During the first experimentation of the Randomness activity sequence two main cultural and contextual issues raised. The first issue concerns pupils’ tendency to reject randomness as a pursuable strategy for problem solving; the second issue concerns teacher’s resistance to accept the production by the class of partial encyclopaedia documents. In the following we are going to focus mainly on the first issues, and will conclude by adding a few details concerning the latter.

Can randomness be a pursuable strategy?

Some of the activities within the Randomness activity sequence aim at developing random strategies for problem solving. In particular we propose to pupils two similar games, based on the same device, the LEGO RCX robot ShakerBot. In the two games pupils are required to drive the ShakerBot, in the first game the goal is to drive it over certain targets in order to score points, while in the second game the goal is to drive the robot over as many black spots as possible. In the first case the best strategy is to point targets and drive the robot toward them on purpose; in the second case, to drive the robot upon black spots on purpose is very difficult (but still possible) and a random strategy may turn out to be the winning one, or at least a good one. In fact, due to the properties of random walks (in an infinite time a random walk covers all the available space), it may be the case that just by driving the ShakerBot randomly one walks upon many black spots, thus scoring many points. Of course, it is also a matter of available time, and of luck, however the random strategy can be a good strategy for such a game. According to our plans, the two games should foster the idea that it is possible to follow random strategies (as opposed to non random ones), and the idea that random strategies can be good for solving some specific problems.

When we set up the two games in our first experimentation, we could observe that in both games some pupils scored many points just by driving the ShakerBot randomly, and in particular in the second game some of the highest scores were obtained following a random (or semi-random) strategy. However this didn’t seem to result in pupils accepting random strategies as good ones and pupils didn’t seem to give to random strategies the same status of deterministic strategies. This was suggested by pupils’ reports, and made clearer by a set of interviews that we conducted a week after pupils had played the second game. In general we individuated three main trends within the groups of pupils rejecting randomness as a good strategy for the ShakerBot games, that can be synthesized as follows:

1.      Pupils not ascribing any good property to the random strategy: they do not believe that it is possible to score many points by driving the ShakerBot randomly. Some of these pupils were asked, when interviewed, to play the second game twice, once using their own strategy, and the other time going randomly; the obtained results contrasted with their opinions (in fact the random strategy led them to score more points then their own strategies), resulting, for some of them, in a slight change of opinion towards the trends described below.

2.      Some pupils recognize that it is possible to score many points driving the ShakerBot randomly, but they wouldn’t adopt such a strategy because “it is only a matter of luck”.

3.      Some pupils recognize that it is possible to score many points driving the ShakerBot randomly, but they wouldn’t adopt such a strategy because it is less interesting/fun than a deterministic strategy.

In other words, pupils may accept randomness as a good strategy, but would not adopt it. We believe that such a position is the result of many possible factors, some of them culturally rooted. Before the experiment, we had individuated the following factors that were later supported also by the randomness related examples brought by our pupils in the first phase. (The Randomness Small Talks activities) of the experiment:

1.      A socially shared tendency towards determinism in contrast to randomness. We believe that in general, randomness is considered to be less valuable then non randomness, as shown also by the examples brought by our pupils, sometimes randomness has a negative connotation. For instance in the phrase “I answered randomly to the test because I had not studied”, randomness is associated to the socially negative behaviour of not having studied.

2.      Lack of experiences involving randomness as a strategy; in fact pupils previous experiences concerning randomness consisted mainly in chance game situations, or in daily life situations driven by loss of control or lack of information. In none of the examples of randomness related situations brought by our pupils can we find random strategies. For instance a chance game (eg. Dices, bingo, etc.) is based on some random phenomenon, but a player is never involved in choosing between a random or non random strategy; in the same stream, also in daily life situations like “I chose a jacket at random because they were all the same” (this is an example brought by pupils), the subject is not involved in choosing between a random and a non random strategy.

Such lack of experience can be individuated at a more global social level, in the sense that if we exclude chance games, there are really few examples in which randomness plays a key role, and even fewer examples in which it is convenient to use randomness as a problem solving strategy. Significant examples can be found in advanced sciences, but not in daily life.

One of the aims of the ShakerBot activities was to overcome such factors, providing pupils with a situation in which randomness could be individuated either as a strategy and as a good strategy. If on one side the first objective was somehow reached, fostering the idea that one could adopt a random strategy, the goal to give positive connotations to random strategies was not reached.

A first analysis of the data suggested to us some more possible factors that influenced pupils behaviour:

1. The sense of “fun”: driving the ShakerBot randomly was not perceived as fun, because it was not under the control of the user.
2. The sense of “control”: most of the pupils that moved the ShakerBot randomly did it because they were unable to drive it non randomly (in fact the device is designed to facilitate random strategies). Some pupils switched to non random movements as soon as they were able to do it, and some of them did not go back to random movements even if they had scored more points when moving randomly. Perhaps pupils need to feel they are controlling the object.
3. The tasks proposed to pupils were too much oriented towards a deterministic approach: in fact pupils were required to explain the functioning of the ShakerBot and how to drive it, we believe that this shifted their attention, and the focus of the discussion, away from the randomness issue.
4. The proposed tasks did not highlight enough the good properties of random strategies as opposed to non random strategies: for the next experimentations we plan to set up games, or situations, where random strategies are much better then non random strategies.

