Data from 82 teachers and 1,021 parents and students in their classrooms were used to explore the correlates of homework activities and the effects of homework on elementary school students' achievements and behaviors in school. Six groups of variables that concern homework were examined: homework time; homework appropriateness; student attitudes; teacher practices regarding parent involvement in learning activities at home; parent abilities and resources; and other student and family background variables. Although findings seemed to be counterintuitive, they indicated that at the elementary school level, low achievement in reading and mathematics, in comparison with high achievement, is associated with more time spent doing homework, more minutes of parent help, and more frequent requests from teachers for parent involvement. Thus the findings serve as a good example of the inadequacy of correlations to address questions of effects on students. Questions are raised about ways in which elementary school homework can be designed, with parents' help, to prepare students for the skills needed in the upper grades. (RH)