This study's findings may have important implications for understanding how students learn in the classroom. Consonant with previous research, they indicate that both engagement in school and students' perception of their own academic competence influence achievement in mathematics for high school students. But the study departs from earlier work in suggesting that perceived academic competence may be more influential than engagement in boosting achievement in both mathematics and reading. Indeed, analyses indicate that perceived competence had a stronger influence on subsequent engagement than engagement had on students' perceptions of themselves as competent learners. The findings also make clear that supportive teachers and clear and high expectations about behavior are key to the development of both student engagement and perceived competence. This study suggests that the earlier schools and teachers begin to build students' confidence in their ability to do well, the better off students will be. Because students' perceptions of their capacity for success are key to their engagement in school and learning, schools should be designed to enhance students' feelings of accomplishment. Teachers whom students see as supportive and who set clear expectations about behavior help create an atmosphere in which students feel in control and confident about their ability to succeed in future educational endeavors. Appended is: Survey Items Used to Create Student Attitudes and Behavior Scales and School Context Scales. (Contains 8 tables and 7 figures.)