Shawn's abusive behavior toward Tara seems to be triggered by her increasing independence and maturity. Like his father, Shawn needs to have complete control and authority at all times. He seems to be particularly triggered by women disrespecting his authority, since, as his comments to Tara reveal, he does not respect or trust women. Shawn thinks women are inherently sinful and need to submit themselves to masculine authority; as Tara undergoes puberty, she shifts in his mind from a little girl he needs to take care of to a woman whom he wants to control and dominate. The first time Shawn physically lashes out at Tara is because she will not show him the same subservience he has come to expect based on the young woman he is dating. Tara does not feel the need to do everything a man tells her to do; perhaps she resists because of the independence she has gained while performing, or because she has watched her mother develop her own skills. Shawn will not tolerate Tara's assertiveness or rebellion, and he wants to make it clear that he can dominate her physically, while her father has always dominated her psychologically.
While it is unclear whether it changes his personality, Shawn's accident shows that the Westover siblings are leading a dangerous life. Despite the fact that his initial fall is clearly severe, no one calls for help until Shawn's second collapse, which shows that the other men are more focused on respecting Gene and his values than ensuring Shawn gets the help he needs. Taking Shawn to the hospital represents a desperate compromise which would only be undertaken under very dire circumstances. Tara's uncertainty about whether the brain injury impacted Shawn's behavior reveals that she is unclear about how much responsibility to assign to her brother. She seems to be at least partially tempted to blame Shawn's subsequent violence on the injury he suffered, because that would make Shawn less culpable. At the same time, Tara is forced to admit that Shawn was already being abusive before the injury, which means he likely would have hurt her no matter what.
While one brother is making Tara's life hell, her other brother becomes a force urging her toward independence. Tyler seems to know that he cannot control Shawn's behavior, or change the way his brother treats Tara. Instead, Tyler focuses on supporting Tara's independence, and he knows that the best way for her to break free of her family involves expanding her education. Tyler's choice to urge Tara to go to college and get away—rather than confronting Shawn or their parents—does shift the burden of changing her life onto Tara herself. By this time, Tara is so entangled with her loyalty to her family and their values that she is hesitant to pursue Tyler's plan. Her hesitation about whether to seriously consider college shows that the abuse she is experiencing is eroding her self-confidence, and making her feel unworthy. However, her love for music finally persuades her to start working toward a new goal.
Tara's road to getting an education does not begin easily. She has some basic knowledge but she has to significantly retrain her mind to take in information in a new way. She also has to grapple with learning skills that have no immediate applicability. Growing up on the farm, Tara has only ever had to learn manual labor and practical tasks. Trigonometry (and other academic subjects) is the first truly intellectual work she has had to do, and this is part of why she finds it so challenging. Nonetheless, Tara also takes a certain satisfaction and pride in the hard work, and building her confidence in what she is capable of.