We have to remember no education is "free", though I understand why it's often referred to as so.
Essentially, "free education" is the pooling of a society's resources to provide educational services to all of those that live within the society. Certainly if education were not socially funded, class warfare among other issues of inequality would ensue, since many families would not be able to afford the education, if even allowed to attend.
Education in the United States suffers a few issues. The funding is there, not well allocated in some respects such as unnecessary paid positions in government and schools in place of outdated textbooks. Teachers are paid well and receive many many protections and benefits relative to other developed nations. However, money doesn't fix the societal and cultural defects that interact with the educational system. For instance, countries that are more cohesive, many of which are located in East Asia, are mostly homogeneous in comparison to the United States and are able to excel with less funding since the parents, teachers, and students have clear expectations of their duties and are VERY reverent toward duties. Parents from family to family share common traditions and roles in their childrens' education. In the United States, there is not a strong social cohesion by which binds and obligates that parents perform their duties in a uniform fashion. Thus, some parents will be more active while others will be less active, in addition a difference in the fashion of these interactions. It would seem the bar is raise by societal pressure in Eastern Asian whereas the United States, "the land of the free" is more heterogeneous in customs and cultures and hasn't dealt with these differences as Canada has, in that they do more uniformly maintain expectations fairly ubiquitously. Essentially, the United States likely won't improve or keep pace with Eastern nations if the real problem, the social structure, is not addressed.
Spending on Education to Standardized Test Scoring