Analytical thinking is a transversal learning skill that helps learners build knowledge independently of subject area. The capacity to synthesize a solution to a problem, as opposed to memorize a correct answer, has wide applicability in themes ranging from mathematics, science, and technology to arts and culture. The ability to approach a problem critically, to deconstruct it, to evaluate alternative implementations, and to introduce a viable solution is valuable not only in academics but also professionally as well as in daily life. Current educational trends underline the importance of analytical thinking in learning; however, formal curricula in many cases fail to introduce educational recommendations that focus on the active development of this skill. The work presented in this paper introduces a problem-based didactical approach for building analytical thinking among young learners by deploying visual programming concepts. The proposed cMinds learning method exploits the structured nature of programming, which is inherently logical and transcends cultural barriers, towards the introduction of algorithmic thinking early in life and specifically among primary education learners. A game-based, visual programming environment has been developed aimed for classroom use. The proposed tool maximizes graphical presentations of programming constructs and all but eliminates programming language-like syntax. Learners are presented with carefully selected learning exercises that introduce them to algorithmic solving approaches, including brute force, divide-and-conquer, and reduce-and-conquer. As a first step, learners explore potential solutions to a given problem in a manner similar to drawing sketches on paper. Once they have developed a basic intuition on the solution, they build graphically in a handson, step-wise manner an algorithm that solves the problem at hand; learners achieve a solution by dragging and dropping from a toolbox of graphically presented programming constructs, conditions, and actions to a programming area. Learners get visually feedback on their efforts through an animation that precisely executes the steps of their "program". Real-time system interaction helps learners identify and correct errors in an iterative manner, gradually scaffolding knowledge. Finally, learners can compare their solution to an "optimal" one through a comparison zone. On-going validation in real-life learning experiments engaging learners and teachers in Greece, Sweden, Romania, and the Czech Republic has demonstrated positive results of the learning methodologies and virtual tools in terms of relevance with existing educational processes as well as effectiveness, enriching the learning process in the context of mathematics and science education.