Connecting the dots: children's use of a systematic figure to facilitate mapping and search.

Organizing locations into a systematic figure was predicted to facilitate children's use of spatial relations in a mapping task. In Study 1, 3-, 4-, and 5-year-olds used a map to find a sticker hidden under 1 of 27 locations. The search locations formed a systematic figure, the outline of a dog. Half of the children were shown that the locations formed a dog. Seeing the dog pattern facilitated the performance of 5-year-olds but not that of the younger children. Study 2 indicated that children had to see a systematic figure to gain an advantage; adding lines to an unsystematic figure did not convey an advantage. Study 3 indicated that a verbal label alone could not convey an advantage. Study 4 revealed that seeing the dog pattern could also facilitate performance when the map was rotated relative to the represented space. The importance of organizing spatial information to facilitate relational thinking and mapping is discussed.

The initial segment strategy: a heuristic for route selection.

People often choose one route when traveling from point A to point B and a different route when traveling from point B to point A. To explain these route asymmetries, we propose that people rely on a heuristic (the initial segment strategy, or ISS) during route planning. This heuristic involves basing decisions disproportionately on the straightness of the initial segments of the routes. Asymmetries arise because the characteristics that favor selection of a particular route in one direction will usually differ from those that favor selection when traveling in the opposite direction. Results from five experiments supported these claims. In the first three experiments, we found that subjects' decisions were asymmetric and involved a preference for initially straight routes. In Experiment 4, we confirmed that the ISS is a heuristic by demonstrating that people rely on it more when under time pressure. However, people can choose the optimal route when instructed to do so. In Experiment 5, we generalized the findings by having subjects select routes on maps of college campuses. Taken together, the results indicate that the ISS can account for asymmetries in route choices on both real and artificial maps.

Beliefs about genetic influences on mathematics achievement: a cross-cultural comparison.

The poor mathematics performance of children in the United States has become a topic of national concern. Numerous studies have shown that American children consistently perform worse than their counterparts in many parts of the world. In contrast, children in China, Japan, Taiwan, and other Asian countries consistently perform at or near the top in international comparisons. This paper examines possible causes of the poor performance of American children and the excellent performance of Asian children. Contrary to the beliefs of many Americans, the East Asian advantage in mathematics is probably not due to a genetically-based advantage in mathematics. Instead, differences in beliefs about the role of genetics may be partly responsible. Asians strongly believe that effort plays a key role in determining a child's level of achievement, whereas Americans believe that innate ability is most important. In addition, despite the relatively poor performance of their children, American parents are substantially more satisfied with their children's performance than Asian parents. The American emphasis on the role of innate ability may have several consequences for children's achievement. For example, it may lead children to fear making errors and to expend less effort on mathematics than their Asian counterparts. As research on genetic influences on behavior, traits, and abilities increases scientists should be careful to ensure that the public understands that genetics does not directly determine the exact level of a child's potential achievement.

Angles and distances: children's and adults' reconstruction and scaling of spatial configurations.

Young children have performed poorly in spatial tasks that require the scaling and reconstruction of a configuration. The present research investigated whether or not children's reconstructions nevertheless preserved the relative positions of objects within the configuration. In Experiment 1, preschoolers (ages 4 and 5), young elementary school children (ages 6 and 7), and adults were asked to reconstruct symmetric configurations of six objects that were depicted on simple maps of an empty room. Most subjects preserved the overall configuration of objects, but preschoolers placed the objects far from the correct locations. Many of the preschoolers' reconstructions contained systematic transformations; many reconstructions were off-center and too small or too large. In Experiment 2, the configurations were asymmetric, and preschoolers performed substantially worse than in Experiment 1. Experiment 3 demonstrated that preschoolers could reconstruct the asymmetric configurations when scaling was not required. Taken together, the results reveal that even young children can represent and transform an entire configuration of objects. At the same time, the results reveal important developmental differences.

Beliefs and achievement: a study of black, white, and Hispanic children.

School achievement among black, white, and Hispanic elementary school children was investigated, and efforts were made to study the beliefs about academic achievement of the children and their mothers. A total of approximately 3,000 first, third, and fifth graders enrolled in 20 schools in the Chicago metropolitan area were given achievement tests in mathematics and reading. Black and Hispanic children performed at a significantly lower level than white children, but at fifth grade ethnic differences in mathematics scores were no longer significant when mothers' education was statistically controlled. This was not the case in reading, where differences were found after controlling for the effects of mothers' education. Interviews with subsamples of approximately 1,000 mothers and children revealed greater emphasis on and concern about education among minority families than among white families. Black and Hispanic children and mothers evaluated the children and their academic abilities highly; they were positive about education and held high expectations about the children's future prospects for education. Mothers of minority children and teachers in minority schools believed more strongly than white mothers and teachers in the value of homework, competency testing, and a longer school day as means of improving children's education.