The prisoner in the cave is not blind. They can see perfectly well. What they lack is direction: they are chained to face the wall. Education is the unchaining, the rotation, the painful process of reorienting the whole self toward what is real. The eye of the soul already has the power of sight — it only needs to be turned.
Plato's educational programme — gymnastics and music in early childhood, then mathematics (arithmetic, geometry, astronomy, harmonics), then dialectic — is structured as a progressive turning. Each stage loosens the soul from its attachment to a lower level of reality. Mathematics trains the mind to grasp what is unchanging and perfect, preparing it for a further ascent toward the Forms.
The deepest implication is that education should not aim primarily to transmit information — though it does this. It should aim to transform what the student loves. The student who genuinely learns mathematics begins to love what is eternal; the one who genuinely practices dialectic begins to love truth itself. Education is complete when the soul's desire has been permanently redirected from the shadows toward the sun.
Education as soul-turning (periagoge) appears in Book VII of The Republic. Plato's word for this rotation — periagoge — is the same word used for a military about-face, suggesting the violence of the transformation he has in mind.