Mathematics Teachers’ Changes in Knowledge for Teaching Conditional Probability Through Lesson Study

Understanding what knowledge mathematics teachers develop during lesson study is crucial for improving teaching practices and student learning outcomes. Despite widespread use of lesson study as a professional development approach, limited research has explored the specific types of teacher knowledge that emerge through this collaborative process, especially in secondary education contexts. This study explores the types of knowledge developed by mathematics teachers during the implementation of Lesson Study. Using a qualitative case study design, data were collected from three Lesson Study cycles involving four junior secondary school mathematics teachers. Data sources included classroom observations, video recordings of planning and reflection sessions, and teaching documents. Transcript-based lesson analysis was employed to examine changes in teachers’ knowledge across three key domains: mathematical content knowledge, pedagogical content knowledge (PCK), and awareness of student thinking. Findings indicate that participation in Lesson Study encouraged deeper conceptual understanding, more deliberate instructional decisions, and greater sensitivity to students’ learning processes and misconceptions. These outcomes highlight the transformative potential of Lesson Study in fostering collaborative, practice-based professional growth. The study concludes by recommending the strengthening of school–university partnerships and the institutionalization of Lesson Study as an effective and context-responsive approach to mathematics teacher development in Indonesia.

PurposeTeachers in the USA have been conducting lesson study for more than ten years since it was introduced from Japan in the late 1990s. Although interest in conducting lesson study in the USA is still strong and greater numbers of teachers have become involved in this professional learning, there are significant obstacles to conducting high quality and effective lesson study that enhances teachers’ content and pedagogical knowledge, as well as improving their instruction and student learning in classrooms. Because of the needs of improvement in lesson study in the USA, so it can be administered effectively and sustained, the purpose of this paper is to discuss the current status of lesson study in the USA, what high quality and effective lesson study is, and what ideas might be help to improve lesson study in the USA.Design/methodology/approachIn this paper, issues that are common barriers to conducting effective lesson study, such as: US teachers’ misunderstanding or lack of understanding of lesson study; teachers’ insufficient knowledge of content, pedagogical content, curriculum knowledge; lack of support from administrators for lesson study; non‐systematic approach to implement lesson study; and having short‐sighted vision to conduct lesson study will be discussed. The discussions are based on the author's 12 years of experience working with teachers, schools, and school districts in the USA, interactions and information exchanges with other lesson study educators and researchers and professional development coordinators in schools and districts in the USA, and existing research documents in the USA. Through this discussion, the author attempts to provide suggestions for improving lesson study in the USA.FindingsIn order for lesson study to be successful, teachers need to think of lesson study as a way to improve their own learning as well as student learning. Spending more time studying mathematical content and curriculum, developing a strong pedagogical content knowledge with colleagues, and establishing a professional community of learning through lesson study will help it to be effective for improving classroom teaching and learning.Originality/valueThe paper provides some helpful suggestions for improving quality and effectiveness of lesson study in order to improve: classroom teaching – teacher's content, pedagogical content and curriculum knowledge; and student learning. The paper is particularly valuable for lesson study practitioners, and administrators and staff developers who are implementing lesson study in schools.

The lesson study is a collaborative model of teacher professional development originating in Japan, which has received growing international attention. This multifaceted model can be considered from many points of view. This research aims to understand what physics and chemistry pre-service teachers learn, in the domain of the pedagogical content knowledge on the speed of sound, in a lesson study. Participants were all pre-service teachers (three) attending the first year of their initial teaching education programme. The lesson study, had two cycles, took place over the course of twelve sessions and a total of 36 hours of work. The first cycle consisted of ten sessions: the first eight sessions aimed at defining the topic and lesson planning; this was followed by the first research lesson taught by the cooperating teacher; and finally, there was a post-lesson reflection. The second cycle consisted of two sessions; a second research lesson was also taught by the cooperating teacher; and subsequent to this, there was a post-lesson reflection. This is a qualitative and interpretative study. Data were collected from participant observation of all sessions using field notes and video recording, individual interviews and individual written reflections. Results showed that the pre-service teachers developed the pedagogical teacher knowledge (PCK) to teach the topic in the planning phase, when they identified the students’ prior knowledge, which would help them learn the topic, and in the post-lesson reflection sessions, when they discussed strategies that could help students overcome their learning difficulties.

