A commonly accepted definition of online learning is that students have access to learning experiences in: time, place, pace, learning style, content, assessment, and pathways (Chen, 2003). Although this is true, there is a considerable concern about the level of abstraction involved in online education. Critics of flexible learning call it just…

This article reports on the use of a unique number system to facilitate teachers' understanding of the concepts of place value. Teachers' mastery of base-ten may hinder their recognition of the difficulties students have with place value, so the authors created a number system that used five symbols to represent values. Using this system, teachers…