In a catechetical manner; by means of catechesis or systematic religious instruction through questions and answers.
From 'catechetical' + '-ly' (adverbial suffix). This forms the adverbial version of the Greek-derived adjective, indicating how something is done in a methodical, question-based teaching style.
Using words this way—catechetically, pedagogically, didactically—shows how English took Greek teaching methods and turned them into fancy adverbs to describe how any kind of knowledge transfer happens.
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