ive reasoning and problem solving is error-prone. One such pattern is manifested in that people err more often when problems are indeterminate than when problems are determinate W e suggest that an incomplete problem representation could account for the observed pattern of errors. W e further contend that in verbal reasoning such incomplete representation stems from a lack of systematic representations of connectives (e.g., and, or, if, etc.), and, therefore, extemalization of relations denoted by sentential connectives should improve people's representations of multiple possibilities. These predictions were tested in three reported experiments. Results indicate that determinate problems were easier to represent and recall than indeterminate problems. Furthermore, there was a tendency to represent and recall indeterminate problems as if they were determinate ones by fruncating the number of possibilities compatible with the problem. Finally, external aids dramatically improved representation and recall of indeterminate problems. These results are discussed in relation to theories of representation and reasoning.

Although an understanding of fractions is a critical precursorfor other mathematical concepts, including proportionalreasoning, algebra, and success in STEM fields, surveys ofmathematics education in the United States indicate thatschool-age children lack age-appropriate math skills andproficiency. Thus, understanding the critical precursors offraction knowledge is important for the development ofinstructional materials. The aim of the present study was toexamine whether instructional format affected children’slearning and transfer of fraction concepts, and whetherindividual variables such as executive function and mathknowledge moderated these effects. Six- to 8-year-oldchildren participated in a longitudinal, pre/post test design, inwhich they received a fraction-training intervention.Critically, we manipulated the extent to which real-worldinstruction was grounded in visual vs. symbolicrepresentations. We find that 1 st and 2 nd graders were able tolearn fraction concepts following this intervention, despitehaving no formal fraction education. The extent to which theinstructional stimuli were grounded in visual vs. symbolicrepresentations affected children’s proportional reasoningknowledge in a transfer task, and condition effects weremoderated my children’s working memory and prior mathknowledge. This work has implications for instructionaldesign and curriculum development in the classroom.

The overlap of numerical and non-numerical properties in concrete object arrays raises the question of how these input dimensions interact. Two studies were conducted to address this question and showed that changing the object identity (while retaining the numerosity) and changing the numerosity (while retaining the object identity) both resulted in attenuated recognition of object arrays. However, this interference differed across development. In adults interference was asymmetrical (i.e. changing the object identity has greater effect on memory for numerosity than changed numerosity had on object identity). In contrast, children showed a symmetrical pattern of interference. These results imply that for adults, processing numerosity might be an attention-demanding process compared to a spontaneous object perception. Children, however, processed neither the object identity nor numerosity independently.

Categorization, the process of grouping distinguishable entities into equivalence classes, is an essential component of human cognition. Although it has been often argued that selective attention is an important component of categorization, organism with immature selective attention (such as human infants or young children) exhibit the ability to learn categories. This research addresses this apparent paradox by examining attention allocation in the course of category learning across development. Results suggest that while some young children are able to attend selectively, adults more flexibly deploy selective attention according to task demands.

Categories are essential for thinking, learning, and communi-cating. Research has shown that young children and adultstreat categories very differently, with young children favor-ing whole objects while adults focus on the key informationin most cases. If so, then how can young children learn cat-egories requiring focused attention to key features? Studieshave shown that drawing attention to rules had facilitative ef-fects. We sought to identify whether the effect was driven byinstruction about rules or by stimulus-driven factors. Our re-sults suggest that even with instruction, 4-year-olds were notable to attend to key information. Simply making importantinformation more salient, however, allowed them to learn thecategory and transfer to situations when the key feature wasno longer salient.