Objection 1. It would seem that Christ did not advance in this knowledge. For even as Christ knew all things by His beatific and His infused knowledge, so also did He by this acquired knowledge, as is plain from what has been said (1). But He did not advance in these knowledges. Therefore neither in this.
Objection 2. Further, to advance belongs to the imperfect, since the perfect cannot be added to. Now we cannot suppose an imperfect knowledge in Christ. Therefore Christ did not advance in this knowledge.
Objection 3. Further, Damascene says (De Fide Orth. iii, 22): "Whoever say that Christ advanced in wisdom and grace, as if receiving additional sensations, do not venerate the union which is in hypostasis." But it is impious not to venerate this union. Therefore it is impious to say that His knowledge received increase.
On the contrary, It is written (Luke 2:52): "Jesus advanced in wisdom and age and grace with God and men"; and Ambrose says (De Incar. Dom. vii) that "He advanced in human wisdom." Now human wisdom is that which is acquired in a human manner, i.e. by the light of the active intellect. Therefore Christ advanced in this knowledge.
I answer that, There is a twofold advancement in knowledge: one in essence, inasmuch as the habit of knowledge is increased; the other in effect--e.g. if someone were with one and the same habit of knowledge to prove to someone else some minor truths at first, and afterwards greater and more subtle conclusions. Now in this second way it is plain that Christ advanced in knowledge and grace, even as in age, since as His age increased He wrought greater deeds, and showed greater knowledge and grace.
But as regards the habit of knowledge, it is plain that His habit of infused knowledge did not increase, since from the beginning He had perfect infused knowledge of all things; and still less could His beatific knowledge increase; while in I, 14, 15, we have already said that His Divine knowledge could not increase. Therefore, if in the soul of Christ there was no habit of acquired knowledge, beyond the habit of infused knowledge, as appears to some [Blessed Albert the Great, Alexander of Hales, St. Bonaventure, and sometime appeared to me (Sent. iii, D, xiv), no knowledge in Christ increased in essence, but merely by experience, i.e. by comparing the infused intelligible species with phantasms. And in this way they maintain that Christ's knowledge grew in experience, e.g. by comparing the infused intelligible species with what He received through the senses for the first time. But because it seems unfitting that any natural intelligible action should be wanting to Christ, and because to extract intelligible species from phantasms is a natural action of man's active intellect, it seems becoming to place even this action in Christ. And it follows from this that in the soul of Christ there was a habit of knowledge which could increase by this abstraction of species; inasmuch as the active intellect, after abstracting the first intelligible species from phantasms, could abstract others, and others again.
Reply to Objection 1. Both the infused knowledge and the beatific knowledge of Christ's soul were the effects of an agent of infinite power, which could produce the whole at once; and thus in neither knowledge did Christ advance; since from the beginning He had them perfectly. But the acquired knowledge of Christ is caused by the active intellect which does not produce the whole at once, but successively; and hence by this knowledge Christ did not know everything from the beginning, but step by step, and after a time, i.e. in His perfect age; and this is plain from what the Evangelist says, viz. that He increased in "knowledge and age" together.
Reply to Objection 2. Even this knowledge was always perfect for the time being, although it was not always perfect, simply and in comparison to the nature; hence it could increase.
Reply to Objection 3. This saying of Damascene regards those who say absolutely that addition was made to Christ's knowledge, i.e. as regards any knowledge of His, and especially as regards the infused knowledge which is caused in Christ's soul by union with the Word; but it does not regard the increase of knowledge caused by the natural agent.
Source: Summa Theologica (New Advent)