The purposes of this study were (1) to determine the difference between the cognitive style of low and high achieving students in an algebra course in a traditional high school and the cognitive style of low and high achieving students in an algebra course in a high school for dropouts, and (2) to determine the difference between the cognitive styles of low and high achieving males and females in an algebra class in a traditional high school and in a high school for dropouts. It was hypothesized that (1) low achieving mathematics students are more field-dependent than high achieving mathematics students in both the traditional high school and in the high school for dropouts, (2) female students are more field-dependent than male students in the mathematics classes of both schools, and (3) there will be a significant interaction on the achievement variable and the sex variable with respect to field-dependence in both schools.

The problem of this study was to discover the relationship between field-independent and field-dependent cognitive styles and social behaviors during free-play of preschool children in a school setting. This study also compared the field-independent and field-dependent cognitive styles and social behaviors during free-play between age-groups and sex-groups. Thirty-six children from a university child development laboratory were subjects. They were selected from a 3-year-old classroom and a 4-year-old classroom. The research instrument, the Preschool Embedded Figures Test, was utilized to measure field-independent and field-dependent cognitive styles. The children's social behaviors were observed during free-play for four consecutive weeks. The nine categories of social behavior were solitary, parallel, and group play; .unoccupied, onlooker, transitional, and aggressive behaviors; and conversations with teachers and conversations with peers. Correlations between field-independent and field-dependent cognitive styles and social behaviors indicated that field-independence/field-dependence was related to social orientations in preschool children and also related to the choice of play activity. Field-dependent children tended to engage in conversations with teachers more often than field-independent children. Four-year-old children who were field-independent tended to spend more time in solitary play than 4-year-old children who were field-dependent. Four-year-old boys who were field-independent tended to play more often in the manipulative learning center than 4-year-old boys who were field-dependent. There were significant differences between age-groups but not significant differences between sex-groups in field-independence/field-dependence. Some social behaviors were significantly different between age-groups and sex-groups. Three-year-old children participated significantly more in physically aggressive behavior and less in conversations with peers than 4-year-old children. Boys engaged significantly more in aggressive behavior than girls.