Teacher and Learner

This flow traces the reciprocal bond through which teaching directs attention while learning turns direction into independent understanding.

increasingBearing stren­gth in each eventdecreasing

Instructional Distance

Instructional Distance Misalignment The teacher names a figure while the learner searches for the named parts. Attention becomes delayed and easily broken. Fragile Bond The classroom relationship suffers because teacher intention does not immediately become student perception.

Common Colours

Common Colours Shared Vocabulary Teacher and learner receive the same visible names through colour. The diagram reduces the distance between instruction and recognition. Trust The learner can follow the teacher without first mastering a separate code of letters.

Guided Attention

Guided Attention Sequential Focus The teacher directs the class from one coloured part to another as the proof develops. The learner's attention follows a path rather than wandering among labels. Collaboration The proof becomes an activity shared by voice eye and diagram.

Independent Seeing

Independent Seeing Internalized Method The learner gradually identifies equal and corresponding parts without constant verbal prompting. The teacher's guidance has become a habit of visual analysis. Development Dependence on instruction gives way to independent inspection.

Shared Reasoning

Shared Reasoning Mutual Achievement The teacher supplies a visible structure, while the learner supplies attention and judgment. Neither role is passive. Educational Bond The success of the method lies in turning instruction into a partnership in proof.

during the critique of ordinary classrooms

during the first coloured class example

during oral demonstrations of triangle properties

during the propositions on circles and parallels

near the educational conclusion