Set in 1998, Critical Thinking tells the true story of a Cuban-American teacher named Mario Martinez (known to his students as Mr. T) and his national championship-winning chess club at Miami Jackson High School.
Sedrick, an African-American student living in a single-parent household, takes up chess as an elective and meets Mr. T along with Ito, a student who works after school to support his education. The class also includes Rodelay, the class clown, and Gil, who is of Spanish descent.
Mr. T deals with opposition from Principal Kestel, who believes that the class is made up of academic misfits and that the chess club brings little to no glory to the school. Kestel threatens to redirect funding from the chess club to the school's football team. To offset the price of the registration for the regional competition, Mr. T. uses his personal savings. At the end of the road trip[clarification needed], Sedrick happily tells his dad about his victory. Sedrick's father tells him to get his life straight and decide on his future rather than waste his time on chess. Ito loses his job and his mother throws him out of her apartment, leading him to quit the chess team. The rest of the team realizes that they need money to register for the state championship. They also need Ito, who previously qualified for the regional. If they can't achieve both, they risk forfeiting.
The boys face interrogation from police officers who believe that their friend Andre murdered another student. Soon after, Ito, dealing with financial troubles, is recruited by a drug kingpin because of his knack with numbers. The boys raise funds for the state championship by washing cars. They also recruit a new member, Marcel, whom Mr. T calls Duchamp. At the last minute, Ito changes his mind and travels with the boys to the tournament. An airline company had promised free tickets via sponsorship for them if they made it to the nationals, which they narrowly qualify for due to Rodelay's refusal to accept a draw, after which he loses due to a zugzwang. He stays at home to fix his life, with a drug dealer, Andre, threatening to hand him over to the police if he tries to quit.
The boys' progress well and are pitted against Akopyan, the three-time, back-to-back reigning champion. Akopyan plays individually against Marcel, who has the best record on the team. At some point in the game, Akopyan, who is having a difficult time beating Marcel, decides to take a bathroom break and suggests that Marcel should do the same. However, Akopyan mistakenly leaves his clock timer running. In the bathroom, Akopyan tries to talk Marcel into accepting a draw, and Marcel replies that a win is all his team needs to win the tournament. When the game resumes, Akopyan is upset to find his clock running which puts Marcel up in a time advantage. However, Marcel waits five minutes without a move to level the game time, and the two finalists resume the game on an equal footing. Eventually, Akopyan has to resign as his position is obviously losing. Marcel is crowned as the new champion alongside the boys and Mr. T.
Back home, Ito invites Donny and Andre over under the pretense of talking about business, but Andre suspects something to be off about the meeting. He seizes Ito's Walkman and forbids him from answering the phone, and talks about Sedrick and his girl Chanakya and what he might do to them. Ito gets angry and grabs Andre, bashing his head on a refrigerator until Andre is unconscious, and then leaves the store and walks into the street.
