This research project investigated manifestations of critical thinking in pupils 10 to 12 years of age during their group discussions held in the context of Philosophy for Children Adapted to Mathematics. The objective of the research project was to examine, through the pupils' discussions, the development of dialogical critical thinking processes. The research was conducted during an entire school year. The research method was based on the Grounded Theory approach; the material used consisted of transcripts of verbal exchanges among the pupils (at the beginning, middle and end of the school year). Analysis of the transcripts revealed that: (1) critical thinking appears to the extent that a "dia-logue" is established among pupils; (2) on the cognitive level, dialogical critical thinking is comprised of four thinking modes: logical, creative, responsible and meta-cognitive; and (3) on the epistemological level, dialogical critical thinking is only manifested in a context where egocentricity of perspective and relativism of beliefs are transcended.