We explored the cognitive structure of students in grade 1-grade 4 using word association in three topics (science, energy sources, and health) with six-six keywords (stimulus words) per topic. Based on the common associations given to the stimulus words, we calculated the relatedness coefficient for the stimulus word pairs. This was used to draw a cognitive structure, the conceptual network, characteristic of each group of learners. We found that the verbal version of the word association test is suitable for studying the cognitive structure of young schoolchildren. The typical conceptual network of the student groups shows a strong correlation with the knowledge structure of experts in grade 4 (in all three topics), as well as in grade 1 and grade 3 (in the topic of health). Using word association tests, we have been able to demonstrate that the number and strength of connections in the conceptual networks for groups of learners increases with the learners’ grade and their everyday experience of the topic.