Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Programme

TSG 4 from ICME 13 aimed at connecting people from around the world who share interests in recognizing, developing and supporting gifted, talented and promising mathematics students. TSG 4 built on the work of several previous ICME Topic Study Groups. The programme included approximately sixty presenters from twenty different countries in regular presentations, oral communications and poster sessions. The presenters updated colleagues on their most recent work in a relaxed climate where questions and discussions of results were addressed. The TSG 4 co-chairs, team members and IPC liaison collaborated in person as well as electronically before, during and after the conference and all contributed to a smooth management and friendly atmosphere.

To offer a foundation for the discussions in each TSG4 session, a forty-page survey paper, Research On and Activities For Mathematically Gifted Students by Florence Mihaela Singer, Linda Jensen Sheffield, Viktor Freiman, and Matthias Brandl (Singer et al. 2016) has been published by Springer as an Open Access book and is available along with survey papers from other Topic Study Groups at http://icme13.org/publications/topical-surveys as well as on the MCG website at www.igmcg.org. The aim of this Topical Survey was to give a brief overview of the current state of research on and activities for mathematically gifted students around the world, being of interest to mathematics educators, educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. The focal topics include empirical, theoretical and methodological issues related to the following themes: Nature of Mathematical Giftedness; Mathematical Promise in Students of Various Ages; Pedagogy and Programs that contribute to the development of mathematical talent, gifts and passion; and Teacher Education. Current and historical research and suggestions for new research paths are included in each category.

The four main themes in the survey were also the themes for our TSG 4 sessions at ICME. These are briefly presented below.

  1. 1.

    Nature of Mathematical Giftedness. This session was organized around the following questions:

    • What do we know and what do we need to know about mathematical giftedness?

    • Is mathematical giftedness a discovery or a creation?

    • What theoretical frameworks and methodologies are helpful in identifying, creating, valuing, and educating mathematically gifted students in different contexts/societies?

Answers to these questions were offered by the presenters of the following papers: Distinguishing Between Gifted and High Achievers at University Level (authors: Florence Mihaela Singer, Cristian Voica, Ildiko Pelczer); Characteristics of Mathematical Giftedness: Learning from Extraordinary Minds (author: Carmel Diezmann); Characteristics of Mathematical Giftedness in Early Primary School Age (author: Daniela Assmus), as well as by Matthias Brandl, as chair of the session.

Discussions during this session included differing definitions of mathematical giftedness and frequently used terms such as mathematically promising, talented, high-achieving, high ability, and precocious as well as questions of nature vs. nurture. Differing answers to these questions often influence how gifted students are identified and served.

  1. 2.

    Mathematical Promise in Students of Various Ages. This session addressed questions such as:

    • What does recent research in cognitive science and neuroscience bring to understanding the development of mathematical talent and innovation?

    • In what ways are cognitive, social, and affective aspects connected in gifted students?

    • What are the differences between novices and experts?

    • How are mathematical creativity and giftedness connected?

    • What are new research paths?

Answers to these questions were offered by the presenters of the following papers: Using Discourse Theory to Analyze Mathematical Giftedness within the South African Education System (author Michael Mhlolo); Analysis of the Cognitive Demand of a Gifted Student’s Strategies to Solve Geometric Patterns Problems (authors: Clara Benedicto, Eva Arbona, Adela Jaime, Angel Gutierrez); Mathematical Problem Solving Techniques Employed by Gifted Students (author: Andreas Poulos); Pathways and Dead Ends in the Kingdom of Numbers: Problem Solving Strategies Used by Students in Mathematical Olympiad (authors: Ingrida Veilande, Liga Ramana, Sandra Krauze), in collaboration with Florence Mihaela Singer, who chaired this session.

One common theme in this session was an emphasis on the problem solving techniques and strategies used by mathematically promising students. Discussions included whether these were innate or teachable as well as their prevalence in students of all ages and from all socio-economic backgrounds.

  1. 3.

