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The purpose of this paper is to report a case study of how learning study was incorporated in teacher education programs in Hong Kong. It aims to share the success of the program and to disseminate how pre‐service teachers enhanced their mathematical content knowledge and pedagogical content knowledge by practising learning study. Building on the work, this paper suggests incorporating the framework of learning study, a theory‐guided pedagogical principle, as an integrated subject of mathematics pedagogy and teaching practice in teacher education programs.

In total 32 pre‐service teachers’ learning journals of their reflections of learning processes were analyzed. The analysis of data and reporting of findings are linked tightly to how pre‐service teachers enhanced their mathematical content knowledge and pedagogical content knowledge by practising learning study.

The 32 pre‐service teachers noted that the learning study subject fostered their understanding of relationship between theory and practice and their understanding of transforming knowledge into action. In particular, they came to understand that knowledge of pupils and content involves a particular mathematical idea or procedure and familiarity with students’ prior knowledge and misconceptions. They also reported that they understood better what mathematics pedagogy content knowledge means and what components it includes.

The suggestions of incorporating the framework of learning study in teacher education programs is supported and manifested by the positive feedback and comments of the 32 pre‐service teachers who underwent the entire learning process of learning study in Hong Kong. The findings demonstrate how pre‐service teachers’ mathematical content knowledge and pedagogical content knowledge were enhanced by practising learning study.

Teachers 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.

In 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.

In 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.

The 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.

Elementary teachers' understanding of mathematics is a significant contributor to student success with mathematics. Consequently, teacher educators are frequently charged with the responsibility of supporting the development of prospective elementary teachers' mathematics content knowledge as they re‐learn concepts in ways they are required to teach. The purpose of this paper is to describe one teacher educator's efforts to support prospective elementary teachers' tenuous understanding of rational numbers.

Given the variety of factors influencing the development of teacher knowledge, a mixed method research design was utilized. Research participants were prospective elementary teachers enrolled in a nine‐week elective course who agreed to participate in the study (n=40); while the control group were prospective elementary teachers not enrolled in the elective course (n=35).

The results of this study indicate that it may be possible to improve prospective teachers' conceptual understanding of mathematics by providing additional short‐term support, such as an elective course and/or web‐based video clips. However, the program intervention can only build upon the existing knowledge that prospective teachers bring when they begin their Bachelor of Education programs.

For prospective teachers with a limited foundation in mathematics (e.g. less than four secondary school mathematics courses), short‐term support may be insufficient to compensate for their nebulous understanding of rational numbers. Based on this finding, one‐year Bachelor of Education programs might consider, either: including Grade 12 mathematics as a pre‐requisite for elementary teacher applicants; or mandating enrolment in a full‐year math content course similar to the elective course described in this paper.

The national mathematics curriculum of Pakistan has emphasized on improving content knowledge, reasoning abilities and problem-solving skills of students about thinking, communicating and solving mathematics (national mathematics curriculum of Pakistan, 2006). Whereas, there is a need to understand the point of view of teachers about the challenges they face in achieving the goals of national mathematics curriculum. This will help leading teacher training institutions to revisit their math teacher continuous professional development (CPD) programs and facilitate school leadership in improving the quality of math education in rural schools of the province. However, the purpose of this research study is to figure out the challenges that teachers are facing while achieving the goals of the national curriculum by teaching mathematics at the primary level in educational institutes of Pakistan.

In this research study qualitative research approaches have been utilized, in which focus group discussions (FGDs) were used as data collection techniques. Furthermore, thematic analysis of the data led toward the development of four overarching themes such as teachers' knowledge about mathematics curriculum, challenges relating to mathematics content and pedagogy, difficulties in developing conceptual understanding and designing lesson plans to address students' diversity.

The overall findings of this research study suggested that the majority of teachers are facing difficulties in mathematics content teaching such as decimal fraction, unitary method, measurement principles, practical geometry and data handling. Moreover, teachers are also facing challenges and difficulties in developing hands-on and minds-on activities in the teaching of mathematical concepts to the students of primary level in educational institutes of Pakistan.

This research study will facilitate the teachers and stakeholders to address the problematic issues in the domain of content delivery of mathematics. Whereas, this study recommends educating teachers about national mathematics curriculum and to develop a CPD framework for mathematics teachers for the enhancement of their pedagogical content knowledge. The study also recommends orientating school heads about the different aspects of math curriculum so that they can mentor math teachers in achieving math curriculum goals.

This is the first research study of its nature, which targets and highlights the teacher's perceptions toward the achieving the goals of national mathematics curriculum of Pakistan and addressing the pedagogical challenges faced in mathematics teachers. There is a dearth of studies in mathematics education in Sindh province. The issue is of immense importance, the findings will help teachers to improve mathematics instructions at primary level.

This study aims to explore how the theories of professional capital and decisional capital can be extended to introduce “professional mathematics capital” and “decisional mathematics capital”.

Professional development (PD) efforts in one school district in elementary mathematics education are described to illustrate these extensions and to contemplate ways to enhance teacher learning of mathematics pedagogy.

Both theoretical extensions provided useful frameworks for conceptualizing mathematics PD. Preliminary evidence suggests that participants demonstrated the emergence of professional and decisional mathematics capital.

While there were observed and reported changes to teacher practice, further research is needed to explore the implications of these theoretical extensions on student learning.

