ABSTRACT
The evidence is growing, however, from analyses of performance within the United States (US), as well as international comparisons of mathematical knowledge and performance, that deep understanding versus broad coverage, experiential learning versus drill and practice, elegance in addition to utility, and mathematics as a frame of mind for understanding the world versus an organized set of algorithms are among the underpinnings of success in the discipline and also generate defensible mathematical curricula. Contemporary rich mathematics curricula may not necessarily be an elite topic under suitable circumstances. The directions of contemporary thinking within the discipline reveal many similarities to curricular advice in gifted education. The Study of Mathematically Precocious Youth (SMPY) experience has shown that high achieving seventh- and eighth-grade students can learn the high school mathematics curriculum in a quarter to a third of the usual time.
