Language used by students in mathematics for quantitative and numerical comparisons

Chapter 4 : Weigh Up cont.
 
Table 4.25 Logical connectives between Physical Consequence – Consequence.
Logical Connectives
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
so
17
8
7
18
4
11
10
25
so then
2
1 1 2 0 2 1 3
and 5 2 3 4 3 1 3 7
and then 1 1 1 1 0 1 1 2
then 1 1 1 1 1 0 1 2
   

'So' is used by more students to join a Physical Consequence to a Consequence. All but one girl who used this combination of text elements used a 'so' as a logical connective. Although they used an equal number of these combinations, boys consistently used fewer logical connectives than girls. Although Year 8 students used this combination more often than Year 4 students, they also used more logical connectives proportionally than did the Year 4 students. All but one student from a middle decile school who used this combination also connected it with a 'so'. This was proportionally more than for students attending high or low decile schools.

Why is there a change in the logical connectives used in this particular combination? It is difficult to know and difficult to investigate. However, it may be that the students chose to use 'so', with its meaning of 'as a result', to emphasise the logical link between an action and the consequence drawn as a result of the action. For example, a Year 8 girl from a low decile school said this in her response:

I'm guessing that um, that D is heavier than, I mean C is heavier, heavier than D, and it is, so D will go there and C will go there

'And' connects a Premise to the Physical Consequence but 'so' is chosen by the student to connect the Physical Consequence to its Consequence. The 'and' could be left out and the meaning would not change very much but if the 'so' was removed the link between the ideas is not transparent.

In looking at the overall picture of who used which logical connectives where in the Description responses, it would seem that girls and Year 8 students were more likely 57 to use them to connect different text elements together. This is different to the situation in the Plan where the distribution was much more evenly spread.

 
aText structures and clarity of language

In order to determine the relationship between using particular text structures and being judged on accuracy of response and clarity of language, there was a need to have large enough groups for meaningful comments to be made. Unfortunately the distribution of students within Table 4.1 did not match the distribution of students in Table 4.14. In the Description responses, the only groups with large enough numbers to comment upon were those deemed to have an accurate clear response, those who were accurate but elliptical and those who were moderately clear and approaching accuracy.

It would appear that certain text elements and combinations of elements occur more frequently when students gave clear accurate answers and less frequently when giving elliptical but accurate answers or moderately clear answers which were approaching accuracy. These are the use of Conclusions (implicit or explicit), Premise - Consequence - Elaborator and Physical Consequence - Consequence combinations.

   
 
Table 4.26 Percentage of each group[ of students who used particular text elements and combinations.
 
Description responses
Premise – Conseq
Premise – Conseq – Elaborator
Conclusion
Physical Conseq – Conseq Supposition
Accurate and clear n = 17
53%
41%
35%
94%
6%
Accurate and elliptical n = 7
0%
0%
0%
0%
14%
Approaching Accuracy and moderately clear n = 12
25%
8%
17%
58%
25%
   

Table 4.26 provides details of which students were deemed to have accurate and clear responses and their use of various combinations of text elements. Of the 17 students, who were deemed to have accurate answers and clear language, nine included a Premise - Consequence combination with a further two students using a Consequence - Premise combination. There were only two cases when the Premise - Consequence combination was not followed by an Elaborator. Six students, five of which were in Year 8, also used a Conclusion (implicit or explicit). However, a more common combination was that of Physical Consequence - Consequence with 16 of the 17 students using this combination. 'So' was the most common logical connective between these elements.

Only seven students, with five being in Year 8, were deemed to have elliptical but accurate answers. Of these, none contained a Premise - Consequence (- Elaborator) combination, a Conclusion or a Physical Consequence - Consequence combination. This is not particularly significant, as in being labelled as elliptical, these students were unlikely to give extended answers. Two students, in fact, said nothing while all 58 except one of the other students used at least a Physical Consequence. These students were unwilling or unable to discuss what they were doing while they were doing it.

Table 4.26 also provides information on the text elements used by the twelve students who were deemed as having a moderately clear response which was approaching accuracy. It can be seen that the proportion of students using these text elements or combinations is significantly lower than was for the case for students who were accurate with clear language. It may well be that, if students are explicitly taught to include these combinations in their response, they would be more likely to be able to use language to support their thinking.

