focused on providing teacher candidates with increased opportunities for action and expression during in-class instruction. This collaborative lesson study inquiry (Fernandez et al. , 2003; Fernandez and Yoshida, 2004; Murata, 2011) involved the four-step process of planning, doing, checking and acting (PDCA) (Cheng, 2019). Several data collection methods were adopted and data sources analyzed.
Findings
Challenges the group encountered during the study included ascertaining the goals of lesson study and offering critical feedback to each other. While this made decision-making more intricate and intentional, there was exceptional value in participating in the lesson study process. The results revealed three overarching themes: 1) challenges in classroom observations; 2) hesitation in providing supportive feedback to colleagues and 3) deliberations regarding what constitutes expertise within subject-specific preservice teacher education.
Originality/value
While lesson study has been adopted fairly extensively in K-12 settings, its adoption in postsecondary education is limited (Chenault, 2017). Considering the merits of lesson study for K-12 practitioners, this research investigated the similar advantages that lesson study might have for postsecondary education faculty, students and programs.
... The studies by Norwich et al. (2016Norwich et al. ( , 2018 report that the LS group was joined by both the researchers and additional experts. Some researchers accompanied the process as active participants in the LS process and simultaneously acted as authors of the research paper (e.g., Leong et al., 2016;Ni Shuilleabhain and Seery, 2018), while others described their role as researchers being that of invisible observers (Moghaddam et al., 2015). This diversity made it difficult to clearly understand the role of researchers and external experts in articles that mentioned external instructors or experts, but neither identified them nor explained their role in the LS process. ...
Lesson Study is a method of professional development for teachers that has gained traction in recent decades. However, publications routinely fail to describe crucial details of the implementation or to link the mechanisms that facilitate teachers learning in Lesson Study to theory. This makes it difficult to meaningfully synthesize and replicate research findings. Using a protocol based on three dimensions of transparency, this systematic review examines 129 articles on Lesson Study published between 2015 and 2020 to identify how transparent they were in their reporting of how teachers observed and reflected together. The findings indicate a lack of transparency across several dimensions of how the Lesson Study intervention is reported and highlight a current lack of theorization and coherence in the field. To address some of these issues, we propose a framing structure that empirical papers on Lesson Study should give critical attention to in order to ensure relevance and transferability.
... The respondents were asked to rate the questions on a 5-point scale (5 = strongly agree, 1 = strongly disagree). The scale developed by [62], [63], and [18] assessed public entrepreneurship. It has 25 questions. ...
Organizational performance is an expected public outcome, particularly in the challenging context of Thailand’s public transformation into the twenty-first century. Entrepreneurial leadership is critical in developing public entrepreneurship and, ultimately organizational performance. This research study aims to investigate the influence of entrepreneurial leadership on public entrepreneurship and organizational performance as well as the influence of public entrepreneurship on organizational performance of local administrative organizations in the northeastern region of Thailand. A cross-sectional questionnaire study is used in this study. Data were collected from 400 people through five-point Likert scale questionnaires with validity and reliability analyses. Descriptive statistics and inferential statistics were used to analyze the data in preparation for ordinary least square regression analysis. According to the findings of the study, entrepreneurial leadership has a significant direct influence on public entrepreneurship with a standardized coefficient of 0.852. Public entrepreneurship has a significant direct influence on organizational performance with a standardized coefficient of 0.775. Entrepreneurial leadership has a significant direct influence on organizational performance with a standardized coefficient of 0.735 at a 0.05 significance level. In order to accomplish the desired public results for local administrative organizations, local administrative organizations should encourage leadership styles of entrepreneurial orientation to turn Thailand’s public sector into a competitive public entrepreneurial sector.
... It only shows that the proper implication of the social aspect of the students exposed in the Two Cubed Approach performs better in Algebra. It is supported by research results that students working cooperatively with enhanced social skills accomplish a consolidated better yield than students working independently [30]- [32]. The advantages increment further when students share their reasoning and other Mathematical ideas during the activity. ...
Working in joint effort empowers students' dynamic social connection and helps oversee intellectual and behavioral improvements. This study focused on assessing the effectiveness of the Two Cubed Approach as an introduced Collaborative teaching practice in enhancing the Algebra and the social skills of the students. One group pretest and posttest experimental research design was used to 38 College of Teacher Education first-year Mathematics major students, during the second semester of the academic year 2018-2019. The students experienced working in two cubed collaboration, quartic discussion, paired sharing, and individual verification. Its ultimate goal is to make them become independent learners who mastered the competencies set. The result shows a significant positive increase from pretest to posttest scores in the algebra skills of the respondents, which implies enhanced skills in recalling, simplifying, analyzing, solving, and applying the concepts learned from poor to fair level reached very good to excellent performances. This study also showed that the use of two cubed approaches in the classroom enhanced the social attributes of the learners. They were able to establish good working relationships and shared relevant ideas in accomplishing the tasks provided, leading to a more productive learning experience. The use of two cubed approaches in learning algebraic concepts enhances the students' skill for them to achieve better performances, and its collaborative segments led to a positive view in dealing with their group mates in attaining a high level of social skills.
