|
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 |
|
|
|
|
|
|