aTask and acceptable answers

The first portion, labelled Plan, was scored as 'clear, logical, complete', 'nearly complete', 'on the right track but substantially incomplete', or 'other'. The second portion, labelled Description, was scored as 'all correct', 'one inversion' or 'worse'. The third portion, labelled Explanation, was scored as 'clear, logical and complete', 'nearly complete', 'on the right track but substantially incomplete', or 'other'.

There were equal numbers of students who were judged as being accurate as there were students who were only deemed as approaching accuracy. A further nine students seemed unsure of what was involved, either by providing a minimal response or by attempting to answer a completely different question. Quite often it seemed that they were trying to ensure that two boxes equalled the weight of the other two boxes. The following comes from a Year 4 girl attending a middle decile school:

Uh, Ok … what I'd do is I'd measure two of the Pebbles in one and if they don't equal up to the same I'd put one of the Pebbles down and get another box and put it on the weight, and if that weighed exactly right then I knew that that was the right balance.

The distribution of students does not show any major trends. Five of the six Year 8 boys attending a high decile school were judged as having a correct answer but none were considered to have a clear explanation. There was only one Year 8 girl from a high decile school who had an accurate response. There were equal numbers of Year 4 boys and girls from high decile schools who gave accurate responses. The only group of students not to be unclear about the task were boys attending a middle decile school.

By looking more carefully at the text structures which made up the students' responses, it is possible to investigate whether there was any correlation between judgements about the clarity of the explanation and their accuracy. The following section, therefore, describes the text elements and the common combinations found in these responses as well as the logical connectives joining these combinations.

In the Plan, like in other aspects of this task, there were many elements used in a variety of combinations. This may have been related to the extended answers required by the task. It would seem sensible for longer responses to be more likely to use a variety of elements. Yet in the Bank Account task where an extended response was often provided, there was not as great a variety of elements. It seems more likely that the variety of text elements was related to the fact that there were several ways that the Plan could be answered. Students were told that they could handle the boxes but that they were not allowed to use the balance, just describe what they would do with the balance. Some students, therefore, talked about their estimation of the order from their handling of the box, whilst others concentrated on what they would do once they were allowed to use the balance. As a result, the answers were quite varied. The following excerpts provide examples of these different types of answers.

In the first example, a Year 8 girl from a middle decile school described what she did as she weighed the boxes in her hands.

Well, right now, by just shaking them, umm, I think there's the lightest amount of Pebbles in this box because I can hear them the most whilst they're moving quite a lot and then see, I don't think that there's that many in that box

As a response to comments and questions by the teacher, she began with a Premise which was followed by a Supposition, 'I think', with an elaboration, 'there's the lightest amount of Pebbles in this box'. This was followed by a Consequence 'because I can hear them the most' which actually preceded its Premise 'whilst they're moving quite a lot'. Another Consequence 'and then see' follows before the Supposition' I don't think' with its Elaborator 'that there's that many in that box'. Suppositions are elements that are described in greater detail below.

The second example illustrates what a Year 8 boy from a high decile school would have done with the balance:

Umm, you'd get those two and find out the heavier one and put that like that and then test those two and the heavier one would go there and then you could test those two and the heavier one would go there and you'd keep doing it until they're all right.

This response began with a Premise which was followed by a Consequence and this combination was then repeated. The response was completed with an implicit Conclusion followed by an Elaborator.

The elements used were Premise, Consequence and Conclusions, both explicit and implicit, as there had been in the Better Buy task. But there were also Introductions, Elaborators, Suppositions and Physical Consequences. The students who used these elements is given in Table 4.3 and the elements themselves are described in the next paragraphs.

In Table 4.2, it can be seen that Premises were used by most students. However, unlike Better Buy, Motorway and Bank Account where every student used a Premise, there were six students who did not use a Premise in responding to this part of the Weigh Up task. One Year 4 boy from a low decile school did not answer at all but the remaining five students gave a response which did not include a Premise. Often these students used a Physical Consequence instead. For example, the following response is from a Year 8 boy from a high decile school:

This one feels the lightest and then
Q
That's the lightest, that's the second lightest and then that one and that one

The boy began with a Physical Consequence and after the teacher's comment gave an implicit Conclusion describing the order of the boxes from lightest to heaviest.

In this section of the task, there were more Year 8 students who used Elaborators, implicit Conclusions and Suppositions than Year 4 students. More girls used Suppositions than boys. However, more boys appeared to use Consequences than girls. There did not seem to be any other major differences in the distribution of elements between the groups.

In the Motorway task, an Introduction only provided a personal response. In this task, the Introduction was an element that set up whether the student was giving a personal or generalised response. As is seen in Table 4.2, there were three students who used Introductions. Two students began their responses with 'what I'd do is' and 'what you could do is'. These both included an Elaborator embedded within the main clause. In both clauses 'is' is the main verb and 'what I'd do' and 'what you could do' are the Elaborators. The use of 'you' suggests a more generalised response than when the students uses the first person, 'I'.

