A decision to allow a Catholic school to become a publicly funded charter would profoundly impact American education, experts say.

The justices have allowed vouchers for religious schools and required equal treatment in tuition programs. But direct government payments to religious public schools pose a new test.

The Supreme Court will hear arguments Wednesday in a blockbuster dispute over the nation’s first religious charter school, a case that critics say has prompted a “crisis of identity” in the school choice movement and that could vastly expand taxpayer funding for religious education.