To explain the tumultuous events of recent days, Tracy Merlin used an analogy her second-grade class would understand: the eternal struggle between dog people and cat people.

“Let’s say that half of the country thinks dogs are the best, and half of the country thinks cats are the best,” said Ms. Merlin, who teaches in Broward County, Fla. “But then it just turns out that the dogs won the election.”

“Do you think that people can still like cats and that maybe there can be some conversation?” she asked. “They can still like cats,” ventured Ander, 8, his blue headphones clamped over his ears.

Ms. Merlin scanned the sea of little heads floating in their individual squares. “Do you think it’s OK for the cat people to break into all the pet stores when they’re upset?” she asked.

“No,” Ander said. “Because that’s illegal.”

A riot at the U.S. Capitol. The second impeachment of Donald J. Trump. And, despite it all, a transfer of power. The events of the past few weeks have been mind-boggling for many adults.

How, then, to explain them to students, be they preschoolers meeting on socially distanced circle rugs or college students peering anxiously into seminar videochats?

Across the United States, educators have rerouted their syllabuses toward the news. They have turned to science fiction, Shakespearean tragedy and the fall of Rome in search of parallels to help their students process the often frightening and surely historic events.

“When I was a kid, the Challenger blew up,” Ms. Merlin, 46, said the day before the inauguration of President Biden. She remembers exactly what she was doing when the space shuttle exploded after liftoff in 1986 — just as her parents remember exactly what they were doing when John F. Kennedy was assassinated.

“I don’t know if this is this generation’s moment,” she continued. “But I know there are things that stick with them from a very young age. If I can let them know that it’s important to know about what is happening around you, and be informed, and have the facts, then I feel like I’ve done my job.”

College students have needed help framing these turbulent weeks, too.

On Wednesday, the morning of the inauguration, 180 students logged on to Steven G. Noll’s introductory American history class at the University of Florida. The lecture topic was post-Civil War Reconstruction.

Professor Noll, 68, easily plucked out uncomfortable parallels to the present.

“Words matter,” he said. What were once called “riots” that culminated in the killing of newly freed and enfranchised Black people are now called “massacres,” he said.

He showed a picture of a stone monument in Louisiana, erected in the memory of three “heroes,” who in 1873, the monument said, “fell in the Colfax riot fighting for white supremacy.” Those rioters killed 150 Black people.

He said that carrying the Confederate flag, as one of the Trump supporters in the mob that took over the Capitol on Jan. 6 was photographed doing, tells us “that they are fighting for white supremacy.”

The night of the Capitol riot, many of Melissa Deokaran’s middle school students in Washington, had lain awake, some hearing Trump supporters shouting in their alleys. At least three have parents in the D.C. National Guard who went to protect the Capitol.

So the day after, Ms. Deokaran used her Latin class to discuss the etymology of “invasion,” “insurrection” and “coup.” Then on Thursday, after Mr. Biden had assumed office, Ms. Deokaran taught the root of “inauguration,” “resilient” and “union.”

“I think it’s important for us to understand what a union means and what it means to be unified,” Ms. Deokaran, 32, told her class. In Latin, she said, “it means ‘one.’ In English, union means being ‘joined as one.’”

Across the country, schools occupy a fraught political space. The ways that children learn history, civics and literature can shape the votes they will one day cast. Teachers work hard to ensure their classrooms are safe for everyone to express opinions and disagree.

But the pandemic has eroded that four-walls privacy. Teachers have had to navigate the political passions of their communities in a time of intense division. Parents with strong opinions might be nearby as students learn virtually — and objecting to characterizations of polarizing events.

“I’ve had constant meetings and emails and such with a fairly aggressive contingent of parents that feels very strongly about the way that I am dealing with these issues in my classroom,” said James Mayne, who teaches at a Seventh-day Adventist school in Clark County, Wash., that he said leans conservative.

On Thursday, Mr. Mayne asked his 11th-grade U.S. history students to compare Mr. Biden’s inaugural speech with Abraham Lincoln’s second inaugural. Then he opened the floor for discussion, steering students toward the struggles both presidents faced in reuniting the country.

“I would have a very difficult time finding ground with white supremacists,” said Jordan, 16.

“White supremacists are an extreme part,” retorted Talia, 16, who called herself a liberal. “I have a bunch of people on the other side of my life that are not racists. They may have a bad way of explaining things sometimes, but in their hearts they are good people and they love everyone.”

If you cannot look past language, Talia said, you cannot find middle ground.

In politically conservative or even just politically mixed places, some schools have shied away from political discussions. Some school districts, like Bangor, Maine, did not broadcast Mr. Biden’s inauguration because they feared violence. And teachers who live in divided areas must work hard to avoid seeming biased.

Alyssa Kelly teaches 11th- and 12th-grade English in a conservative-leaning, rural district about 35 miles southwest of Bangor.

The day after the riot, one of her students, a vocal Trump supporter, came to class confused. He had spent the evening trying to parse memes, sound bites and his social media feeds. He just wanted a straight answer.

What had actually happened, he asked. After they spoke about it as a class, Ms. Kelly said, he was frustrated with how his fellow Trump supporters had acted.

“I am not necessarily confident that if he hadn’t had the space to wrestle with his own ignorance for a minute — in a way I didn’t judge him at all — he would have got to the same conclusion,” Ms. Kelly said. “I didn’t have to say anything political, really. I just had to unpack it for him, or help him unpack it.”

Ms. Kelly, who teaches in a majority-white district, hung a print of “Golden Rule,” a Norman Rockwell piece depicting a racially and religiously diverse group of people under the American flag. When her students turn to say the Pledge of Allegiance, she hopes they remember who else lives in the country.

“My students are going to graduate and, most likely, remain in their homogeneous perspectives and convenient, familiar contexts,” Ms. Kelly said. “This is one last chance to remind them that befriending someone who disagrees with you is actually possible.”

To scythe through confusion, several teachers said they used a three-part query system: What do I know? What do I think I know? And what do I want to know? Whenever possible, they directed discussions back toward the curriculum, using primary sources as a guide.

The day after the Capitol rampage, Nicole Hix turned class discussion in her Advanced Placement world history class toward the violence. Instead of asking her students at a private Catholic school in Houston to analyze documents from the reign of Louis XIV, Ms. Hix asked them to discuss recent pictures, headlines and tweets, just as they would any other primary source.

“When it got awkward, I moved on,” Ms. Hix, 46, said. “It was a tough day. It was hard to swallow. A lot of them didn’t have questions, so I turned it into an Advanced Placement skills day.”

One student, Sophia, said her peers kept their heads down and their mouths closed. She answered direct questions but mostly steered clear of sharing her opinion.

“It’s our age,” said Sophia, 15. “We don’t want to lose any friends, but we also have beliefs. We can all tell that it’s very tense.”

Back in Ms. Merlin’s second-grade class, she directed the discussion about cats and dogs toward the riot at the U.S. Capitol. It had happened two weeks before — eons in second-grade time.

“We saw a lot of violence,” said Ms. Merlin, a local activist for gun violence prevention. “Do you girls and boys remember the pushing and the shoving? How did that make you feel?”

“It was kind of sad to see that,” Logan, 8, said. “They could probably talk to people and just sort of figure this out, instead of breaking into the Capitol.”

“What is something that you have to do with your ears when the other person is talking?” Ms. Merlin asked.

Sierra, who is 7, unmuted herself. “You need to listen,” she said.

By Amelia Nierenberg for the New York Times
Anemona Hartocollis contributed reporting.