he Virtual Playground: an Educational Virtual Reality Environment for Evaluating Interactivity and Conceptual Learning

6.2 Substituting the denominator

Another common mistake, made by more than half of the participants in the
study, was the use of the denominator of a fraction as the resulting number
required by the task. This problem was faced with two of the playground
elements, the slide and the monkey bars, which involved tasks that required
finding 1/5 of 10 and 1/6 of 12 respectively. For example, initially the
monkey bars occupy an area of six blocks, placed in a long strip. The rule
communicated to the participant states that the current area is too long and
that it must be decreased by 1/6 of the area of the sandpit (which occupies
twelve blocks). David, an 11 year-old participant in the passive VR condition,
immediately concluded that the correct answer is six.

29. Observer: What did the bird say?

30. David: That ...it’s too long [the monkey bars] and that they have to be 1/6 of
the area of the sandpit...

31. Observer: How much is that?

32. David: Six.

He was certain that six was 1/6 of twelve. However, the layout of the
playground provoked an internal contradiction, since the monkey bars were
already six blocks long, so if the robot took out six this would leave no blocks
on the ground. When the robot removed four blocks leaving a total of two
blocks on the ground and the blocks were correctly switched to monkey bars,
David exclaimed that he had known all along that the correct answer was two
but hadn’t thought of it from the start. When asked later why he was confused
even though he knew that 1/6 of 12 is two, he responded that the correct result
(two blocks) did not make sense to him, because “in real life the area for the
monkey bars could not have been so short”. However, after seeing Spike (the
robot) performing the task, he was able to explain why the correct answer was
two blocks.

Cherry, a confident and very talkative 9 year old girl who participated in the
passive VR condition, had a similar response to the slide task (which involved
increasing the existing area of 10 blocks by one fifth). As soon as the blue
bird finished presenting the rule for the slide, Cherry began counting aloud in
order to direct Spike on what to do:

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