In regard to age, unlike the Better Buy task, it would seem that Year 4 students were more likely to place 'if' before a Premise. Five more Year 8 than Year 4 students had used more than just a Premise in their responses, but it would seem that proportionally there is no significant difference in the use of logical connectives according to age.

A similar situation happens when decile level of schools is considered. As so few Pacific students used more than a Premise in their response, it is not surprising that they used few logical connectives. However, it was expected that as students who attended high decile school used more complex text structures, that they would also use more logical connectives than non-Pacific students attending low decile schools. However, this was not the case, with both groups using almost equivalent amounts of logical connectives.

Within the text structures, there were also clauses which provided more information to particular elements. For example within a mathematical Premise such as '98 is almost a hundred, so it's just two away', 'so it's just two away' adds more information about 98 being almost a hundred. This extra information is a known fact rather than as a consequence of working with 98. Therefore, it cannot be considered as a second Premise, as it does not add new information. Nor can it be considered as a Consequence, as nothing was done to 98 for a new idea to be developed as a Consequence. Consequently, these types of clauses have been labelled as Elaborators. Other Elaborators were clauses following what Halliday (1986) calls mental processes such as 'say', 'think' or other verbs that were followed by 'that' or 'which' clauses. These following clauses have also been labelled as Elaborators. For example, one child responded with 'I counted all the twos that were needed to go all the way up to nine hundred'. 'That were needed' and 'to go all the way up to nine hundred' both provide an elaboration of the previous clause by providing more information about it. These are considered cohesive devices (Hudson & Shapiro, 1991). Where these Elaborators occurred is set out in Table 5.14.

Of the fifteen students who used clear language and also provided a good estimate or exact answer, six of them only used Premises and four used a Premise, Consequence and a Conclusion structure. This would tend to suggest that for this task there was not a high correlation between getting a correct answer and using a more complex text structure containing a series of different elements. However, the use of mathematical Premises did seem to be important. It is worth noting that Pacific students who were able to get a correct answer were all students who only provided mathematical Premises within their answers.

There were a further 15 students out of the sample of 72 who were able to respond to this task correctly. These students gave a moderately clear or vague response. As can be seen in Table 5.16, Year 8 students attending high decile schools were the most likely groups to give these responses, but their combinations of text elements were much more varied than those given with clear language. For example, some students used a factual rather than a mathematical Premise as the basis for their explanation. In giving clear explanations, only 6 students did not have a Consequence as one of the elements in their response. However, out of the 15 students who gave an unclear response, 6 students also did not include a Consequence but only 3 just gave a Premise.

The text structures used students who gave incorrect answers generally only contained Premises. At Year 8, many students, especially from low decile schools were unable to give an estimate, but did give the mathematical Premise '9 times 98' or the equivalent. Year 4 students were more likely to give a factual Premise such as 'Heaps a go, heaps a cars go down the road every day and in nine minutes … more cars come in' or a personal Premise such as 'I don't know I just guessed.'

In the responses to the previous tasks, students who gave accurate answers were more likely to use a complex text structure involving the combination of several text elements. In the Motorway responses, it would also seem that it was mostly Year 8 students who could do the mathematics who would use more complex text structures. What Motorway also illustrates is that just providing a Premise can sometimes be considered a clear response. However, on the whole students, who just gave a Premise, who were predominantly Pacific students were most likely to be unable to provide an accurate response.

It was apparent that many students were hesitant in giving their responses, either because they were uncertain about their own mathematics or because they felt that the situation required them to show deference to the teacher administrator. In the Weigh Up task, showing hesitancy is discussed with the use of Suppositions. In the response to this task, there appeared to be two different ways that students made their responses seem hesitant or vague. The first way was in regard to expressing uncertainty about the correctness of their thinking. Making a response vague can decrease a student's risk of losing face. The second relates to the 'estimation' element of the task and illustrates how students mark the approximation of their calculations and answers.

By using hesitant language to limit a potential loss of face, students are exhibiting signs of what Grob, Meyers and Shuh (1997) labelled powerless language. 'Powerless language typically has been defined as speech marked by hesitancy and tentativeness … it often contains more polite forms, hedges, hesitations, disclaimers, intensifiers, empty adjectives, tag questions, and hypercorrect grammar' (p. 284). In the responses given by students to this task there were examples of hesitations through verbal fillers, hedges and disclaimers. The distribution of these is given in Tables 5.17, 5.18, 5.19. There were also two uses of intensifiers. One Year 8 boy from a high decile school recruited support for his answer by including the word 'obviously' in his response.

Well, each minute ninety-eight cars come down, says about, so obviously that's about nine hundred, says nine minutes and then one minute goes ninety-eight cars.

A Year 4 girl used 'basically' in a similar way, although it did not have the strength of 'obviously'.

Um.. because the motorway's kind of busy and people don't really um hold up on the motorway, because you can kind of, because there basically isn't a speed limit on the motorway, they go quite fast.

Burton and Morgan (2000), in their study of the professional writing of mathematicians, found intensifiers were used quite frequently as authority claims. It is interesting to see that students in responding to this task do not claim authority for the correctness of what they have done in the same way. The same student who used 'obviously' was also one of only two students who referred to the question as support for what they had done. The other student was also a Year 8 boy from a high decile school.

Um, because it says nine minutes so I just went up to nine hundred.

The 'it' has become the authority on which the student is basing his argument. This would be what Sowder and Harel (1998) had described as an external based proof as it calls on an outside authority to authenticate the evidence.

