According to many books and articles, New England's leaders established the basic themes and preoccupations of an unfolding, dominant Puritan tradition in American intellectual life. To take this approach to the New Englanders normally means to start with the Puritans’ theological innovations and their distinctive ideas about the church—-important subjects that we may not neglect.
I know "approach" means "way/method" or "getting closer", but here I don't know what "take this approach to" means. "To 'way/method' the New Englanders"? "To get close to the New Englanders"? Someone told me it should be considered as "To 'study' the New Englanders". However, I don't know if this holds in English.