Why is asking 'what is this chord doing?' a more powerful analytical question than 'what Roman numeral is this?'
Think about your answer, then reveal below.
Model answer: Roman numerals identify chords by their scale position, but the same chord can serve different functions depending on context. A vi chord usually provides tonic-substitute function, but the same pitches in a different harmonic context could behave differently. Functional thinking reveals the underlying drama of tonal music — departure from home (subdominant), accumulation of tension (dominant), return to rest (tonic) — which is the real engine of progression. It also explains exceptions: why a deceptive cadence works, why ii substitutes for IV, why diminished chords are so restless.
Functional analysis unlocks harmonic substitution, explains cadence types, and reveals the emotional logic behind progressions. A student who only knows Roman numerals can label chords; a student who understands function can explain why progressions move the way they do and compose convincing music. The three functions (tonic, subdominant, dominant) act as a grammar for tonal music — knowing the grammar lets you understand and generate sentences, not just label individual words.