It was expected that children would perform better on the problems needing an auxiliary task when presented with the problems without an auxiliary task first. However, results revealed that children performed significantly better overall with the analogy based object with adaptation when they received the problems needing an auxiliary task first (of the 42 per cent overall use of the analogy based object with adaptation - 26 per cent and 16 per cent, respectively) χ2
(1, N = 17) = 3.014; p<.05. Overall analysis did not support the prediction that children presented with the problems without an auxiliary task first. Order of presentation did not seem to affect children in the video condition when presented with problems without an auxiliary task first; this made very little difference to children’s performance on the problems needing an auxiliary task (7 percent and 9 per cent). Similar results were found in the control condition (5 percent and 0 per cent). This suggests that children were not transferring what they had learned from the problems without an auxiliary task to those needing an auxiliary task.
No predictions were made for performance on the problems without an auxiliary task due to order effects because of the simple nature of the problems. It was expected that
children would perform well on them regardless of the order in which children received them. However, of interest, those presented with problems needing an
auxiliary task first performed significantly better on the problems without an auxiliary task than those who received the problems needing an auxiliary task first χ2
(1, N = 17) = 11.636; p<.05 (57 per cent and 33 per cent, respectively). The findings indicate that children receiving the problems without an auxiliary task first were not
necessarily benefiting from practice with the problems needing an auxiliary task; whereas the presentation of the problems needing an auxiliary task first improved performance with the analogy based object with adaptation in both conditions. It is unclear why this was the case. It may be that children were more motivated to do well after they had failed to solve the problems needing an auxiliary task. This finding is at odds with Seligman’s (1974) learned helplessness and current teaching practice.
To determine why performance on the problems needing an auxiliary task was not benefiting from the problems without an auxiliary task first, children’s alternative strategy use was explored. If children were selecting incorrect strategies in the problems without an auxiliary task, this may explain why they were not transferring the analogy based object with adaptation onto the problems needing an auxiliary task. Table 6 presents the findings by order.
Table 6 reveals that children in the video condition who received the problems without an auxiliary task first relied on the analogy based object but without adaptation strategy and level 2 errors on a number of responses in the problems without an auxiliary task (37 per cent and 23 per cent, respectively).
Table 6: The Percentage of Children’s Strategic Choices by Order, Problem Type and Condition
Without Auxiliary first Auxiliary first
Without auxiliary Auxiliary Without auxiliary Auxiliary
Strategy Video Control Video Control Video Control Video Control________
No solution attempt 7 29 23 33 19 0 43 17
Level 1 error 0 0 7 5 0 0 5 17
Level 2 errors 23 5 43 47 0 14 29 53 Analogy based object without adapting 37 52 20 10 24 43 14 13
Analogy based object with adaptation 33 14 7 5 57 43 9 0
Since these children only used the analogy based object with adaptation with correct action to solve the problems without an auxiliary task on 33 per cent of responses suggests that two thirds of the responses were incorrect (non-analogous) and would not benefit their performance on the problems needing an auxiliary task. Therefore, if children’s analogical ability was to transfer (or improve) onto the problems needing an auxiliary task then it would be expected that children’s performance in the problems needing an auxiliary task would match (or better) the 33 percent correct responses in the problems without an auxiliary task. This was not the case, only 7 per cent of responses were analogous (the analogy based object with adaptation) in the problems needing an auxiliary task. This suggests that children were not benefiting from receiving the problems without an auxiliary task first and children were finding tasks in the problems needing an auxiliary task more difficult than those in the problems without an auxiliary task even when they had practice with less difficult analogies.
5.3.2 Representation
Overall, 41 percent (42/102) of children who received the video analogue described both the problem and solution to the problem. This finding suggests that over half of the children were finding representation of the base information difficult. It seems that children were able to describe the solution to the problem (36 per cent), but not the problem and solution. Overall results showed that 46 per cent (22/48) of 3-year-olds and 37 per cent (20/54) of 4-year-olds descriptions included both the problem and solution to the problem. A chi square analysis revealed no significant difference in children’s representational ability across age χ2
(2, N = 17) = 1.668; p>.05, suggesting that children in both age groups represented the problem to a similar degree.
