Most teachers know of pupils who have used social media to share sexual messages, pictures or videos, a survey by a teachers' union suggests.
A poll of 1,304 teachers by the NASUWT union indicated most pupils involved in such incidents were aged 13 to 16, but some were aged as young as seven.
The government said young people must be made aware of the risks and dangers.
The survey comes after the Labour Party accused the government of "refusing to protect the smartphone generation".
Labour called for compulsory age-appropriate sex education in all of England's schools and for official guidance to be updated.
Currently, sex-and-relationships education is compulsory from age 11 under the national curriculum - but this does not apply in academies, and the government announced last week that all schools in England must have plans in place to become academies by 2022.
Half of those who responded to the survey were aware of pupils using social media to send insulting or bullying messages of a racist nature, and most (53%) were aware of messages of a homophobic nature.
Most said they had come across pupils sending sexist messages.
The survey on social media abuse also found half of the teachers had had adverse comments posted about themselves by pupils and parents.
Most reported being on the receiving end of online abuse from parents in the past year, compared with 40% in 2015.
There has also been an apparent rise in the number of teachers receiving online abuse from pupils - 55% compared with 48% in 2015.
Teachers' reported online abuse by parents:
"Parent got child to take a photograph of me whilst teaching.
"I used to teach the parent many years ago.
"The parent then posted the picture along with derogatory comments, 'I can't believe he is still teaching.
"'He couldn't teach anybody.'"
"She made comments about my capabilities, made up lies about the state of the pupils in my class, she discussed with her friends and husband about knocking me out, her friends called me abusive names and added to the threats of violence."
"Told daughter off at school, mum put on Facebook that she was going to come to school to punch me."
"Parent threatened to come in and 'sort that bitch out'."
NASUWT general secretary Chris Keates said: "Online abuse has a devastating impact on teachers' and pupils' lives, and yet no serious action is taken by government to ensure that schools are responding appropriately to this abuse.
"There are still too many cases where no appropriate action is taken when abuse is reported to head teachers, the police or the social networks themselves.
"The level of abuse that teachers are suffering at the hands of parents online is simply unacceptable.
"How can pupils be expected to use social media sensibly and safely when parents are using it inappropriately?
"Online abuse is traumatic and potentially life-changing. Victims need strong support through a zero tolerance approach."
A Department for Education spokeswoman said: "Young people and teachers should be able to take advantage of the vast potential that the internet and social media offers to their lives and education.
"But they also have a right to feel safe.
"We want to make sure young people are aware of the risks and dangers - including sending inappropriate images.
"That's why schools should deliver high quality personal, social, health and economic education which is an important opportunity to teach young people about how to stay safe and avoid risks.
"The law is also crystal clear that where teachers find indecent images of children, they must report this to the police."
She added: "No teacher should be subjected to abuse or threatened online.
"Where teachers are, we would urge them to report it to the relevant authority so the appropriate action can be taken."