The Teacher's Changing Role

This flow traces the teacher's movement from verbal lecturer to coordinator of shared visual attention and reasoning.

increasingBearing stren­gth in each eventdecreasing

Verbal Lecturer

Verbal Lecturer Conventional Practice The teacher names points lines and angles through strings of letters. Students must reconstruct the intended figure while listening. Risk A small failure of attention can produce confusion before the proof has begun.

Diagram Organizer

Diagram Organizer Coordinated Colour The teacher assigns colours to corresponding parts and maintains those assignments across the argument. The figure becomes a prepared field of attention. Shared Focus Every pupil can be directed toward the same visible magnitude at the same moment.

Oral and Visual Guide

Oral and Visual Guide Dual Address The teacher speaks while the class sees the relevant colour and form. Sound explains sequence while vision locates the objects under discussion. Efficiency The two channels reinforce rather than compete with one another.

Proof Facilitator

Proof Facilitator Guided Comparison The teacher can direct attention to equal coloured sides and angles before stating the inference. Students see the data while hearing its consequence. Less Recitation The teacher's role shifts from enforcing memory to arranging evidence.

Classroom Reformer

Classroom Reformer Broader Reach The teacher is imagined as capable of instructing large groups without multiplying verbal confusion. The method supports public and private instruction alike. New Authority Teaching becomes the art of making reasoning visible.

before the proposed method is introduced

during the explanation of coloured diagrams

during the discussion of classroom demonstrations

during the propositions on congruent triangles

at the educational conclusion of the introduction