Set in 1998, Critical Thinking tells the true story of a Cuban-American teacher named Mario Martinez (known to students as Mr. T) and his national championship-winning chess club at Miami Jackson High School. Martinez finds himself working with minority students as a chess teacher. Sedrick, an African-American child, 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 interference from Principal Kestel, who feels the class is made up of academic misfits. Kestel believes that the chess club brings little to no glory to the school. Principal Kestel threatens to cut funding from the chess club and use it to fund the school’s football team. To offset the registration ticket for the Regionals, Mr. T. uses his personal savings. At the end of the road trip, 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. He loses his job, and his mother throws him out of her apartment. He quits the team because he lost everything. It dawns on the boys that they need money to register for the State Championship. They also need Ito, who previously qualified for the regionals. If they can’t achieve both, they risk forfeiting.
They face interrogation from police officers who believe their friend Andre murdered one of the students, and they told him that he would be exonerated if he confesses that Andre did it. Soon thereafter, Ito, dealing with financial troubles, is recruited by the street drug kingpin for his knack with numbers. The boys were able to raise funds for the state championships by washing cars. They also recruit a new super player, Marcel, whom Mr. T calls Duchamp. At the last minute, Ito changes his mind and goes on a road trip with the boys for the tournament. An airline company had promised free flight 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, thereby causing him to be 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 with good numbers to be pitted against Akopyan, the three-time, back-to-back reigning champion. Akopyan was played individually by Marcel, who had the best record on the team. At some point in the game, Akopyan, who was having a difficult time beating Marcel, decides to take a bathroom break and suggests that Marcel should do the same too, whilst he mistakenly leaves his clock timer running. Inside the bathroom, Akopyan tries to talk Marcel into accepting a draw, who replies that a win is all his team needs to win the tournament. The game is resumed, but Akopyan is upset to find his clock running, which puts Marcel up in time advantage. However, Marcel waits about five minutes without a move to level the game time, and the two finalists can resume the game on an equal footing. Eventually, Marcel checkmates Akopyan, and he is crowned 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, talks about Sedrick and his girl Chanakya and what he might do to them. Ito gets angry and grabs Andre, bashing his head on the refrigerator glass until Andre is unconscious, and then leaves the store and walks into the street. During the end credits, the movie returns to modern-day Ito and Marcel.