Which of the following is NOT true according to Piaget’s view of children’s…

Jean Piaget and Bärbel Inhelder, in The Child's Conception of Space, held that a child's grasp of spatial ideas unfolds through a fixed sequence of cognitive stages: topological relations (nearness, separation, order, enclosure) grasped first through direct sensorimotor and tactile-kinaesthetic action, then projective space (viewpoint-dependent relations, built by coordinating different visual and tactile experiences), and finally Euclidean space with fixed distances and angles.

Piaget was explicit that this sequence is fixed by the logical structure of the child's developing mental operations — a logical, psychological order — and not by the sequence in which geometry was historically worked out by mathematicians (topology and projective ideas were in fact formalised well after Euclidean geometry). Checking each statement against this account:

• Progression of geometric ideas follows a definite order — matches Piaget's fixed stage sequence exactly.

• Progression follows a historical rather than a logical order — reverses Piaget's actual claim, since he grounded the sequence in logical necessity, not in the history of geometry.

• Early understanding of space is formed by sensorimotor experiences — matches the first, topological stage of his account.

• Co-ordination of different visual and tactile experiences is required for projective space — matches how Piaget described the construction of projective space.

This lines up with Piaget's wider topological-primacy thesis, that children master topological properties before projective and Euclidean ones purely because of increasing logical complexity, independent of how those ideas arose historically in mathematics.

So the statement that swaps a logical order for a historical one is the one that is not true according to Piaget's view.