Unasked But Answered: Comparing the Relative Probabilities of Coin Flip Sequence Attributes

The objective of this article is to contribute to research on teachers’ probabilistic knowledge and reasoning. To meet this objective, prospective mathematics teachers were presented coin flip sequences and were asked to determine and explain which of the sequences was least likely to occur. This research suggests that certain individuals, when presented with a particular question, answer different questions instead. More specifically, we found that participants, instead of making the intended relative probability comparison, compared the relative probability of a number of particular attributes associated with coin flip sequences. Further, we interpret participants’ attempts to reduce levels of abstraction in order to reason about probability, in a relative sense. Embracing the research literature suggesting that responses reflect individuals’ understandings of the question they were asked, this article suggests potential questions that participants have not been asked but are answering. In doing so, this article suggests that participants are providing reasonable relative probability comparisons for questions that are unasked. Finally, implications for future research are also discussed.