In particular the latter two factors are supported by the final class discussion aimed at updating the Randomness Encyclopaedia. Such a discussion was structured by the teacher (under our advice) as a review of the past activities, each example episode, or object encountered during the activity sequence was discussed in terms of its randomness related properties. In particular items where classified in terms of their randomness/non-randomness and predictability/unpredictability in order to insert them as new elements of the corresponding Encyclopaedia items “random”, “non random”, “predictable”, “unpredictable”. The final part of the discussion is quite interesting for what concerns the issue of negative/positive connotations of random strategies. After pupils have discussed the case of the Sweeper Bot, and had agreed that if it is left alone moving, after a while it will have covered all the available space, the teacher poses the following question:

T: Thus, suppose you are an unintelligent animal searching for food…could it be a good strategy to move randomly?

Chorus: no

T:

T: So, what about an animal with no sense of smell?

C5: Does it have eyes?

…some confusion

T: So, let’s suppose this instead, let’s give it some sense of smell

C1: With some sense of smell…yes…depends

T: There is a big field with very little food, is it better to go randomly or to use the sense of smell?

Chorus: to use the sense of smell!

C1: To use the sense of smell…thus not to go randomly

…some confusion

C1: In fact, it would go where there isn’t anything

T: What if the food is more diffused?

…confusion and several contemporary answers, we can distinguish some voices pronouncing the word “randomly”

C1: …Diffused…I would go anyway using my smell

T: Pardon?

C1: I would go around anyway following my sense of smell

T: So, suppose instead that the food is odourless

… confusion and several contemporary answers, most of pupils seem to pronounce the word “randomly”

C1:Well, in some situations you are…you must go randomly because you do not have enough information, enough…abilities…to find the food

C1 Shows a resistance to accept randomness as a good strategy, or simply she doesn’t think it can be a good strategy, however, she finally accepts it in the extreme case of a total lack of information. At this point the teacher tries to push the discussion towards the idea that random strategies not only can be good when one doesn’t have enough information to solve a problem; in fact in some cases randomness can be a very good strategy to generalize a solution to a problem, in particular for problems where some crucial information remains unknown. For instance, suppose we want to program a robot that is able to paint (or to sweep) a figure, no matter what the topology and the shape of the figure is. Thus the teacher proposes:

 

T: Another question, suppose that you have a machine that paints the floor

C?: What is it?

T: A machine for painting…

C5: That one, like…like that one of the telly advertisement that vacuums, the vacuum cleaner…

[…]

T: So, there is this little object, you put it on the floor, you press a button, and it starts going round, vacuuming…

C?: Ah, yes, I saw it!

T: When it hits the floor it changes direction

We can hear confused voices recalling the advertisement

T: Do you think that, the person that programmed that object, put inside the object information about the house in the advertisement?

Chorus: noo…

[…]

C6: It goes randomly

C7: It must have a sensor that as soon as it sees the walls…

T: So it has a sensor

C1: It has a sensor like the Sweeper Bot which sees the wall, hits the wall, but it realizes that there is a wall and then moves backwards.

T: And what happens when there is no wall?

C1: It goes straight on!...doesn’t find any obstacle and goes straight on

C8: But I think that also that robot goes randomly, that is, yes, when it hits a wall it changes direction, but it goes randomly…thus…thus in the end…

[…]

C8: That is, I think that in the end it must wait… it must wait a lot of time before the house is cleaned, I think…because if it continues…if it continues hitting walls, eh!...you do it with a normal sweep and you do it quicker, eh, you do it yourself!

 

C8 believes that the only reason for the robot to go randomly is that it doesn’t have enough information, it doesn’t have a map of the house. She thinks the best solution, for her, would be to clean up herself with no robot. The problem C8 is thinking of solving is that of cleaning her house, or a specific given house.

 

[…]

C8: That robot […] goes randomly because it doesn’t have enough information, if the progr…what’s it’s name…the inventor had the map of the city and he could…

C?: Of the house?

C8: Yes, of the house…in fact, it would clean quicker, it would do better…that is, it goes randomly because it doesn’t have information

T: But the vacuum seller, can he put inside the robot the maps of all those houses?

Chorus: no!

 

The teacher’s observation moves the focus of the discussion towards a generalisation of the problem of cleaning a house, the new problem now is to be able to clean up any house. As a result of such generalisation, the class produced the following excert of Randomness Encyclopaedia item “random”:

 

“Ciuf ciuf brought a little robot “briciola” which moves on its own and going randomly it is able to clean up all the flat. Jeka said that if the robot had in its memory the map of the flat maybe it would clean it up more quickly; Teo said that the program would be more complicated and one would need a different program for each flat. This is an example where randomness is convenient”.

