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Issues in Teaching Mathematics to Aboriginal Students
Peter Howard Bob Perry
Australian Catholic University University of Western Sydney
p.howard@mary.acu.edu.au b.perry@uws.edu.au
This paper reports on the espoused views of a group of primary teachers as they discuss
issues related to the teaching of school mathematics to Australian Aboriginal students.
They believe that their teaching is significantly affected by trying to program and cater for
the wide range of abilities, the amount of mathematics content to be covered and the lack
of teaching time. They report a lack of teacher education preparation for teaching
mathematics across ability groups and the difficulty of inventing appropriate teaching
strategies to meet the learning needs of Aboriginal children.
Australian Aboriginal people continue to be the poorest, most incarcerated, most
unemployed and least educated people in Australia (Kemp, 2001). Aboriginal students
continue to achieve lower educational levels than those of other Australian students (NSW
Aboriginal Education Consultative Group Inc./NSW Department of Education and
Training, 2004). Over the last 20 years, “there has been little improvement in the
educational outcomes for Aboriginal students” (Cavanagh, 2005, p. 285).
In NSW primary schools, Aboriginal students meet the mathematics derived from the
state syllabus (Board of Studies, NSW, 2002) with the assistance of their teachers. Most of
these teachers in NSW are non-Aboriginal. While this is not, of itself, a cause for concern,
there is the potential for cultural conflicts in terms of the understandings and views of the
Aboriginal students (and their families) and those of the teachers (Howard, 2001;
Matthews, Howard, & Perry, 2003).
The view that mathematics and mathematics learning is context and value-free in its
nature, content and practice has been long challenged (Barton, 1992; Bishop, 1994) with
the acknowledgment that the continuing evolution of mathematics takes place in socially
and culturally laden contexts (Zevenbergen, 2003). Sfard and Prusak (2005) suggest that
learning is a process of sociocultural interaction. School mathematics is constructed in a
social context governed by rules. These rules reflect the social and cultural rules of the
wider society as interpreted by the individual classroom teacher. School mathematics,
though taught within social and cultural practices, may not acknowledge the mathematics of
the student’s cultural origins. “The ‘one mathematics’ curricula common in our schools
must be seriously questioned because it limits the possibility of mathematics” (Barton,
1992, p. 9). Teachers need to acknowledge the social and cultural contexts in which learning
takes place. They have to appreciate the learning environment through the eyes of the
learner and thus begin to develop a curriculum that results from negotiation between
students, teachers and community. This is particularly so for Aboriginal students placed in
classrooms with non-Aboriginal students (Howard, Perry, Lowe, Ziems, & McKnight,
2003; NSW Aboriginal Education Consultative Group Inc./NSW Department of Education
and Training, 2004).
Teacher beliefs about mathematics, mathematics learning and mathematics teaching
play a critical role in determining how teachers help their students develop their
mathematics (Pajares, 1992; Schuck & Grootenboer, 2004). A number of researchers have
linked the success, or lack of success, of reform movements in mathematics to the efforts to
adequately address teacher beliefs (Battista, 1994; Beswick, 2005; Stipek & Byler, 1997).
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Hence, it is appropriate when considering the mathematical learning and teaching of
Aboriginal students in primary classrooms to study the beliefs of the teachers in these
classrooms. Thus, this paper considers the question, What do teachers believe to be the
important issues in teaching mathematics to Aboriginal students? In considering this overall
question the following sub-questions provide the foci of this paper:
•Is teaching mathematics to Aboriginal students different from teaching mathematics
to other students?
•What impact does the context of the lives of the Aboriginal students have on the
teaching of mathematics?
Methodology
Data for this paper were collected as part of a 9-month ethnographic study involving
Aboriginal students, their parents, Aboriginal educators and non-Aboriginal teachers living
in a remote rural community in New South Wales, Australia (Howard, 2001). The levels of
cultural sensitivity, awareness and knowledge of the people processes required to maintain
effective ethnographic research in this specific context required the author to relate to
Aboriginal and non-Aboriginal people, to appreciate the contextual social and cultural
factors and to develop mutual trust and respect with the participants over time. The study
investigated the espoused beliefs about the nature and learning of mathematics stated by
Years 5 and 6 teachers in a primary school in Tremayne, a farming town dependent upon
wool, wheat and cotton. The town’s population comprised significant numbers of
Aboriginal and non-Aboriginal people. Tremayne has a history of recurring conflicts
between these two groups. Ellen Road Public School was a two-stream primary school,
with a staff of 19 teachers (18 non-Aboriginal; 1 Aboriginal) and an enrolment of 412
students, 32% of whom were Aboriginal. The school had three Aboriginal Education
Assistants with specific roles and responsibilities in Aboriginal education. Over a period of
6 years, the lead author had established significant levels of trustworthiness within the
school and community through acknowledging and following appropriate negotiation and
consultation protocols in undertaking the research.
