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Parents have raised their concerns after children were told to stay away from windows and doors and crouch under tables at school.
Meopham School, in Wrotham Road, Meopham, implemented its emergency plan last Wednesday after two boys were spotted in the grounds. The heads say they did so because "the safety of our school community is at the heart of every decision we make".
A concerned mum – who asked not to be named – said her terrified son was calling her and begging to be picked up.
She said: "They were frightened for their lives. For a whole hour I was out of my mind. It caused absolute pandemonium.
"My son was begging me to come and pick him up. He did not want to go to school the next day."
She believes the lockdown protocol was unnecessary and caused more anxiety to the students.
The parent explained children were told on their first day about a code they would hear over the tannoy if the secondary school needed to instigate the lockdown procedure because a serious incident was ongoing or there was an emergency.
She added: "The children did not need to be dragged into this. My son called me and was in tears, screaming down the phone and I could hear screaming in the background.
"They are old enough to understand. They did not need to be so cryptic. It was not the right thing to do to scare the children."
She said teachers should have told pupils what was going on so they did not assume the worst and that it could have been handled differently.
In a letter issued to parents last Thursday, executive head teacher Suzanne Dickinson and head of school Kate Girling said it was a "precautionary measure".
They added: "As we made you aware yesterday, two youths unknown to the school, accessed the school playing fields at lunchtime on scooters.
"The youths did not leave the school site when asked to do so, and were behaving in a manner which could have posed a potential threat to the safety of our students and staff.
"As we are sure you will understand, the safety of our school community is at the heart of every decision we make. As a consequence we decided to take the precautionary measure of deploying our lockdown procedures.
"We understand that taking a decision to instigate our emergency lockdown procedures is likely to cause concern to all members of the school community."
The letter explained every school in the country is required to have a plan: "Government guidance states that when a lockdown is called, students and staff should be ushered into the nearest classroom, doors and windows locked, blinds drawn, and every effort should be made to get out of the line of sight of a potential attacker.
"This includes asking students to move to the back of the classrooms, away from the door, and to get underneath tables as an added precaution."
Police were called at 1.21pm to the incident to reports that two boys had trespassed onto the school. They said later the suspects had left the area and officers were making inquiries into the circumstances.
Meopham School was contacted for more information.