The Co-ordination of Meanings for Randomness

l. The stochastic: a pedagogical challenge (l) The domain of probability points particularly sharply to a fundamental difficulty in mathematical pedagogy. On the one hand, it is deceptively close to everyday intuitions and experience, even language: chance encounters, random behaviours, likely occurrences. One might easily suppose that these culturally embedded meanings could facilitate the transition to a mathematical way of thinking. Yet this is not the case. Probability is a notoriously difficult topic and it might appear that the only way for students to achieve satisfactory grades is to ignore the relationship of probability to everyday notions of chance altogether. Perhaps more than in any branch of mathematics, the gap between potential everyday applicability and formal understanding is at its greatest in the domain of stochastics and probability. There are multiple opportunities to apply such knowledge as people go about their everyday lives; the playing of games with explicit random number generation (do I take the finesse of the queen of hearts?), in sport (should I adopt a long ball strategy?) and in parenting (should I let my daughter walk to school?). Yet such opportunities do not seem to have led to widespread construction of meaning for stochastic concepts. On the contrary, the research reported later in this opening section suggests that adults9 understanding of such ideas is often impoverished, even misconceived.