Well, technically, it is neither. This is a quote/reference to 2 Timothy 2:15. The word in Greek means "to cut straight; to set forth truthfully, without perversion or distortion". In older translations it would be rendered "to divide rightly (correctly)". Here, grammatically, it is an present active participle (accusative singular masculine), which is describing the (arch)bishop (or in this case Pope and (arch) bishop). The text can be rendered (from Greek):
Among the first be mindful, O Lord, of our Archbishop (name), whom grant-for thy Churches in peace-(that he be) safe, honored, healthful, increasing in days, and dividing rightly the word of thy truth.
I would say that (if I read rightly) that this a petition that he teach the word rightly, although in St Paul, this is an attribute he should already possess, so it would be a petition for him to retain the attribute. It a way, it is asking for both-that they are teaching rightly and that they continue to do so.