The students used one of ten different combinations in giving their reasoning. Table 3.6 provides examples of each of these combinations and the number of students who used the different types of Premises. In the examples, Q stands for a question or prompt from the teacher administrator.

By looking at how text elements were combined, we hoped to better understand children's perceptions of the situation in which they were operating. It would appear that when students are required to respond to the 'why is that box better value for money?', every child provided a Premise. This is an obligatory feature of every child's response, regardless of year level, gender or decile level of their school. Optional elements were Consequences and Conclusions, as not every child included these elements. In this sample, in regard to sequencing, Premises always came before Consequences, but they were also found after or before Conclusions. Consequences, unsurprisingly, do not occur in students' explanations unless preceded by a Premise. As can be seen from Table 3.6, Consequences were more likely to occur when preceded by a hypothetical Premise. In regard to iteration, Premises and Consequences occurred repeatedly within a student's explanation, so that there have been Premise, Premise, Consequence, Premise, Consequence or Premise, Premise or Premise, Consequence, Premise, Consequence. Conclusions, whether explicit or implicit, only occurred once in any child's explanation except with one Year 4 boy who began and then ended his explanation with a Conclusion.

As can be seen from the examples given in Table 3.6, logical connectives had a role in the combination or iteration of the different elements. Bills and Grey (2001) had also found that the use of logical connectives was related to the likelihood of students providing an accurate response. From the 72 samples, when a beginning clause such as 'this box would be' is ignored, 62 students prefaced their explanations with 'because'. One began with 'so', three with 'well' and two with 'if'. Table 3.7 shows that there were no apparent patterns across groups for those who used 'because'.

It would certainly seem that many students believed that a response to a 'why' question should begin with a 'because' in a school setting. However, it does not appear that the children who began their answer with 'because' but then completed it by giving a repeated fact understood that this answer would be considered inadequate. The following two excerpts illustrate this:

.....Um, because it, that box has more Pebbles than that box (Year 4 girl from a high decile school)

Because it says a hundred gram, ah no, because it's, I don't know, they've just got, because it's got a hundred in it, and, ah no, because, well they're both the same really, because that's only thirty cents away from a dollar and that's only, ah, this one probably. (Year 4 girl from a middle decile school)

At a superficial level, these students appeared to have appropriate language resources. However, when contrasted with students who can use language to develop their thinking, there are significant differences. A student is more likely to be able to think through a problem if they recognise that a 'because' is needed and know that to use it appropriately requires a speaker to provide a logical reason. The following excerpt provides an instance of this:

The most significant difference in who used 'because' in a deductive explanation is between Year 4 and Year 8 students. Donaldson's (1986) research suggested that 'because' and 'so' in deductive explanations were acquired at about eight years old, which is much later than their use with empirical explanations. The results in Table 3.8 suggest that most Year 4 students are unable to use 'because' appropriately in deductive explanations. However, age alone is not the only determiner. Twenty-one percent of students attending low decile schools followed 'because' with a logical reason compared with 63% of students attending high decile schools.

Other text elements were also preceded or followed by logical connectives. Hypothetical Premises are most likely preceded by 'if'. 22 out of 23 students who used a hypothetical Premise began with 'if' whilst the final student began with 'when'. The distribution of students using these logical connectives can be seen in Table 3.9. Factual Premises were not preceded by a logical connective.

Thirty-eight students followed a Premise with a Consequence. Of the 23 students who used Consequences which were preceded by hypothetical Premises, 22 could have begun them with a 'then' to follow the 'if' which began the Premise. However, only one student used 'then' to join the Consequence to the Premise. Table 3.10 shows the distribution of students who joined a Premise to a Consequence or a Consequence to a Consequence with a connective. When there was iteration of Premises and Consequences within the responses to this task, there was a variety of connectives which joined them together as well as instances when no connectives were used at all. Therefore, sometimes one student may have used more than one connective within their response whilst other students may have used none.

The most noticeable thing about Table 3.10 is the lack of students who used logical connectives in front of Consequences. Although 38 students used Consequences, only 7 joined Premises to Consequences with a logical connective. Of these 7 students, two used a causal connective, 'so'. More students joined Consequences together with logical connectives, but there were still only 13. Most of these used 'and' which is narrative rather than causal. When the distribution of students is considered overall, it would appear that Year 8 students are more likely to use logical connectives with Consequences. It would also seem that they are least likely to be used by students attending low decile schools. There were no differences according to gender. The number of students were small and no clear trend can be given. However, a similar pattern was evident in the logical connectives used in front of Premises.

Conclusions were also often preceded by logical connectives. 34 students followed a Premise or a Consequence with a Conclusion or an implicit Conclusion. The distribution of students who used logical connectives to join these Conclusions to their preceding text elements is given in Table 3.11. In the 11 times that Conclusions (explicit and implicit) started the utterances, 'because' always followed.