It would seem that the use of Premise - Consequence (and to a lesser degree combined with an Elaborator) and Physical Consequence - Consequence combinations support providing an accurate, clear response. To a lesser extent, the inclusion of a Conclusion may also increase the likelihood that the response would be judged clear. Although the use of Premise - Consequence (- Elaborator) combination was equally useful in the Plan responses, the other combinations were not so. This reinforces the belief that students need to know how to combine different text elements but also need an awareness of the appropriate situations in which these combinations should be used.

The Description part of the task produced responses which were more likely to revolve around Physical Consequences than Premises. As such, there were differences in the use of text elements generally and in regard to which responses were most likely to be considered accurate and clear. The high use of Physical Consequences also affected the proportion of students using logical connectives and the likelihood of them being used in different positions.

   
aWeigh Up Explanation

In this part of the task, students were asked how they would explain this task to a class-mate. On the whole, students were more expansive in their explanations than when they had responded in the Plan section, where they had to describe what they would do before doing it. NEMP's report on this task stated that '[e]xplanations improved a little after the students did the task' (Flockton & Crooks, 1997, p. 38). As was the case in the previous sections of this task, Table 4.27 is provided to give background about students' accuracy and clarity.

For this part of Weigh Up task, it was not possible to transcribe the responses of six Year 4 boys from middle decile schools. This was because, in the sample which were kept by NEMP, there was only 5 students with these demographics who were asked all three questions. As a result the total sample size is 71. As well, one Year 4 boy from a low decile school did not say anything except 'Umm.... Q No' when asked the question.

   
 
Table 4.27. Clarity of language vs correctness of explanation*.
 
 
Clear Language
Moderately clear but vague on specific details
Unclear, multiple reruns, vague
Elliptical
Accurate Answer 2 Yr 8 LG 3 Yr 8 LGs 1 Yr 8 LG  
  1 Yr 8 MG 3 Yr 8 LBs 2 Yr 8 MGs  
  2 Yr 8 HBs 3 Yr 8 MGs 1 Yr 8 HG  
  1 Yr 4 HB 1 Yr 8 MB 4 Yr 8 MBs  
    3 Yr 8 HGs 3 Yr 8 MBs  
    2 Yr 8 HBs 1 Yr 8 HB  
    2 Yr 4 LGs 1 Yr 4 MG  
    1 Yr 4 MG 2 Yr 4 MBs  
    1 Yr 8 MB    
    1 Yr 4 HG    
    2 Yr 8 HBs    
         
Approaching accuracy 1 Yr 8 MB 1 Yr 8 HGs 2 Yr 4 LGs 1 Yr 4 LB
  1 Yr 8 HG 1 Yr 8 HB 2 Yr 4 LBs  
  1 Yr 4 LG 1 Yr 4 LB 1 Yr 4 MG  
  1 Yr 4 LB 1 Yr 4 MB 1 Yr 4 HG  
  3 Yr 4 MGs 1 Yr 4 MG 1 Yr 4 HB  
  2 Yr 4 HGs 3 Yr 4 HGs    
    1 Yr 4 HB    
         
Unclear about the task       1 Yr 4 LB
*student identification as in Table 3.1
   

Although the NEMP report suggested improvement in students' responses in this part of the task, Table 4.27 shows that it was still difficult for many students. Although more students were considered to have accurate responses, very few were deemed to have clear language. This is probably due to the high linguistic demands placed on students. In this part of the task, they had to describe a complex set of instructions for a peer and make distinctions between the four boxes. The most successful were those who were able to make general rather than specific references to the boxes. The following is from a Year 8 girl from a low decile school who was judged as using clear language and providing an accurate answer:

Um, to weigh two of them, and then take leave .. leave the lighter one, no take the lighter one off .. and, no take both of them off and then put on the other two on, and then take the two heaviest from both of those different ones, put them on and find out which is the heaviest, then put it down the end, and then measure between the two middle ones and find out what was the heaviest, and then put the heaviest, the next heaviest on the next bit, then figure out between the lightest and the other one, like from D and B, figure out which was the lightest from them and then put the lightest there and the next one there.