The only other student who used an Introduction did not do so at the beginning of the response. This year 8 boy from a middle decile school began with an Implicit Conclusion, 'I've done it', and it was only after a prompt from the teacher administrator that the student re-started with 'I went like', which made it clear that this was a description of what this student had done rather than a generalised statement. This last example was much closer to the Introductions used in the Motorway task which were all related to the calculation being described.

Suppositions were clauses which put forth a proposition. There were several ways that students did this. Using 'say', 'perhaps', 'probably' or 'you think' seemed to set up a hypothetical situation whilst 'I think' was more likely to show uncertainty about the validity of a result or the suggestion being made. In this part of the task, there were 15 students who used Suppositions.

Four students used 'say' which was coded as a Supposition. A Year 8 boy from a low decile school used 'say' to make a suggestion which could then be further developed in the following utterance, 'Um, just pick any one and put them on, and then, say that that one was heavier than this one'. A Year 8 boy from a middle decile school also used 'say' in the following extract from his response: 'say A's the next heaviest, it feels like..'. A Year 8 girl from a middle decile school also said, '...and then, C, say if this was the lightest then I'll go C and D'. Another Year 8 girl from a high decile school also used 'say' in the following, 'measure ah, say A and B together and see which one's heavier'. 'Say' therefore was a marker to show that it was a hypothetical rather than an actual situation being described. In these cases, 'say' appeared to be used as an intermediate step between only talking about the specific situation in which the student is involved and being able to produce a generalisation which would cover any possibility. This similar to the 'general' category that Bills and Grey (2001) found in their research.

In a similar manner, a Year 8 boy from a middle decile school said, 'if I say that that's lightest...'. Although coded as a Premise because of it being the basis for his argument, it shared many similarities with Suppositions. There were two other suppositions which used the expression 'you think' which also seemed to fit this category. A Year 8 boy from a low decile school said, 'by grabbing ... um, ah just one that you think it is' and a Year 4 girl from a high decile school said, 'and you'd put down the one that you thought was the heaviest'. These students were responding to the part of the question about what would you do if you were able to use the balance.

A Year 8 boy from a high decile school who had used 'say' in his response, also used the expression 'perhaps B's still heavier' which was coded as a Premise but shared many of the characteristics of a Supposition by suggesting a possibility. This student was the only one to use 'perhaps' in this way. As well, there were three students who used 'probably' to suggest uncertainty about the Premise, Physical Consequence, Consequence or Conclusion that they were making. A Year 4 boy from a high decile school said at the end of his response, 'like it won't quite be down there, probably be about there'. A Year 8 girl, also from a high decile school, said in a fairly disjointed response, 'okay, you'd probably put those two on'. The third use of probably was by a Year 8 girl at a low decile school:

Ok, you could go like that, and that one there's lighter than that one .. I think .. yeah, that one there's probably lighter than that one, and, that's probably lightest up there .. and that one there, and that one there.
Q
Probably do it the same way, just put like A there..

It is difficult to know how much this student was using 'probably' to show a suggestion and how much she was using it as a hedge to lessen the likelihood of losing face in front of the teacher administrator.

A similar difficulty in making judgements about the purpose of these elements also arose with students' use of 'I think'. The other nine students who used Suppositions used 'I think' to express uncertainty about the correctness of their order of the boxes after they had weighed them by hand. As was the case with 'I think' in the Motorway and Bank Account tasks, these expressions can be used as hedges to reduce the possibility of the student losing face. In these situations, the students could have been certain about the result, but did not want to appear too assertive. For example, they may have been able to guess that the next part of the task required them to actually use the balance to find a definitive answer so they did not want to pre-empt doing this. As was seen in the example of the Year 8 girl above, it is difficult to determine how much the 'I think' reflects genuine uncertainty and how much it is used to acknowledge the power relationship between the student and the teacher. This kind of difficulty is not uncommon in research on hedges (Meyerhoff, 1987). As a result, 'I think' was labelled as a Supposition rather than a hedge. The following table shows the distribution of Suppositions and other proposing devices.

There were far more uses of 'I think' than any other types of Suppositions. Although the numbers are small, it would seem that students from high decile schools were less likely to use 'I think'. It would also seem that girls were more likely to use Suppositions than boys and they were used predominantly by students in Year 8. This last trend is interesting because it would be anticipated that more Year 4 students than Year 8 students would have difficulty in making an accurate judgement by hand of the order of the boxes, but they are not the ones to express uncertainty about their estimation. It may be, of course, that there were fewer students in Year 4 who responded to this question by estimating the order of the boxes. However, Table 4.2 shows that equal numbers of students in Year 4 and Year 8 used a Physical Consequence to describe the results of an action that they had undertaken. This suggests that equivalent numbers of students chose to respond to this task by weighing the boxes by hand.