Other negative politeness strategies which make the response seem vague were when the speaker added a disclaimer. Disclaimers are expressions such as 'I mean' and 'I think'. These suggest the speakers' uncertainty about the statement which follows, whereas intensifiers tend to recruit the hearer's support for the truth of the statement. Table 5.17 sets out the distribution of disclaimers in the responses to this task. The small numbers of students who use disclaimers make it unclear whether there are any patterns associated with disclaimers, except that five out of seven students were from high decile schools. When the information on disclaimers is combined with intensifiers, it would appear that these are more likely to be used by students from high decile schools. If these linguistics features are markers of powerless language, it is surprising to find that they are more likely to be used by these students, who were the most likely in Table 5.17 to be considered to have clear language.

On the whole, it would seem that there are no large differences in distribution of fillers according to gender. There is a small difference according to gender with slightly more boys using them than girls and according to age with Year 8 students using them slightly more often than Year 4 students. Pacific students were the least likely to use fillers whilst students attending high decile schools were the most likely, especially in regard to use of 'well/okay'. Given that these were the students most likely to have an accurate response, it is surprising to find that they more likely to use these features of hesitant language.

In the Introductions, four of the responses contained 'just' after 'I', such as 'I just went' and 'I just took'. In the rest of the explanations, there was also 17 other students who used 'just'. 'Just' acts as what Rowland (2000. p. 60) described as an approximator which modifies a proposition by 'making it more vague'. The need for such vagueness is, perhaps, more to do with uncertainty about the correctness of their approach rather than uncertainty about what they remember that they did. As the question specifically asks students to 'explain to me how you got your answer', these Introductions could be responding to this personal flavour of the question. Given the power relationship which exists between the student and the teacher administrator, it is not surprising that the student may be more hesitant to talk about how they got their answer than to simply give the numerical result. Brown and Levison (1978) suggested that when the Hearer has high power over the Speaker, the Speaker will tend to use negative politeness strategies, such as those which lessen the strength of the utterance and to use off-the-record strategies such as putting forward ambiguous statements. As well as adding 'just', students also used words such as 'kind of', 'maybe' in their responses to make their responses appear less certain. In mathematics classrooms, Rowland (2000) suggested that students are often vulnerable when responding to teachers because of the fear of ridicule. By suggesting through negative politeness that they are unsure of their thinking process, students reduce the loss of face if their thinking is not appropriate. Table 5.19 provides a description of variety and distribution of hedges used in the responses to this task.

Hedges were used more often by boys, especially 'just', but there was little difference according to age or to decile level of school attended. There seems to be slightly less chance that Pacific students would use hedges than other students.

In considering who uses what examples of hesitant language, it would seem that boys are more likely to use hedges. Year 8 students are more likely to use fillers and Pacific students less likely to use fillers or hedges. This last result could be because these students gave the shortest responses. However, the relationship between short responses and the need for fillers or hedges is not clear.

It has been suggested that 'powerless' language contains more intensifiers, hedges, disclaimers and hesitations and is generally associated with female language (Grob, Meyers & Shuh, 1997). Yet the tables in this section clearly show that boys use more hedges and hesitations than girls do in presenting their responses to this task. This appears to match other research done in this area. Staley (1982) found that for children talking informally in groups, boys aged 4, 8 and 16 used more hedges. It was only with twelve year olds that it was girls who used more hedges. 16 year old boys used significantly more hedges. In work undertaken by Grob et al (1997), female college students used more hedges than males, but the amounts were not significantly different. Even if hedges are considered to show politeness rather than powerlessness (Fishman, 1978), studies by researchers such as Deucher (1990) suggests that women, including girls, generally use politer language than men It is quite surprising then to find that in describing a response to a mathematics task, boys who typically are believed to feel more confident with their mathematics ability (Burton, 2001) expressed themselves in a more hesitant manner.

The other way that students express hesitant ideas is when they provide approximate calculations or answers for the task. Given that the task asked for an approximate answer ('About how many cars would go down the road in 9 minutes?'), it is perhaps more surprising that very few student did this. There are two types of approximators: rounders and adaptors. Rounders are words such as 'about', 'around' and 'approximately', whereas adaptors are words and phrases such as 'a little bit' and 'like'. In giving their answer, students used expressions such as 'really, that's probably about roughly what goes down' and 'probably get around a thousand'. Table 5.20 provides the distribution of students who used the rounder 'about' or an adaptor such as 'like' or a rising intonation to indicate uncertainty about the amounts given in response to the first question of this task.

The numbers are small, with the only discernable trend being that students from high decile schools are more likely to use rounders or adaptors than students from low decile schools, particularly Pacific students. It may also be that Year 8 students were more likely to use a rounder than Year 4 students. However, these results are not as clear cut as those reported by Rowland (2000), which had shown that students could determine when it was appropriate to use a rounder by the age of eight, which would be the age of most students in Year 4.

Students also used approximations in their explanations of how they had determined their answers in discussing their calculations. In discussing amounts, students used expressions such as 'like, really big', 'only three', 'heaps of cars'.

There appears to be no obvious patterns in who asked questions. Slightly more Year 8 students asked questions of the teacher administrator than Year 4, but the difference is not great.

It would seem that in responding to this task, students used a range of different strategies to make their responses seem more vague. Although there were a few differences in the distribution of groups using them, there appears to be no clear pattern. For example, Year 8 students from high decile schools were most likely to use approximators, but Pacific students were least likely to use hedges. As an area which is likely to influence teachers' perceptions of students' ability, this area of mathematical language use requires more investigation.