Table 2 Synthesis of PSTs' use of... | Emerald Publishing

Table 2

Synthesis of PSTs' use of visualisations, patterns of variation, and reflection

Phase in learning cycle	Type of visualisation	Patterns of variation	Didactical function	Sustainable problem-solving focus	Reflective orientation
Planning	Representational line segments drawings pie charts	Separation Contrast	Making intended critical aspects visible	Maintaining invariant solving methods while varying problem contexts	Anticipating difficulties
	Representational line segments drawings pie charts	Separation Contrast	Making intended critical aspects visible		Aligning with prior knowledge
	Transformational ratio schemas	Similarity	Structuring proportional relationships	Supporting transfer and sustainability of methods	Sequencing and scaffolding
	Transformational ratio schemas	Generalisation Fusion	Structuring proportional relationships	Supporting transfer and sustainability of methods	Sequencing and scaffolding
Enactment	Invariant structural rectanglesratio schemas	Similarity Generalisation	Supporting relational reasoning	Linking method to structure rather than procedure
	Representational Invariant structural dynamic use	Contrast	Adapting explanations; clarifying misunderstandings	Stepwise and holistic reasoning; transfer across tasks	Monitoring and adapting instruction
		Separation
		Fusion
Post-lesson	All types evaluated comparatively	Contrast Separation	Identifying gaps between intended and lived critical aspects	Preventing superficial strategy use Strengthening conceptual focus	Refining future instruction
Individual reflection	Invariant structural Transformational valued retrospectively	Fusion	Support generalisation, dialogue, metacognition	Developing sustainable teaching strategies and professional judgement	Theory–practice integration

Phase in learning cycle	Type of visualisation	Patterns of variation	Didactical function	Sustainable problem-solving focus	Reflective orientation
Planning	Representational line segments drawings pie charts	Separation Contrast	Making intended critical aspects visible	Maintaining invariant solving methods while varying problem contexts	Anticipating difficulties
	Representational line segments drawings pie charts	Separation Contrast	Making intended critical aspects visible		Aligning with prior knowledge
	Transformational ratio schemas	Similarity	Structuring proportional relationships	Supporting transfer and sustainability of methods	Sequencing and scaffolding
	Transformational ratio schemas	Generalisation Fusion	Structuring proportional relationships	Supporting transfer and sustainability of methods	Sequencing and scaffolding
Enactment	Invariant structural rectanglesratio schemas	Similarity Generalisation	Supporting relational reasoning	Linking method to structure rather than procedure
	Representational Invariant structural dynamic use	Contrast	Adapting explanations; clarifying misunderstandings	Stepwise and holistic reasoning; transfer across tasks	Monitoring and adapting instruction
		Separation
		Fusion
Post-lesson	All types evaluated comparatively	Contrast Separation	Identifying gaps between intended and lived critical aspects	Preventing superficial strategy use Strengthening conceptual focus	Refining future instruction
Individual reflection	Invariant structural Transformational valued retrospectively	Fusion	Support generalisation, dialogue, metacognition	Developing sustainable teaching strategies and professional judgement	Theory–practice integration