ENHANCING THE QUALITY of mathematics learning is important to educators. Consider the nature of the learning tasks and teaching practices.

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.

Keller describes the relevance strategies with the following terms: 

Solving challenging problems enhances motivation and develops appropriate dispositions to learning and achievement. Thus incorporating Keller's second and third strategies- Present Worth and Future Usefulness.
Keller's Needs Matching has particular value for "future Mathematicians." The most important part of the work is to look back at the completed solution. Students may meditate upon the difficulty of the problem. He/she may try to see what hampered him/her and what helped. He/she may compare and develop various methods. Digesting the problems he/she solved as completely as he/she can. He/she may acquire well ordered knowledge ready to use. These task lead to build upon the remaining strategies Modeling and Choice. 

 Patricia Brown
Graduate Student
SDSU Educational Technology