drought in Taiwan and a cold snap in Texas that temporarily shut down factories operated by Samsung Electronics, NXP Semiconductors and Infineon.

“It’s hell on earth right now,” said Frank McKay, chief procurement officer at Jabil, which buys billions of dollars’ worth of chips each year to assemble products for customers that include Apple, Amazon, Cisco Systems and Tesla.

On any given day, he said, his company is facing shortages of 100 or so components and has to use all its negotiating power to get them — successfully so far. “But it’s a roller-coaster ride every day,” Mr. McKay said.

Fixing other issues is likely to stretch into 2022. Mr. Gelsinger said Intel was talking to auto industry suppliers about shifting some production of their chips to older Intel factories, possibly starting in six to nine months. But adding new production tools to an existing chip plant can take a year. Building a new one takes three years.

“This is going to be a long healing,” said Thomas Caulfield, chief executive of GlobalFoundries, a big U.S. chip manufacturer that is doubling capital spending this year so it can meet demand.

For now, chip delivery schedules have stretched from around 12 weeks to more than a year in some cases, chip buyers and brokers said. That is bad news for companies like the webcam start-up Wyze Labs.

“We’re going to be straight up with you about some bad news we got this week,” the company wrote in a note to customers in January. “Some of our key suppliers informed us they would only be able to supply about one-third of the chips we need to make Wyze Cams.”

The company, which is based in Kirkland, Wash., predicted problems stocking the third version of its flagship webcam. The company website says it is sold out, with more inventory expected in one to two weeks. Wyze did not respond to requests for additional comment.

Supply problems can be a touchy topic, said Zach Supalla, chief executive of Particle, a San Francisco company that buys chips to make communication and computing equipment. It sells its devices to thousands of companies that make products like hot tubs, air-conditioners and industrial and medical equipment.

Particle has so far has secured enough chips to keep making its products, he said. But the company is asking customers to order further and further in advance to ensure it can meet demand, Mr. Supalla said.

When chips can be found, price markups can be stark. One particularly unglamorous widget, a type of ceramic capacitor that ordinarily sells for around 3 cents each, became hard to find when a Covid-19 outbreak temporarily closed a factory in China.

The capacitor shortage hurt production of a popular cellular modem. That modem, which normally sells for $10 to $20, spiraled to $200 on the spot market, Mr. Supalla said. Customers like car companies may be willing to pay such sums to keep producing $40,000 cars, Mr. Supalla said. But not all can.

Some buyers suspect profiteering. Jens Gamperl, chief executive of an online components exchange called Sourcengine, recounted a call from an executive who fumed that a chip normally priced at $1 each was listed for sale by the exchange at $32. Mr. Gamperl had to explain that his own company had been forced to pay $28 for the component.

“That is the kind of craziness that we see left and right now,” he said.

Besides the direct effect on hardware makers, chip shortages can reduce shipments and raise the cost of servers and networking equipment to offer services like streaming entertainment, remote learning and medicine. They can also affect software makers.

Tripp, a Los Angeles start-up that makes a kind of meditation app that exploits virtual-reality headsets from Sony and others, was banking on the new PlayStation 5 to lift software demand, said Nanea Reeves, Tripp’s chief executive. But chip shortages helped to hobble that console launch.

“We were expecting a bigger bump from the PS5,” she said. The company is hoping more consoles arrive in the second quarter.

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Online Schools Are Here to Stay, Even After the Pandemic

In a study by the RAND Corporation, “Remote Learning Is Here to Stay,” 58 out of 288 district administrators — roughly 20 percent — said their school system had already started an online school, was planning to start one or was considering doing so as a postpandemic offering.

“This is hardly a panacea or a silver bullet for public schooling,” said Heather Schwartz, a senior policy researcher at RAND who directed the study. But, she added, “there is a minority of parents, a minority of students and even a minority of teachers for whom virtual schooling is the preferred mode.

Yet a surge of online schools comes with risks. It could normalize remote learning approaches that have had poor results for many students, education researchers said. It could also further divide a fragile national education system, especially when many Asian, Black and Latino families have been wary of sending their children back to school this year.

“My fear is that it will lead to further fracturing and fragmentation,” said Jack Schneider, an assistant professor of education at the University of Massachusetts, Lowell.

Districts said they were simply responding to demand from parents and children who want to stick with remote learning — some because of student health issues, some because of concerns about bullying or discrimination in their school, and some who just prefer the convenience of learning at home.