The author had worked in the school for 5 months both as teacher and researcher and
established effective inter-personal relationships with staff, students, Aboriginal parents
and community. Conversational interviews were held with all participants ranging from 30
to 70 minutes to enable the teachers to address all issues they wished to raise. The teacher
interviews reported in this paper involved the five teachers on Years 5 and 6, all of whom
were non-Aboriginal. The interviews were then transcribed by the author. Sixteen
categories of responses were determined and analysed using a grounded theory approach
(Glaser & Strauss, 1967). For this paper, one of the categories—the teaching of
mathematics—is considered from the perspective of the teachers. Pseudonyms have been
used for all participants and locations.
The Teachers
Mrs Cotter had been teaching at Ellen Road for the previous 6 years. For the last 3
years she had taught the highest streamed Year 5/6 mathematics group which, at the time of
the interviews, consisted of 34 children, one of whom was Aboriginal. Mrs Cotter was
born in Tremayne and, after completing her teacher education, returned to teach in
Tremayne.
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Mrs Allan was the Assistant Principal at Ellen Road Public School. She, too, had been
born in Tremayne and left to do her teacher education before returning. Mrs Allan taught
the second streamed mathematics class comprising Year 5 and 6 students. There were seven
Aboriginal children in the class - five girls and two boys.
Ms Martin had been at Ellen Road Public School for 7 years. Ms Martin taught the
Year 6 mathematics class comprising those students deemed to be in the middle ability
range. Of these, eight were Aboriginal — four girls and four boys.
Mr Kennedy had been appointed to Ellen Road Public School the previous year as a
new graduate. He had grown up in Sydney, and Tremayne was his first experience of living
in a rural community. Mr Kennedy taught the Year 5 mathematics class comprising those
students deemed to be in the middle ability range, ten of whom were Aboriginal - six girls
and four boys.
Ms Jones was a full-time casual teacher teaching the mathematics class comprising the
lower ability Year 5 and 6 children of whom 12 out of 25 were Aboriginal - five girls and
seven boys.
Results
The category ‘teaching of mathematics’ identified comments related to the organisation
and presentation of teaching and learning activities. The following selection of comments
from the teachers is representative of the comments made which were categorised under
‘teaching of mathematics’. The comments have been grouped into sub-categories for ease of
presentation.
Teaching Aboriginal children mathematics
Mr Kennedy did not believe that Aboriginal children should be taught any differently
from other children. All children, no matter their colour, were to be taught in the same way.
*Mr KENNEDY: I don’t have any problems with that. I just teach kids and if they pick it up they
pick it up no matter what colour they are. But there are issues that are hanging around that we teach
Murris [Aboriginal people from the local area] differently. I’m not a great believer in that.
Ms Martin speculated on the links between Aboriginal children’s learning and their
relationships with mathematics, although she did not see this as something specific to
Aboriginal children.
*I: You’re the first to mention that relationship difficulty with learning maths [for Aboriginal
students]. Does that happen with other kids in the class?
*Ms MARTIN: It would have to, especially the children from average down who are negative in
themselves in a lot of ways. They are negative to learning. I think you have to have problems.
Those above should have the initiative and outlook to learn. I’m sure there are kids that go into a
teacher’s class and don’t ever improve and next year they can get a different teacher and just go
zoom.
Mathematics teaching
Mrs Cotter thought that at the school there had been a push to improve student
achievement in mathematics over the last few years. She liked teaching mathematics but
expressed her personal difficulty in not understanding why children did not understand.
*Mrs COTTER: I like teaching maths. I like it because it’s logical. I like the English side too but I
find maths really logical. Probably where I have the most trouble is that I don’t understand why
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kids don’t understand it. I think that’s why they slotted me into the upper strand.
Mr Kennedy was concerned for what his students would have learnt by the end of the
week. He was also concerned about his teaching performance as measured by what the
children in his class learnt each week.
*Mr KENNEDY: It’s a major concern of mine that at the end of this week, are the kids going to
know the things that I’ve been telling them? Have I been successful? I think they’ll have an idea but
I don’t think they’ll be able to do it.
*I: Perhaps you’re being hard on yourself and what you have to say is, “What do they know?”
*Mr KENNEDY: If I’ve been trying to teach kids for a week and they have no idea, after a week,
I’ve failed to some degree. I haven’t done my job and, as a beginning teacher, I think to myself that
I bet someone else could have taught them. It could have been done. How could I have done it?
Mr Kennedy saw his main task as getting the children to listen during mathematics
lesson.
