By LARA SUKHTIAN and JOSEF FEDERMAN .c The Associated Press

JERUSALEM (AP) - Armed guards stood watch outside Israeli schools. Children in the West Bank climbed over the concrete slabs of an Israeli barrier. Students cowered as warplanes roared overhead in the Gaza Strip. It was back to school, Middle East style, in Israel and the Palestinian territories, where schools have felt the brunt of four years of fighting, budget cuts, and violence.

The school year opened Wednesday under the shadow of new violence, a day after 16 people were killed in a Palestinian suicide bombing in the southern city of Beersheba. The attack ended a months-long lull inside Israel and put a nation already obsessed with security on sudden alert.

``When I see these children, it only strengthens my determination,'' Prime Minister Ariel Sharon said during a visit to a kindergarten class in the West Bank settlement of Maaleh Adumim. ``I want these children, when they grow up, to live in peace and quiet.''

Police stepped up security throughout Beersheba and set up checkpoints to monitor traffic coming in and out of the city, said police spokesman Gil Kleiman.

Police also increased patrols along the ``Green Line,'' the invisible frontier between Israel and the West Bank, Kleiman said. The attackers Tuesday came from the West Bank city of Hebron.

In Beersheba, police cars and armed officers greeted children walking into schools. Schools brought in social workers and psychologists to help children cope.

``The celebratory atmosphere has been ruined,'' said Tamar Shoui, principal of Ben Gurion Elementary School.

In all, 13,000 officers, security guards and soldiers - some armed with submachine guns - were deployed at Israeli schools, well above the typical daily level, Kleiman said.

He noted, however, that police are mobilized every year for the first few days of school, although this year the beefed-up presence will remain in effect for several weeks because of the heightened alert.

In the West Bank, 13-year-old Muntaha Aude spent an hour getting to school just over a mile from her home in the northern West Bank village of Jbara. The village has been surrounded by Israel's separation barrier, leaving one gate and one checkpoint to move in and out of town.

``The whole process takes about an hour,'' she said. In ``normal'' times, she added, she would walk to school in less than 15 minutes.

Israel says it is building the contentious barrier, which is about one-quarter complete, to prevent attacks like Tuesday's suicide bombing. Israeli officials noted that the attackers came through an area where the barrier has not yet been built.

The completed sections, however, have caused hardship for thousands of Palestinians by separating them from schools, jobs and services.

Ziyad al-Nazem, spokesman for the Palestinian Education Ministry, said nearly 3,700 Palestinian students crossed the barrier each day at the end of last school year. ``We expect that the problem will continue to deteriorate as the barrier is built,'' he said.

Altogether, 1.2 million Palestinian children returned to school on Wednesday.

The barrier has hit the Jerusalem suburb of Abu Dis especially hard. Many residents work or study in Jerusalem. Now, the area is almost entirely sealed off by 25-foot concrete slabs.

Early Wednesday, children congregated around an uncompleted section of concrete, where a pile of rocks allowed them to climb over a lower wall. Israeli soldiers stood by, checking identity cards, as parents peeked through cracks in the wall to make sure their children reached the taxis and buses waiting on the other side.

``It's really frustrating when you know you're only a five-minute drive from your school, but it could actually take as long as an hour to get there,'' said Salwa Matouq, 40, a teacher and mother of two children.

In Gaza City, students in crisp new uniforms walked to school as Palestinian police tried to control the area's notorious traffic. An Israeli F-16 warplane roared overhead, causing 6-year-old Rami Karam to burst into tears. ``Their sound scares me,'' he said.

Palestinian Education Minister Naim Abu Humous said Israel's restrictions have aggravated an already desperate situation. The cash-strapped ministry said the average classroom is 35 students, and in some cases large as 50. More than 95,000 students go to school in afternoon shifts to alleviate the overcrowding, officials said.

Israel is grappling with its own education crisis, with test scores dropping and violence on the rise. Israeli education officials recently unveiled a sweeping reform plan to reverse the trends.

At the Kadoori School in northern Israel, students and staff wear a uniform of sorts - purple shirts - to address the problem. ``Discipline starts with things like this,'' said principal Hillel Hillman.