The Education Department is proposing legislation to improve student loan collections by sending aid checks to schools instead of students and by forbidding further aid if a student is in default at any school.

Those were two steps outlined yesterday to a House subcommittee by Edward M. Elmendorf, assistant secretary for post-secondary education.

"We believe such a policy would provide better assurance that loans are used for educational purposes, and would reduce the potential for aid duplication, and the risk of no-show defaults," he said.

Current law provides only that a student in default or owing a refund on a grant may not receive further aid at the same school.

Furthermore, Elmendorf said, the department plans to expand current requirements for exchanging information about defaulters with credit bureaus, enabling state guarantee agencies also to exchange information.

John F. Simonette of the General Accounting Office said the department's total loan collections for fiscal 1982 were about $6 million less than in fiscal 1981, declining from $659 million to $653 million, while its total receivable accounts grew by over 5 percent. "Of the six agencies we reviewed, this was the only instance of an agency reporting declining total collections," he said.

"The decrease in Education's total collections, when factored by the corresponding increase in receivables, computes out to a $41 million relative drop in collections," Simonette added. "In terms of the $225 million target for increasing collections given to Education by the Office of Management and Budget, the agency, therefore, fell short of the goal by $266 million."