Although there were some false starts, it is quite possible to follow her explanation as she makes comparisons between the different boxes. It is only towards the end that she resorts to using box labels to make suggestions about what should be done. The references to the placement mat, 'put the lightest there and the next one there' make sense when watching the video and are entirely appropriate when the teacher administrator and the students are sitting in front of the boxes and the place mat. There are some non-standard terms such as 'heaviest', which was used in 'then take the two heaviest from both of those different ones', which in Standard New Zealand English should have been 'heavier' as it is a referred to a comparison between two boxes. Many students used 'heavier' and 'heaviest' to refer to a comparison between two boxes, although 'heavier' was never used to refer to a comparison of more than two items.

The following example also comes from another Year 8 girl attending a low decile school. It was judged as being accurate but elliptical.

Put one in and then, and then weigh them all, all of them to see if that's the lightest, and then just do it to all of them.

There is much that the listener is required to fill in. Although the student is correct in the first step, the suggestion 'then just do it to all of them', would not enable another person to actually complete the task themselves if they had not seen it being done. However, given that the teacher administrator has just watched this student successfully complete the task, the student is aware that the teacher administrator knows what is involved in this instruction. Heath's (1982) work on adult-child questioning interaction patterns suggests that middle class children are the most likely to provide more detail in their responses in a classroom setting when there is considerable shared knowledge between participants. Children of lower class families are less likely to fulfil the school game of providing details that the other participants in the interaction already know. The results in Table 4.27 suggest that this is not the case in New Zealand. Girls attending low decile schools were as likely as boys from high decile schools to provide a clear or moderately clear and accurate response. It would also seem that students from middle decile schools were more likely to provide a vague but accurate response, regardless of gender.

Although there were equivalent proportions of students getting accurate answers with clear language and with vague language, it would also seem that Year 4 students who provided an accurate answer were more likely to be moderately clear. This also suggests that the linguistic demands of this part of the task were demanding for these students. Some ability to use language was necessary to gain an accurate answer, but to give a clear response required more language ability than most Year 4 students had.

   
aText Structures
Although the same range of text elements (Introductions, Premises, Consequences, Conclusions -implicit/explicit, Elaborators and Suppositions) were used in this part, all texts began with an Introduction (only one Introduction was used) or a Premise and most responses combined at least three of these elements. Table 4.28 provides information on the distribution of students using the different elements.
   
 
Table 4.28. Use of text elements by different groups.
 
Text Elements
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
introduction
0
1
1
0
0
0
1
1
premise
36
24 24 36 23 23 24 70
elaborator 34 30 30 34 18 22 24 64
consequence 35 31 32 34 21 22 23 66
physical consequence 6 1 3 4 2 4 1 7
conclusion 1 0 0 1 1 0 0 1
implicit conclusion 15 10 11 14 7 9 9 25
supposition 7 6 4 9 2 6 5 13
   

All students who made a verbal response included a Premise and almost all students also used an Elaborator and a Consequence. However, the number of students using a Physical Consequence significantly dropped from the earlier parts of the task. Only one of these 7 students was a boy. Most students did choose to describe through words rather than actions what another student would have to do to solve the task. Occasionally, some students resorted to again comparing the boxes on the balance so that their Explanation resembled their Description. The following comes from a Year 8 girl at a middle decile school and gives both her Description and her Explanation.

Description
Okay, I felt that one was the heaviest so I put that in there and ... that one. …
Q
So, right now, I've seen that that one is really heavy, so, because like how much it takes down and that one didn't move nearly at all and this one moved a bit more than that. So that one is the lightest, definitely and B will be the second lightest and … A is next and C comes last because C was the heaviest.

Explanation
I'd take, I'd tell them to take which one they thought was the heaviest, say that was C, to put it in and that would touch the ground. Well, to as much as it would go and then take the, and see which one never, like, that one goes down quite a bit and so it's quite heavy and find out which one doesn't move really, it, which one moves the least. See this one barely moves it at all and this one moves it a bit more and if this one. If this one makes this one, makes it heavier then see that one is a bit heavier and so we know that D is the heaviest and B was lighter than A because it stayed up more and D was the lightest

Although the student started her explanation by just talking about what another student would have to do, in order to clarify her explanation, she began to use the balance again. As a result, there is a close resemblance between her Description and Explanation. Hence, Physical Consequences such as 'this one moves it a bit more' appeared in her response.