*Mr KENNEDY: I liked mathematics at university and teaching last year made me enjoy it cause I
could go off on tangents and do extension work. We could do real life situations and it sunk in
really quick. They were all bright eyed and they understood and that made me enjoy teaching maths
as well. This year I came in with a fairly positive attitude towards it [teaching] and so that’s helped
me survive a bit. Ten minutes of each lesson would be on “This is how you do it” or “Listen to
this person and let them tell you how to do it”, or just listening and being shown what to do. The
biggest thing for me is to just get people to listen.
At times, Mr Kennedy believed himself to be a failure as a teacher.
*Mr KENNEDY: I’m not always a failure. But there is a point. There are good and bad teachers and
the kids in the class learn things and if some of the kids in my class don’t learn anything then I
have to question myself.
Mr Kennedy believed mathematics was more about thinking and reaching the right
answer than having neatly completed work.
*Mr KENNEDY: Because most maths is more thinking about it. Forget how neat it is as long as
you have the right answer or as long as you’re thinking in the right way. For me a big push in
mathematics is not to have it neat, whereas in writing you have to be able to read it so it has to be
good.
Ms Martin discussed how much the children had written in mathematics this year.
*Ms MARTIN: I haven’t had kids write things down in maths this year though we discussed what
we’ve done to see what they’ve retained. I tried it one year and I found that the kids who could
write and being grouped that year in ability levels the bottom group couldn’t do it. The other thing
is that you don’t always have the time to do it.
For Mr Kennedy time was a constraint on the variety of teaching strategies that he
incorporated into his mathematics classroom. He would try group work and he knew the
value of the children using materials in their mathematics learning but did not use them
because of time pressures to cover the mathematics content. Mr Kennedy gave an overview
of the way that he approached his teaching across one week when the topic of ‘area’ was
the focus.
*Mr KENNEDY: Sometimes I do it as a group session and then they’re listening and showing and
improving their knowledge or proving what they thought. It’s maybe more enjoyable and more
interesting for them. That’s why I do it that way but I don’t know. It seems to me from university
too much of it was just give it all to the kids and let them decide what to do with it and if they
come across it well they would. There was never a question that they would not. They will
eventually get to where you want them to get by giving them materials and that. But I don’t have
any time for that at all I’m afraid.
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Mrs Allan reflected on her school days and the place of tables drill stating that, “I think
that if it worked for me it will work for other people. I mean we probably had the threat of
death over us.” Mrs Allan presented a perspective of ‘generational change’ to the
discussion. Mrs Allan had been teaching for 24 years and talked about the changes in
teaching across that time. She believed that children had lost their innocence through the
impact of technology, particularly television and video. These changes had implications for
teaching mathematics. She believed that, though she liked teaching, she would not
recommend it to anyone as a career because teaching was much harder now than when she
first started.
*Mrs ALLAN: It might be more fun now but we’re catering for all the different personalities. When
I first started you just taught the class and everyone did the same sort of thing. We have all
different levels of ability in our classrooms and we’ve taught kids to be outspoken and stand up for
their rights and they’re more aware of everything that goes on. There’s hardly any naive kids
anymore. They have to be streetwise to be aware of stranger danger. You’d like them to be innocent
and be children but then you have to prepare them for all the things that happen now. And they see
everything on TV and video.
Teaching a wide range of abilities
Mr Kennedy had some misgivings about what he had experienced in mathematics
education through his teacher education program. It had not prepared him for the range of
ability that he experienced in his mathematics class. In the previous year he had taught a
higher mathematics class but the range of ability levels in this lower mathematics class had
presented new problems for this teaching.
*Mr KENNEDY: That’s the difficult part isn’t it, covering the range? Yeah I must say that’s my
biggest shock this year. Last year having the top class where everyone wanted to learn and
everybody tries their hardest and didn’t take that much to pick up on things. Anyway to this year
where you’ve got the whole range from the bottom up to a bit over half and those top kids who
finish faster and pick things up quicker than others, to those who don’t listen and are behaviour
problems.
Ms Jones, too, had difficulty programming for the range of children’s mathematical
ability levels in her class.
*Ms JONES: I get a bit stuck with the ones that finish quickly and get it straight away. I had to
move one kid out. What I normally do is put them to use like “I want you to sit next to…” or I
send them around marking. It is hard. I tried it once to split them up into ability groups but it was
really hard to keep getting round to them all.
Ms Jones’ taught the lowest Year 5/6 mathematics’ class in which 12 of the 24 children
were Aboriginal. She had difficulty finding mathematics problems appropriate to the
children’s ability level. The wide range of the Year 5 children’s mathematical ability also
influenced Mr Kennedy’s teaching.
*Mr KENNEDY: I like to think that I can explain it as simply as I can so that some amount of it
will sink in. I spend extra time with those who are having trouble during the course of the lesson.
There are kids where I could say, “This is how you do it. Go and do it,” and leave them for a week
doing worksheets and have them know exactly what I want them to know without even coming to
see how they went. Then there are those who don’t have a clue unless I’m one on one and they’re
forced to think because they’re thinking of what they’re going to do when they get home.
