Weaving Mathematical Connections from Counting to Calculus: Knowledge Clusters and The Quantile® Framework for Mathematics

“Swiss cheese mathematics.” This metaphor aptly describes some students’ cognitive mathematical landscapes. When students miss connections among mathematical ideas, they may seem to have some substantive grasp and intuition on a topic at hand, yet they may still have major holes in their knowledge which prevent mastery of interrelated concepts. Those holes become limitations to the development of further mathematical knowledge.