This research focused on preservice elementary teachers' understanding and reconstruction of understanding about multiplication in the domain of fractions. At the start of the study, 44% of the 50 preservice teachers studied reported that they had a method for reasoning about multiplication with fractions, and 28% were able to describe a situation modeled by multiplication with a fraction operator. Although reasoning individually, the preservice teachers revealed common dimensions of understanding--about taking fractional parts of non-unit wholes and about numerical effects, referents for results, and the invariance of multiplication--as they reconceputalized multiplication with fractions. "Sense" of multiplication and "sense" of fraction relationships were forms of reasoning that supported the re-conceptualization process. (Author/MKR)