Districts that fail to start online schools could lose students — along with government education funding — to virtual academies run by neighboring districts, companies or nonprofits, administrators said. To pay for the new online offerings, some districts said, they are using federal coronavirus relief funds or shifting resources from other programs.

Online schools began opening in the 1990s, some run by states or districts and others by private companies or nonprofit charter management organizations. But until recently, they played a niche role in many states.

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N.Y.C.’s mayor says a new virus rule will reduce temporary public school closures.

Mayor Bill de Blasio of New York City announced a plan on Thursday that he said would significantly reduce the temporary public school closures that have frustrated parents and educators across city over the last few months.

Starting on Monday, public schools will have to close for 10 days only if four or more coronavirus cases in separate classrooms are confirmed within a seven-day period, and only if the city’s contact tracing program determines that the infections originated inside the school. Until now, schools had to close for 10 days when two unlinked cases were detected, regardless of the source of infection.

The mayor said earlier this week that he would get rid of the so-called two-case rule, which had prompted more than 200 temporary school closures during the last two weeks of March.

The new rule now applies to individual schools, rather than entire buildings. Because many school buildings in New York house multiple schools, two virus cases in one middle school could force an elementary school with no cases on another floor to switch to remote learning for days under the old rule.

Schools with suspected cases will no longer close for 24 hours while health detectives determine whether cases are linked, a change that will eliminate the frequent short-term closures that were sometimes announced just a few hours before the start of the school day. One or more cases found in individual classrooms will continue to prompt temporary closures of that classroom, but not necessarily the whole school.

The city will increase testing in schools where at least two cases are found.

Fully vaccinated teachers — along with older high school students who will be eligible for vaccines this week — will no longer have to isolate even when classrooms quarantine. As of last Friday, well over 65,000 of the roughly 147,000 Department of Education employees had been vaccinated.

New York City parents have until the end of the day Friday to decide if they want to switch their children from remote learning to in-person classes.

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How to Virtually Become a Doctor

Jerrel Catlett’s eyes narrowed on the large intestine, a gloppy, glow stick-like object whose color matched the stool stored inside of it. He chose to isolate the organ, and it expanded on his screen as the body parts surrounding it receded — the gall bladder bright green with bile, the ribs white and curved like half moons.

“My old boss used to tell me that when I did this, I’d be so wowed by how complex the human body is,” said Mr. Catlett, 25, a first-year student at Icahn School of Medicine at Mount Sinai, gesturing to the image of a body on his laptop screen. “But it feels like there’s something missing from the experience right now.”

For generations, medical students were initiated to their training by a ritual as gory as it was awe-inducing: the cadaver dissection. Since at least the 14th century, physicians have honed their understanding of human anatomy by examining dead bodies. But amid the coronavirus pandemic, the cadaver dissection — like many hands-on aspects of the medical curriculum — turned virtual, using a three-dimensional simulation software.

Of the country’s 155 medical schools, a majority transitioned at least part of their first and second-year curriculums to remote learning during the pandemic. Nearly three-quarters offered lectures virtually, according to a survey by the Association of American Medical Colleges, and 40 percent used virtual platforms to teach students how to interview patients about their symptoms and take their medical histories. Though the cadaver dissection posed a trickier challenge, nearly 30 percent of medical schools, including Mount Sinai, used online platforms to teach anatomy.

expands. Through remote clerkships at schools like Sidney Kimmel Medical College at Thomas Jefferson University, medical students assisted hospital staff by following up virtually with patients who had been discharged earlier than usual because of the pandemic.

“Other doctors got thrown into the deep end but we get to practice using this technology,” said Ernesto Rojas, a second-year student at University of California San Francisco School of Medicine. “We learned how to build rapport and ask the patient things like, ‘Are you in a place where you can talk privately?’”

Students have also said they’ve felt particularly motivated to complete their training amid the pandemic. Medical school applications are up by 18 percent compared with this time last year, according to the A.A.M.C.

For Prerana Katiyar, 22, a first-year medical student at Columbia, the first few months of medical school didn’t look anything like she had anticipated. She started the semester living in her childhood home in Fairfax, Va., where she shared lessons from her anatomy classes with her family over dinner. “When my dad said his abdomen hurt, I was able to talk to him about the quadrants of the abdomen,” Ms. Katiyar said.

Halfway into the semester, she had an exciting update for her parents. “My skull finally arrived in the mail,” she said. Ms. Katiyar’s anatomy professor arranged for each student to order a plastic model of the skull.

