experiencing difficulty in reconciling their past knowledge of probability e.g. that probabilities add up to 100%, that things work out over time with how they use this knowledge to judge what to do in the case of a single trial.
We found evidence of strong personal beliefs in luck. One pair who had conducted experiments to show that changing was always more likely to be beneficial, in the post test said they would still not change although they knew it would increase their chance of success because "it would be worse to lose if you changed from the right answer."
There was a strong tendency to over generalise the concept of randomness. One subject in particular had a very strong view of the concept of randomness. She interpreted it as meaning that as her choice of which door to open had been made randomly, it was not possible for any outside event to influence whether or not this choice was correct or not. "I can't really see what the point is in trying to work out a strategy if it's all totally random."
One pair ran 12 trials always changing, and one always "sticking". When encouraged to review their data they commented:
'We only won twice when we stuck.... We won once up there and then we changed, we've won three, we've won four times when we've changed I still think my first...I still think there's no strategy.
Although the data was in conflict with thesubject's view she persisted with it because of a belief that there could not be a strategy which would be of benefit.
Using the simulation with a partner was successful in moving the subjects' perception of what would be a successful strategy in four out of the five pairs. The fifth pair started with conflicting views about what would be the correct strategy to employ. One of them was so fixed in his view that either strategy was equivalent, resisted attempts to design an investigation to check this, rejected disconfirming data and succeeded in persuading his partner that his view was correct.
We are interested in how using this system has laid bare the prior conceptions held by our subjects on the topic of probability. We have presented evidence on how our subjects' interaction with each other and with the simulation influenced their understanding of the problem they were asked to solve. We are interested in exploring the possibility of scaffolding students at work on the simulation by augmenting the note taking and record keeping tools which they have available to them, and considering what further support we can offer students to help them visualise the problem more effectively. More generally we are interested in the usability of such systems for learning.
Environments such as Kansas that support synchronous distributed collaboration could play an important role in the support of distance learners. This potential role depends on the existence of working examples which allow us to study how much larger numbers of simultaneously active learners, distributed as individuals and small groups can productively learn together. On the other hand, there are simple arguments that say there must be threshold limits to the number of individuals and groups who can usefully be co-active. We are exploring whether scaling up of collaborative group size works and exploring the limits of this scaleability. We are interested in exploring further the ideas of scaleability. Some teaching and learning approaches scale much more easily than others. It is necessary to analyse each new example of computer supported collaborative learning with respect to how many students should be associated with each running instance, whether human support is necessary and what the effective human learning guide support arrangements should be.
Our initial findings indicate that the groups can become less effective in both process and product terms as the number of group participants increases above two or three. Larger groups find it harder to engage in constructive task division and in situations where there is a lot of initial consensus the larger groups display inordinate cognitive fixity and become totally committed to erroneous solutions that are contradicted by the operation of the micro-world. On the other hand, larger heterogeneous groups that are not dominated by individuals can display more flexibility and creativity than smaller groups. These findings are similar to those found in co-present groups working together but our preliminary finding is that these differences in group problem-solving dynamics are amplified by the use of the collaborative support technology. We are currently continuing with our experiments involving larger groups and our experiments involving video as well as audio communication so that we can further explore the