Language used by students in mathematics for quantitative and numerical comparisons

Chapter 6 : Bank Account cont.

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.

   
 
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.


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