Of the 41 percent who correctly represented the base problem, 71 per cent (30/42) of the correct representations were in the problems without an auxiliary task. Chi square analysis revealed significant differences in children’s ability to represent the base problem across paradigm χ2
(1, N = 17) = 13.114; p<.05. This indicates that children found the tasks in the problems without an auxiliary task significantly easier to represent than the problems needing an auxiliary task.
Table 7: The Percentage of Children’s Descriptions of the Base Analogue in the Video Condition as a Function of Problem Type and Age
____________________________________________________________________________________________________________ Without Auxiliary tasks Auxiliary task____________________________
3-yr-olds 4-yr-olds 3-yr-olds 4-yr-olds
_____________________________________________________________________________________________________________
No response/Irrelevant 8 22 37.5 11
Problem only 4 7 0 0
Solution only 21 19 37.5 67
Problem and solution 67 52 25 22
Table 7 shows that both 3- and 4-year-olds found representation easier in the problems without an auxiliary task compared to the problems needing an auxiliary task. To explore whether differences in paradigm extended across age, chi square analysis was carried out on 3-year-olds and 4-year-olds separately. Chi square analysis revealed significant differences in 3-year-olds’ representational ability between the problems without an auxiliary task and problems needing an auxiliary task χ2
(1, N = 8) = 11.089; p<.05 (67 per cent and 25 per cent, respectively). Significant differences were also observed in 4-year-olds between the problems without an auxiliary task and problems needing an auxiliary task χ2
(1, N = 9) = 6.289;
p<.05 (52 per cent and 22 per cent, respectively). This reiterates the difficulty faced
by both age groups in representing the problems needing an auxiliary task.
Interestingly, 3-year-olds represented more base problems than 4-year-olds in both problem types. However, only in the problems without an auxiliary task were differences significant between 3-and 4-year-olds χ2
(1, N = 17) = 4.669; p<.05. This indicates that 3-year-olds were able to represent more problems without an auxiliary task than 4-year-olds, but 3- and 4-year-olds found problems needing an auxiliary task equally as difficult to represent. Table 7 also reveals that both age groups relied more heavily on representing the solution only in the problems needing an auxiliary task. However, the results reveal that 3-year-olds relied on solution and no response /irrelevant information equally, whereas 4-year-olds relied on solution only significantly more than 3-year-olds χ2
(1, N = 17) = 17.380; p<.05 (67 per cent and 37.5 per cent, respectively).
To explore the benefit of representation on children’s ability to solve the target problem, children’s representational ability and solution on the target problem was matched. Of the 41 percent (42/102) correct representations, 40 percent were used to solve the target problem. Thus, just under half went on to use this information to solve the target problem.
Children who represented the base problem were more likely to solve the target problem (40 per cent) than those who did not represent the base problem (15 per cent) χ2
able to represent the base problem. However, not all children who represented the base analogue went on to solve the target problem. Eleven correct representations (26 per cent) were followed by the level 2 errors strategy in the target problem and 11 (26 per cent) were followed by analogy based object but without adaptation.
.
Since there were no differences in representational ability between 3- and 4-year-olds, no age differences in children’s ability to use the representation in the target problem were predicted. The figures reveal that 24 per cent of the 3-year-olds who gave correct representations went on to solve the target problem with the analogy based object with adaptation and 17 per cent of 4-year-olds. However, the differences did not reach significance χ2
(1, N = 8) = 1.503; p>.05. Although the figure was low, both 3- and 4- year-olds used the representation in the target problem to a similar degree. Children were able to form a representation and use it to solve the target problem more in the problems without an auxiliary task (50 per cent) than in the problems needing an auxiliary task (17 per cent) χ2
(1, N = 17) = 24.442; p<.05.
These findings highlight the fact that children's lack of representational ability may explain why children performed poorly on the problems needing an auxiliary task. However, this does not explain why some children unable to represent the base problem, were able to solve the target problem (35 per cent- 9/26 responses). As indicated at the beginning of this sub-section, the majority of 4-year-olds in the problems needing an auxiliary task represented the solution only (67 per cent). If representing the solution only (one transformation) is related to recognising just one aspect (transformation) of the base problem, then it would be expected that children’s performance on the target problem would only include one transformation (level 2 errors). This occurred in 33 per cent of 4-year-olds problems needing an auxiliary task. However, 67 per cent of 4-year-olds who represented the solution only used strategies other than level 2 errors. This suggests that children were not basing their selection of objects on their representation.