Beginning Monday, more than 100,000 struggling Brooklyn students will stay at school longer for a new tutoring program. Department of Education officials say the 37 and a half-minute sessions will create a small class setting by having no more than 10 students per teacher. In most schools the lessons will be held four times a week. The extended school day is a part of the teachers? new labor contract. The extra time adds up to an extra two weeks worth of class time for Brooklyn and city students. Officials estimate Brooklyn taxpayers will have to pay an extra $48 million a year to cover the cost of extra school buses.