Real Engagement in Active Problem Solving (REAPS) is an evidence-based model for building on and extending the characteristics of gifted learners, enabling them to develop their exceptional talents. The purposes of this study were to (a) identify teachers who implemented the method at a high level of fidelity and (b) describe their ways of…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…