There was a big push for reform of all kinds, military, political, etc. which is called the Tanzimat. This was kicked off officially by the Gulhane Edict (1839) which, in some ways, tried to shift the Ottoman self-definition from an empire to a modern-nation state. The reforms that followed included declaring that the citizens of the empire were equal regardless of faith, establishing an Academy of Science, establishing post offices and telegraph lines, opening factories, etc.

One area which the state tried expanding into during the Tanzimate period was education. The reason given for this was usually that foreign schools, especially of the missionary variety, were possible sources of nationalism and foreign allegiances which undermined. The push for these schools came from both local actors such as concerned parents and community leaders who thought that these missionary schools would convert good Muslim/Maronite/etc. kids to Protestantism or other forms of Christianity. Still, many families would send their children to these foreign-run schools to give them an education in foreign languages (i.e. French) needed for a successful business.

In response to this, there was a push to increase the reach of public education. The languages taught in such schools were Ottoman Turkish and Arabic. The textbooks and morality primers, by the late 19th century, were provided by the Ministry of Public Education. There were also schools for military and schools for medicine and schools for the children of Anatolian nomadic peoples (in order to bring them further into the fold of the Ottoman State and away from whatever subversive foreign power that might try to influence them). Mind you, all this effort was sometimes a bit spotty and not always carried out to the fullest extent due to funding issues. The buildings used for schools were sometimes old, re-purposed medresses and good qualified, trained professional teachers were in low supply, partly due to the lack of many training programs. I recommend Selim Deringil's "The Invention of Tradition as Public Image in the Late Ottoman Empire, 1808 to 1908" on such matters.

Edit 1: Centuries all look the same to me. Derp.