Infants and toddlers experience the world in interaction with others. Likewise, social interactions are important in learning about math--concepts of number ("one," "two," "three"), space ("on top," "upside-down," "round"), and magnitude ("more," "big,"…

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

In an age of scientific method much of any individual's thinking is quantitative. He lives in a world in which every situation involves concepts of quantity, amount, size, or number. He employs number language, that is, number names and signs to express his quantitative ideas. These various number names and signs constitute the medium for his…