Language researchers have identified a number of elements related to language performance. One of these factors is individual attributes of the language learners or their cognitive ability. In the fall semester 2015, 18 undergraduates of Greek for academic purposes language course of a public university in Cyprus participated in the study. This research work attempts to investigate the relationship between students' Field Dependence-Independence (FDI) cognitive ability and learning strategies within a Computer-Assisted Language Learning (CALL) environment. Students FDI cognitive style was measured on their performance on the Hidden Figures Test (HFT) psychometric tool and classified into Field- Dependent (FD), Field-Mixed or Neutral (FM/FN), and Field-Independent (FI) learners. Statistics and mainly qualitative analyses were used to interpret the data. With the end goal of understanding how learners' FDI cognitive ability intersects in learning within a CALL environment, the article concludes with some directions for further areas of research. [For the complete volume of short papers, see ED572005.]