As with the use of other logical connectives, it is Year 4 students attending low decile schools who are least likely to join Conclusions to their preceding text elements. There is no gender difference in those who used logical connectives in this situation.

This analysis presents a far more complex situation than that suggested by Bills (2002). His research had shown that, although students had been exposed to procedural and explanatory language and could use it in other situations, they did not always choose to do so in explaining how they arrived at their calculations. Our data suggests that the use of certain text elements clearly correlated with the features identified by Bills. For example, students almost always used 'you' or 'I' in a hypothetical Premise. 'You' was used by 52 students. Only six students did not use them in either a hypothetical Premise, a Consequence or a Conclusion. In all cases 'you' could have been replaced by the more formal 'one' as it was not used to refer to the teacher administrator but to a generalised person. Rowland (1995) commented on a similar use of 'you' in his research and suggested that it pointed to an expression of a generalisation. In the responses to this task, the students seemed to use it more to provide a description of the conditions under which something would be true. 'If you got two of those it will be the same as that but it would be ten cents less' enables the cost and mass of both boxes to be made equivalent, thus allowing a comparison of cost, which is a necessary part of illustrating which box is better value. This suggests that in responses to this task that 'you' was used in a very specific part, the Premise. If it is not used in the Premise, it very rarely appeared in other elements of the text structure. However, if it was used in the Premise, it was also likely to be continued to be used in the other elements found in that response. Not all groups of students used the same combinations of text elements, as can be seen in Table 3.12. 31

In Table 3.3, of the 29 students who gained an accurate answer, 22 were considered to have clear language. Of these, 7 used the Premise - Consequence - Conclusion 32 structure, while a further 11 used a Premise - Consequence - implicit Conclusion structure. A further two students use a Conclusion - Premise - Consequence structure. The remaining 2 students used a Premise - Consequence combination. It would appear then that clear language which accompanies an accurate answer is most likely to be a combination of all three elements. Of the remaining 7 students who gained a correct answer, only 2 students included all three elements in their responses.

If the social environment is similar for all students, why is it that there are these differences between students in the structures of their explanations that they give? Certainly understanding and ability to solve the problem seems to allow students to make use of the Conclusion element of the text structure. In some ways, it is obvious that if a student is unable to resolve the problem then they would have nothing to conclude. However, there also seem to be differences between boys and girls in their perceptions of the explicitness of the Conclusion which is required. What makes boys chose to be more explicit than girls? This was a task in which there was a lot of shared experience between the teacher administrator and the student, yet these boys chose to be very explicit in their reasoning. We can consider the text structures that were used in explaining students' reasoning, as being on a continuum from requiring little of the listener to requiring the listener to provide a large amount of their background knowledge to the task. Students who only gave a Premise in their response require the listener to back-fill in most of the necessary information in order for the reasoning to be considered acceptable. As has been suggested elsewhere (Meaney, 2002), students' perceptions of who their audience is will have an impact on the information they provide in their responses. It may well be that students who provide very explicit responses are aware that an assessment situation requires them to presume that the listener has no prior knowledge and that they need to provide as much information as possible. Students who gave an unclear or elliptical answer may have been judged to have not solved the problem correctly even when they had chosen the 50 gram box because they could not provide a clear explanation. This has implications for teachers in regard to what they should provide in the way of modelling appropriate answers in the classroom.

Would students who knew about an expected text structure be able to use it to their advantage in helping them solve the problem? Or would a similar situation occur to that where students obviously knew that 'because' begins a response to a 'why' question but did not understand that it needed to be accompanied by a logical reason? Bills (2002) suggested that as students could use linguistic features in nonmathematical explanations, their use or non-use in mathematical explanations reflected their thinking about mathematical concepts. Our results certainly suggest that, on the whole, Year 4 students were unable to determine a successful strategy to solve this problem and providing them with a text structure for their answers may not be useful. However, some Year 8 students, by knowing about an appropriate text structure, may be able to use it to help them solve the task appropriately. Further research is needed to see whether such an intervention is beneficial.

It was also surprising to find that responses which provided a Conclusion, either explicit or implicit, were most likely to have had a hypothetical Premise, often making use of a 'you' as the doer of the action. From considering formal mathematical texts, it was expected that there would be more use of objects as the doers of the actions (see Meaney, forthcoming). Certainly, by the time that students 33 complete high school, it is expected that they would have gained this aspect of the mathematics register. Our research shows, however, that at the end of primary school there are very few students who are clearly explaining their reasoning and who do not have a person as the agent. Yet students who have less extended responses are more likely to only provide information about objects. Is using a generic 'you' in the explanation, a necessary phase that students need to go through in order to be able to give extended explanations using objects as the agents later in their mathematical career? Further research is also needed to see when a change occurs in students' responses and whether all students go through such a sequence in the responses that they give.