 

We think this episode is interesting because on one side it shows pupils resistance to accept randomness as a good strategy, but on the other side it shows that it is possible to overcome such a resistance setting up suitable activities that put pupils in front of situations where randomness is actually a feasible strategy, and a very good one. In this particular case a key role has been played by the tangibles Sweaper Bot and “briciola” (the robot inthe TV advertisement); they served to focus the class discussion on the teachers educational goal, providing sources for a rich discussion concerning randomness, on the basis of their observable functioning, and their programmability (actual or supposed). Finally, we observe that if on one side experiences (direct or indirect ones) with the robots brought sources for discussion, on the other side, it is thanks to the class discussion aimed at updating the encyclopaedia that we could observe an evolution of pupils ideas concerning randomness and its usability and validity as a strategy for problem solving.

 

Contextual and cultural resistance to the idea of an evolving Encyclopaedia

In the episode presented above a key role is played by the Randomness Weblabspaedia, and in particular by the activity of updating such an encyclopaedia. Such an activity can be exploited by the teacher in order to stimulate class discussions and direct them towards the construction of items of the encyclopaedia that are the result of an agreement between pupils and of their collective reflection. In the particular episode the activity of updating the encyclopaedia was exploited as a means for discussing randomness as a strategy for problem solving, and it lead to overcoming pupils resistance to accept that a random strategy can be a good one. The agreement reached by the pupils is crystallized in the extract of the Encyclopaedia item “random”, as reported above. At this stage the encyclopaedia has been updated only by appending new stuff to the existent items, without discussing its previously included contents, and without checking the coherence of new contents with the rest of the encyclopaedia.

However, the teacher plans to set up a new revision at the beginning of the next school year, in order to systematize it and eventually change its contents. The fact that the teacher herself plans to set up such a revision is to considered as a result of the experiment, in the sense that at the beginning of the activity sequence we witnessed strong resistances from her side with respect to the idea of publishing encyclopaedia items that were not “perfect”. In fact in the first phases of the experimentation, we received from the teacher in several occasions, requests to not publish reports collectively produced by the pupils, the reasons for such a request were expressed in phrases like:

-         “I send you the description of the school that was written by pupils together with their English teacher, I did not do any corrections, I shall let you judge it in this case and make any corrections before publishing the document on the website”

-         “I send you the reports collected today […] please do not publish them because pupils have to work more on them” (emphasis not added by the author)”

-         “wait before inserting them on the web site: they need another discussion; there are some issues pending”

-         “I send you some reports on games, produced by a pupil: if you think it is the case we can refine them a little”

The phrases are extracted from our mailing correspondence with the teacher, and are in chronological order; all of them are in the first 3 months of experimentation, then the teacher gave up requiring us not to publish “unfinished” documents, but at the same time we witnessed a drastic decrease of the number of activities aimed at producing collective reports (like those of the Randomness Weblabspaedia). Our interpretation of this phenomenon is that there is a resistance of the teacher with respect to the idea of publishing documents that are not “perfect” or “definitive”, possible social factors for such a behaviour are:

-         the school context, in which “incorrect” or “unfinished” works are usually negatively valued

-         a cultural tendency to consider valuable, and sharable with other people, only “correct” and “finished” works

-         a fear for the judgement of external readers (meaning also members of the project that are not directly involved in this experiment).

Besides such social factors, we want to observe that for this experiment, it was crucial that the idea of publishing “unfinished” works, in the sense that Encyclopaedia items were supposed to represent the evolving culture of the class; it was one of our educational goals that of introducing pupils to the idea that culture can be socially built and shared, and that, even in science, it is important to fix and publish for the community also non definitive results. We hypothesize that this educational goal contrasted to the usual scholastic tendency to consider valuable and publishable only correct and finished works. In other words, for us it was important that the process of producing and updating the encyclopaedia, and this we believe contrasts with the usual scholastic tendency to consider the final product as the most important thing. Thus our interpretation of the witnessed phenomenon is that probably at the beginning the teacher regarded at the Encyclopaedia mainly as a final result, with no particular attention to the process leading to its production. Nevertheless the teacher put a lot of effort in all the activities, included collective discussions and the production of collective reports, and we assisted to an evolution of her behaviour, leading to the last Encyclopaedia update activity that we partially mentioned in the episode described above. The fact that at the end she asks us to publish Encyclopaedia items that she already knows are not going to be definitive, is a clear sign of an evolution toward our ideas of Encyclopaedia interpreted as an entity that evolves together with the class culture.

We believe this learning snapshot, which involves mainly the teacher, is important for the project because it shows possible difficulties related to the use of an information sharing system like the phone. When we set up experiments that involve teachers that are immersed in the school context, it is important to take into account the kind of resistance to publishing non definitive documents that we described in this section.