Computer programming is considered an important competence for the development of higher-order thinking in addition to algorithmic problem solving skills. Its horizontal integration throughout all educational levels is considered worthwhile and attracts the attention of researchers. Towards this direction, an exploratory case study is presented concerning dimensions of problem solving using computer programming by 5-6 years old kindergarten children. After a short introductory experiential game the children were involved in solving a series of analogous computer programming problems, using a Logo-based environment on an Interactive White Board. The intervention was designed as a part of the structured learning activities of the kindergarten which are teacher-guided and are conducted in a whole-class social mode. The observation of the video recording of the intervention along with the analysis of teacher's interview and the researcher's notes allow for a realistic evaluation of the feasibility, the appropriateness and the learning value of integrating computer programming in such a context. The research evidence supports the view that children enjoyed the engaging learning activities and had opportunities to develop mathematical concepts, problem solving and social skills. Interesting results about children learning, difficulties, interactions, problem solving strategies and the teacher's role are reported. The study also provides proposals for the design of future research. (Contains 7 figures and 3 tables.)