This study aimed to explore how secondary school science and mathematics teachers in Qatar integrate Technological Pedagogical Content Knowledge (TPACK) into their teaching practices. The study examined the relationships between the subcomponents of TPACK using structural equation modeling (SEM), complemented by an analysis of additional categorical variables. A total of 245 science and mathematics teachers from Qatar participated in the research. The model’s findings showed that the internal components—technological knowledge, pedagogical knowledge, and content knowledge—had a significant and positive direct effect on the external factors: technological pedagogical knowledge, technological content knowledge, and pedagogical content knowledge. However, these internal components did not directly impact TPACK itself. Together, these variables accounted for 77% of the variance in TPACK. Among the findings, Technological Content Knowledge (TCK) emerged as one of the most influential variables affecting TPACK, emphasizing its importance in teachers’ TPACK integration. On the other hand, it was found that Pedagogical Content Knowledge (PCK) did not have a direct and significant effect on TPACK. Categorical variables like certificates and postgraduate education significantly impact TPACK and its subcomponents, while gender, field of study, and teaching experience do not. This finding underscores the importance of structured training and postgraduate education in enhancing TPACK skills for science and mathematics teachers. Participation in technology-based certification programs and postgraduate studies in STEM is crucial for their TPACK development in teaching STEM subjects. Future studies could explore the long-term impact of structured, technology-based training programs on enhancing STEM teachers’ TPACK development and assess how this improvement influences student learning outcomes in science and mathematics classrooms. This would provide deeper insights into the effectiveness of such programs and their potential to transform teaching practices and student achievement in STEM education.

Traditionally, engineering lecturers do not have sufficient training and background in teaching although training and passion toward teaching could help to make them good engineering educators. However, it takes time for them to learn by themselves by attending training and continuously improving their practice. Recently, Lesson Study is practiced in universities to help improve teaching and learning among lecturers collaboratively. Lesson Study is a form of continuous professional development for educators where a group of educators come together to plan lessons, observe each other’s classes, analyze the classes, and give feedback as well as reflection of the lessons. The learning and development of educators can be faster and more meaningful as Lesson Study is directly improving classroom teaching. This paper describes how Lesson Study was practiced by eight engineering lecturers to teach “Introduction to Engineering” among chemical engineering students that utilize a problem with a sustainable development theme. Frequent meetings and classroom observations were conducted throughout one semester. At the end of the semester, reflections were collected from the lecturers to study the benefits and challenges they encountered. Most of them agreed that Lesson Study helps to improve their lesson planning, time management, collaboration among lecturers, and confidence in teaching. However, Lesson Study requires time to meet, discuss, and plan. Lesson Study is seen as a quick way for experienced lecturers to mentor and coach new lecturers especially in shifting them from a teacher-centered approach to a student-centered approach in engineering education.

This study sought to examine the use of learner-centered approaches in mathematics Subject at Pugu Secondary School in Ilala District, Tanzania. The study employed a qualitative approach through interviews, focus group discussions, documentary review and classroom observations. The study involved 30 students who participated in classroom observations and FGD and two teachers through interviews and the classroom observations. The study established that advanced mathematics teachers and students equally positively perceived the use of learner-centered approaches in the mathematics subject. Teachers integrated teacher-centered and learner-centered approaches but they lacked competence on how to effectively integrate different strategies when facilitating the lessons. Teachers either prepared lesson plans without following it or did not prepare the lesson plans at all. The study recommends that school administrators should make sure that teachers prepare and use lesson plans to guide the teaching and learning processes for better results. Finally, there is a need for frequent in-service training to mathematics teachers on how to effectively integrate different teaching and learning strategies in order to enhance students’ achievement in mathematics.

Lesson study (LS), a teacher-oriented, student-focused professional development approach that originated in Asia, has spread globally. However, findings related to the effect of LS on teacher learning and growth have varied widely. This suggests a need to review current research on LS in the field of mathematics education. This paper focuses on mathematics teachers’ learning and professional growth through LS using Clarke and Hollingworth’s interconnected model of professional growth (IMPG) that contains three components: domains of change, mediating mechanisms, and change environment. With regard to domains of change, we found that although previous LS studies—often small scaled, qualitative studies—attended to all domains of change, they have more frequently reported changes in the personal (or collective) domain (e.g., teacher knowledge) but have relatively less frequently reported changes in other domains. In fact, there is a lack of research on systematic changes across domains in the IMPG. Regarding the mediating mechanisms, research has well explored both enactment (planning and teaching) and reflection (debriefing). For enactment, the planning process is less appreciated, and there is an inconsistent understanding of the role of the knowledgeable others. For reflection, there is a lack of focus on student thinking and constructive feedback during this process. Finally, research has suggested that LS has received support from the change environment but that tensions (e.g., time limits) have remained. These challenges call for systemic support and cross-cultural collaborations to develop sustainable and large-scale LS. We suggest future directions for continued research and practice.