The following comes from a Year 8 boy at a middle decile school. It shows considerable difference between the Description and the Explanation responses. Although there is still some reference to the actual situation, as in 'put them on there', none of the Consequences in the Explanation are drawn from using the balance.

Description
Ok....well, A's still heavier....C, A..B, D.

Explanation
I'd say, ah, use your hands to find the two heaviest, then measure them then put .. then, get the heaviest one put it at the end, and then put the second heaviest one after it, then get the lightest one, then get the other two and put them on there and just find which one's heaviest from there .. oh, and with the heaviest ones, you put them on the scales as well to find out which one is the heaviest.

Although there were only 7 students who gave Physical Consequences in their responses, it is interesting to find that 6 of these were girls. More research needs to be done to see whether, on the whole, girls are more inclined to discuss what they are actually doing than to abstractly talk about instructions for another person.

As can be seen in Table 4.29, similar numbers of students used Suppositions in this part of the task as they had done in the other two sections. In the previous two parts of this task, more girls had used Suppositions or other propositional devices than boys. In this part of the task, there is no distinction between girls and boys. However, it would seem that Year 8 students used Suppositions more than Year 4 students. This was most evident, in this part of the task, in the use of 'you think'. Across the three sections of this task, it would seem that being able to use linguistic features to set up a proposition is something which students learn as they get older. As with other features like the Premise - Consequence - Conclusion combination in responses to the Better Buy task, the decile level of school attended also has an affect on the likelihood of the use of Suppositions. Students attending low decile schools are less likely to use them than other groups.

   
 
Table 4.29. Use of Suppositions by different groups.
 
Suppositions
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
say
4
1
3
2
0
2
3
5
imagine
0
1 1 0 0 0 1 1
guess/estimate 1 1 0 2 1 0 1 2
you think 3 5 1 7 1 4 3 8
they think / thought 1 1 1 1 1 1 0 2
   

As well, compared to the Suppositions used in the previous two sections, the expressions used to give propositional status to a clause were different. Whereas previously 'I think' had been the most common expression used, there were no examples of this in this part of the response. However, 'you think' or 'they think' was used by similar numbers of students as 'I think' had been in the earlier two sections of this task. Given that this task specifically asks students about what they would tell another student, it is not surprising that first person references were replaced. What is interesting is that students chose to use a second person pronoun rather than a third person one. The following example comes from a Year 8 girl from a middle decile school: 'until you think you know which one's lightest and heaviest'. The use of 'you' is unlikely to refer to the teacher administrator but to a generic 'you' as was the case 63 in the Better Buy task. It, however, may be that students are rehearsing what they would say to another child rather than giving a generic response.

In the example, 'you think' suggests that the doer of the actions does not need to be absolutely certain of the lightest and heaviest box. The following example, also from a Year 8 girl from a middle decile school, does not provide this uncertainty: 'and just do that with each one until, eventually you've got it figured out', although the 'eventually' does suggest that the process might take some time. The numbers are fairly small, but it would seem that Year 8 students were most likely to use 'you think' and students from low decile schools were least likely.

It was also interesting to note that there were no uses of 'perhaps' or 'probably', but a student used 'imagine' in a similar manner to 'say', thus suggesting a proposition . 'Guess' and 'estimate' were each used by a student. Although these were not coded as Suppositions but rather as Premises, there is a sense that the doer of the action does not have to be correct.

Table 4.30 provides information of the most common combination of elements which were used at the beginning of student responses. This table shows that Premise, Consequence and Elaborator were used in different combinations at the beginning of almost all responses.

   
 
Table 4.30. Use of text structures by different groups.
 
