Three
boys, all from low decile schools, refused to attempt the task at
all. Two were from non-Pacific communities whilst the third was
a Pacific. Two were in Year 8 whilst the third was in Year 4. Many
students also used a range of different linguistic features to mark
hesitant language. Many of them would occur in the same utterance,
as in the following:
Umm .. well,
here he had like not much money in his bank account then he must
of saved a bit more and got another ten dollars in his bank account,
and on Wednesday he didn't save any, any money, and he just kept
the same in his bank account, then on Thursday he must have spent
some, then on Friday he mustn't have spent any, and just left
it, and on Saturday he must spent some.
As with the
responses to the Motorway task, hesitant language featured hedges,
fillers, approximators, questions and disclaimers. The following
table provides information on the fillers that students used to
gain themselves time. |
|
|
|
Table
6.14. Showing the distribution of fillers by different groups. |
|
|
Fillers |
Gender |
Year
Level |
School
Decile and Ethnicity |
Total
|
Girls |
Boys |
Year
4 |
Year
8 |
Low
PI |
Low
Non- PI |
High |
 |
umm |
21 |
11 |
10 |
22 |
11 |
10 |
11 |
32 |
oh
/ ah |
5 |
7 |
4 |
8 |
3 |
2 |
7 |
12 |
well |
4 |
3 |
3 |
4 |
0 |
1 |
6 |
7 |
okay |
1 |
3 |
0 |
4 |
1 |
1 |
2 |
4 |
hang
on, hold on |
1 |
2 |
0 |
3 |
1 |
1 |
1 |
3 |
yeah |
0 |
2 |
0 |
2 |
1 |
1 |
0 |
2 |
|
|
|
There
was more variety in the fillers that students used in their responses
to this task than those used to respond to the Motorway task. However,
the use of 'umm' is quite different to how it is used in responses
to the Motorway task. In the Motorway task, the numbers were fairly
evenly spread between boys and girls, and between Year 4 and Year
8 students. For the Bank Account task, there were twice as many girls
and Year 8 students using 'umm' as there were boys or Year 4 students.
For the other fillers, the results are similar to those used in the
Motorway responses. |
|
|
|
Table
6.15. Showing the distribution of hedges by different groups. |
|
|
Hedges |
Gender |
Year
Level |
School
Decile and Ethnicity |
Total
|
Girls |
Boys |
Year
4 |
Year
8 |
Low
PI |
Low
Non- PI |
High |
 |
just |
2 |
5 |
3 |
4 |
0 |
3 |
4 |
7 |
like |
5 |
7 |
4 |
8 |
3 |
2 |
7 |
12 |
kind
of |
2 |
0 |
2 |
0 |
0 |
1 |
1 |
2 |
probably |
2 |
3 |
1 |
4 |
2 |
1 |
2 |
5 |
say |
2 |
0 |
0 |
2 |
0 |
1 |
1 |
2 |
I
mean, I think, that meant, which means, lets see, as I say |
5 |
1 |
2 |
4 |
2 |
1 |
2 |
6 |
|
|
|
The
results in Table 6.15 show similarities between the use of fillers
and hedges in this task and in responses to the Motorway task, although
there are many more students using them in this task. Some of these
hedges were used to approximate the amounts that students were discussing.
The following table shows the distribution of the approximators used
to lessen the exactness of the amounts discussed. |
|
|
|
Table
6.16. Showing the distribution of approximators by different
groups. |
|
|
Approximators |
Gender |
Year
Level |
School
Decile and Ethnicity |
Total
|
Girls |
Boys |
Year
4 |
Year
8 |
Low
PI |
Low
Non- PI |
High |
 |
a
little (bit), a wee bit |
3 |
3 |
2 |
4 |
3 |
2 |
1 |
6 |
like |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
some
(more) money |
3 |
5 |
3 |
5 |
0 |
5 |
3 |
8 |
just |
2 |
0 |
1 |
1 |
1 |
1 |
0 |
2 |
kind
of |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
a
bit more |
1 |
2 |
2 |
1 |
0 |
0 |
3 |
3 |
lots
of money |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
quite |
2 |
0 |
0 |
2 |
0 |
0 |
2 |
2 |
about
/ almost |
4 |
0 |
0 |
4 |
2 |
1 |
1 |
4 |
|
|
Students
used a greater variety of approximators than they did for the Motorway
task. This probably reflects the differences in the types of answers
expected of them for these two tasks. In this task, students were
not given any specific instructions on what details they should
include in their graph stories. The requirements for the Motorway
task constrained the types of response that students gave thus limiting
the types of approximators that they used.
The four Year
8 girls who used 'about'/'almost' did so in regard to the amounts
in the bank account on Thursday and Friday which required them to
make an estimate against the scale. All the other students who referred
to the graph and gave mathematically sensible stories either gave
exact amounts or used broad approximators such as 'some'. The following
response was by one of these girls who used 'about'.
Well, if this
is the amount of money, and these are the days. Say he came into
the bank on Monday, and he like put ten dollars into his bank
account then it shows that he's got ten dollars, and he came on
the next day and he put um, ten more dollars in, and then he came
in the next day he didn't put any money in, because it's the same
amount, and then he came in on a Thursday. Lets see, he obviously
took out some money ... he took out about .. umm, four dollars,
and then he didn't put any more money in on a Friday, and took
out some more money...umm .. he took out about six dollars.
