How does Shakespeare show Kate's transformation throughout the Taming of the Shrew?

Kate's transformation occurs over the length of the play. She transforms from the harsh shrew we meet in the beginning of the story into a submissive yet spirited wife. This change is made possible when Kate learns and experiences love..... thus, we see that her harsh behavior was most often linked with feeling of inadequacy rather than jealousy.

Petruchio's arrival brings the attention and compliments she craves, but even after their marriage she doesn't recognize the love. In fact, Kate will need to recognize and demonstrate her own love for others before she is able to relate it to herself. Eventually, she is able to discern what love really is and display her emotions, she also learns how to empathize and see that others don't always do it right themselves. An example of this is shown when Kate chides her sister for her childish behavior and disrespect of her own husband.

By the end of the play, Kate is a changed woman, but by no means a different woman. She's still spunky and playful, but no longer finds it necessary to throw tantrums in order to make a point. She understands and feels love, but also understands that deference to one's husband is not the same as the way in which she once defined submission.