She questions Joel using his chalk, possessed of no magic, for part of the maze. Crucially, Melody doesn't understand what's happening at first. They work together to trap enemy chalklings inside said maze.
What they end up doing requires both of them, as she draws the maze he tells her to, while he waits and times when to get the Scribbler's attention. Joel can't defend himself without Rithmatic powers, and Melody panics, unsure what to do with the powers she has. The dorm fight makes it clear that neither alone is enough. The book traces their growing friendship and trust, leading up to the twin climaxes: the dorm fight and the melee. However by the end, they can work in harmony to be more than the sum of their parts and act as a capable Rithmatist. Alone, neither could be called a fully competent Rithmatist, even on the level expected of a student. As we are introduced to them at the beginning, he's an ordinary non-Rithmatist (just a student attending the general school who is obsessed with Rithmatics) and she's a failing Rithmatist (struggling with the basics and wishing she could drop out). Joel and Melody are arguably the two most major characters in the novel. This answer will lack nice direct quotes because I only managed to get my hands on an audiobook. Coming at this after another re-read, I think that there's something clever going on with this title: when it says "The Rithmatist", it's actually referring to two people together (Joel and Melody).
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