This open access Topical Survey offers a brief overview of the current
state of research on and activities for mathematically gifted students
around the world. This is of interest to a broad readership, including
educational researchers, research mathematicians, mathematics teachers,
teacher educators, curriculum designers, doctoral students, and other
stakeholders. It first discusses research concerning the nature of
mathematical giftedness, including theoretical frameworks and
methodologies that are helpful in identifying and/or creating
mathematically gifted students, which is described in this section. It
also focuses on research on and the development of mathematical talent
and innovation in students, including connections between cognitive,
social and affective aspects of mathematically gifted students.
Exemplary teaching and learning practices, curricula and a variety of
programs that contribute to the development of mathematical talent,
gifts, and passion are described as well as the pedagogy and mathematics
content suitable for educating pre-service and in-service teachers of
mathematically gifted students. The final section provides a brief
summary of the paper along with suggestions for the research,
activities, and resources that should be available to support
mathematically gifted students and their teachers, parents, and other
stakeholders.