Problem Solving (PS) skills allow students to handle problems within an educational context. PS is a core competence of Computer Science education and affects programming success. In this vein, this paper aims to investigate PS ability performance in primary school pupils of a computer course, implemented according to the Neo-Piagetian theory of cognitive development. The study included 945 Slovenian pupils, ranging from fourth to sixth grade. The effects of gender, age and consecutive years of attending the course were examined on pupils' PS ability at the pre-operational and concrete operational stages. Pupils completed a survey questionnaire with four types of tasks (a series of statements, if-statements, loops and variables) at both stages. The analysis revealed three findings: the performance of PS ability in all tasks was, at the pre-operational stage, associated positively with performance at the concrete operational stage; there were no gender differences in PS performance at both stages, and both the grade and consecutive year of taking the computer course had an effect on PS ability performance at both stages. Those in the lowest grade and those taking the course for the first year reported lower performances than their older counterparts. These findings may help curriculum designers across the world develop efficient approaches to teaching computer courses.