Abstract An informal mathematical module integrating Arts (modifying STEM to STEAM) and following an inquiry-based learning approach was applied to a sample of 392 students (aged 12–13 years). The three lesson module dealt with mathematical phenomena providing participants with the commercially available hands-on construction kit, aiming to advance STEAM education. Pupils built original, personal, and individual geometrical structures by using plastic pipes in allowing high levels of creativity as well as of autonomy. Tutors supervised the construction process and intervened only on demand. A pre-/post-test design monitored the cognitive knowledge and the variables of relative autonomy, visual reasoning, formal operations as well as creativity. Our informal intervention produced newly acquired cognitive knowledge which as a process was shown of being supported by a broad basis of (soft) factors as described above. A path analysis elaborated the role of creativity (measured with two subscale: act and flow) to cognitive learning (post-knowledge), when flow was shown to lead. Pre-knowledge scores were significantly influenced by both creativity subscales: act and flow. However, relative autonomy, visual reasoning and formal operations contributed, too. In consequence, cognitive learning within STEAM modules was shown dependent on external triggers. Conclusions for appropriate educational settings to foster STEAM environments are discussed.