Consider the nature of the learning tasks and teaching practices. Research Research indicates that challenging tasks provide opportunities for students to develop mathematical power through high level thinking and reasoning. Challenging mathematical tasks for gifted students should be authentic tasks that provide opportunities for them to emulate the practices of mathematicians.
All learners require challenging tasks to facilitate deep learning and develop autonomy.
Students should engage in challenging tasks for three reasons related to cognition, metacognition, and motivation. Challenging tasks cater to preferences of mathematically gifted students for exploring patterns and relationships, producing holistic and lateral solutions, and for working abstractly. Even at the elementary level, students' capabilities and preferences for working abstractly should be accommodated. To view movie of example of students actively engaged in a mathematics activity, click on the start button of QuickTime movie. Thus incorporating Keller's second and third strategies- Present Worth and Future Usefulness.