Digital inequality has been intensively studied in recent decades, due to the considerable social significance of this phenomenon. Research has struggled with finding quality and profound ways to measure digital literacy of people from different social groups, due to the dynamic character of digital technology, which results in ever-changing, nuanced types of digital inequality. This study proposes an innovative method for examining how users approach and accomplish digital tasks by introducing eye tracking for measuring user scan patterns, gaze and attention during completion of tasks. Eye tracking as a measurement of attention and focus reflects the processes that occur while users are performing required tasks, and therefore may be a useful tool to comprehend digital literacy. We apply this innovative methodology in a repeated measures observation study of digital skills of low-skilled participants in a computer introductory course. 19 participants were requested to perform several online tasks before and after completing the course. The paper describes the results, which demonstrate that although participants' skills have improved, the improvement is manifest in basic, trivial uses, while advance uses, such as understanding of efficient searching, or using the Internet in sophisticated ways as an environmental resource supporting one's situational awareness, are only slightly improved, as data based on tracking user gaze and mouse movements reveals.