While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young children's tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development…

Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students' difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the…

Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model predicts…

This study investigates children's metarepresentational competence with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2003) work on metarepresentational competence in mathematics and sciences as theoretical and empirical background, it aims to assess children's criteria for representational adequacy of graphical…

This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…

This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level.…

In a 3-year longitudinal, mixed-method study, 67 children in two schools were observed during literacy activities in Grades 1-3. Children and their teachers were interviewed each year about the children's motivation to read and write. Taking a grounded theory approach, content analysis of the child interview protocols identified the motivations…

This study was designed to identify the types of understandings, skills, and beliefs that affect pre-service teachers' evaluations of students' mathematical arguments in classroom contexts. Thirty-four pre-service teachers read a transcript of a third grade lesson in which the students were expected to prove a generalization. To investigate…

This study provided 5 weeks of direct strategy instruction about narrative elements and relations in 4 first-grade classrooms (n = 83), all with materials that made minimal decoding demands on children's reading. Two comparison classrooms (n = 40) received comparable instruction on language development and poetry. A battery of assessments given at…

In this article I detail the conceptual trajectory of a classroom of 2nd- and 3rd-grade students as they reinvent topographical lines to represent height in a map within the constraints of an overhead perspective. In my analysis I pay special attention to the role of social interaction--and in particular the role of the teacher--in the process of…

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…