1. a. The board of education or trustees of each school district and the city school district of the city of New York shall ascertain under regulations prescribed by the commissioner and approved by the regents of the university, the number of children with handicapping conditions in such district under the age of twenty-one years and the nature of the handicapping condition of each such child in accordance with the provisions of this section, and shall maintain a register containing the name of each child with a handicap- ping condition who resides in the district, the nature of such child's handicapping condition, the educational placement and setting, if any, of such child.