Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

Five- to six-year-old children estimated the size of Euclidian objects using an addition rule of Height plus Width, rather than a multiplying rule. Within the framework of information integration theory, tested whether intensive handling of objects would facilitate shift from addition rule to multiplication rule. Found that following handling,…