Only teachers who possess problem-solving skills can develop them in their students. These skills therefore need to be accentuated during teachers’ pre-service training. In this study, attention was given to pre-service chemistry teachers’ (students) problem-solving skills measured with the use of two sets of problem tasks–chemistry and general science tasks. Based on a pre-test consisting of both types of tasks, one successful, one partially successful and one unsuccessful solver was selected from a group of first-year bachelor chemistry teacher students. To compare, the tasks were also given to three experts (post-docs in the field of chemistry education). All the participants solved two tasks on a computer with their eye movements recorded. After the procedure, retrospective think-aloud and interviews were conducted to provide data about the problem-solving process. The results showed several trends. (1) Students–novices considered the chemistry task more difficult than the science task, which correlated with their task results. (2) Experts considered the science task more complex, therefore more difficult, however scored better than the students. (3) Even the successful student only solved the chemistry task using memorized facts without the support provided. (4) Experts’ direct focus on relevant parts was confirmed, whereas unsuccessful (novice) students distributed their focus toward other task parts too. (5) When students faced a problem during task solving, they used limiting strategies. This behavior was not identified in the expert group. The results thus showed a need to support students’ problem-solving strategies in several areas, especially careful reading, and identifying the main problem and supporting information. Moreover, the results showed a need to present chemistry tasks to students with more variability and explain their reasoning rather than testing field-specific, separated, memorized information.