This study describes the implementation and effects of a 32-week teacher-led spatial reasoning intervention in K-2 classrooms. The intervention targeted spatial visualization skills as an integrated feature of regular mathematics instruction. Compared to an active control group, children in the spatial intervention demonstrated gains in spatial…

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 of…

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…

Children's estimation patterns on a number line estimation task may provide information about the mental representation of the magnitude of numbers. Siegler and his colleagues concluded that children's mental representations shift from a logarithmic-ruler representation to a linear-ruler representation. However, there are important methodological…

Reasoning about mechanisms is one of the hallmarks of disciplined inquiry in science and engineering, but comparatively little is known about its precursors and development. Children at grades 2 and 5 predicted and explained the motion of simple mechanical systems composed entirely of visible linkages (levers). Students' explanations of device…

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.…

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 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…

The aim of the study was to analyze the development of children's adaptive expertise in computing sums and differences up to 100. We defined the adaptive nature of children's strategy choices on the basis of problem (addition, subtraction), achievement, and strategy performance (accuracy, speed). Sixty-nine 2nd graders of high, above-average, or…

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…

Simple arithmetic word problems are often featured in elementary school education. One type of problem, "compare with unknown reference set," ranks among the most difficult to solve. Differences in item difficulty for compare problems with unknown reference set are observed depending on the direction of the relational statement (more than vs. less…

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…

The study examined children's understanding of scientific inquiry, through the lens of their conceptualization of uncertainty in investigations they had designed and implemented with a partner. These largely student-regulated investigations followed a unit about animal behavior that emphasized the scaffolding of independent inquiry. Participants…