... LS began to draw attention outside of Japan starting with Stigler and Hiebert's work (1999), which identified best practices from around the globe for improving education in the classroom. Since that time, linking the good results of Japanese students to the training and teaching culture in the country (Ingersoll, 2004), LS has been embraced and studied by teachers and researchers around the world (Lewis & Lee, 2017), including educational contexts as varied as Hong Kong (Hargreaves & O'Connor, 2018), Iran (Moghaddam, Sarkar Arani & Kuno, 2015), Uganda (Fujii, 2014), the U.K. (Dudley, 2013) and the U.S. (Akiba & Wilkinson, 2016), being these last two contexts where we find more examples of the put into practice of LS and of related studies (for the history and development of LS in the U.K., see Dudley [2011;). ...
Lesson study (LS) is a collaborative practice of inquiry in which teachers design a lesson plan and work to improve it and its execution after observing its instruction. Originating in Japan, LS is recognized in international research as a useful mechanism for teachers’ training and professional development. However, research reveals that misconceptions arise when LS is adopted outside of Japan, and different authors have called for further theoretical development to increase comprehension of the process. In response, we analyse three LS’ key components (phases, product and teachers’ cooperation) from the perspective of the epistemology of complexity, highlighting the role of emergence, the ecology of action, and joint reflection. We suggest that viewing LS through the lens of complexity can allow teachers to gain a deeper understanding of this practice and to apply it more successfully. Free eprint link of the published version (without changes):
https://www.tandfonline.com/eprint/WEFXNJ6W9BB7YUZB4MDI/full?target=10.1080/13540602.2020.1745174
... Page 312 AICLL 2019professional development activity and they plan to continue using Lesson Study in the future.This finding is in line with whatEktefaei (2006)suggested where the reason may be from the idea that teachers found a significant different between lesson study and other traditional professional development. Additionally, they also noticed the strong and weak points of their teaching, since Lesson Study provided teachers to talk about ideas they never thought through their experience in a collaborative teaching practice(Moghaddam et al, 2015). ...
Lesson Study (LS) assists teachers and lecturers to improve their professionalism within the idea of collaborative work through collegiality. Not all lecturers have enough competencies dealing with pedagogical content knowledge. Nevertheless, some of them seem to be reluctant to get involved in the program. This study aims to explore lecturers’ perception on the use of LS process in improving pedagogical content knowledge. It employs a qualitative method by applying descriptive study as its framework. Three EFL lecturers who teach at one of the state universities in Bandung who previously experienced LS process were being respondents in the study. The data were obtained from open-ended and close-ended questionnaire focusing on two themes, the steps and processes of the LS cycle and its effectiveness in improving pedagogical skill in teaching EFL. The result of the study revealed that the lecturers had a positive perception on using LS in improving pedagogical content knowledge in teaching EFL. However, time management of conducting the discussion still became the main problem in the program. The findings above suggest that the lecturers should have more desire and enthusiasm in conducting LS in order to promote their teaching and to help them get the characteristics of effective professional developments in their work.
... Not surprisingly, in the light of the above, there were cases in which it became part of a centralised educational system, whereas in others, it became a means of directly extending the teacher's autonomy. In certain places, lesson study started to make an immense contribution to the development of educational science as such, whilst, in others, it became a dominant form of teachers' social experience-based knowledge-community development (Moghaddam, Sarkar Arani, & Kuno, 2015;Saye, Kohlmeier, Brush, Maddox, & Howell, 2008). ...
It would be difficult to find any pedagogical story that is comparable to that of jugyou kenkyuu (or lesson study in English) that has been practised for over a century in Japan in isolation and became a method that was used worldwide in less than 10 years. Because of its uniqueness and its history, it is an irrefutable challenge to understand what it is really about, how its basic aspects such as a lesson or teachers' knowledge and its development, the culture of education, the measurability of educational activities and other main aspects of education are or can be conceptualised and in which ways these can travel in a globalised arena of education. In this article, we try to give answers to these and some other relevant issues related to lesson study via the author's subjective view and individually‐constructed narrative.
... Not surprisingly, in the light of the above, there were cases in which it became part of a centralised educational system, whereas in others, it became a means of directly extending the teacher's autonomy. In certain places, lesson study started to make an immense contribution to the development of educational science as such, whilst, in others, it became a dominant form of teachers' social experience-based knowledge-community development (Moghaddam, Sarkar Arani, & Kuno, 2015;Saye, Kohlmeier, Brush, Maddox, & Howell, 2008). ...