This study serves to enhance the literature related to PD and teachers' mathematical content knowledge. The theoretical extensions of professional and decisional mathematics capital are a novel and promising concept that allows for a unique approach to be laid out for those designing PD in mathematics.

The purpose of this paper is to examine how elementary school teachers integrated technology into their mathematics teaching in classroom settings that were one-to-one computer environments for most of the day. Following a series of classroom observations and interviews, inductive qualitative analyses of data indicated that teachers felt that technology supported students’ mathematics learning and prepared them for their future where technology was important. However, observations indicated that despite teaching in one-to-one environments, students only used technology on rare occasions or if they finished activities early. Further, these technology-based activities were low-level review of mathematics computations. Implications include the need to provide effective support to teachers about integrating technology in meaningful ways.

This study involved classroom observations of two-third grade teachers.

Findings indicate that teachers used Chromebooks in one-to-one classrooms to provide students with extra practice on computational skills.

There is a need for future studies to look at teachers’ use of technology and its influence on student learning.

Teacher education programs and school leaders should provide opportunities for current and future teachers to learn about technology with content specific examples.

This study provided an examination of all of the third grade teachers in a school who all were teaching mathematics in one-to-one classroom environments.

This paper reports on experiences of university-level mathematics teacher educators (MTEs) from participating in lesson study to improving mathematics teacher preparation. The authors investigate the questions: “What did MTEs report as benefits of participating in cross-departmental lesson study?” and “What considerations did MTEs report for stakeholders interested in lesson study?”

This study employed qualitative methodologies on one cycle of lesson study where the authors served as lesson study participants. Debrief and focus group interview data were analyzed for emergent codes on benefits, supports and challenges from a university-level lesson study.

Engaging in university-level lesson study provided MTEs firsthand professional development, created community, enabled attention to detail, improved knowledge of issues related to teaching mathematics, improved curricular materials and extended beyond one lesson. Institutional support, a natural evolution of the process, alignment of goals among members and support within the group supported their university-level lesson study. Challenges of time and funding, imposition, misalignment of goals and building trust are discussed.

The paper contributes insights about benefits for MTEs who use lesson study to examine their own teaching practice for mathematics teacher preparation. The importance of supports and constraints is highlighted.

This study aims to describe the pedagogical content knowledge (PCK) of a kindergarten educator who implements a lesson plan about informal inferential reasoning designed in a lesson study group.

To this end, we analyzed teaching interventions in two kindergarten lessons focused on the playful task of tossing two coins, associated with inferential statistical reasoning. The study highlights the importance of arguing and promoting this reasoning to develop statistical thinking. It is crucial to recognize how early students can be subject to learning experiences that promote a language of uncertainty, assess the evidence provided by the data, and make generalizations.

The results reveal that while the educator demonstrated knowledge and skills relevant to the curriculum and conceptual teaching strategies, the understanding of the content by the students and the integration of the PCK components still present a challenge.

The lesson study collaborative teaching practices that promote PCK have proven effective for informing the design and implementation of instructional practices supporting the development of early statistical thinking in young children.

The study enriches the knowledge regarding the potential of the lesson study (LS) in the professional learning of kindergarten educators. It also contributes to a comprehensive approach based on authentic playful experiences in grade K that supports the development of early statistical thinking in young children.

The purpose of this paper is to highlight the ways racialization in K-12 mathematics classrooms has narrowed the understanding of mathematical learning for Black children.

Drawing on situated learning theory and funds of knowledge, the authors argue that the social learning context of mathematics classrooms has limited the understanding of what Black children are capable of mathematically. The authors suggest that as a community of practice, mathematics classrooms may be marginalizing Black children, as well as other students of color, by devaluing their community-based knowledge and ways of knowing.

The extant literature portrays Black children as struggling in mathematics; however, this research is overwhelmingly conducted based on school performance measures. Yet, if one looks beyond the classroom to Black children's homes and communities, a plethora of mathematical knowledge tied to cultural and community practices may be found. As such, Black children who struggle in mathematics classroom may be experiencing misalignment across contexts, rather than a lack of mathematical knowledge altogether.

This paper has implications for classroom practice, particularly teacher ideologies pertaining to community-based knowledge. The authors urge mathematics education researchers and practitioners to look beyond the classroom, as community-based mathematical practices may provide more insight into students’ mathematical capabilities. These implications are particularly important for educating students of color, who often experience a subpar classroom education.

In this paper, the authors provide a critical lens to situated learning theory, pushing mathematics education research to examine the underexplored topic of Black children's out-of-school mathematical practices.

The purpose of this paper is to examine practicing mathematics teachers’ learning through parallel lesson study in China. Lesson study in China has been practiced for decades. Parallel lesson is an enriched mode of lesson study to address the implementation of new curriculum.

The expansive learning perspective has been used to explore the ways practicing teachers learned to improve teaching through the transformation of learning objects and boundary crossing.

Two cases are illustrated and compared to highlight features of teachers’ learning through parallel lesson study. The practicing teachers developed their competence in transforming instructional objectives and task selection and implementation. In addition, they also developed professional vision in alignment with the reform-oriented curriculum.

This study makes significant contribution to understanding teachers’ learning through lesson study in China. Meanwhile, it also demonstrates how the theory of expansive learning could be used as a conceptual framework to examine teachers’ learning through lesson study.