The purpose of this study was to investigate whether anomalous cases of argumentation by gifted eighth-grade students enrolled in a Science and Art Center (SAC) affected their scientific creativity. Anomalies are exceptional situations that contradict theoretically established universal laws (Schulz, Goodman, Tenenbaum ve Jenkins, 2008). Argumentation is a model that is formed by systematizing claims arising from data and supported by justifications and parameters (Erduran, Simon ve Osborn, 2004). The participants in the study were 13 gifted eighth-grade students enrolled in a SAC. A one-group experimental design was used. As data collection instruments, “Scientific Creativity Question Form,” “Inventory-I for Views on Anomalous Cases” and “InventoryII for Views on Anomalous Cases” were utilized. For analyzing the quantitative data, the Wilcoxon Sign Test, graphics, and determinations of frequency, mean, and standard deviations were utilized. Finally, for the qualitative data, descriptive analysis profiling student answers in terms of Toulmin’s argument model was applied. The analysis showed that the students accepted all of the cases as anomalous for themselves at the beginning of the study. After application of the argument model, there was no statistically significant difference in pre- and posttest measurements of fluency and flexibility with regard to scientific creativity. There was, however, a statistically significant difference in pre- and posttest measurements of originality and elaboration in favor of the latter. In addition, students who experienced an effective argumentation process presented detailed and differing argumentation frames. In conclusion, effective argumentation processes of anomalous cases by gifted students increased their scientific creativity levels in terms of originality and elaboration.