We tested whether analogical training could help children learn a key principle of elementary engineering—namely, the use of a diagonal brace to stabilize a structure. The context for this learning was a construction activity at the Chicago Children's Museum, in which children and their families build a model skyscraper together. The results indicate that even a single brief analogical comparison can confer insight. The results also reveal conditions that support analogical learning.

We examined the effects of three different training conditions, all of which involve the motor system, on kindergarteners’ mental transformation skill. We focused on three main questions. First, we asked whether training that involves making a motor movement that is relevant to the mental transformation—either concretely through action or more abstractly through gestural movements that represent the action —resulted in greater gains than training using motor movements irrelevant to the mental transformation. We tested children prior to training, immediately after training, (...) and 1 week after training, and we found greater improvement in mental transformation skill in both the action and move-gesture training conditions than in the point-gesture condition, at both posttest and retest. Second, we asked whether the total gain made by retest differed depending on the abstractness of the movement-relevant training, and we found that it did not. Finally, we asked whether the time course of improvement differed for the two movement-relevant conditions, and we found that it did—gains in the action condition were realized immediately at posttest, with no further gains at retest; gains in the move-gesture condition were realized throughout, with comparable gains from pretest-to-posttest and from posttest-to-retest. Training that involves movement, whether concrete or abstract, can thus benefit children's mental transformation skill. However, the benefits unfold differently over time—the benefits of concrete training unfold immediately after training ; the benefits of more abstract training unfold in equal steps immediately after training and during the intervening week with no additional training. These findings have implications for the kinds of instruction that can best support spatial learning. (shrink)

In this article, we review approaches to modeling a connection between spatial and mathematical thinking across development. We critically evaluate the strengths and weaknesses of factor analyses, meta-analyses, and experimental literatures. We examine those studies that set out to describe the nature and number of spatial and mathematical skills and specific connections between these abilities, especially those that included children as participants. We also find evidence of strong spatial-mathematical connections and transfer from spatial interventions to mathematical understanding. Finally, we map (...) out the kinds of studies that could enhance our understanding of the mechanisms by which spatial and mathematical processing are connected and the principles by which mathematical outcomes could be enhanced through spatial training in educational settings. (shrink)

Thomas & Karmiloff- Smith show that the assumption of residual normality does not hold in connectionist simulations, and argue that RN has been inappropriately applied to childhood disorders. We agree. However, we suggest that the RN hypothesis may never have been fully viable, either empirically or computationally.

The proposal of Rips et al. is motivated by discontinuity and input claims. The discontinuity claim is that no continuity exists between early (nonverbal) numerical representations and natural number. The input claim is that particular experiences (e.g., cardinality-related talk and object-based activities) do not aid in natural number construction. We discuss reasons to doubt both claims in their strongest forms.