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Current efforts for teacher education reform in several Asia-Pacific countries suggest that preservice teachers need to develop a better understanding of learning. One way to do this is to have preservice teachers reflect upon themselves as learners in their teacher education classes. In this study, students in a course in an Australian university teacher education program used a World Wide Web site that was designed to incorporate a three-phase reflective framework — analysis, synthesis, and theorizing — to assist them to reflect on their experiences as learners in university classes. The web environment included a database to help the students structure their reflections to collect data and theorize about their experiences. In the third phase of the framework — theorizing — the students developed a metaphor to represent the complexity of their own learning and labelled it with key learning factors. Most students believed that the design of the website guided them in their reflections and the metaphor enabled them to represent the complexity of their own classroom learning. Students in other Asia-Pacific countries would also be able to use the reflective framework in their teacher education classes and it could be adapted to include other influences such as culture on learning.

Transformation in teacher education is seen as crucial for creating change within the educational system. In this article, we explore how members in a teacher education program interpret new ideas and tools such as portfolio assessment, case-based methods, and ICT. These ideas and tools are important conditions for the collective change of the institution, where portfolio assessment emerges as a new object between the subject-oriented communities. In activity theoretical terms, we suggest that learning is a matter of acting on and talking about the object within and between communities. These sideways movements lead to transformations on the object. This conception also gives us an alternative perspective on the classical theory/practice problem.

At the Muenster University, teaching–learning labs have been integrated into teacher education as part of a joint initiative by the German federal and state governments in order to improve the quality of teacher education. Because of the great potential in natural differentiation and the particular challenge in teaching, mathematical modeling was placed at the focus of the teaching–learning lab. The paper deals with the structure of an innovative and supportive learning environment that fosters the diagnostic competence of mathematical modeling as part of the professional competence of pre-service teachers. With the help of a newly developed test instrument, it was shown that the development of modeling-specific diagnostic competence increases significantly and with a large effect size in the teaching–learning lab for mathematical modeling, while no significant changes occur in a control group (CG).

This report presents a summary of the content of the various presentation by the participants in ICME-14 under the Topical Study Group 17: Problem Posing and Solving in Mathematics Education. Some trends in the research on problem solving and problem posing are identified through this study. Other areas which were less explored were also highlighted

In the field of applications and mathematical modelling there is intensive research. Within the TSG, we have thematically addressed the teaching of mathematical modelling, teacher education, and modelling processes and competencies of school and university students. Future research directions are expected to consider theory building, empirical studies, including developing standardized research instruments, and the use of technology.

The aim of TSG-36 was to share the experiences of research on classroom practice at the primary level, address its research methods and theories, describe innovative classroom practice, and discuss the impact of research on classroom teaching and learning mathematics in different countries. A total of 32 submissions of research articles, project reports, and posters addressed related topics.

According to UNESCO (2015), the equity gap in education is exacerbated by the shortage and uneven distribution of professionally trained teachers, especially in disadvantaged areas. Target 4.c (MOI) of the SDG 4 is therefore aimed at substantially increasing the supply of qualified teachers, including through international cooperation for teacher training in developing countries, especially least developed countries and Small Island developing States by 2030. It further states that teachers are one of the fundamental conditions for guaranteeing quality education and therefore there is need to empower and adequately recruit, remunerate and motivate professionally qualified teachers and educators, and support them within a well-resourced, efficient and effectively governed systems (UNESCO, 2015). The knowledge of teachers in the last three decades was mainly influenced by a well-known scholar Lee Shulman who categorized teacher knowledge into seven categories among which content knowledge is included. However, much research on in-service teachers focused on the pedagogical content knowledge hypothesizing the mastery of content as much as they are graduated from recognized training institutions. Based on this categorization, the present paper presents an analysis of Rwandan mathematics school subject leaders’ Content Knowledge (CK). The presentation is based on partnership established between governmental and nongovernmental institutions led to development and implementation of certified Continuous Professional Development (CPD) programs for primary and secondary mathematics teachers. Findings reveal a lack of teachers’ preparedness to adopt the new curriculum teaching approaches, there is also lack of appropriate physical facilities in schools to accommodate every leaner’s individual needs among other hindering factors. Recommendations include systematic CPD programs for in service teachers to complement preservice training so that they can adapt various reforms and in-service teachers to establish their individual professional development plans.

