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The aim of TSG 25 at ICME-12 was to discuss the experiences and approaches developed in different countries to support the professional development of teachers for practice, in practice and from practice. The study group 25 received 74 paper submissions from scholars, graduates, and practitioners in various countries and regions, and accepted 69 papers. A total of 63 papers were presented at 10 sessions at ICME 12 conference. Participants discussed research based practices and state-of-the-art approaches to the in-service education and professional development of teachers from a multi-national and globe perspectives.

The topic study group on pre-service mathematical education of teachers is dedicated to sharing and discussing of significant new trends and development in research and practice about the various kinds of education of pre-service mathematics teachers and of pre-service primary teachers who teach mathematics and are trained as generalists. It aimed to provide both an overview of the current state-of-the-art as well as outstanding recent research reports from an international perspective. The group discussed research experiences with different practices of pre-service mathematical education of (mathematics) teachers throughout the world, i.e. similarities and differences concerning the formal mathematical education of teachers, types and routes of teacher education, curricula of (mathematics) teacher education, facets of knowledge and differences in their achievements and beliefs about the nature of their training, and a variety of factors that influence these differences.

Affect has been a topic of interest in mathematics education research for more than 30 years. More recently, and as emphasized in the last ICME 11 report, beliefs has turned from a ‘hidden’ to a more ‘visible’ variable. Today we know that affective variables can be regarded as explicit factors which influence mathematics learning outcomes as well as instructional practice. The different research perspectives used in studies of affect include psychological, social, philosophical, and linguistic. Those various views were represented in the ICME 12 research presentations. It also became clear during the conference, and this was expected, that the construct of ‘affect’ encompasses related constructs such as ‘motivation’, ‘beliefs’, ‘values’ and ‘attitudes’, to name but a few. We invited, and received, presentation proposals on all areas of affect in mathematics learning and teaching.

The topic of “Language and Communication in Mathematics Education” covers a wide range of areas of interest, ranging from the question of what constitutes “language” in mathematics, through investigations of communicative interactions in mathematics classrooms and study of issues involved in teaching and learning mathematics in multilingual settings. This breadth was well represented in the papers accepted for presentation in the Topic Study Group at ICME12. In order to facilitate discussion, the paper presentations in each session were divided into two sets, with participants choosing which set to attend. This allowed the discussion to focus in greater depth on common themes. In addition, one session of the TSG was devoted to a panel discussion on the topic of “Theoretical and methodological issues in studying language in mathematics education” and a final plenary meeting enabled participants to reflect on the TSG as a whole, the common issues addressed, the lessons learnt and aspirations for future work on the topic. In this report, we present an overview of the major themes arising in the papers presented and in the discussions during the congress.

While mathematics are universal, it appears that delicate process in the classroom, but not only there, lead boys and girls to perceive things differently. And from this perception at school depends the future of the jobs.

For this topic study group, 35 papers were accepted from a range of different cultural, linguistic and country contexts. The papers were discussed under specific thematic questions. These themes provide an organizing framework for this report that draws its content from the papers and the discussion in the TSG 30 sessions. The submissions illustrated the rich diversity in the kinds of issues that arise in mathematics education in multilingual and multicultural environments. These include challenges for teaching, learning, curriculum, pedagogy, teacher education and use of technology in and for multilingual and multicultural settings. Issues were at the level of policy (e.g. language of instruction) and at the level of classrooms (e.g. teaching methods, curriculum) and teacher education (e.g. models of pre-service and teacher professional development). Diversity was also seen in terms of the geographical spread of the contexts from where papers were presented. The diversity of contexts reflects technologically advanced countries with increasingly large immigrant populations (e.g. Australia, Canada, Germany, Sweden, USA, UK), postcolonial countries with concomitant colonial languages as the medium of instruction (e.g. Ghana, Pakistan, Malaysia, South Africa, Tanzania) and countries with varied indigenous and official languages (e.g. China, India, Indonesia, Mexico, New Zealand). The overwhelming prevalence of issues related to quality of mathematics education in multilingual and multilingual contexts illustrates its significance.

A critical topic in mathematics education is the design and analysis of open-ended, realistic, and exemplary tasks. Task design and analysis is a relatively new field, appearing for the first time as a topic of study (TSG 34) at ICME-11 in Monterrey, Mexico. It is developing quickly and dynamically as an area of international attention and active research.

The purpose of TSG 32 was to gather congress participants who are interested in research, policy or design that focuses on mathematics curriculum development. The TSG aimed at including presentations and discussions of the state-of-the-art in this topic area and new trends and developments in research and practice in mathematics education. Curriculum was perceived at two levels. On a national or state level, where the focus is on content and goals for the primary or secondary school mathematics curriculum. And on a more specific level of curriculum design which concerns the developmental trajectories of mathematics content and the best ways to represent them. In relation to this theme, we especially solicited papers that might foster the deliberation on the varied aims of the curriculum and bring concerns and experiences from different contexts.

The purpose of Topic Study Group 33 was to address issues related to assessment in mathematics at all levels and in a variety of forms. Assessment and evaluation play an important role in mathematics education as they often define the mathematics that is valued and worth knowing. Furthermore, sound assessment provides important feedback about students’ mathematical thinking that prompts student and teacher actions to improve student learning.

The organizing group and the participants come to challenging mathematics from many different perspectives, but all firmly believe that mathematics education for the twenty-first century requires all teachers, schools and extra-curricular experiences to provide structure and support that allow and entice each student and citizen to strive to reach his or her personal best in mathematics. In the words of the discussion document for ICMI Study 16, “Mathematics is engaging, useful, and creative. What can we do to make it (engaging, useful and creative mathematics) accessible to more people?”