We are shown how they should and should not behave, as a daughter, wife, and widow. In the induction scene, the lord lectures his page on the duties of a wife, instructing him to bear himself with honorable action and uses key words such as duty and humble wife. We are then quickly confronted with katherina, quick witted, and seemingly willing to do anything to get her own way, even at the expense of her own reputation, and that of her sister and father. In contrast to Kate, Bianca is a model daughter and women. She is demure, quiet, respectful, and has many suitors, yet she is the one who uses her femininity to manipulate her tutors, and eventually elopes, potentially bringing great shame to her father. Katerina as supposed shrewish nature is built mainly on reputation. True, she is sharp with her tongue, and speaks out when perhaps convention tells her to be quiet, but she does her duty to her father and husband, agreeing to marry petruchio despite his eccentric behavior, and in so doing, allows her sister the chance to marry.
It is important to note an interesting point with regards to katherina. The oxford dictionary defines a shrew as a brawling, troublesome women, yet also say as that it now usually means someone of keen practical judgment, as in the word ëshrewisha. This is a modern development, and it is not unlikely that this relates to Shakespeare as treatment of Katherina in the play, especially since etymologists claim Shakespeare to be personally responsible for coining over two thousand words, not to mention phrases into our language, such as obscene, majestic, lonely .
It is also important to note katherina as final speech. In it, she lectures the other wives, including her sister, on the duty of a wife. In it, she mirrors the lord as original speech as to the dutiful behavior of a wife, claiming .
Thy husband is thy lord, thy life, thy keeper,.
Thy head, thy sovereign she emplores her fellow wives to behave just as convention states, to be obedient, fair, amiable.