During the progressive education reform movement what were the theories that came out of the progressive era? What do they look like in practice, when attempted? And what are the obstacles to Progressive reform in some areas?

In the early twentieth century, progressive education reform entailed the reconstruction of teaching methods, curricula and academic standards to reflect stronger democratic ideals; the ultimate goal was to turn American citizens into more engaged participants in democracy by creating greater access to education that promoted intellectual, creative, and psychological growth.
The roots of progressive reform theory lie in the works of European thinkers such as Rousseau and Locke, but were expanded on by later proponents in both America and Europe, including John Dewey, Helen Pankhurst, Rudolf Steiner, and Maria Montessori. By far the most influential of these was Dewey, who prioritized the needs and individuality of the student over the sanctity of a school as a domineering institutional voice. Dewey considered it the responsibility of the education system to consider a student's psychological as well as intellectual development by nurturing children's instincts, curiosity, and inquiry. In practice, the Dewey system entailed classroom discussion and student engagement rather than reliance on rote memorization, straightforward textbook learning, or lectures. Implementing Dewey's educational theories also resulted in a proliferation of studies in creative arts and manual skills that would encourage a more balanced and autonomous individual. 
Dewey's ideas resemble those of Rudolf Steiner, the inspiration for Waldorf education. Steiner viewed childhood development and learning as comprising three stages: practical activity and creative experiences in early childhood; artistic identity and social awareness in elementary school; and critical reasoning and empathy in secondary school. Thus, Steiner wanted education to cultivate children's intellectual, artistic, and practical skills. In practice, Waldorf schools function very differently than conventional ones. For example, Waldorf education encourages a non-competitive environment, there are no textbooks from kindergarten through fifth grade, arts classes are considered essential and not a 'frill' or 'privilege,' and teachers often stay with a certain class for several consecutive years. The ultimate goal is to create ethically mature, socially adjusted citizens.
One of the primary obstacles to progressive educational reform lies in its accessibility; many progressive schools are elite, private institutions that are inherently segregated along racial and economic lines because only certain families can afford the tuition. This is antithetical to progressive education values of democracy, equality, and tolerance. Furthermore, standardized testing, which is aimed at 'objectively' assessing intellectual skill regardless of academic background, creates pressure across institutions that creates undemocratic disadvantages; economically privileged students are able to tutor and prepare for such tests, skewing access to college and scholarship opportunities that use the test results as benchmarks of aptitude.