He identifies three different stages or rhythms in educational methodology that happen in tandem and in rotation (I visualize a geocentric universe filled with epicycles of rotating moons and planets to illustrate the layers and rings of motion in teaching). He bases these stages on Hegel's Thesis, Antithesis and Synthesis, but he adapts them to the classroom and human learning. He calls these rhythms Romance, Precision, and Generalization. In Romance, the teacher needs to awake the sense of wonder and curiosity in a student's mind. This will provide the impetus to pursue the learning to the next stage: Precision. In the second stage, the student studies by drill and repetition the formulae, rules, and grammars that build upon a thorough knowledge of a filed. In the third stage, Whitehead declares that the student needs to move into a realm of Generaliztion. In this rhythm, the student makes connections, applications, and full, mature usage of the material and ideas.
I wish more teachers and teachers interested in developing their pedagogical methodolgy would take the time to read this short masterful book.