Reform has always been a tradition in America. From the Revolutionary period through today, Americans believed in the idea that they could raise their quality of life. This seems to be an essay question therefore I cannot compare and contrast four reform movements however I can provide you with topic information.
1. The Abolition Movement- became a crusade between the 1830's and 1860's to end slavery. The movement moved into the political realm when the slavery question became connected to the admission of new states into the union. The 13th Amendment abolishing slavery in 1865 was their victory.
2. The Suffrage Movement- women began to vocalize their demand for equal rights, especially the right to vote. The first Women's rights Convention was held in 1848 at Seneca Falls, NY. The passage of the 19th Amendment was a great victory for their reform.
3. Reform of the spoils system- elected officials awarded political jobs to those who were loyal to their campaign regardless of ability. After President Garfield was assassinated by a disgruntled person who was promised a job but forgotten Congress passed The Pendleton Act 1883 creating the Civil Service Examination System. Appointments to jobs were based upon the scores recieved.
4. Settlement Houses- were created to assist the urban poor, mainly immigrants. They were located in the poor neighborhoods and offered some education, English classes, clinicis, and job training programs.
Public Education arrives later than the mid-1800s. But, if you are looking for nineteenth century reform movements, how about: women's rights, temperence, abolitionism, and the various denominational and religious reforms that occured in the wake of the Second Great Awakening.
To an extent, these four movements amplified and 'caused' each other. Women were active participants in the Second Great Awakening Methodist tent meetings that led to a reconsideration of the morality of slavery. As women fought to free slaves, they realized that they lacked the very rights that they sought for slaves. So, women organized the Seneca Fall Convention in 1848. The women's movement in the nineteenth century was partly about freedom from abuse in the home. So, women led the charge for temperance in order to stop drunken husbands from beating their wives.
Government schooling is a recent phenomenon. Formerly, schooling was in the home from tutors if the family was well off, and in store-loft and old-field academies if the family was not well off. The leaders who raised this country to greatness came from the old method of schooling, while it has been placed in its present state by leaders who come from the new method.
If you take Thomas Jefferson's argument for separation of church and state and substitute "school" every place that that argument says "church," you will have a very good argument for separation of school and state.
Here are some citations: two about the old way of schooling, one about the rigor of the curriculum, and one about education without schooling.
Joynes, Edward Southy. 1902. "School Training in the Early Days," extract from "The ‘Old Field’ School," in The Educational, May, 1902, reprinted in Library of Southern Literature, VII, 2870-2872, The Martin & Holt Company, 1907 & 1909.
Poe, Edgar Allen. 1836. "The Classics," Southern Literary Messenger, 2, 4 (Mar.), 221-233. This one is on the Internet at a University of Michigan site.
Pudner, H. Peter. 1971. "People Not Pedagogy: Education in Old Virginia," Georgia Review, 25 (Oct.), 263-285.
Zettler, B. M. 1912. "School Days" in War Stories and School-Day Incidents for the Children. New York: The Neal Publishing Company, 23-31. This one is on the Internet.