“Now I can see the bony landmarks and where the nerves are,” she continued. “I’m a very visual person so it’s been helpful to trace it with my finger.”

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Teachers’ Unions Uncertain on C.D.C.’s New 3-Feet Limit

Proponents of fully reopening schools got a major boost when the Centers for Disease Control and Prevention announced that elementary school students and some middle and high school students could be spaced three feet apart in classrooms.

The previous guidance of keeping most students six feet apart had in many school districts become a big obstacle to welcoming students back for full-time instruction because it severely limited capacity. Many experts now say a growing body of research shows that six feet is not much more protective than three, as long as other safety measures are in place, like mask wearing.

Public health experts, parents and school officials cheered the new recommendation. Teachers’ unions, which have used the six-foot guidance to oppose bringing children back for normal schedules, did not.

Randi Weingarten, president of the American Federation of Teachers, the nation’s second-largest educators’ union, said in a statement that she would “reserve judgment” on the new guidelines pending further review of research on how the virus behaves in schools, especially those in cities or that are under-resourced. Becky Pringle, president of the largest teachers’ union, the National Education Association, raised similar concerns.

for example, is planning to reopen elementary schools in the coming weeks on a half-day schedule that would avoid meal times, giving students less than three hours per day of in-person schooling, only four days per week.

Meanwhile, some districts have kept schools closed one day a week for what is sometimes described as a day of “deep cleaning,” a practice that experts have said has no benefit. In Anne Arundel County, the cleaning day is why the district is aiming to bring students back four days a week this spring, rather than five.

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N.Y.C. Students To Be Able to Opt Into In-Person Learning in Public Schools, Mayor Says

New York City’s public school system, the nation’s largest, will give families another chance to enroll their children in in-person classes following new guidance released by the Centers for Disease Control and Prevention, Mayor Bill de Blasio said on Friday.

The new C.D.C. guidance allows elementary school students wearing masks to be spaced three feet apart, rather than six feet, in reopened schools. The city’s elementary schools, prekindergarten programs and programs for children with complex disabilities will adopt the new distancing guidelines in April, Mr. de Blasio said, allowing classrooms that have been operating at one-third capacity for many months to accommodate more students. With less distancing required between students, schools will be able to fit more children into each city classroom.

The city will continue to assess the risks of adjusting distancing rules for middle and high school students, Mr. de Blasio said. The C.D.C. said that its relaxed three-foot guideline only applies to to students in middle schools and high schools where community transmission is not high. (New York State has more recent cases per capita than any state except New Jersey, and the New York City metro area has the country’s second-highest rate of new cases behind only Idaho Falls, Idaho.)

The guidance still holds that adults in schools should keep six feet of distance from each other, and from students. New York City teachers have been eligible for the coronavirus vaccine since January.

many nonwhite families in particular are still wary of in-person learning, and it is likely that a significant number of parents will keep their children at home through the end of the school year in June.

New York’s schools, some of the first in the nation to reopen, have had extremely low positive test rates. Mr. de Blasio has committed to fully reopening the city’s school system this September for full-time instruction for any child who wants it. He has also said he expects the city to maintain a full-time remote option for some children this fall.

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Child Dies in Accident Involving Peloton Treadmill

An accident involving a Peloton treadmill has left a child dead, the company’s chief executive announced on Thursday.

In a letter posted on the company’s website, John Foley, Peloton’s C.E.O. and a co-founder, said that the company, known for its wildly popular interactive stationary bikes, had recently learned of the fatal accident and was aware of “a small handful of incidents” involving children hurt by its Tread+ treadmill.

“While we are aware of only a small handful of incidents involving the Tread+ where children have been hurt, each one is devastating to all of us at Peloton, and our hearts go out to the families involved,” Mr. Foley said.

The company urged Peloton users to adhere to safety warnings concerning Peloton products, asking members to keep them where children can’t get to them and to store safety keys away from children when the machines are not in use.

at-home treadmill injuries occurred in children under 16 and that the coronavirus pandemic presented a unique risk for injuries as more adults were working from home and children were taking part in remote learning. Common injuries, the study found, included damage to the hands and fingers, such as friction burns or degloving, where part of the skin tissue detaches from underlying muscle.

closed down 4.6 percent amid the news of the fatal treadmill accident.

Last year the company faced another setback when it recalled pedals on about 27,000 of its stationary bikes after it received reports that clip-in pedals had caused injuries that required stitches or other medical care.

Susan Beachy contributed research.

