Systematic and Sustained: Powerful Approaches for Enhancing Deep Mathematical Thinking

Developing appropriate curriculum to challenge gifted students can be difficult, whether in a mixed-ability classroom or in a self-contained gifted classroom. Four potential ways that a curriculum can be modified for gifted students have been suggested: (1) acceleration; (2) enrichment; (3) sophistication; and (4) novelty. This article proposes several specific strategies that take two typical approaches for gifted students--enrichment and novelty--and transforms those experiences into a highly sophisticated approach that may more strongly enhance students' abilities for deep mathematical thinking. Two features of the proposed sophisticated curricular experiences are that students engage with systematic and sustained experiences. This article employs a strategy that will be one of those recommended for use with students to enhance the characteristics of "systematic and sustained." A few particular examples are selected for presentation in some depth, from which larger pedagogical implications and impacts are discussed. These examples are chosen simply because they offer an opportunity to illustrate some of the more fundamental concepts being raised and not because they are inherently more useful or valuable than any number of other possible choices that might serve equally well. (Contains 3 tables and 4 figures.)