Society today presents a civilising equation where it is crucial to unveil and guide the imbricated relationship between what is technical and what is human. Therefore, the study of contemporary variables is central to the interpretation of this reality. By considering that critical mathematics education (CME) is the most developed approach to treating such themes in mathematics classes, we present a landscape of investigation developed with high-school students, step by step, based on reflective didactic transposition (RDT) of a Scientific Initiation (SI) project in high school. SI enables the investigation of contemporary themes that, in turn, approach the concerns of CME by fostering questions, autonomy, decision-making and a critical interpretation of reality. This proposal evidenced the approximation of SI concepts with landscapes of investigation, just as it was possible to perceive the urgency of the imbrication between the different milieus of learning and the contemporary variables of this complex civilising equation.