A new element found in the responses to this task was one which described the consequence of an action but was not related to a Premise. These were labelled as Physical Consequences and an example of one is the following from a Year 8 Pacific boy: 'and these two kind of feel the same'. Although more common in the second part of this task, there were instances in responding to the first question where students began with or only used Physical Consequences in their responses.

There were also quite varied combinations of text elements in the structures. For example, a Year 4 girl attending a high decile school said the following:

Pick it up and if they're heavy, leave it by itself, and if the other one's are light, umm, if they are like this one
Q
B and, C is the heaviest and B, A and D are light and um
Q
You'd pick them up and feel the weight, and there's the second one …
Q
The two last ones down there put them in the same one, oh no, the big one, the small one goes down there and the big one, the big one and the small one goes down …

This response contains a Premise - Consequence - Premise - Physical Consequence - Premise - Consequence - Physical Consequence - Premise - Physical Consequence combination. Although some students used simple text structures, complex combinations were common and can be seen in the Table 4.4. One Year 4 boy from a low decile school only replied 'no' to all teacher prompting. The '+' indicates that the text combination could also be followed by other elements.

The most interesting thing about the results in Table 4.4 is the lack of any clear patterns in their distribution. This is partly because of the small numbers of students who used many of these combinations of elements. There are only three combinations which were used by more than 9 students. Of these, two had similar distributions 41 across gender, year level and decile level of school attended. Only the text structure which began with Premise - Elaborator, with other elements following, was clearly used by more girls than boys and by Year 8 students more than Year 4 students. This pattern is emphasised when another 4 students who also used a Premise - Elaborator combination are added to these results. It is interesting to note that two Year 4 students began their responses with Consequence - Premise combination joined with 'because'. Donaldson (1986) stated that this combination was more common in her research that than ones where the action was joined to its result with a 'so'. Although very few students used 'so', as can be seen in Table 4.7, the Premise - Consequence combination was far more prevalent in responses to all tasks.

Table 4.5 sets out the combinations which included an Elaborator. The first number in each box gives the number of students using that combination with an Elaborator, whilst the second number after the '/' provides information about the total numbers of students who used the original element from Table 4.2.

Table 4.2 shows that equivalent numbers of boys and girls used Elaborators. However, from Table 4.5 it can be seen that girls used more combinations with elaborators in them (37 to 29), with the main difference being in the use of a Premise - Elaborator combination. When comparisons are made between the initial numbers of students who used Premises, Consequences, etc and those who used these elements in combination with Elaborators, there are some major differences between groups. If girls used Consequences in their responses, they were more likely to follow them with an Elaborator than boys were. Although the numbers are small, there also seems to be a tendency for students attending middle decile schools to combine Suppositions with Elaborators than any other group. Year 8 students also seemed more likely than Year 4 students to combine a Supposition with an Elaborator. However, the number of Year 4 students who used a Supposition was very small (3) and it is difficult to know how reliable this conclusion is. What could be said is that if a Year 8 student used a Supposition then they were quite likely to follow it with an Elaborator. Students who used Physical Consequences and, to a lesser extent, implicit Conclusions were less likely to combine these elements with an Elaborator than with other text elements.

The relationship between Consequence and Elaborator elements is strongly influenced by the distribution of the Premise - Consequence - Elaborator combination. This combination was frequently used by students in their responses to all parts of the Weigh Up task. For example, a common response was something like the following which came from a Year 4 boy in a middle decile school; 'you could pick them up and see if they are heavy or light'. 'You could pick then up' is the Premise 'and see' is the Consequence with 'if they are heavy or light' as the Elaborator of the Consequence.

The way that different combinations of text elements are joined can support the cohesion of the student's text. The following sets of tables show the distribution of various combinations of elements and the logical connectives used to join them together. The first pair of tables is about the combination of Premise - Consequence (with and without an Elaborator as the next element) and Premise - Elaborator - Consequence. It looks at who used them anywhere within their responses.

It appears that there are more students using logical connectives than students using text elements, because sometimes the same student might have several combinations of Premise (- Elaborator) - Consequence within a response and have different logical connectives between elements. This can be clearly seen in the students who came from middle decile schools. This group used the least number of these text combinations, although not by a large amount, but were the group who used the most logical connectives, although once again not by a large amount.

Table 4.7 suggest that there were few uses of 'so' and these were all by Year 8 students. There did not seem to be any major differences between the users of other logical connectives. In this part of the Weigh Up task, it was most common for 'and' to join Premises, with or without Elaborators, to Consequences. It may be that boys use 'and' in this way slightly more than girls do and that Year 4 students do so slightly more than Year 8 students. However, the differences in the numbers are not so great as to be definitive. This use of 'and' would be related to the 'put another one on and see if it's um, different weight', Premise - Consequence - Elaborator combination which was very common, especially amongst students from low decile schools. The following table shows what logical connectives were used between different text elements and Elaborators. This includes the use of 'if' in the Premise - Consequence - Elaborator combination.