This thesis documents the design, implementation and evaluation of a professional learning programme to support teachers in developing their ability to teach mathematics through problem solving. Teaching mathematics through problem solving is recognised as an effective way to teach mathematics. However, there are a number of different approaches with different descriptors such as problem posing and problem-based learning. In this study, teaching mathematics through problem solving is an approach where learners explore a problem or a task and their responses to the task are ‘orchestrated’ by the teacher to introduce and develop the mathematics to be learned. The development of this teaching approach involves the principles of task design and planning the sequencing of anticipated responses to be orchestrated. The professional development programme was informed by research on task design and the features of effective professional learning for teachers. The programme was built around the professional learning programme Lesson Study and was modified with a ‘pause’ in the research lesson and the use of remote visualisers to observe and analyse the work of the pupils. This latter feature was an adaption of the original programme design to respond to conditions arising in schools during the Covid-19 pandemic. Also a number of additional modifications were made to accommodate the ambitions of the programme. A qualitative approach was adopted using the methodology of design research and comprising two research cycles. The cohort in the first cycle were secondary school teachers and in the second cycle they were primary school teachers, all working in England. The aim of the study was to understand the effect of the programme on the participants’ knowledge, skills and confidence in teaching mathematics through problem solving. Existing frameworks in the literature on the known characteristics of effective professional learning were synthesised to evaluate the effectiveness of the programme. The main outcomes from this research confirm that the designed features of the PD programme were effective in supporting teachers in developing their ability to teach mathematics through problem solving. The use of task design principles in conjunction with the development of the teaching technique of orchestration resulted in gains in teacher confidence and subject and pedagogical knowledge. The pause in the research lesson and the use of visualisers to observe and analyse the pupils’ work provided the participants with a focused learning opportunity to develop the teaching approach. The evaluation of the programme using the designed analytical framework for CPD identified [a range of] known characteristics of effective CPD in the programme as designed and implemented. Three main implications emerged from the study, the first of which concerns the future development of teaching mathematics through problem solving. It was apparent that there were contextual barriers to the approach becoming an established part of teachers’ practice. To address these, the design of mathematics teaching resources would need to reflect the ambition to teach mathematics through problem solving. This is an issue for curriculum designers. There would also need to be recognition of the problem-solving skills that pupils require to access the problems, which would need to be taught either as part of teaching through problem solving or as a separate approach known as teaching for problem solving. The second implication identifies the challenges associated with introducing this type of programme into the current landscape of professional learning for teachers of mathematics in England, including the need for greater coherence between the professional learning of teachers of mathematics and their own workplace contexts. Finally, the third implication relates to the use of Lesson Study. This study described how the use of design research can develop Lesson Study variants that can make a positive contribution to professional learning environments for teachers without compromising the key principles of Lesson Study.

Research on teachers' knowledge for teaching is an essential domain in teacher education. This article used a Japanese Lesson Study to develop prospective mathematics teachers' knowledge for teaching measures of central tendency from bar charts and histograms. More specifically, the research focuses on developing specific content knowledge (Specialized Content Knowledge, SCK), knowledge of content and student (Knowledge of Content and Students, KCS), and knowledge of content and teaching (Knowledge of Content and Teaching, KCT) for prospective mathematics teachers through a lesson study process. The research results indicated that the prospective mathematics teachers had improved their knowledge for teaching through a lesson study cycle. The results provide insights into the effectiveness of the implementation of lesson study in initial mathematics teacher education.

Features of two lesson study contexts, one with prospective secondary teachers engaged in microteaching lesson study and one with prospective elementary teachers engaged in field experiences, were investigated for providing US prospective teachers with opportunities for growth as teachers of mathematics. In both contexts, the prospective teachers (PTs) exposed their knowledge, beliefs and practices to the scrutiny of peers and other experts, developing and reconsidering their thinking and practices through the shared teaching experiences. Similarities and differences in features of the two contexts are discussed with respect to PT learning. Similarities included the importance of negotiation during teaching cycles as catalysts for PT learning, the value of the cooperative nature of the experiences for sharing varying ideas and perspectives among PTs, the merits of overarching student learning goals for PT lesson planning, and the contributions of the group products (written or oral reports of the lesson study) to the learnercenteredness of the experiences. Differences influencing prospective teacher learning included the extent of focus on mathematics knowledge, extent of focus on classroom processes and management, use of videotaped lessons as part of formative feedback, and participation of knowledgeable advisors during or at the end of the cycles.

The paper clarified the developing lesson plan of fertilizer dilemma story for integrated knowledge practicing through lesson study. Through the PD program using lesson study, the theoretical framework of dilemma story was adopted to reference of the developing lesson plan. Methodology regarded paradigm. Participants included primary school teachers as team teachers, supervisors, expertise university lecturer, and school director. The primary school teachers as team teachers include a science teacher, a mathematics teacher, a technology teacher, and an art teacher in Nongsonghong district, Khon Kaen, Thailand. The developing lesson plan of fertilizer dilemma story for integrated knowledge practicing through lesson study will be interpreted through document analysis and participant observation. The innovation lesson plan of fertilizer dilemma story for integrated knowledge practicing could be summarized through the outcomes of lesson study design – plan, see, and reflect. The results provided the overview of the lesson plan of fertilizer dilemma story for integrated knowledge practicing that could be viewed through the structuring questions for ethical dilemma fertilizer story and example of dilemma story chemical fertilizer. This study may have implications for development program for integrate the curriculum in Thailand.

