Open Access

Dinah Reuter, Frank Reinhold

• Mathematical thinking involves recognizing patterns and structures, and students differ in how they perceive and interpret such regularities. In this study, we investigated the pattern recognition abilities of N  = 387 primary school students (grades 1 to 4). Building on Vitz and Todd’s (1967, 1969) item set for repeating patterns, we developed supplementary growing additive patterns and systematically varied complexity-inducing features such as stimuli with complete vs. incomplete basic units. We assessed pattern recognition using three measures: regular continuation in any pattern, structural completion in incomplete repeating patterns, and recognition of growth in complete growing patterns. As shown in previous studies, all three abilities improved with age. But it becomes apparent that more than 20% of fourth graders could not complete incomplete repeating patterns as intended, and over 60% failed to recognize additive growth structures. Beyond that, we found that recognition of growing structures followed a binary pattern: students either recognized the structure in both complete and incomplete stimuli or not at all. In contrast, continuing repeating patterns was notably more difficult when the pattern was incomplete. Regarding complexity-inducing features, we found that the number of different symbols in a pattern’s basic unit significantly impacted item difficulty, rather than the length of the unit or the frequency of those symbols. This challenges prior assumptions that unit length is the primary driver of complexity. Our findings highlight the need to differentiate between sources of item complexity, such as structural completeness and symbol variety and to assess distinct levels of pattern recognition.