As the students
were expected to give a story about an imaginary bank account, it
was anticipated that many students would use modal verbs such as
'might', 'would'. However, as Table 6.17 shows, this was not the
case. |
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|
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Table
6.17. Showing the distribution of modal verbs by different groups. |
|
|
Modal
verbs |
Gender |
Year
Level |
School
Decile and Ethnicity |
Total
|
Girls |
Boys |
Year
4 |
Year
8 |
Low
PI |
Low
Non- PI |
High |
 |
might |
1 |
4 |
3 |
2 |
1 |
2 |
2 |
5 |
could |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
2 |
must |
0 |
2 |
0 |
2 |
1 |
0 |
1 |
2 |
would |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
|
|
|
The
numbers are once again very small. Boys used more of these verb
forms than girls, but there seem to be no other major differences
between the different groups.
Another way
that students showed their uncertainty about what they had to do
during the task was through asking questions or stating their uncertainty.
Students asked questions, either of themselves or of the teacher
administrator. The questions that they asked of the teacher administrator
were either about the task itself or about something on the graph.
Often these questions could just be a more subtle way of asking
for reassurance about the task. This can be seen in the following
example:
Is this how
much money he's got in his bank account?
|
|
|
|
Table
6.18. Use of questions by different groups. |
|
|
Questions |
Gender |
Year
Level |
School
Decile and Ethnicity |
Total
|
Girls |
Boys |
Year
4 |
Year
8 |
Low
PI |
Low
Non- PI |
High |
 |
Question
of TA about task |
5 |
3 |
2 |
6 |
1 |
3 |
4 |
8 |
Question
of TA about graph |
5 |
2 |
0 |
7 |
5 |
0 |
2 |
7 |
Question
of themselves |
0 |
2 |
1 |
1 |
0 |
1 |
1 |
2 |
|
|
|
The
results for the different groups asking questions are given in Table
6.18. Rowland (2000) reported research which showed that students
were reluctant to ask questions because they felt they would lose
face in front of their teachers. Similarly, in research looking
at Pacific girls in an Auckland high school, Jones (1988) found
that these girls were far less likely to question their teachers
than their non-Pacific peers. This was not only because of the risk
of losing face, but also because they felt that it was disrespectful.
It is, therefore, very interesting to find that it is girls rather
than boys who are prepared to take such risks, but only once they
are in Year 8. There is, however, other research (Langvogt, Leder
& Forgasz, 2002) which suggests that girls are less confident with
their own ability in doing mathematics and so it could be a lack
of confidence which results in them checking what they are doing.
Boys, on the other hand, will launch into an explanation even when
they are answering a very different question than the one which
was asked. This is in contrast to the boys who refused to attempt
the task at all. By not attempting it, they cannot be considered
to have 'failed' and so resemble the boys in Langvogt et al.'s (2002)
research, which suggested that boys thought they failed because
they had not studied rather than because of a lack of talent. Girls
were more likely to consider that they lacked talent.
As well as asking
questions to indicate their uncertainty about what to do, some students
expressed their uncertainty about what was expected of them. The
following table outlines this. |
|
|
|
Table
6.19. Use of disclaimers by different groups. |
|
|
Disclaimers |
Gender |
Year
Level |
School
Decile and Ethnicity |
Total
|
Girls |
Boys |
Year
4 |
Year
8 |
Low
PI |
Low
Non- PI |
High |
 |
I
don't know |
3 |
4 |
3 |
4 |
3 |
4 |
0 |
7 |
I'm
not sure |
0 |
2 |
1 |
1 |
1 |
0 |
1 |
2 |
|
|
|
These
results suggest that boys express their uncertainty in different
ways to girls. Women are known to ask more questions as part of
their interactional style (Fishman 1978) and, therefore, if boys
and girls follow the language patterns of adults, and there is research
to suggest that this is true (Deuchar, 1990 and Coates, 1993), it
is not surprising to find this also occurs in how boys and girls
express uncertainty. However, what is surprising is that this is
compounded by socio-economic background. Boys from high decile schools
are less likely to express their uncertainty either as a statement
or as a question. On the other hand, 4 out of the 6 Year 8 girls
from high decile schools asked a question. Boys who did express
their uncertainty by either: refusing to do the task; asking a question;
or making a statement about it, were all from low decile schools.
3 out of the 6 Year 8, Pacific boys from low decile schools asked
a question.
Koehler (1990)
reported research which showed that classrooms where girls were
encouraged to ask questions resulted in them having poorer results
than those in which students were encouraged to be more autonomous
in their learning. If, for students in low decile schools, it is
acceptable to opt out of participating in tasks, then it may that
these students, boys or girls, are not being encouraged to be autonomous
learners and this would have an effect on their learning. Alison
Jones' (1988) research on Pacific girls found that, compared to
their Pakeha peers, they 'avoid[ed] eye contact with the teacher,
they spoke up very little, muttered more often and rarely called
out an answer as an individual' (p. 148). She felt that these behaviours
were reinforced by the demands made on the teachers' time by Pakeha
girls thus reducing Pacific girls' opportunities for engaging in
ways of behaving which were more likely to produce the learning
valued by schools. Although our research suggests that primary students
in low decile schools do not express themselves in the ways suggested
by Jones, there are differences in how groups of students choose
to provide mathematical stories and interact in assessment situations.
If these inhibit students' access to the experiences which are most
likely to result in them gaining the learning valued in classrooms,
these students could be unfairly disadvantaged. More work needs
to be carried out to discover how much these different ways of talking
affect the learning situations offered to students. |
|