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.

"The best source I have seen challenging mathematically talented students. The activities are thought provoking and enjoyable. I will recommend this book to parents as well as educators of mathematically talented students!"
Sally Reis
Past President of The National Association for Gifted Children

Combining theory and practice, Sheffield expertly guides the reader through the process of mathematical talent development from identifying students with mathematical potential, to finding and creating first-rate problems for exploration and strategies for assessment.

The multi-level investigations in this book are designed to challenge students and inspire deeper and more original mathematical thinking in Number and Operations, Algebra, Geometry and Measurement, and Data Analysis and Probability.

Each investigation is developed in the following easy-to-follow format:

Relate?sets the stage for the investigation by connecting it to prior learning and the NCTM Principles and Standards

Investigate?poses the initial problem to start students thinking about the investigation

Evaluate and Communicate?provides solutions, probing assessment questions, and suggestions for teacher responses

Create?offers ideas for extending and deepening the investigation, allowing even the most accomplished students to add depth and complexity to their reasoning

Discussion?gives teachers hints on what to look for in student solutions, as well as ideas for encouraging students to dig more deeply into the mathematical concepts that are presented

Mathematically promising students have the potential to become the leaders and problem solvers of the future. Extending the Challenge in Mathematics provides the practical tips and tools educators need to help their students develop this potential to the fullest.