Introduction: Enhancing creative capacities in mathematically promising students. Challenges and Limits.- 1. Frameworks for Studying Mathematical Creativity and Giftedness.- Mathematical Creativity: Product, Process, Person and Press.- The Nature and Use of Theories on Giftedness in Mathematics Education Research: A Review on ICME Activities in the 21st Century.- High Talent and High Achievement in Mathematics - the Connection, the Difference and the Problems.- Mathematical Giftedness and Creativity in Primary Grades.- 2. Characteristics of Mathematically Gifted.- Characteristics of Mathematical Giftedness in Early Primary School Age.- Twice Exceptional Children - Mathematically Promising Children with Special Needs Marianne Nolte.- Mathematical Promise, Gender and Achievement Motivation. The Significance of Mathematical Self-Concept, Attributions and Interest in the Identification of Mathematically Promising Swedish Girls and Boys.- Cognitive Variety in Rich-Challenging Tasks.- 3. Teaching Strategies to Foster Creative Learning.- Encouraging Creativity in Heterogeneous Mathematics Classrooms.- Promoting Creativity with Procedural Tasks: Task Characteristics and Student Impact.- Flexibility of Pre-Services Teachers in Problem Posing in Different Environments.- A Gifted Student Learning Algebra by Means of Geometric Patterns Problems. Analysis of the Cognitive Demand.- 4. Tasks and Techniques to Enhance Creative Capacities.- About the Techniques of Gifted Students on Solving Challenging Mathematical Problems.- Repeated Participation at the Mathematical Olympiad: Does it Ensure the Students' Progress in the Use of Problem-Solving Strategies?.- Development and Implementation of Creativity-in-Progress Rubric on Proving.- Technology-rich Environments for Mathematically Gifted: What is an Add-On Value?.- Commentary paper.