FIGURE 16 (S803F): Pseudoconceptual reasoning of volume and proportion

The eight-year-old participant (S803F) in Figure 16 noticed size almost immediately and she went about sorting the blocks according to size because she maintained that size made the blocks related to one another and that this being related was what made sense.

This participant’s attempts to demonstrate her understanding of volume and proportion by making use of the concrete characteristics of the blocks was most intriguing: her descriptions and explanations would have made Piaget’s head spin – because conservation of volume had been achieved, but not when it came to proportion. She had spoken about volume and attempted to explain why a different principle applied to the three groups cev, mur, and lag, but she was unable to “see” beyond the perceptually obvious: that even though the lag tower would be bigger in volume than cev or mur towers, the concept of proportion involves a different focus. For her, the volume of the lag tower would be greater than the volume of a cev or mur tower. Therefore, the proportionate relationship between the lag tower and the constituent lag blocks would be different to the proportionate relationship of the cev tower to the constituent cev blocks: because the lag blocks were bigger, the proportionate relationship to the tower would be larger than the proportionate relationship of the cev blocks to the cev tower.