“Educational facilities will be extended and better standards of morality will be established. Political institutions, too, will be improved. In this way a backward nation can develop into a progressive state.”

Source: Dictionary of political economy, 1818, p. 159, as cited in: Zabieglik (2002).

Widely attributed to Gandhi, sometimes citing Ramachandra Krishna Prabhu, The Moral Basis of Vegetarianism (1959). (Cf. Ralph Keyes, The Quote Verifier (2006), p. 74.) However, it is not found in that essay http://www.mkgandhi.org/ebks/moralbasis_vegetarianism.pdf nor in any of Gandhi's Complete works. http://animalsmattertogod.com/2013/09/13/mahatma-gandhi-hoax-quote-greatness-of-a-nation-and-its-moral-progress-can-be-judged-by-the-way-that-its-animals-are-treated/
The original quote seems to be by David Strauss, The Old Faith and the New (Der alte und der neue Glaube, 1872, trans. by M. Blind, New York: Henry Holt & Co., 1873), vol. II, ch. 71, p. 59 https://archive.org/stream/oldfaithnewconfe01stra#page/59/mode/2up: The manner in which a nation in the aggregate treats animals, is one chief measure of its real civilization.
Similar quotes, not attributed to Gandhi, are found throughout the twentieth century: e.g. The great actress, Mrs Fiske, once said to me, "The civilization of any country can be told by the way it treats its animals" (Zoe Berkeley, "Zoe Berkeley's Corner", Salinas Index-Journal, 1933-07-01, p. 8).
Attributed to Gandhi since at least 1980: The seal hunt truly is Canada's shame and we would do well to think of the words of Gandhi when he said, "The greatness of a nation and its moral progress can be judged by the way its animals are treated" (Doris Potter, Letter to the editor, The Gazette (Montreal), 1980-03-18, p. 8).
Disputed

Special Message to the Congress on Education (20 February 1961) http://www.jfklink.com/speeches/jfk/publicpapers/1961/jfk46_61.html
1961
Context: Our progress as a nation can be no swifter than our progress in education. Our requirements for world leadership, our hopes for economic growth, and the demands of citizenship itself in an era such as this all require the maximum development of every young American's capacity. The human mind is our fundamental resource.

Source: The Natural System of Political Economy (1837), p. 30

Gemba Kaizen: A Commonsense Approach to a Continuous Improvement Strategy, Second Edition (ed. McGraw Hill Professional, 2012), ISBN 9780071790352

Charles Dupin (1831), Discours sur le Sort des Ouvriers [Discourse on the Condition of the Workers] Paris: Bachelier Librairie. p. 1. ; Translation Wren & Bedeian (2005, 73)

Source: Ethics and Education (1912), The Call of the Past, pp. 9–10

Source: The Evolution of Civilizations (1961) (Second Edition 1979), Chapter 4, Historical Analysis, p. 122

1920s, Address at the Black Hills (1927)