Literacy rates in the United States were very high during the late 19th Century. I still have my Grandfather's school books from that era. They are written at a much higher level than any University Text printed today. The average 6th grade education in 1900 was far, far more complete than graduating High School today. Elementary level math problems then were based on real world applications. Word problems about if you were paid X amount per day and your rent was X and this was X and you needed a new pair of shoes that cost 50 Cents and you have a nickel left over each day, how long must you save your nickels to buy the pair of shoes. Examples such as this and how to write checks, how compound interest works. The virtue of work and thrift. All of this was found in a third or fourth grade level math book.
Reading the Prefaces of these books is most informative. They all stressed the need to learn how to think, that facts meant nothing without the ability to think.
Of course education was not compulsory then. You had to have the desire to go and you had to pay for your own books. My grandfather worked in a saw mill to pay for his education. He also had to work from a young age to support a house hold with 12 younger brothers and sisters. By age 16 he was a clerk in a dry goods store. By age twenty he was a book keeper. By the time the 20's rolled around he was an accountant and owned his own home and had the most expensive Pontiac you could get at that time.
He lived in a World where nobody handed you anything, you had to have the desire to earn it and then do so. Life was tough for the average person then and perhaps that hardness is what made them able to accomplish so much.