For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

The relationship between a cognitive style variable, field-dependence-independence, and instructional treatments that differed in two dimensions of discovery learning, level of guidance and level of abstraction, was investigated with 116 prospective elementary teachers. As predicted, field-independent students did better with minimum guidance,…

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…