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Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N= 52) saw combinations of cherry juice and water in displays that highlighted either part–whole or part–part relations. Their task was to indicate on a continuous rating scale how much each mixture would taste of cherries. Ratings suggested the use of a proportional integration rule for both kinds of displays, although more robustly and accurately for part–whole displays. The findings indicate that children may be more likely to scale proportional components when being presented with part–whole as compared with part–part displays. Crucially, ratings for part–whole problems correlated with fraction knowledge, even after controlling for age, suggesting that a sense of spatial proportions is associated with an understanding of fractional quantities. [ABSTRACT FROM PUBLISHER]

How do toddlers learn the names of geometric forms? Previous work suggests that preschoolers have fragmentary knowledge and that defining properties are not understood until well into elementary school. The current study investigated when children first begin to understand shape names and how they apply those labels to unusual instances. We tested 25- and 30-month-old children’s (N= 30 each) understanding of names forcanonicalshapes (commonly encountered instances, e.g., equilateral triangles),noncanonicalshapes (more irregular instances, e.g., scalene triangles), andembeddedshapes (shapes within a larger picture, e.g., triangular slices of pizza). At 25 months, children knew very few names, including those for canonical shapes. By 30 months, however, children had acquired more shape names and were beginning to apply them to some of the less typical instances of the shapes. Possible mechanisms driving this initial development of shape knowledge and implications of that development for school readiness are explored. [ABSTRACT FROM PUBLISHER]