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The ability to perceive structures in sets and to use them to determine cardinality is one important basis for arithmetical learning. This study is based on a theoretical model that distinguishes between the two processes of perception and determination. A total of 95 5-year-old children were interviewed individually to find out whether and how children of this age perceive structures in a visually presented set and whether and how they use these structures to determine the cardinality of the set. To gain insights into the invisible process of perception, eye-tracking was used. Known structures, such as the pattern of a dice-four, seem to play a role in these processes. With the help of an analyzing process consisting of three different types of data, final interpretations were generated that suggest that 5-year-old children can already perceive structures and use them to determine cardinalities. There also seem to be children who are already aware of a structure, but cannot use it to determine the cardinality. This leads to the conclusion that perception and use of structures are possible elements for early mathematical education at this age.

Children’s perception of structures when determining cardinality of sets—results of an eye-tracking study with 5-year-old children