This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing meaning for the formal symbols used in mathematics. Therefore, the meaning that students attach to the fraction symbol and their ideas about the utility of fractions were assessed through a written pretest and individualized interviews. The relationships of the fraction concept to what had been experienced and learned in the past and students' perceptions of the value in using various representational models of fractions were explored for the fractions 1/2, 1/3, and 3/4. Subjects were 15 fourth-grade girls from a private school. Seven research questions are reviewed with reference to two students, identified as novices, and an expert fraction student. Findings are discussed for their definitions of fraction, utility of fractions, comparisons of fraction and whole number, syntax and semantics of the fraction symbol, models of fractions, metacognitions, and the relationship of standardized achievement to performance. Appendices contain a four-page reference list, the interview questions and questions and responses, pretest with data, and observed performance and judged ranks. (MNS)