There is a crucial debate concerning the nature of chess chunks: One current possibility states that chunks are built by encoding particular combinations of pieces-on-squares (POSs), and that chunks are formed mostly by "close" pieces (in a "Euclidean" sense). A complementary hypothesis is that chunks are encoded by abstract,…

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…