As elementary students begin to program using tangible blocks, they must coordinate their use of counting with the movements, directions, and numbers they use to move a character. In our study, we analyzed 13 first graders' first attempts at coordinating these elements when playing a programming game on the iPad that used tangible programming…

This article examines prospective elementary teachers' conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. Student work samples and classroom conversations are used to illustrate the types of unitizing understandings that prospective teachers bring to teacher…

When to introduce negative integers to children is an important issue in school mathematics; delaying their introduction can lead to lasting misconceptions such as one cannot subtract a larger whole number from a smaller. Yet understanding negatives involves a complex extension of whole-number knowledge. It is not known whether this extension is…

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…

Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…

As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate…

In a recent study, Gevers and colleagues (2010, "Journal of Experimental Psychology: General," Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are…

This paper focuses on the kinds of notations young children make for fractional numbers. The extant literature in the area of fractional numbers acknowledges children's difficulties in conceptualizing fractional numbers. Some of the research suggests possibly delaying an introduction to conventional notations for algorithms and fractions until…

This study had two purposes: (a) to investigate the developmental relationship between students' uses of fractions notation and their understandings of part-whole relations; and (b) to produce an analysis of the role of fractions instruction in students' use of notation to represent parts of an area. Elementary students (n = 384) in 19 classes…