to the sources...

A personal view...

Generally we speak of "Christian education;" the phrase "teaching Christianly" is not as widespread - perhaps because Christian makes a tidier adjective than adverb.  However, teaching Christianly has a fresh and vivid character that I find lacking in Christian education.  It isn't that Christian education is wrong but it has been cheapened with abuse.  Many words share a similar history: 'awesome' isn't quite as grand since its gradual equivalence to anything 'good'; 'radical' isn't quite as revolutionary since its flippant use during 1980s.

There are those who argue that we need to rescue these abused words from their semantic slavery, and they are probably are right.  But until those adjective abolitionists secure emancipation, I succumb to the stronger adverb.  Besides, I do like 'teaching Christianly' which portrays active education versus its counterpart which suggests an established product.  Finally, if 'teaching Christianly' means that I (as a teacher) need to teach as a Christian, in a Christian way, and to Christian ends, then 'learning Christianly' means that students need to learn as Christians, in a Christian way, and to Christian ends.