Students' understanding of the meaning of the equal sign develops slowly over the primary grades. In addition to updating their representations of equations to recognize that the equal sign represents an equivalence relation rather than signaling an operation, students need to move beyond full computation to efficiently solve equivalence problems.…

The principle of "inversion," that a + b - b "must" equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005). Hypothesis 1 is that…

In this study the authors investigated whether children demonstrated the "underconfidence-with-practice" (UWP) effect. This effect is a highly robust metacognitive illusion in which adults become underconfident in their memory performance when asked to predict their memory for the same items across multiple study-test trials. One…

Data collection can be the most time- and cost-intensive part of developmental research. This article describes some long-proposed but little-used research designs that have the potential to maximize data quality (reliability and validity) while minimizing research cost. In "planned missing data designs", missing data are used…

The present study examined whether younger and older children differ in the use of the goal-related information in a continuous performance task (AX-CPT), and if so, whether those age differences are due to the ability to represent and/or maintain goal information. Experiment 1 compared third- and sixth-grade children in their ability to transform…