We study how students and teachers conceptualize the notion of ‘algorithm’, a fundamental concept in computer science and computer science curricula. We analyze the work produced by CS students and teachers during a workshop conducted repeatedly over several years in some outreach activities for schools, computing education courses, and professional development opportunities for teachers. Participants were divided into groups, given some procedures written in natural language, and asked to decide together which of the procedures might be taken as algorithms. The procedures were purposely designed to present flaws or features that could activate discussion. After that, groups were asked to agree upon a definition of `algorithm’ and make its fundamental properties explicit. The activity triggered reflections around the idea of algorithm and its interpreter, going beyond stereotyped definitions, and leading participants to deepen their comprehension of the notion. We report on the aspects that were more debated by the groups, and those that were recurrent in the resulting definitions. We argue that this kind of activities should be offered more often both to students during their study career, and to teachers in professional development opportunities, to prompt them to reflect on computing foundations also in a non-technical, more holistic way.