This article offers a detailed reading of chapter II.2 of Finnegans Wake, the “Night Lessons” section in which three children (Shem, Shaun, and Isabel) practice their grammar and arithmetic. It begins by tracing the history of the medieval Trivium/Quadrivium system on which Joyce models the children’s lessons. Joyce was first made aware of the pedagogical and iconographic history of the “triv and quad” in 1898, through his reading of John Ruskin’s Mornings in Florence. As is demonstrated, Ruskin’s influence on Joyce persisted from Joyce’s early college essay “The Study of Languages” to FW II.2 written forty years later. Joyce’s longstanding interest in “triv and quad” reflects his sense of a profound union between grammar and arithmetic. In Finnegans Wake, this results in a primitive language based on the archaic sense of “de-nomination” in which numbering and naming are still thought of as a single practice. Ultimately, Joyce’s re-coupling of grammar and arithmetic helps us better to comprehend his own sense of the new language of “wakese” as both verbally suggestive (or polysemous) and arithmetically precise.