Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three…

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…

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…

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…

Looking away from an interlocutor's face during demanding cognitive activity can help adults and children answer challenging mental arithmetic and verbal-reasoning questions (Glenberg, Schroeder, & Robertson, 1998; Phelps, Doherty-Sneddon, & Warnock, 2006). While such "gaze aversion" (GA) is used far less by 5-year-old school children, its use…

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…

The nature and evolution of intertextuality was studied in 2 urban primary-grade classrooms, focusing on read-alouds of an integrated science-literacy unit. The study provides evidence that both debunks deficit theories for urban children by highlighting funds of knowledge that these children bring to the classroom and the sense they make of them…