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The DG has prepared a questionnaire to collect data of teachers’ practise in China, Taiwan, Hong Kong, and Korea. The results, together with the literature search in theory and practice in mathematics education was prepared into a booklet of 90 pages for discussion during the ICME-12. There were two sessions of discussion during the ICME-12 and the following is a report of work and discussion of the DG during the ICME-12.

This group discussed the potential value of using technology-supported geometric transformations to introduce and develop function concepts. This approach (referred to here as ) and related representations can be used to help students develop intuitive understandings, avoid and overcome misconceptions, and deepen their understanding of variables and functions.

The principal aims of the discussion group were to discuss the development of a variety of mathematical software applications developed during the past decades. Among the most often utilised software types in education are Computer Algebra Systems (e.g. Derive, Mathematica, Maple, Maxima), Dynamic Geometry Systems (e.g. Cabri Geometry, Geometer’s Sketchpad, Cinderella, GeoNEXT, GeoGebra), Spreadsheet and Statistics Software (e.g. Excel, SPSS, Fathom, R). Most of this software has been designed by keeping in sight primarily their usability for research purposes while others were predominantly aimed for their use in teaching. In the recent years we could observe, among others, three important trends in the development of these software tools: (1) Designers of research oriented software products started to involve features and support for educational purposes; at the same time teaching oriented software have been becoming increasingly more powerful so their use in some research is increasing; (2) The distinction between different types of software has begun to blur as many products integrate features from other types of software; (3) The computer platforms are diversifying; with the appearance of smart phones, tablets, and Interactive Whiteboards (IWB) in recent years, as well as online services such as Wolfram Alpha, challenging the design and development of mathematics software.

The main question addressed in this Discussion Group is whether professional development can have a positive effect on the retention of mathematics teacher, and if so what is the nature of professional development that leads to teacher retention and how (what are the mechanisms by which) such professional development supports teacher retention.

The aims of DG12 were to: Facilitate discussion of key issues related to the knowledge required by mathematics teacher educators (MTEs), Identify different emergent strands in research that can be related to this area.

There were 30 participants from 17 countries. The challenge presented to the group was as follows: “The data revolution is everywhere except the classroom. In general, students finish their schooling seriously under-prepared to participate in the emerging data-driven society. This represents an enormous loss of scientific discovery, solutions to social problems, economic advancement, ….”.

In recent years, achieving mathematics proficiency has received notable attention [RAND 2003; National Research Council (NRC) 2001] What useful, appropriate, practical, and effective strategies can be developed and used to enhance student proficiency in mathematics is still a puzzle to mathematics educators. This urgent need becomes a challenging task for mathematics educators seeking research-based strategies to support classroom teachers to enhance their teaching leading to student proficiency.

The aims of the discussion group are to (1) discuss the findings of the three indigenous authors (Mamangon, Moses and Velasquez) investigations thus far relative to mathematics and culture in Micronesia, (2) explore the challenges and successess achieved in using elders to uncover and validate indigenous knowledge and practices, (3) explore the pedagogical issues of how to translate the findings into materials and approaches suitable for elementary school children, and (4) consider implications for future research in other indigenous cultures. Indigenous mathematics, ethnomathematics, cultural-based mathematics.

“Can art save the world?” is a well-known catchphrase in art circles. As most participants to the ICME are mathematicians, the title of this DG was reformulated more modestly as: “Can art save mathematics?” Indeed, some call mathematics a supreme art form as it enjoys total freedom, unrestricted by material limitations. An art form with the “collateral advantage” of having many real life applications, sure.

The 1980s saw a world-wide push for problem solving to be the central focus of the school mathematics curriculum since the publication of Polya’s book about solving mathematics problems in 1954. However, attempts to teach problem solving typically emphasised the learning of heuristics and not the kind of mathematical thinking used by mathematicians. There appears to be a lack of success of any attempt to teach problem solving within school curriculum. Problem solving strategies learned at lower levels tended to be ignored instead of being applied in their mathematical engagements at the higher levels, possibly because of the routine nature of the high-stake national examinations.