As used in this chapter, an "annual average full-time equivalent student" means an eligible student who is a full-time equivalent student on each of the count dates in October through June: Provided, That a student electing to attend the summer quarter in lieu of attending the autumn, winter, or spring quarter will be counted during the summer months of June through August. No individual student shall be counted as more than one full-time equivalent student on any count date or more than one annual average full-time equivalent student in any September 1 through August 31 period for the purposes of claiming and allocating state and federal kindergarten through twelfth grade moneys to school districts and to the University of Washington.