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History of mathematics teaching and learning is a subject that concerns two domains of research and may generate fruitful synergies between them. In 2000, during the International Symposium celebrating the centenary of the first international journal on mathematics teaching ( ), the interplay between the present educational problems in mathematics and their historical evolution through the twentieth century brought to the fore the potentialities of the field of research, “History of mathematics teaching and learning,” not only for historians, but also for educators.

Kay Owens (Charles Stuart University, Dubbo, NSW, Australia) presented a paper illustrating how schools can change when funds are available to assist schools and communities to implement appropriate and effective professional development, to establish partnerships between school and community, to revise teaching approaches and curriculum, to overcome disadvantage, and to value family and Aboriginal cultural heritage.

In the last decade, the issue of theories has been raised more than once in international conferences on mathematics education (e.g. PME 2005, 2010; CERME since 2005; ICME 11). Since 2006, a European group for the networking of theories has researched the question how mathematics education can deal with different theories (Bikner-Ahsbahs et al. ). This contribution addresses the issue of how to deal with the diversity of theories in mathematics education and gives an overview about the presentations and the discussion of the Topic Study Group on this topic held at ICME 12.

The countries represented during the discussion group’s meetings included: Australia, Canada, China, Iran, Israel, Philippines, Singapore, the United Arab Emirates, and the United States. The types of institutions varied among the countries and included: two and four-year vocational institutions, community colleges, programs related to retraining adults, and a one-year preparatory program in Israel for individuals coming out of military service and interested in attending university.

The Discussion Group 2 on Creativity in Mathematics Education at ICME-12 in Seoul, affiliated with MCG, was a great success. Co-chaired by Board members Emily Velikova and Vince Matsko, the group focused on issues relating to creativity in the classroom as well as training both pre-service and in-service teachers regarding effective ways of fostering creativity.

Linear Algebra is one of the most important courses in the education of mathematicians, scientists, engineers and economists. DG 3 was organized by The Education Committee of International Linear Algebra Society (ILAS) in order to give mathematicians and mathematics educators the opportunity to discuss several issues on teaching and learning Linear Algebra including motivation, challenging problems, visualization, learning technology, preparation in high school, history of Linear algebra and research topics at different levels. Some of these problems were discussed. Around 50 participants participated in the discussion.

A successful implementation of educational change depends on teachers’ professional development, and their ability to translate innovative ideas into practice. Although teaching, by its very nature, is a complex practice, most teachers work in isolation, making their own planning and decisions, and solve pedagogical problems having limited consultation with and feedback from their colleagues. The past decade has seen increasing demand to improve school mathematics, which, as a result, generated a need for teachers to join forces and share individual knowledge and experience with the community. Thus, the need to nurture mathematics teachers’ communities of practice became a primary goal.

Activities concerning history of mathematics have been a part of ICMEs since ICME2 in Exeter in 1972. They are now regular features of ICMEs, organized by the HPM (International Study Group on Relations between History and Pedagogy of Mathematics). The premise of this discussion group was that research on history of mathematics in education tends to have older pupils and students in mind, and that there is a lack of both research and resources on how to include a historical perspective when teaching younger pupils.

The goal was to elucidate the nature of postmodern mathematics and mathematics education, including the multiplicity of the subject of mathematics; and to explore and share ideas of how postmodern perspectives offer new ways of seeing mathematics, teachers, learners, mathematics education theories, research and practice. The two key themes originally used to organizer the sessions are as follows.

The purpose of this proposed Discussion Group is to facilitate discussion and initiate collaborative research with colleagues around the world to seek effective ways to improve teacher professional development through Lesson Study.