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Learning Apps Have Boomed During the Pandemic. Now Comes the Real Test

After a tough year of toggling between remote and in-person schooling, many students, teachers and their families feel burned out from pandemic learning. But companies that market digital learning tools to schools are enjoying a coronavirus windfall.

Venture and equity financing for education technology start-ups has more than doubled, surging to $12.58 billion worldwide last year from $4.81 billion in 2019, according to a report from CB Insights, a firm that tracks start-ups and venture capital.

During the same period, the number of laptops and tablets shipped to primary and secondary schools in the United States nearly doubled to 26.7 million, from 14 million, according to data from Futuresource Consulting, a market research company in Britain.

“We’ve seen a real explosion in demand,” said Michael Boreham, a senior market analyst at Futuresource. “It’s been a massive, massive sea change out of necessity.”

co-founded Blackboard, now one of the largest learning management systems for schools and colleges. “You can’t train hundreds of thousands of teachers and millions of students in online education and not expect there to be profound effects.”

Tech evangelists have long predicted that computers would transform education. The future of learning, many promised, involved apps powered by artificial intelligence that would adjust lessons to children’s abilities faster and more precisely than their human teachers ever could.

improve students’ outcomes.

Instead, during the pandemic, many schools simply turned to digital tools like videoconferencing to transfer traditional practices and schedules online. Critics say that push to replicate the school day for remote students has only exacerbated disparities for many children facing pandemic challenges at home.

“We will never again in our lifetime see a more powerful demonstration of the conservatism of educational systems,” said Justin Reich, an assistant professor at the Massachusetts Institute of Technology who studies online learning and recently wrote the book “Failure to Disrupt: Why Technology Alone Can’t Transform Education.”

Apps that enable online interactions between teachers and students are reporting extraordinary growth, and investors have followed.

Among the biggest deals, CB Insights said: Zuoyebang, a Chinese ed-tech giant that offers live online lessons and homework help for students in kindergarten through 12th grade, raised a total of $2.35 billion last year from investors including Alibaba and Sequoia Capital China.

Yuanfudao, another Chinese tutoring start-up, raised a total of $3.5 billion from investors like Tencent. And Kahoot, a quiz app from Norway used by millions of teachers, recently raised about $215 million from SoftBank.

raised $100 million. Now Newsela is valued at $1 billion, a milestone that may be common among consumer apps like Instacart and Deliveroo but is still relatively rare for education apps aimed at American public schools.

Nearpod also reported exponential growth. After making the video lesson app free, the start-up saw its user base surge to 1.2 million teachers at the end of last year — a fivefold jump over 2019. Last month, Nearpod announced that it had agreed to be acquired by Renaissance, a company that sells academic assessment software to schools, for $650 million.

Some consumer tech giants that provided free services to schools also reaped benefits, gaining audience share and getting millions of students accustomed to using their product.

more than 150 million students and educators, up from 40 million early last year. And Zoom Video Communications says it has provided free services during the pandemic to more than 125,000 schools in 25 countries.

But whether tools that teachers have come to rely on for remote learning can maintain their popularity will hinge on how useful the apps are in the classroom.

Nesi Harold, an eighth-grade science teacher in the Houston area, have used features on the app to poll students, create quizzes or ask students to use a drawing tool to sketch the solar system — digital tools that work for both live classroom and remote instruction.

“It allows me to broadcast the lesson to all of my learners, no matter where they are,” said Ms. Harold, who simultaneously teaches in-person and remote students.

one complaint: She can’t store more than a few lessons at a time on Nearpod because her school hasn’t bought a license. “It’s still pricey,” she said.

The future in education is less clear for enterprise services, like Zoom, that were designed for business use and adopted by schools out of pandemic necessity.

In an email, Kelly Steckelberg, Zoom’s chief financial officer, said she expected educational institutions would invest in “new ways to virtually communicate” beyond remote teaching — such as using Zoom for Parent Teacher Association meetings, school board meetings and parent-teacher conferences.

Mr. Chasen, the ed-tech entrepreneur, is counting on it. He recently founded Class Technologies, a start-up that offers online course management tools — like attendance-taking and grading features — for educators and corporate trainers holding live classes on Zoom. The company has raised $46 million from investors including Bill Tai, one of the earliest backers of Zoom.

“I’m not coming up with some new advanced A.I. methodology,” Mr. Chasen said of his new app for video classrooms. “You know what teachers needed? They needed the ability to hand out work in class, give a quiz and grade it.”