... It has forced teachers to shift their teaching from "teacher-centered" and "content-centered" to "student-centered" approaches. To improve teachers' knowledge and skills, the Ministry of Education's Bureau for the Scientific Promotion of Human Resources has developed short-term courses and workshops for teachers (Aliakbari and Sadeghi, 2014;Moghaddam et al., 2015;Navidinia et al., 2015;National Study Center for TIMSS and PIRLS, 2015;Saberi and Amiri, 2016;UNESCO, 2016). These new expectations also highlight the need for principals who are more active in leading teachers in the development of teaching and learning (Aliakbari and Sadeghi, 2014). ...
The purpose of this study is to understand and describe patterns of principal instructional leadership practice in Iranian primary schools and to then assess whether there are differences between the high- and low-rated principals. A mixed methods design was used to collect both qualitative and quantitative data from principals and teachers within Iranian primary schools. The quantitative data were collected and analyzed from 535 teachers and 70 principals across the 70 primary schools. Next, we used ratings on the Principal Instructional Management Rating Scale to identify four of the highest and lowest performing principals. We then conducted open-ended interviews with teachers and principals in these schools. The key findings showed that, despite working in a highly centralized context, the highly ranked principals in the sample were also differentiated from their lower ranked peers on specific instructional leadership practices. They appeared to give more emphasis to their role in developing the quality of teaching and learning and monitoring student progress. In this setting, ensuring a collegial and collaborative environment for teachers is commonly articulated by the successful principals in our study as an important aspect of instructional leadership.
... To raise instructional effectiveness, language teaching experts have recently been encouraged to borrow and apply a range of theoretical and practical ideas to base their instruction not only on specific language structures, generic, and discoursal features, but also on practices that address disciplinespecific needs and expertise of students. Generally, these practices aspire to embrace the notion of specificity that emphasizes the literacy skills applicable to the academic principles of particular disciplines (Hyland, 2002;Moghaddam, Sarkar Arani, & Kuno, 2015;Wardle, 2009). Therefore, Hyland (2002) warns against the assumption of an "autonomous" view of literacy that "misleads learners into believing that they simply have to master a set of rules which can be transferred across fields" (p. ...
... To raise instructional effectiveness, language teaching experts have recently been encouraged to borrow and apply a range of theoretical and practical ideas to base their instruction not only on specific language structures, generic, and discoursal features, but also on practices that address disciplinespecific needs and expertise of students. Generally, these practices aspire to embrace the notion of specificity that emphasizes the literacy skills applicable to the academic principles of particular disciplines (Hyland, 2002;Moghaddam, Sarkar Arani, & Kuno, 2015;Wardle, 2009). Therefore, Hyland (2002) warns against the assumption of an "autonomous" view of literacy that "misleads learners into believing that they simply have to master a set of rules which can be transferred across fields" (p. ...
This study aimed to explore how a collaborative approach in teaching for disciplinary academic writing would influence the transfer of learning in postgraduate students with varied writing proficiency levels. For this purpose, a sample population of 58 medical students majoring in four different medical sciences participated in this research. Throughout a whole semester, discipline-specific writing skills that were collaboratively planned were instructed. Meanwhile, the trace of variance in students’ writing practices was recorded and finally correlated with the students’ initial proficiency scores. To benefit the merits of qualitative analysis and to obtain specific information about the values and opinions of the population, focus group interviews were also conducted after each training session. The obtained results indicated that owing to the collaborative design of the program, the participants could attain significant levels of writing skills and finally transfer their received instruction to authentic practices. Further analyses of the results implied that age, university admission criteria, and level of professional involvement could have a determining interplay with students’ varied writing proficiency levels.
Students' errors are causally determined, and very often systematic. Systematic errors are usually a consequence of student misconceptions. These can include failure to make connections with what they already know. There are beliefs held by students that inhibit learning from errors, such as they cannot learn from the mistakes and that mathematics consists of disconnected rules and procedures. Student errors are unique and they reflect their understanding of a concept, problem or a procedure. This study investigated how much mathematics have been understood and remembered by Year 11 repeating students, how their confidence level affects their responses to test items, and the causes for errors and misconceptions. A total of 74 Year 11 repeating students participated in this study and nine Year 11 mathematics teachers were surveyed. The sets of data were collected from the student test performance, student confidence level scale, and student and teacher questionnaires. The quantitative analyses of the students' results suggested that their test performance was not notably affected by their confidence. However, students' misconceptions seemed to have a significant impact on their progress and achievement in the test. The findings also suggested that students' errors and misconceptions were not only varied but there exist different causes as well.
