What were the roles of the catechetical schools in education during the middle ages​

Initially, Christianity found most of its adherents among the poor and illiterate, making little headway—as St. Paul observed (1 Corinthians 1:26)—among the worldly-wise, the mighty, and those of high rank. But during the 2nd century CE and afterward, it appealed more and more to the educated class and to leading citizens. These individuals naturally wanted their children to have at least as good an education as they themselves had, but the only schools available were the grammar and rhetoric schools with their Greco-Roman, non-Christian culture. There were different opinions among Christian leaders about the right attitude to this dilemma that confronted all Christians who sought a good education for their children. The Greek Fathers—especially the Christian Platonists Clement of Alexandria and Origen—sought to prove that the Christian view of the universe was compatible with Greek thought and even regarded Christianity as the culmination of philosophy,

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(1)representation based on state population (2)all states have equal representation apex