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Learning Apps Have Boomed in the Pandemic. Now Comes the Real Test.

After a tough year of toggling between remote and in-person schooling, many students, teachers and their families feel burned out from pandemic learning. But companies that market digital learning tools to schools are enjoying a coronavirus windfall.

Venture and equity financing for education technology start-ups has more than doubled, surging to $12.58 billion worldwide last year from $4.81 billion in 2019, according to a report from CB Insights, a firm that tracks start-ups and venture capital.

During the same period, the number of laptops and tablets shipped to primary and secondary schools in the United States nearly doubled to 26.7 million, from 14 million, according to data from Futuresource Consulting, a market research company in Britain.

“We’ve seen a real explosion in demand,” said Michael Boreham, a senior market analyst at Futuresource. “It’s been a massive, massive sea change out of necessity.”

co-founded Blackboard, now one of the largest learning management systems for schools and colleges. “You can’t train hundreds of thousands of teachers and millions of students in online education and not expect there to be profound effects.”

Tech evangelists have long predicted that computers would transform education. The future of learning, many promised, involved apps powered by artificial intelligence that would adjust lessons to children’s abilities faster and more precisely than their human teachers ever could.

improve students’ outcomes.

Instead, during the pandemic, many schools simply turned to digital tools like videoconferencing to transfer traditional practices and schedules online. Critics say that push to replicate the school day for remote students has only exacerbated disparities for many children facing pandemic challenges at home.

“We will never again in our lifetime see a more powerful demonstration of the conservatism of educational systems,” said Justin Reich, an assistant professor at the Massachusetts Institute of Technology who studies online learning and recently wrote the book “Failure to Disrupt: Why Technology Alone Can’t Transform Education.”

Apps that enable online interactions between teachers and students are reporting extraordinary growth, and investors have followed.

Among the biggest deals, CB Insights said: Zuoyebang, a Chinese ed-tech giant that offers live online lessons and homework help for students in kindergarten through 12th grade, raised a total of $2.35 billion last year from investors including Alibaba and Sequoia Capital China.

Yuanfudao, another Chinese tutoring start-up, raised a total of $3.5 billion from investors like Tencent. And Kahoot, a quiz app from Norway used by millions of teachers, recently raised about $215 million from SoftBank.

raised $100 million. Now Newsela is valued at $1 billion, a milestone that may be common among consumer apps like Instacart and Deliveroo but is still relatively rare for education apps aimed at American public schools.

Nearpod also reported exponential growth. After making the video lesson app free, the start-up saw its user base surge to 1.2 million teachers at the end of last year — a fivefold jump over 2019. Last month, Nearpod announced that it had agreed to be acquired by Renaissance, a company that sells academic assessment software to schools, for $650 million.

Some consumer tech giants that provided free services to schools also reaped benefits, gaining audience share and getting millions of students accustomed to using their product.

more than 150 million students and educators, up from 40 million early last year. And Zoom Video Communications says it has provided free services during the pandemic to more than 125,000 schools in 25 countries.

But whether tools that teachers have come to rely on for remote learning can maintain their popularity will hinge on how useful the apps are in the classroom.

Nesi Harold, an eighth-grade science teacher in the Houston area, have used features on the app to poll students, create quizzes or ask students to use a drawing tool to sketch the solar system — digital tools that work for both live classroom and remote instruction.

“It allows me to broadcast the lesson to all of my learners, no matter where they are,” said Ms. Harold, who simultaneously teaches in-person and remote students.

one complaint: She can’t store more than a few lessons at a time on Nearpod because her school hasn’t bought a license. “It’s still pricey,” she said.

The future in education is less clear for enterprise services, like Zoom, that were designed for business use and adopted by schools out of pandemic necessity.

In an email, Kelly Steckelberg, Zoom’s chief financial officer, said she expected educational institutions would invest in “new ways to virtually communicate” beyond remote teaching — such as using Zoom for Parent Teacher Association meetings, school board meetings and parent-teacher conferences.

Mr. Chasen, the ed-tech entrepreneur, is counting on it. He recently founded Class Technologies, a start-up that offers online course management tools — like attendance-taking and grading features — for educators and corporate trainers holding live classes on Zoom. The company has raised $46 million from investors including Bill Tai, one of the earliest backers of Zoom.

“I’m not coming up with some new advanced A.I. methodology,” Mr. Chasen said of his new app for video classrooms. “You know what teachers needed? They needed the ability to hand out work in class, give a quiz and grade it.”

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