Infectious diseases ranging from the common cold to cholera affect our society physically, emotionally, ecologically, and economically. Yet despite their importance and impact, there remains a lack of effective teaching materials for epidemiology and disease ecology in K-12, undergraduate, and graduate curricula [2]. To address this deficit, we’ve developed a classroom lesson with three instructional goals: (1) Familiarize students on basic concepts of infectious disease ecology; (2) Introduce students to a classic compartmental model and its applications in epidemiology; (3) Demonstrate the application and importance of mathematical modeling as a tool in biology. The instructional strategy uses a game-based mathematical manipulative designed to engage students in the concepts of infectious disease spread. It has the potential to be modified for target audiences ranging from Kindergarten to professional schools in science, public health, policy, medical, and veterinarian programs. In addition, we’ve provided variations of the activity to enhance the transfer of fundamental concepts covered in the initial lesson to more complex concepts associated with vaccination and waning immunity. While 10 variations are presented here, the true number of directions in which the game might extend will only be limited by the imagination of its students [6].
This paper states three claims dealing with the relationship between mathematics education researchers and mathematics teachers: (1) Mathematics education research is a highly diverse field; (2) Teachers have various roles as stakeholders in mathematics education research; (3) Regarding teachers as stakeholders in mathematics education research affords reflecting some (fruitful) "cultural differences". The paper claims the necessity to regard researchers as key stakeholders in practice, and teachers as key stakeholders in research. © 2014, The Author(s) & Dept. of Mathematical Sciences-The University of Montana.
The central role of teachers and instructors in enhancing education quality and promoting education reform has been largely acknowledged by various researchers. However, professional development for university instructors in Iran is far from satisfactory. This paper initially outlines major shifts in professional development. It then provides a critical appraisal of professional development in Iran in both pre service and in service education. It then concludes by offering ways to revitalize continuing teacher professional development.
This chapter describes the purpose of the Framework for the PISA surveys of mathematical literacy and its evolution from 2000 to 2012. It also describes some of the analysis and scholarship on which the key constructs of the Framework are based, and links to kindred concepts in the wider mathematics education literature. The chapter does not intend to present the Framework but instead to share insights into its creation by successive Mathematics Expert Groups. The main Framework concept is that of mathematical literacy which has its roots in recognition of the increasing importance of mathematical proficiency in the modern world. The chapter describes mathematical literacy, its evolving definition and the origin of the term within broadened notions of literacies and its relationship to other terms such as quantitative literacy and numeracy. It describes the central constructs of the Framework, which are used to describe what abilities make up mathematical literacy and are also used to ensure that the item pool is comprehensive and balanced. These are the real–world context categories that group the source of mathematical challenges, the phenomenologically–based content categories, the fundamental mathematical capabilities and a set of processes based on the mathematical modelling cycle. The way in which new technologies have expanded the view of mathematical literacy and how this has been assessed through the 2012 computer–based assessment of mathematics is also discussed.
In this paper the research team proposes that classroom-based teacher training is more effective when embedded in the instructional context of the classroom. Instructional context can be defined as the relation between academic instruction and motivation to learn. Hence, we were interested in understanding how the classroom-based professional development training provided to teachers who integrated Crystal Island, a game-based learning environment, influenced teaching, learning and motivation. © 2013 © 2013 International Professional Development Association (IPDA).
There is much debate within mathematics teacher education over ways in which professional and academic foci could be made to complement each other. On one hand, teachers' craft knowledge is emphasised, mainly as this relates to the particular and local level of teaching; on the other, the importance of academic subject knowledge cannot be denied. In this chapter the focus will be on how to blend and balance the two through activities in which teachers learn from other teachers, particularly the co-learning of teachers and teacher educators. It will discuss professional relationships, reflective practice, community building, and research in practice. Examples of research-based programs involving Lesson Study (LS) and Learner's Perspective Study (LPS) research projects have moved the relevant research in this area to yet another theoretical level. Projects such as these and others from diverse parts of the world will be presented and discussed.
In recent years, a growing interest has developed in lesson study, a Japanese form of professional development that centers on teachers coming together to examine their practice by planning and trying out lessons. This article examines the lesson study work of a group of elementary mathematics teachers to speculate about the educative value of lesson study. Specifically, this article explores whether lesson study can afford teachers opportunities to learn about mathematics in a way that is useful for the enactment of reform-minded teaching. What hinders teachers in taking advantage of such opportunities and how such obstacles can be overcome are also addressed. Implications for future research on lesson study and for our broader understanding of what teachers learn from examinations of practice are discussed.
In recent years, there has been a feeling that effective teachers can be fostered by grounding professional development in actual classroom practice. This paper reports how a group of teachers adopted a lesson study approach and worked collaboratively so as to improve their class instruction on wh-question formation. Teachers’ reflections indicate that the collaborative environment throughout the study enabled them to gain insights into how to improve their teaching strategies. Also identified are some of the problems faced by teachers, which may undermine the gains of lesson study.