Text Structures
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
none
0
1
1
0
1
0
0
1
intro +
0
1 1 0 0 0 1 1
premise 0 1 1 0 2 0 0 2
premise – elaborator – premise +, + 8 7 8 7 6 4 5 15
premise – elaborator – consequence + 12 11 8 15 6 10 7 23
premise – elaborator – supposition + 2 3 2 3 2 3 0 5
premise – consequence 0 2 1 1 2 0 0 2
premise – consequence – premise 1 0 1 0 0 1 0 1
premise – consequence – elaborator 10 9 11 8 6 3 10 19
premise – consequence – supposition 1 0 0 1 0 0 1 1
premise – supposition + 1 0 0 1 0 1 0 1
premise – implicit conclusion 1 0 0 1 0 0 1 1
   
The three combinations which were used by most students were Premise - Elaborator - Premise, Premise - Elaborator - Consequence and Premise - Consequence - Elaborator. 42 students out of the possible 71 students gave responses which began with Premise - Elaborator and were completed with other elements. A further 22 students gave responses which began with Premise - Consequence and were completed with other elements. Although it appears that students attending middle decile schools are less likely to use this last combination than students attending high decile schools, there do not appear to be any other distinctions between groups. When the combination of elements is examined more carefully, twice as many Year 8 students as Year 4 students used the Premise - Elaborator - Consequence combination. However, the most notable feature of the results in Table 4.30 are the lack of differences in groups using various combinations.
   
 
Table 4.31. Text structures with combinations including an Elaborator.
 
Text Structures containing
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
premise – elaborator
24/36
21/34
18/34
27/36
16/23
16/23
13/24
45/70
consequence – elaborator
29/34
25/30 25/30 29/34 18/18 16/22 20/24 54/64
supposition – elaborator 5/7 2/6 3/4 4/9 0/2 3/6 4/5 7/13
physical consequence – elaborator 2/6 0/1 1/3 1/4 1/2 1/4 0/1 2/7
implicit conclusion – elaborator 3/15 3/10 4/11 2/14 3/7 2/9 1/9 6/25
   

As Elaborators were once again a feature of most students' responses, Table 4.31 provides information on the distribution of students using different elements with Elaborators. In the Explanation, there were significantly more students who combined an Elaborator with a Premise. In the Plan, the percentage of students using Premise - Elaborator combinations compared to those using just Premises was 27% and for the Description part of the task, it was 26%. However, in the Explanation, this rose to 45%. This increase was because 75% of Year 8 students who used a Premise combined it with an Elaborator. This increase in the number of students using this combination is probably related to the opening Premise which was often something like 'You'd tell them to use one of these' or 'Well to check first of all to find out which is the heaviest one'. As the students were asked 'If you had to explain to someone else in your class how to work out the order from lightest to heaviest, what would you tell them to do?' both Introductions and these opening Premises respond directly to the question by setting the scene for the explanation to come. However, unlike an Introduction, these Premises describe a specific action, such as telling or checking. This is different to 'What you do is' which was the only clause coded as an Introduction in this part of the task. There were only two students who did not begin their responses with Premise - Elaborator but who incorporated this combination in their responses later. This emphasises just how prevalent this combination was at the beginning of the responses. The research done by Hass and Wepman (1974) suggested that older children would incorporate more 'embeddedness' into their responses. However, it is only in the Premise - Elaborator combination in this part of the task that there appears to be a difference based on age. Their research analysed samples of students' oral stories based on picture cards. It may be that narratives, which are what the children produced in the Hass and Wepman (1974) study, provided fewer possibilities for using a Consequence - Elaborator combination but encouraged more elaboration around Premises.

For this part of the task, not only did more students use a Consequence within their response but they were more likely to combine them with Elaborators. 84% of students who used a Consequence combined it with an Elaborator at least once within their response. All students attending a low decile school, if they used a Consequence, combined it with an Elaborator. Although the differences are not great, it would also seem that, as was the case in the Plan and in the Description, students attending middle decile schools were the least likely to combine a Consequence with an Elaborator.

Students who used implicit Conclusions were less likely to combine them with Elaborators than with any other text element. There do not appear to be any other major distinctions between groups using elements with Elaborators.

It would seem that the elaboration seen in the responses to this part of the task was due to the increased use of Elaborators with Premises and Consequences. This element enables students to keep the main thread of their argument clear with the Premise - Consequence combination but give essential details through the addition of Elaborators with either of these elements. It may be that Elaborators can be considered part of Krummheuer's (1995) backings as they provide details about the constraints on ideas.

Other information which provides details of the conditions under which claims are valid comes in the use of causal connectives such as 'if' and 'so'. The following set of tables looks at the likelihood of students using particular sets of combinations and the logical connectives used between them.

   
 
Table 4.32. Premise and Consequence combinations.
 
