Understanding, Mathematics, and Scientific Education

The purpose of this paper is to state what the author believes is a good way to develop the powers of understanding of talented college science students. After making a careful and somewhat novel distinction between knowledge and understanding, the paper closely defines the main problem in terms of the new interpretation of "understanding." A short discussion follows which concludes that what is needed is more and better schooling in the central ideas of mathematics. At this point, the tenor of the paper is changed and a semipopular discussion is given on the fundamental type of mathematics the author has in mind. Finally, a proposal is made which is general enough to be adapted to a wide variety of situations.     

Psychological consequences of child maltreatment in homeless adolescents: untangling the unique effects of maltreatment and family environment

OBJECTIVE: This study examined the differential effects of various forms of abuse, as well as their combined effects. The study also sought to separate the factors uniquely associated with abuse from those associated with the more general problems present in an abusive family environment. METHODOLOGY: Data were collected from 329 homeless adolescents. Preliminary analyses indicated some degree of matching for family background variables. Any differences in demographic or family characteristics were controlled for statistically. RESULTS: Chi-square analyses revealed significant differences across groups for rates of assault, rape, depression/dysthymia, and attempted suicide. Multivariate analyses (MANOVAs) indicated significant differences in severity of internalizing problems and cognitive problems. Without exception, the group with histories of both physical and sexual abuse exhibited the most severe symptomatology and was at greatest risk for revictimization. Multiple regression analyses suggested that abuse histories were predictive of internalizing problems while family characteristics were more predictive of externalizing problems. CONCLUSIONS: The findings indicate that both abuse type and family characteristics contribute to the development of symptomatology. Future prospective and longitudinal studies are needed to clarify the sequelae of abuse, as well as the possible cause and effect relations between abuse, family characteristics, and psychological outcome.     

A secure base in adolescence: markers of attachment security in the mother-adolescent relationship

This study sought to identify ways in which adolescent attachment security, as assessed via the Adult Attachment Interview, is manifest in qualities of the secure base provided by the mother-adolescent relationship. Assessments included data coded from mother-adolescent interactions, test-based data, and adolescent self-reports obtained from an ethnically and socioeconomically diverse sample of moderately at-risk 9th and 10th graders. This study found several robust markers of adolescent attachment security in the mother-adolescent relationship. Each of these markers was found to contribute unique variance to explaining adolescent security, and in combination, they accounted for as much as 40% of the raw variance in adolescent security. These findings suggest that security is closely connected to the workings of the mother-adolescent relationship via a secure-base phenomenon, in which the teen can explore independence in thought and speech from the secure base of a maternal relationship characterized by maternal attunement to the adolescent and maternal supportiveness.