Lists some ways that sequences were incorporated into mathematics lessons and explains a teacher's observations about the caliber of thinking and questioning that students develop as they learn appropriate ways to use numbers. Provides a number of questions that have been raised by students and the thinking prompted by a discussion of those…

Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)

Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)

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)

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

This preliminary study examined the meanings, models, and strategies of rural students in grades 3-8 for solving simple, whole number division problems. Findings suggested that students have multiple meanings for division words such as "share" and "fair share." Cultural factors and diversity in the classroom may be associated…

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)

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

This paper discusses the central thesis that new research on estimation and mental computation will benefit from more focused attention on the situations in which they are used. In the first section of the paper, a brief discussion of cognitive theory, with special attention to the emerging notion of situated cognition is presented. Three sources…

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…