chapter  7
Estimation and Uncertainty
Pages 27

From time to time a pupil may feel obliged to make an assertion, perhaps in answer to a question, yet without certainty that what s/he is claiming is entirely accurate or true. The 10-and 11-year-old children considered in the previous chapter had available a repertoire of hedging strategies for maintaining cooperative interaction whilst being appropriately vague, thereby conveying a lack of full commitment to the prepositional content of their utterances. When is this linguistic repertoire developed, and are there identifiable milestones on the way to confident mastery? The vague language identified and discussed in earlier chapters arose in contexts where pupils were engaged in activities involving prediction and generalization. This required extended, contingent interviews, in order to prepare the ground, i.e. the problem environment, for these mathematical processes to come into play. Much of Channell’s book (1994) on the pragmatics of vague language is concerned with approximating quantities. The study reported in this chapter focuses on that dimension of vague language, specifically on estimation of the number of objects in a set. This choice of focus is partly for the sake of addressing what is perhaps the most obvious aspect of mathematical activity in which one would expect vague language to play a part. Moreover, it is possible in a short (5-10 minute) interview to present appropriate estimation tasks to children in a meaningful way, to obtain responses, and to follow these up from a restricted menu of probes. It is therefore convenient, in designing an age-related study, to use estimation rather than generalization tasks to elicit vague language when dealing with a pupil sample numbered in hundreds rather than tens.