"Discovery learning" is not unlike Rousseau's belief that individuals should make sense of the world by reasoning their own way to their own conclusions, and that every mind has its own form.
The power of the environment for learning, one supported by Dewey, originates, also, with Jean-Jacques Rousseau. And, it is argued that child-centered educational theory is "a series of footnotes in Rousseau."
Rousseau's philosophy of education is most clearly seen today in some aspects of the homeschooling movement which takes the child out of mainstream education and what the states says they need to learn and gives them more independence, freedom and space to learn at their own speed and to focus on the topics that they want to study. Rousseau presents a challenge that is still relevant to today's system of education and argues that schools are a bit like sausage making machines. They aim to take different unique children and put them through the factory of education, producing identical sausages.
Rousseau has influenced many movements in American education. For example, the unschooling movement and homeschooling. There are also schools that have based their structure on Rousseau's teachings. The idea of practical education has been popular off and on, and is coming back into favor now to a certain extent. For example, you could argue that project-based learning is an extension of Rousseau's teachings.
Rousseau's effect on the actual educational system of course depends on how inclusive you are in discussing that system. The public education system in the United States is still based almost entirely on the Prussian Model brought here by Horace Mann and still in many ways the opposite of the model that Rousseau favored which allowed for individual interest and motivation to drive the program.
Rousseau's model was one in which the child was not coerced into learning certain things but he suggested that the child will learn what it needs to learn in order to interact with the environment it lives in. Poor children learn from life itself and have no time for formal "education," and he suggested they don't need it. His opposition to a system that children were pushed into stemmed from his feeling that such a system creates slaves rather than free thinking beings.