Text Structures containing :
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
premise – consequence (without elaborator)
11
113
14
10
4
12
8
24
premise – consequence – elaborator
18
20 19 19 13 10 15 38
premise – elaborator – consequence 6 3 4 5 3 3 3 9
premise – elaborator – consequence – elaborator 8 8 6 10 4 8 4 16
   
Table 4.32 shows that there were no major differences between groups based on gender or age. There are some minor differences according to decile level of school attended, with students at middle decile schools more likely than others to just use a Premise - Consequence combination.
   
 
Table 4.33. Logical connectives between Premise and Consequence and Premise - Elaborator and Consequence.
 
Logical connectives
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
then
3
8
2
9
2
6
3
11
and
24
12 21 15 10 13 13 36
and then 12 12 8 16 8 6 10 24
so 1 0 0 1 0 0 1 1
because 0 1 0 1 0 1 0 1
but 0 1 0 1 0 0 1 1
   
The logical connectives which join Premises with Consequences provide information on how the students saw the relationship between these two elements. This is shown in Table 4.33. 'And', 'and then' and 'then' were used by substantially more students than any other logical connective. Donaldson (1986) suggested that although primary school students often use 'and' to join many ideas together in a one, long sentence, their spoken language used a far greater range of connectives. However, the results in Table 4.33 repute this, as it shows that a very limited range of logical connectives were used by the large numbers of students who used a Premise and a Consequence combination, often more than once in their responses. Unsworth (2001) stated that 'Consequential and Theoretical Explanations obviously entail greater use of conjunctions indicating cause while conjunctions in Sequential Explanations are predominantly those of temporal relations' (p. 136). Although it would be expected that most explanations in mathematics would emphasise causality, over all three parts of the Weigh Up task there was limited use of logical connectives showing causality, such as 'so'. In this part of the task, there was only one student who used 'so' between the Premise and the Consequence, but there was also a student who used 'because' inappropriately. The results in Table 4.33 suggest that most students used one logical connective consistently throughout their response. If some students had chosen to use two, then it would mean that an equal number of students did not use any logical connection in this situation. The use of narrative (temporal) connectives rather than causal connectives suggests that students perceived these explanations as being about listing the order of what they had to do rather than giving information about why they are doing it. The situation for logical connectives used between Consequences is very similar and is shown in Table 4.34.
   
 
Table 4.34. Logical connectives between Consequences.
 
Logical connectives
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
and
19
21
61
24
11
14
15
40
then
10
4 6 8 3 8 3 14
and then 17 15 12 20 7 10 15 32
so 2 3 4 1 2 1 2 5
and so 0 1 0 1 0 0 1 1
but 2 1 3 0 1 1 1 3
or 1 0 1 0 1 0 0 1
until 1 0 0 1 1 0 0 1
   
Students used a greater range of logical connectives between Consequences than between Premises and Consequences. However, students still chose most often to use 'and', 'and then' and 'then', which did not provide information on causality. There are some differences between the groups in who uses logical connectives between Consequences. Between Premises and Consequences, 'and' is used by substantially more girls than boys but this is not the case between Consequences. Although boys used slightly more logical connectives between Premise - Consequence combinations, girls used more between Consequences. Year 8 students also used more between Consequences than between Premises and Consequences. In both Premise - Consequence and Consequence - Consequence combinations, fewer students from low decile schools used logical connectives.
   
 
Table 4.35. Logical connectives between Physical Consequences and Consequence.
 
Logical connectives
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
and
3
0
1
2
1
2
0
3
so
4
0 1 3 1 2 1 4
   
Table 4.35 shows the attributes of the few students who used a logical connective between a Physical Consequence and a Consequence. Although there were many fewer Physical Consequences used in this part of the task, it is interesting to see what logical connectives were used to join them to Consequences. As there was only one boy who used a Physical Consequence in his response, it is not surprising to find that it is only girls who used logical connectives in this situation. The numbers are small and so it is not possible to draw any conclusions from this table.
   
 
Table 4.36. Logical connectives between Consequence and Premise.
 
Logical connectives
Gender
Year Level
School Decile Level
Total
Girls Boys Year 4 Year 8 Low Medium High
because
5
2
4
3
1
4
2
7
if
2
0 1 1 0 1 1 2
when 0 1 1 0 0 0 1 1
   
 

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