Recognizing patterns is an essential skill in early mathematics education. However, first graders often have difficulties with tasks such as extending patterns of the form ABCABC. Studies show that this pattern-recognition ability is a good predictor of later pre-algebraic skills and mathematical achievement in general, or the development of mathematical difficulties on the other hand. To be able to foster children's pattern-recognition ability, it is crucial to investigate and understand their pattern-recognition processes early on. However, only a few studies have investigated the processes used to recognize patterns and how these processes are adapted to different patterns. These studies used external observations or relied on children's self-reports, yet young students often lack the ability to properly report their strategies. This paper presents the results of an empirical study using eye-tracking technology to investigate the pattern-recognition processes of 22 first-grade students. In particular, we investigated students with and without the risk of developing mathematical difficulties. The analyses of the students' eye movements reveal that the students used four different processes to recognize patterns--a finding that refines knowledge about pattern-recognition processes from previous research. In addition, we found that for patterns with different units of repeat (i.e. ABABAB versus ABCABCABC), the pattern-recognition processes used differed significantly for students at risk of developing mathematical difficulties but not for students without such risk. Our study contributes to a better understanding of the pattern-recognition processes of first-grade students, laying the foundation for enhanced, targeted support, especially for students at risk of developing mathematical difficulties.