Expectancy-Value & Motivation

At first, solving math questions on the blackboard was valuable and attractive to Will Hunting because he enjoyed the tasks, which demonstrated interest value/intrinsic motivation, while incurring minimal costs. Even if he got caught doing it, he was not likely to face punishment. Moreover, since Will was good at math, both his perception of competence in math and the expectancy for him to solve the problems were high. According to Expectancy-Value Theory, Motivation = personal expectancies for success (E) X personal values (V), he generated a high motivation, which led to an approach choice as a result.

However, Will chose to withdraw from the research project after he showed Professor Gerald Lambeau his solution to a math problem while Lambeau disagreed with the result. Will became inpatient and said that the math was too easy and he was tired of explaining his methods to all the other people who didn't have a clue. From the perspective of Expectancy-Value Theory, the interest value/intrinsic value was low because the math questions were easy for him, while he didn't have any motivation associated with any utility or personal identity purposes. Therefore, even though the expectation of solving the questions was high, his overall motivation decreased. 

Additionally, Professor Gerald Lambeau wasn't able to motivate Will by using the methods that worked for Will. For example, Lambeau stressed the utility value of math, such as helping him be successful in the field and having lots of work opportunities. However, Will didn't find these goals to be attractive, but rather contradictory to his moral standards and his upbringing experiences. Will perceived working for the NSA as contributing to the misfortune of others, so the value of working there was low. Besides, Lambeau constantly attributed success to Will's talent in math instead of his efforts in solving the problems, which adopted a fixed mindset and didn't foster an atmosphere for Will to develop mastery goals to enjoy the process of further development. On the other hand, Will didn't have performance goals to outperform others. 

Will & Skylar

Meanwhile, regarding Will's attitude towards his girlfriend Skylar, he was ambivalent, even though he valued the happiness the relationship brought to him and the feelings of belonging (value). Due to the differences in the backgrounds of he and Skylar, Will was afraid of the failure of their relationship. Will was an orphan who had lived in several foster homes and experienced physical abuse, but Skylar came from a rich family, inherited lots of wealth, attended Harvard, and will continue to study at Stanford Medical School. Will experienced low self-efficacy and expectancies for success because of his past experiences, and so did his motivation (Expectancy-Value Theory). He also adopted a fixed mindset, focusing on their differences rather than future growth and change. As a result, his performance-avoidant motivation led him to leave Skylar, which contributed to his negative emotions and behavior. However, Will reevaluated his views on his life and past, gaining a healthier perspective on himself and the relationship. He valued this relationship; he also believed that Skylar was still in love with him (expectancy), despite their breakup and her move to California. As a result, Will had a strong motivation to move to California to chase Skylar, outweighing the job he had just landed.