In Singapore, a city-nation, the education system is centrally run and, in general, all the teachers in the school system are employees of the Ministry of Education. There is only one institution, the National Institute of Education (NIE), which provides teacher education for all the teachers in the education system and thus, there is very close working relationship between the NIE and the Ministry of Education. The story of mathematics teacher education is primarily based on the teacher education programmes provided by the NIE. This chapter describes mathematics teacher education in Singapore in four sections. The first section sets the context of teacher education in Singapore, the second gives a description of the pre-service teacher education programmes together with a brief discussion of its evolution and issues, the third does the same for the professional development programmes and the fourth section summarises the research done on mathematics teaching and mathematics teacher education over the last decades.

The purpose of this chapter is to unravel the roles of Teachers Network (TN), the school clusters and zones in promoting mathematics learning among teachers in Singapore. Specifically, the author draws on the concept of Learning Communities to discuss teachers’ continuing learning in mathematics in these communities. The case study on TN in particular looks at how, at the national level, teachers are trained to create an environment for mathematics sharing and learning through the practice of the Learning Circles (LC) methodology in their schools. At the zone level, the author describes the work of a Mathematics Centre of Excellence (COE) in its creation of scaffoldings for collaborative learning and sharing of mathematics for schools in the East Zone. Through their activities and programmes, both the TN and the COE spawn learning communities within schools. Issues challenging the roles of TN and of COE in teachers' continuing professional development and the implications of these issues for policy makers are also discussed.

This chapter presents a study investigating the reasons behind the success of mathematics master teachers in their acclaimed teaching career in the Chinese mainland. Data were collected from 31 mathematics master teachers in four provinces and three municipalities through questionnaires and interviews. The results revealed that the master teachers valued internal factors more than external ones in their professional growth. In particular, dedication to education, inner quality, and true professional care towards students appear to be three most important factors. In contrast, capability in dealing with interpersonal relationship was rated as less crucial by the master teachers. The chapter also documented those master teachers' experiences, reflections, and suggestions concerning teachers' professional development. Implications and interpretations of the findings are discussed.

The study focuses on how training courses were designed and implemented by making the reflective use of research-based cases to assist in-service teachers in identifying and maintaining high-level cognitive demands of mathematics tasks in classroom teaching. Eight in-service teachers enrolling in a university course “Theory and Practice of Case Method (TPCM)” in summer M.A. program participated in the study. Data were mainly collected from case analyses, reflective journals and video-tapes of classroom observation. It is found that the use of research-based cases enhanced the teachers' awareness of differentiating levels of cognitive demand of tasks determining students thinking and their ability in maintaining highlevel cognitive demands of tasks in classroom instruction. The major factors associated with maintaining the high level of cognitive demands were related to teachers' expertise of mathematics instruction, such as selecting and sequencing the tasks, selecting and sequencing students' various solution for advancing students' high-level thinking, and encouraging students to make mathematical connections between other student responses. The factors associated with the decline in the high level of cognitive demands were related to the tasks, teachers, students, and time to explore in classroom.

This book documents the journey undertaken by educators from the Mathematics and Mathematics Education (MME) Academic Group in the National Institute of Education (NIE) and Singapore schools during a Mathematical Modelling Outreach (MMO) event in June 2010 under the guidance of renowned experts in the field of mathematical modelling. In this introductory chapter, we provide the context in which MMO was organised, the theoretical framework of mathematical modelling adopted for MMO, and outline the focuses of mathematical modelling during MMO in relation to the Singapore mathematics curriculum framework. We will also present an overview of the chapters in this book, summarise the progress of modelling efforts in schools to date, and draw implications for future directions on mathematical modelling in schools.

In Singapore, unlike in many other parts of the world, the practice of mathematical modelling in the classroom is still in its infancy stage. However, interest in this area has grown rapidly in the last few years, and many local mathematics teachers and teacher educators have been exposed to a variety of views, interpretations and philosophies of modelling in schools. In this chapter, a framework for the practice of mathematical modelling in Singapore schools is proposed along with examples on how the framework may be used as a guide to design modelling learning experiences in local schools.

The change process with any educational innovation does not appear to be something that can be shortened no matter how heightened our awareness of the nature of the change or issues previously met and dealt with in other implementations in other systems according to educational change researchers and theorists. We can, however, benefit from such knowledge of other implementations and the changes teachers underwent by a more in-depth level of implementation in the usual change timeframe. To this end, the change of the Queensland senior secondary mathematics curriculum from a purely mathematical one emphasising content, skills and process to one focusing on applications and mathematical modelling is explored using the voices of teachers reflecting on that change.

The following sections are included:

• Introduction
• Facilitating Students' Modelling Competencies
• Significance of Study and Method
• Findings
• Discussion and Conclusion
• References