Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving…

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual…

Adults overestimate the detail and depth of their explanatory knowledge, but through providing explanations they recognize their initial illusion of understanding. By contrast, they are much more accurate in making self-assessments for other kinds of knowledge, such as for procedures, narratives, and facts. Two studies examined this "illusion of…