Experience is the best of schoolmasters; only the school-fees are heavy.

Thomas Carlyle (1795–1881) Scottish essayist and historian

Essay (1828-04), “Goethe’s Helena,” Foreign Review, No. 2, Art. 5
    (Source)

The essay reviews Goethe's Sämmtliche Werke, Vollständige Ausgabe Letzter Hand, First Portion (1827). Collected in Carlyle, Critical and Miscellaneous Essays (1838–1839).

Carlyle enclosed the phrase in quotation marks, which may mean it was from someone else or a common adage at the time. On the other hand, Carlyle sometimes similarly quoted himself.

Also attributed to Jean-Paul Richter, Samuel Taylor Coleridge, Heinrich Heine, and Minna Antrim. See, as a predecessor, Franklin (1743).

For more discussion about this quote's origin and variants, see Quote Origin: Experience Is the Best of Schoolmasters; Only the School-Fees Are Heavy – Quote Investigator®.