Fractions and division are two topics that receive considerable attention in elementary school mathematics, particularly in grade three and beyond. Despite this attention, fraction and division concepts and skills prove difficult for many middle school students to learn and for teachers to teach. This paper reports on part of a larger study involving 387 middle school students with regard to their performance on an assessment focusing specifically on concepts and skills relating to division and fractions. The study sought to determine how middle school students conceptualize fractions and division. The study also examined to what extent middle school students can recognize, identify, and apply the concepts and skills that stem from the mathematical definition of a fraction found in James and James' Mathematics Dictionary. It concludes that in order to help students and teachers and to refocus mathematics education research and textbook presentations of fractions and division, there must be a new conceptualization that includes fractions and division and the connections between them. Evaluation instrument is appended. (Contains 23 references.) (ASK)