A 4-year-old builds a block tower while commenting to herself about stability…

Concept: a single play episode is classified on three independent axes, one per theorist. Parten classifies the SOCIAL participation of the play, Piaget classifies the COGNITIVE structure of the activity, and Vygotsky classifies the REGULATORY function of the child's speech. A classification is correct only if it holds on all three axes at once.

• Parten's social axis: unoccupied, then solitary (alone and absorbed, not attending to nearby children), onlooker (watching, and perhaps talking to, players without joining), parallel (independent activity beside peers, aware of them, often with similar materials), associative, and cooperative (organised, shared goal, differentiated roles).

• Piaget's cognitive axis: practice or functional play (movements repeated for sensorimotor pleasure, no product), symbolic or pretend play (one thing stands for another), constructive play (materials manipulated toward a product), and games with rules (play governed by agreed, enforced rules).

• Vygotsky's speech axis: private speech is audible, self-directed talk by which a child plans and regulates her own action (self-regulation); other-regulation is action steered by someone else; the zone of proximal development is the gap between independent and assisted performance; scaffolding is the graded support another person supplies.

Application: read this episode once along each axis.

1. Social axis: she pursues her own tower and enters nobody else's activity, yet she is beside peers and monitors them from time to time. Independent activity with peer awareness but no joint undertaking is parallel play, not solitary play (which requires no attention to nearby children) and not onlooker behaviour (in which watching IS the activity).

2. Cognitive axis: she is assembling blocks into a tower, that is, manipulating materials toward a product. That is constructive play. Nothing in the episode is made to stand for something else, and the building is goal-directed rather than movement repeated for its own sake.

3. Speech axis: her talk is about the stability and balance of her own tower and is addressed to no one. Self-directed talk that guides the speaker's own action is private speech serving self-regulation; no other person is steering her, so the regulation is her own.

Cross-check the remaining triples, each of which fails on more than one axis:

• Solitary; Practice play; Other-regulation: solitary play requires her to disregard the children nearby, practice play requires repetition of movement with no product, and other-regulation requires a second person to be steering her.

• Onlooker; Symbolic play; Private speech scaffolding: onlooker behaviour makes watching the whole activity, symbolic play requires one thing to stand for another, and scaffolding is support given BY another person, which self-talk is not.

• Cooperative; Games with rules; Zone of proximal development: cooperative play requires a shared goal and differentiated roles, games with rules require agreed rules between players, and the zone of proximal development describes assisted rather than independent performance.

Result: the episode is parallel play on Parten's axis, constructive play on Piaget's axis, and self-guided private speech on Vygotsky's axis.