As the Enterprise prepares to take part in a test for a new propulsion system, Worf gets a surprise visit from his adoptive mother, Helena Rozhenko, and his son, Alexander. When Worf asks them how long they plan to stay on the Enterprise, Alexander emphatically states: "I'm not going back!"
Helena explains to Worf that she and her husband, Sergei, are getting too old to continue caring for a child, so they wish to leave Alexander in Worf's care, explaining that he "needs his father" to help temper his behavior. Worf reluctantly obliges and takes Alexander to Miss Kyle, the ship's primary school teacher, to enroll Alexander for classes, where it becomes clear that Worf knows painfully little about his son, not even his birthday.
Dr. Ja'dar briefs the senior staff on the upcoming propulsion system test: a soliton wave would be generated on the surface of the planet Bilana III and envelop a test ship, which would ride along the wave to achieve warp velocity without the need of a warp drive, with the Enterprise following behind the test ship, remaining close behind to deal with subspace interference from the wave to monitor it. The test would conclude at Lemma II, where a scattering field would be generated to dissipate the wave.
At Troi's suggestion, Worf decides to step back from his duties to attempt to connect with Alexander. He accompanies him on a field trip with Miss Kyle's class to the biolabs, which goes poorly for both father and son when Alexander takes a model of an extinct Earth lizard and lies about it. Worf lectures Alexander about how dishonorable his actions are for Klingons. To demonstrate his point, Worf tells Alexander about Kahless and Morath, two brothers from Klingon mythology who fought bitterly for several days after Morath told a lie and dishonored his family: for Klingons, to lie is to dishonor one's family, and Alexander's lie dishonored Worf. Alexander promises his father that he will not lie again.
Afterwards, the soliton wave experiment commences. At first, the experiment seems to work out, as the test vessel achieves warp velocity after becoming enveloped by the soliton wave, with near-total power efficiency. But then the experiment begins to go horribly awry, and the test ship is destroyed by the soliton wave. Unfortunately, their problems extend beyond the destruction of the test ship: the soliton wave is still travelling to Lemma II, gaining speed and power—too much power for the planned dissipation to work. If the wave reaches the planet, it would cause devastation on a massive scale.
Meanwhile, Worf learns that Alexander has continued to steal and lie in class. He finds Alexander in a holodeck running his calisthenics program, attempting to fight with the bat'leth he took from Worf's room. With Alexander continuing to lie and acting rebellious, an exasperated Worf decides the only course of action is to have Alexander sent to a Klingon school. When Alexander protests, Worf orders him back to his quarters.
Worf discusses his difficulties with Alexander to Troi, with Troi speculating that when Worf had sent Alexander to live with the Rozhenkos after the death of his mother, K'Ehleyr, it was like losing both of his parents at the same time. Worf was still emotionally wounded over the fact that K'Ehleyr had kept her pregnancy and Alexander's birth a secret from him. Troi suggests that both father and son should work together on healing. However, Alexander is seen packing his bags in Worf's room. Worf tries to explain why he is sending him to Klingon school, but Alexander is convinced his father resents him. Worf instructs Alexander to stay in his room when he is called to meet with Riker.
The problem with the soliton wave has grown more grave, with the wave gaining both size and strength the longer it travels. La Forge has two ideas on how to stop the wave: an inverse resonance wave, which would be difficult due to the wave's constantly changing frequency and amplitude; or a photon torpedo spread detonated directly in front of the wave. At the wave's present size and velocity, moving around it to intercept is no longer an option: the Enterprise would need to travel through the wave, which poses dangers of its own to the ship.
The Enterprise moves through the soliton wave to intercept, which causes some damage to several decks. One of them is Biolab 4, where a fire has broken out and fire suppressant systems have malfunctioned. Picard orders the lab vented, but to Worf's horror, there is one humanoid occupant in Biolab 4: Alexander Rozhenko! With Alexander not replying to messages from the captain, Picard grants Worf leave to rescue his son with Riker in tow. Time is of the essence, though; thanks to the damaged shields, detonating the torpedoes to stop the wave will flood the lab with ion radiation!
Worf finds Alexander trapped under rubble in the lab. With flames roaring around him and smoke choking him, and Alexander hurt and scared, Worf calls upon all of his strength to remove the debris, take Alexander, and escape from the lab just as Picard orders torpedoes fired at the soliton wave, dissipating it and saving Lemma II from certain destruction.
Alexander is taken to sickbay, where he recovers from a hairline fracture in his tibia. Alexander apologizes to Worf and promises that he will behave at Klingon school. Worf, finally coming to accept fatherhood, explains that Klingon school would be challenging, but should Alexander accept, he can undertake an even greater challenge by remaining on the Enterprise and learning how to be a good son while Worf takes on the challenging of how to be a father. Alexander accepts Worf's proposal, with Worf thinking Alexander's mother would be proud of them both.
Tropes featured in this episode include:
- Bratty Half-Pint: Alexander, who steals toys and starts fights while claiming other kids started it. This behavior stems from his feelings of anger and abandonment regarding his father.
- Bratty Half Pint With a Heart of Gold: Despite being in pain and barely conscious during the climax of the episode, Alexander still pleads with his father and Riker to save the endangered animals the Enterprise is transporting.
- Charles Atlas Superpower: Despite already normally being presented as extremely strong, Worf is capable of lifting a piece of debris that would usually require Data to move when he needs to save his son.
- Extinct in the Future: Miss Kyle mentions that the white rhinoceros went extinct.
- Hilarious in Hindsight: Geordi is almost giddy at witnessing the soliton wave test, calling it a historical moment akin to seeing Chuck Yeager break the sound barrier or Zefram Cochrane fire up the first warp drive. Later on in the series, he actually does (did?) get to take part in the latter.
- Mama Didn't Raise No Criminal: When Alexander's teacher tells Worf that he swiped a model lizard, Worf objects, since stealing is dishonorable. But then, at Miss Kyle's insistence, Worf searches Alexander and finds the model.
- Oh, Crap!: Worf, when the computer says that Alexander is trapped in a fire.
- This Is Going to Be Huge: Geordi begins the story by talking about how the soliton wave is going to change spaceflight forever and potentially render warp drive obsolete. It still might, but the destroyed test ship and danger of an Earth-Shattering Kaboom surely set it back a fair while.