In Act I Scene 1 of The Taming of the Shrew, how is Tranio's intelligence and education recognised even though he is Lucentio's servant?
It is Tranio, let us remember, that seems to try and bring his master down to earth after he has fallen so violently in love with Bianca at first sight. Shakespeare shows that Tranio is more than capable of trying to debate with his love sick master, and that he can quote various texts in support of his argument. Note the following example:
If love have touched you, naught remains but so,
"Redime te captum quam queas minimo."
This is a quote from Terence, which translated means "buy yourself out of bondage for as little as you can." Tranio is here showing his intelligence and how well-read he is as well as gently poking fun at his master, talking about the negatives of being in love.
Likewise note that it is Tranio that points out the various realities of the situation whilst Lucentio looks upon it with his pink lenses of love. It is Tranio that needs to remind Lucentio about the existence of Katharina, and then also it is Tranio who decides to "stir" his master from his "trance" and help him to practically think of how to win Bianca. Although he is careful not to overstep the bounds of his position as servant, one could argue that he cunningly directs his master to the plan that he has already formed, encouraging his master to play the role of tutor and himself to become Lucentio. It is Tranio throughout this scene who is shown to be intelligent and resourceful.