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Are education systems converging toward a global model of teacher education or do local models tend to predominate in spite of attempts to reform them? How much do global, national, and local cultures shape and condition future teachers’ opportunities to learn to teach? How do these opportunities influence teachers’ pedagogical content knowledge? In this chapter we use data from the IEA’s first study of the effectiveness of pre-service teacher education in order to investigate teacher education policy, program structure, and outcomes. Using multilevel modeling we found that across countries individual characteristics have a similar and powerful influence on what future teachers come to know at the end of their pre-service programs. The effects of teacher education curriculum on future teachers’ mathematics pedagogical content knowledge reaffirm the prevalence of local cultures on the implementation of an increasingly globalized ideal. We conclude that while the provision of teacher education shares many common features in goals and structure across countries, it is strongly influenced by local conditions and norms, and by cultural notions of the knowledge that is considered essential – framing how quality is to be defined and operationalized – when learning to teach.

In this chapter, three educators recount experiences of professional development from different perspectives in order to examine the intersection of teacher knowledge and subject matter in the areas of science and mathematics education. Professional development projects are productive avenues for exploring this phenomenon. We share stories of experience from professional develop projects of teachers who were situated in different places on the professional knowledge landscape: one elementary school teacher, one teacher educator, and one mathematics educator. From these various vantage points, the relationship between mathematics and science content knowledge and teacher knowledge holds different complexities and complications. Issues related to balancing teacher knowledge with content knowledge in professional development emerge. Based on the stories of experience and the analysis of the narratives, deliberation of curriculum is seen to be a valuable concept when engaging in professional development with teachers. Further, Pragmatic Intellectual Space is proposed for productive approaches to professional development.

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.

Policymakers have focused on improving STEM outcomes for US high school students for over 50 years. Much of this focus has centered on improving the quality of STEM teachers, particularly in poor and minority schools. Few, if any, of these efforts have considered the importance of the content knowledge of those providing instructional leadership in schools – namely, principals and assistant principals. This chapter examines the percentage of school leaders with teacher certification in mathematics or science and the degree to which teacher and school leader turnover interrupts the leadership–teacher relationships. The study concludes relatively few school leaders have the content knowledge to provide deep instructional leadership. Moreover, the study finds combined teacher and school leader turnover greatly diminishes the sustained relationships between instructional leaders and teachers, particularly in lower-performing schools.

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.

The purpose of this chapter is to examine the challenges of instructional leadership in prekindergarten (PK) programs in the context of small and mid-sized school districts. We first explore issues that characterize current PK education including the need for content standards and curriculum, Developmentally Appropriate Practices (DAP), Mathematics Pedagogical Content Knowledge, and addressing mathematics anxiety and teacher-efficacy. We then turn to instructional leadership for PK education and the challenges that leader preparation and district program structures cause for instructional leadership. Often instructional experts have limited exposure to PK classrooms housed in traditional elementary buildings. Additionally, elementary principals are typically ill-prepared with the knowledge needed to support and develop teacher MPCK and effective learning contexts in PK classrooms. Typical preparation and professional development programs offer limited support for building principals as PK instructional leaders. Implications for building principals include the need to engage professional communities, utilize collaborative processes such as team observations, and leverage the collective efficacy and expertise of PK educators in their schools and districts.

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.

Research over the last decade or so has made it clear that quality teachers matter to student achievement. What is less clear is the ways in which they matter and how we can prepare such high-quality teachers. Nowhere is this lack of clarity more evident than in special education, where we have few studies on teacher quality and even fewer studies on the type of preparation opportunities that would lead to high quality. Thus, it is difficult to make evidence-based decisions about how quality special education teachers should be defined and prepared. As a field, we have to turn to research in general education to provide a sense of some of the dimensions of teacher quality and effective teacher education. In this chapter, we provide a summary of the research on characteristics of highly qualified teachers and what we know from the research on teacher education and professional development that might foster these qualities, both in general and in special education. Part of our discussion centers on the concerns surrounding this body of research and the challenges of applying the findings to the field of special education. Although these challenges pose considerable problems, we are optimistic that potential solutions exist and can be reached through an alignment of initial teacher education and induction.