M.M. Gea, R. Parraguez, R. Roa

University of Granda (SPAIN)
Probability is part of the primary school mathematics curriculum in Spain, since 2006. Given that this topic was introduced only recently at this level, many prospective primary school teachers did not themselves study probability in primary school and may have forgotten the relevant ideas that they learnt in secondary school. Accordingly, courses and workshops designed for prospective teachers should take into account prior assessments of their knowledge.

According the curricula, primary school teachers should teach probability with different approaches, in particular with the frequentist view of probability, where probability is conceived as the limit of relative frequencies for increasing sizes of repetition of the experiment. Although primary school children cannot understand this abstract definition, the curricular guidelines suggest an intuitive introduction can be supported by simulation with which children can get experience with random experiments, observe the data on empirical frequencies and its tendency and variability when the number of experiments increases. The concept of simulation is, however, not so easy, as it is important to distinguish between the real and the simulated experiments as well as understand the conditions in which a simulated experiment is valid for a real situation. All these ideas should be clear for the teachers responsible to teach probability in primary school.
The aim of this research was to evaluate the meaning assigned by 60 prospective Primary Education teachers at the Faculty of Education in Granada to whom we proposed the question: “What is for you the simulation of a random experiment?” These teachers had previously worked with probability and simulation in two practical activities, each of them with a length of 2 hours.

A content analysis of the prospective teachers’ responses suggests that few of them understood the essential features of simulation, where a random experiment is replaced by another equivalent experiment when the study of the first phenomena is difficult. In simulation, we can operate and observe the results in a simulated experiment to obtain information about a real situation. For example, we can estimate the probability of having more than 60% females amongst 100 newborn babies by repeating the experiment of throwing 100 coins a large number of times.

In our study, few teachers discriminated between a real experiment and a simulation. The following different meanings of simulation were observed in the sample:
a) simulating an experiment is reproducing it artificially;
b) simulating an experiment is making it visible with the help of a concrete material, so that we can visualise its results;
c) simulating an experiment is just repeating the experiment in order to estimate the probability for an event using the relative frequency in the long run;
d) simulating an experiment is repeating the experiment.

Although each of the above meanings of simulation is partly true, the main properties of simulation are hidden. Consequently, instructors should start from these different conceptions to reflect with the teachers about the characteristics and advantages of simulation, as well as about its potential in the classroom.