Children's intuitive understanding of variance

This paper discusses the important pedagogical question of by how much experimental probabilities need to deviate from subjective or symmetric probabilities before children consider revising their subjective probabilities. Many children believe that common random generators like coins and dice are subject to mystical or physical powers, or to be inherently opposed to a child's wishes. Even 9% of Year 11 students have been found to believe that a six is the least likely outcome from tossing a die. Providing experiences which encourage children to revise their opinions is difficult. One reason for this difficulty arises from the mathematics of the situation. There are 2500 tosses of a coin necessary to obtain a relative frequency of between 0.48 and 0.52 with 95% confidence. This makes it very difficult to attempt a classroom confirmation of any theory.