FIGURE 21a (S1108M): A highly elaborate diffuse complex with the emergence of “ideas” coupled with pseudoconceptual inconsistencies

The participant in Figures 21a and b was the only one of the eleven-year-olds to formulate the principle of the double dichotomy. During his session, he entertained a good number of sophisticated possibilities for grouping the blocks before he arrived at the simplicity of the double dichotomy. This eleven-year-old was highly articulate and his well-developed language could have been taken as an indication of mature, logical, and abstract thinking. However, regardless of the elaborateness of the approaches that he suggested, two main elements emerged which I took to be indicative of diffuse thinking in complexes and a pseudoconceptual disregard for the need for consistency of principles to be applied across the four groups.

In starting, this participant (S1108M) promptly abandoned the shape approach because he reasoned that the semi-circles were not circles, squares, triangles “or rhombuses”. Colour was also briefly considered and logically discarded. As depicted in Figure 21a, he advanced the following solution as a possibility: the bottom right-hand group of blocks had six sides each; the triangles had five; the circles had three; and the group at top right did not conform to the number-of-sides approach because they were too varied to be grouped together. When four blocks had been turned over (he chose which ones), these seemed only to confirm his hypothesis: “I think I got it right” he exclaimed – until the mur hexagon was turned over. He said “Oh, no!” but moved immediately to turn another block over. I stopped him and asked him to explain “Oh, no!”: and his explanation was “I thought mur would have five faces but this one has six” (there were in fact eight by his original tally which is why his last group above didn’t conform neatly to the number-of-sides hypothesis). We then discussed his number-of-sides idea in relation to the newly turned mur hexagon: when I noted that it had eight sides, he instantly suggested that perhaps the sorting could be on the basis of even numbered sides. A fair amount of discussion followed, mainly because he was thinking things out aloud to himself, and then I allowed him to turn over another block. And even though he hadn’t removed the blocks that he’d placed according to the number-of-sides hypothesis, it wasn’t because he was insisting on their “correctness” so much as that he was otherwise involved in thinking about what he could do next. He said “...it didn’t make sense [the newly turned lag block]” and “it’s probably not working… neither would colour… or angles…”.

At my suggestion that we return the blocks to the middle of the board, and try again, the participant noticed “an interesting pattern” in the numbers of shapes of some of the blocks, and the numbers of colours of some of the others. I asked how complex that type of solution would be, and he answered “Extremely”. From this point on, because this participant advanced a number of combinations and permutations in trying to arrive at the solution, the turned-over blocks seemed (tantalizingly) to support one hypothesis after another.

FIGURE 21b (S1108M)

In Figure 21b it could be construed that this participant (S1108M) had begun to get an idea of height and size. However, his subsequent descriptions for these groups did not include mention of height or size but instead became increasing indicative of a regression to a more diffuse mode of thinking compared with the sophistication of his earlier more logical approaches. For example, the bik group (top right) was described as “This is just smalls and six [sides for] two of them and six and four sides and the semi because the rhombus just looks like them”. The cev group (top left) was described as “Just the rest of them”; the lag group as “Large and six sided”; and the mur group (bottom left) as “Large, and two triangles and then this [hexagon] is kind of like this [the white circle]”. Further, the lag group (bottom right) contained a circle which he quirkily explained as “Because it says ‘lag’ on top of it”. Although Hanfmann and Kasanin’s observation regarding some participants who start with a more logical approach can descend to a less logical one as the session continues could apply to this participant (because it is very easy for any of us to be overwhelmed by the possible combinations of colour, size, shape, and height), it seemed to me that the sophistication of his hypotheses and suggestions was not consistently or uniformly applied across the four groups, and this lack of consistency was a clearer indication of a pseudoconceptual disregard for the totality, in addition to the unclearly formed ideas which he seemed to be “trying on for size”. Shortly after the discussion above, the mur group was analysed as “having only minor differences… related to colour… whereas here [bik], the differences are more pronounced”. Although this was an accurate observation of his groupings, it did not question the validity of the underlying principles or the fact that they were not being logically or consistently applied.

As the session continued, he would ask for a block to be turned over, for example, to see “in which areas bik is differentiated” or he explained that the bik group was “rhombuses and semi-circles”, and that there could be some kind of relationship between the small cylinders as possible mur candidates (where the connection between the triangle, the hexagons, and the circles could be as yet some undiscovered link). He also eliminated groups of different shapes on the basis of one shape per group because it could not be logically applied. When he did discover the solution he exclaimed that “It was an extremely good game… because it tackles you. I’m supposed to be very good at this kind of thing but this one totally got me.” He then explained how other games based on guessing subsequent patterns in terms of colour and a number of other factors “which work on the basis of the process of elimination” had influenced his engagement with the blocks. This participant (S1108M) also admitted that it (Vygotsky’s Blocks) “was supposed to be such a big thing, so it must be extremely hard so you look for all the hard things you could think of”.

This participant’s response to the blocks was indicative to me of being at the crossroads between the use of elaborate possible connections in which attempts were made to follow a trend of thought along abstract lines, coupled with a pseudoconceptual application of these as revealed by their inconsistent application as guiding principles.