Any child entitled to attend the public school of any school district situated on the border of Louisiana, Arkansas, Oklahoma, or New Mexico who finds it more convenient to attend the public school in a district in the contiguous state may have the apportionment of the state and county available school funds paid to the school district of the contiguous state and may have additional tuition, if necessary, paid by the district of the child’s residence on terms agreed on by the trustees of the receiving district and the trustees of the residence district.