    Pedagogy and Programs. Moving towards more pragmatic approaches, the questions that drove the discussions were:

    • How could teaching best encourage and promote mathematical talents?

    • How might classroom interactions and discourse contribute to the development of mathematical reasoning?

    • What teaching strategies, curricula, technology, or other in- and out- of school activities might lead students to discover and realize their mathematical promise and talents?

    • How is high-level mathematical innovation developed?

Answers to these questions were offered by the presenters of the following papers: Instructional Models and Pedagogical Tools to Encourage and Promote Mathematical Talents (author: Ban Har Yeap); Fostering Talent in Mathematics—a German Perspective (author: Stephanie Schiemann); Developing Deductive and Spatial Reasoning with Language-independent Logic Puzzles (author: Jeffrey J. Wanko); Enrichment for the Gifted: Generalizing Some Geometrical Theorems & Objects (author: Michael de Villiers) and by Linda Sheffield, who chaired the session.

Speakers noted that it was important to offer opportunities during the school day as well as extracurricular activities to support and develop mathematical expertise. Several noted the importance of students’ collaboration and active involvement in recognizing patterns and constructing their own rules and generalizations to both solve and pose mathematical tasks and problems, with an emphasis on creativity, innovation, depth and complexity rather than speed.

  1. 4.

    Teacher Education. This session was focused on the following set of questions:

    • What types of mathematics and pedagogy are suitable for educating pre-service and in-service teachers for the gifted?

    • How should lessons/units planning be structured in order to address special needs of gifted?

    • What types of assessment are most effective for identifying, challenging and nurturing mathematical giftedness and innovation?

    • What types of local, regional, national or international co-operation between researchers and educators should be emphasized for the promotion of mathematical talent and giftedness?

Answers to these questions were offered by the presenters of the following papers: Gifted Students’ Expectations and Teachers’ Conceptions of Effective Mathematics Teaching (author: Roza Leikin); A Cross-country Comparison of Professional Development Programs on Mathematical Promise and Talent (Elisabet Mellroth, Ralf Benölken); Examining Ireland’s New Second-level Mathematics Syllabus and How it Caters for the High Achiever (author: Aidan Fitzsimons, Eabhnat Ni Fhloinn); Addressing the Needs of Gifted Students: Opportunities for Students, Teachers and Researchers (authors: Hiroko Kawaguchi Warshauer, Max Leon Warshauer, Christina Starkey, Terence McCabe, Christina Zunker), with the contribution of Viktor Freiman, the session’s chair.

Pre-service and in-service programs for teachers of mathematically gifted students should be linked to research on best practices for developing mathematical talent and passion. Several presenters noted the importance of teachers themselves persisting in a struggle to solve and pose problems with multiple entry points and multiple methods of solution in a respectful, inspiring, demanding, and joyful atmosphere where it is safe to fail, in order to understand how best to structure similar opportunities for their students. The need for familiarity with resources such as opportunities for students’ mathematical competitions, camps, circles, mentors, etc. and sources of rich mathematical tasks and samples of exemplary student work were also cited.

A variety of topics related to the TSG activities were also covered by the short oral communications and posters, among which were the analysis of existing theories in the field of mathematical giftedness; characteristics of motivational factors of mathematically promising students; and metacognitive competencies of mathematically gifted students. Aspects related to the development of mathematical giftedness including identification in primary and secondary school, teachers’ characterization of high achieving students in mathematics, and strategies to enhance the teaching of gifted children were other topics addressed during the poster and short oral communications sessions. In addition, several researchers studied features of solving problems by gifted students, and the nature of tasks and enrichment techniques to address the needs of gifted students.

In order to continue to build on the progress made during the TSG, participants were encouraged to join the International Group for Mathematical Creativity and Giftedness (MCG, www.igmcg.org), an International Study Group Affiliated to the International Commission on Mathematical Instruction (ICMI). MCG is free to join and holds biennial conferences in different locations around the world as well as offering a variety of resources such as periodic newsletters and other links to information on current research, problems, and activities related to mathematical creativity and giftedness.