Literature is replete with different conceptualizations of teacher knowledge, each with their implications on teaching practices. Pivotal among these are conceptualizations of content knowledge, curriculum knowledge, pedagogical knowledge and pedagogical content knowledge. The paper argues that until now, the various conceptualizations of teacher knowledge have been mostly general and not domain specific enough. In addition, researchers who have relied on these earlier conceptualizations have mainly concerned themselves with teacher knowledge qualitatively. In an attempt to shift from these general conceptualizations and the qualitative measures of teacher knowledge, the study on which this paper is based relied on the Knowledge of Algebra for Teaching (KAT) project’s conceptualization of teacher knowledge for teaching algebra and an adaptation of one of the instruments. Two hundred and nine participants comprising 189 prospective and 20 in-service high school mathematics teachers in Ghana took part in the study. From the findings of the study, this paper argues that effective mathematics teachers do not only use the individual conceptualized knowledge but sometimes also blend these types of knowledge into somewhat new forms of knowledge. Consequently, the paper proposes an elaboration of the KAT project’s domain specific conceptualization of teacher knowledge that recognizes overlapping packages of knowledge and lends itself to being assessed both qualitatively and quantitatively.

The study aims to find out the suitability of the mathematics teachers’ lesson plan with the 2013 curriculum, the mathematics teachers’ learning implementation with the 2013 curriculum, and the lesson plan with the mathematics teacher’s learning activities with the 2013 curriculum. The study used descriptive research with qualitative approach. The research subjects were 3 mathematics teachers of class X in the State Senior High School (SMAN) 11 Makassar. The documentation, observation sheet, and interview guidelines were the instruments used in this study. The analysis results of the lesson plan with the learning activities based on the 2013 curriculum in accordance with the cultural and education ministry regulation number 22 of the year 2016 about the Elementary and Secondary Education Standard Processes showed that the suitability of those three mathematics teachers’ lesson plans with the learning implementation of the 2013 curriculum was categorized as very high with the percentage of 94.44%, the suitability of the learning implementation in SMAN 11 Makassar at class X with the learning implementation of the 2013 curriculum was categorized as high with the percentage of 81.68%, and the suitability of the lesson plan with the learning implementation based on the 2013 curriculum in SMAN 11 Makassar at class X was categorized as low with the percentage of 62.17%. The study finding also indicated that there was unsuitability between the lesson plan and the mathematics teachers’ learning implementation of the 2013 curriculum at class X of SMAN 11 Makassar.

This paper analyses the Japanese Lesson Study regarding improving student learning outcomes from the perspective of intellectual capital. In the 2000s, international academic achievement surveys brought attention to Japanese mathematics teaching methods and Lesson Study behind them. Today, Lesson Study has become more prevalent in education. Along with the increasing number of research on Lesson Study, the flipside of Lesson Study has also been emerging. The traditional Japanese Lesson Study produces a detailed lesson plan about ten pages in length. It is arduous work for Japanese teachers, so some teachers may have a sense of aversion to do so. This paper illustrates two cases in which a new lesson plan format was developed to alleviate teacher workload without compromising teaching effectiveness. Teachers can focus more on understanding lesson objectives and preparing a practical lesson with such an innovative format. In addition, their lesson plans became the intellectual capital of the school. The cases show that streamlining Lesson Study can foster structural capital and human capital in a school.

Lesson study has received significant attention as a model of professional development among mathematics teachers. Evidence highlights its effectiveness in improving pedagogical practices and student learning, however, less is known about the predispositions which may encourage teachers’ participation in Lesson Study or the impact of participation on teachers’ attitudes. Such findings are relevant considering the voluntary context of teachers’ participation in professional development in Ireland. This research investigates the motivational variables which impact teachers’ participation in Lesson Study, specifically their self-efficacy in teaching mathematics for conceptual understanding and their attitudes towards self-development in Lesson Study. Post-primary mathematics teachers (N = 64), spanning various levels of experience in Lesson Study, completed a survey using a set of pre-validated scales. Findings indicate that teachers’ mathematics teaching self-efficacy is a significant predictor of their participation in Lesson Study. Furthermore, the research finds that teachers’ familiarity with Lesson Study impacts the likelihood of their participation in this model of teacher education. These findings build upon previous knowledge in this field and demonstrate the significance of teaching self-efficacy as a presage variable for developing a positive disposition towards Lesson Study. The paper discusses the implications of these findings for teacher education in Ireland.