Strengthening critical thinking abilities of citizens in the face of news published on the web represents a key challenge for education. Young citizens appear to be vulnerable in the face of poor quality news or those containing non-explicit ideologies. In the field of data science, computational and statistical techniques have been developed to automatically collect and characterize online news media in real time. Nevertheless, there is still not a lot of interdisciplinary research on how to design data exploration platforms supporting an educational process of critical citizenship. This article explores this opportunity through a case study analyzing critical thinking ability of students when facing news dealing with the social mobilization "No+APF". From data collected through 4 online exercises conducted by 75 secondary school students, 55 university students and 25 communication specialists, we investigate to what extent young citizens are able to classify news headlines and ideological orientation of news media outlets. We also question the influence of the media's brand name and the subjectivity of each participant in regards to the social mobilization "No+APF". The results underline the importance of group work, the influence of the brand name and the correlation between critical-thinking abilities and having a defined opinion.