FIGURE 19 (S1101F): Pseudoconceptual reasoning merging into the classical pseudoconcept “proper” within a diffuse complex

The eleven-year-old participant in Figure 19 (S1101F) started her first attempt by creating four groups based on shape. The groups she created were “all triangles”, “all squares”, “all round and the circles” (including the hexagons), and last group of semi-circles and trapezoids was described as “all the ones that have been cut” (quite an elegant solution, and certainly one that I hadn’t thought of). The participant turned over the lag trapezoid and read its name, and immediately the cev semi-circle and said “Oh! A cev! So it’s not the same one”. She left it there and turned the orange lag circle over “Lag!” she said, “but why these two? [the yellow lag trapezoid and the orange lag circle]”. I assured her that this would be something she would discover for herself in the process of playing the game. I suggested we put the two lag blocks together, and asked if we could move the cev semi-circle to the middle of the board for now. It appeared that she did not pay any attention to this cev block at the time because she was very eager to continue turning over the blocks and she needed to be restrained and reassured about getting things right or wrong. With prompting, she said that she was unable to find another way to sort the blocks, and when asked what the discovery of the cev semi-circle had done to her idea of the cut-off group, she then said it meant “That there is no cut-off group”. We agreed to move the cut-off blocks into the middle of the board and after about a minute she said “Maybe it’s like one of each colour”. She started to sort the blocks in this way, saying the names of the colours as she sorted the blocks in the first group.

The photograph featured in Figure 19 was taken eight minutes into the session, and represented this second attempt to sort the blocks. She started off by suggesting that one of each colour per group (starting at top right) was a possibility: however, when it came to the second group (mur at bottom left), she said “Triangle, square, one cut-off one, and a circle”. These moves revealed quite clearly the fluidity and instability of her approach in that colour was given less importance after only one group had been grouped in this way, and she had created a charming example of a chain in the mur group – shape to same height to similar shape to flat as per the trapezoid. She repeated this with the lag group, but then began to swap quite a few blocks to fit with her emerging approach of one of each colour but particularly one of each shape per group. In starting the fourth group, she noticed that there were not enough colours to go around, and instead of stopping to count the colours and the shapes, she continued with much re-arranging and increasingly random moving of the blocks to get them to fit her idea of one shape per group. It was at this point that the participant (S1101F) noticed that there were (only) two semi-circles (which she had not perhaps been quite conscious of before when she included them in the cut-off group), but this observation did not influence her insistence that there had to be a way to find one shape per group. Her ignoring this fact (as well as her earlier disregard about the cev semi-circle’s effect on her cut-off idea until prompted), led me to see quite clearly that her approach was in fact pseudoconceptual: although her approach seemed to be one of systematic intent, its pseudoconceptual and concrete and factual connections were evident in this matter of the number of semi-circles, a tiny detail that could easily be overlooked by any researcher.