Ms Martin thought that her mathematics lessons should include extension work, some
fun and review of work covered. These were issues related to meeting the individual
mathematics learning needs of the children as a result of the wide range of ability levels
within her class. She identified some of the pressures that she felt as a teacher of
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mathematics, particularly the belief that there was now more content to teach than before.
*Ms MARTIN: There’s so much to cover. The wide range of kids and I suppose the parent
expectations of where they think the children should be at. The only thing that I see is that the
children in Year Two this year when they get to Year Six hopefully the range won’t be that wide.
They would have used a lot more materials because they’ve only arrived in the last few years. We
seem to have more of it and more children can get to it and hopefully you’ll be able to get through
more.
The reality of teaching mathematics and addressing adequately the individual needs
across the range of children’s mathematical abilities was something that Mr Kennedy
believed he was not doing well. He had had to adopt and invent teaching strategies to cope
with the reality of everyday teaching when he did not believe he had the time available to
do everything that he was required to complete.
*Mr KENNEDY: …it just seems to me that having to fit in all the other things as well that I
haven’t got the time that they are saying that you need for mathematics. I just don’t have it so I had
to adopt other ways to teach it. I haven’t invented them all myself by any means.
Mr Kennedy was unsure if he was supporting the ‘bottom kids’ in his mathematics
class. He did not think that giving children materials, asking them to discover and then to
write down what they had found out helped the ‘bottom kids’.
*Mr KENNEDY: I like to think I give the bottom kids more help or explain it to them at the start
so they understand it but I don’t know if I always succeed in that. I don’t think giving them all the
materials and saying what do you notice and leave them to it for forty-five minutes and then getting
them to write down what they noticed is going to help the bottom kids a great deal.
Discussion
The teachers at Ellen Road Public School have worked in a context where 32% of the
412 students in the school are Aboriginal. The length of time in which they have worked in
this context ranges from 1 to 7 years. As well, two of the teachers grew up in Tremayne. It
was well known by all teachers at Ellen Road Public School that the researcher was
focusing on the mathematics learning of Aboriginal students. He had made presentations to
staff meetings and parent groups. He had been present in the school for at least four
months interviewing Aboriginal children and their parents before the teacher interviews
reported in this paper were conducted. In spite of this, the teachers focussed their attention
upon the curriculum issues of teaching mathematics content and the classroom issues of
managing the ability range and endeavouring to involve the students in learning mathematics
with a focus on explaining and having the children listen.
Despite the obvious presence of a substantial number of Aboriginal children in the
school and the teachers’ mathematics classes, Aboriginal children are virtually invisible in
the comments the teachers have made about teaching mathematics. The same teachers made
very few specific comments about Aboriginal children’s learning of mathematics (Howard,
2001) but these are not referred to when the discussion moves to the teaching of
mathematics. These teachers had a range of teaching experience, they were aware of the
Aboriginal population in the school but did not talk about it in the context of teaching
mathematics. These data suggest that the poor mathematics learning outcomes reported for
Aboriginal students in Australian schools (NSW Aboriginal Education Consultative Group
Inc./NSW Department of Education and Training, 2004) could be linked to the lack of
teacher appreciation of the presence of Aboriginal children in mathematics classrooms and
what this presence means for the provision of relevant and appropriate teaching-learning
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activities that support the children’s cultural and learning needs.
Even though they were teaching in streamed classes, the Tremayne teachers believed
teaching to be harder now than it had been previously because of the children’s wide range
of mathematical ability. They perceived that they had not received sufficient teacher
education preparation for teaching mathematics across such a wide range of ability nor for
inventing appropriate teaching strategies for these children in their classes, including
Aboriginal children. Teaching mathematics, managing students and accommodating the
learning needs of Aboriginal students is difficult and complex. Teachers have to know their
mathematics and be quality teachers whilst knowing, appreciating and accommodating the
cultural issues within their mathematics classrooms.
Mathematics lessons in which students share in discussions, undertake collaborative
work, value each others’ ideas, experience relevant community-based mathematics activities
and are encouraged to use their cultural and language resources to solve problems provide
purposeful mathematics learning for Aboriginal students (Howard, 2001). However,
teachers cannot be expected to devise appropriate educational programs for Aboriginal
students on their own. Teachers and educational systems need to listen to and take
direction from Aboriginal people to appreciate and come to know the contexts in which
Aboriginal students are living and learning. Community partnerships need to be reflected in
mathematics teaching and change has to be a whole school and community effort (Howard
et al., 2003). When it comes to the development of mathematics curriculum, systems need
to enact this collaboration by developing documents through community partnership and
shared ownership. If collaboration and change are to occur then the voices of parents,
teachers and Aboriginal children have to be engaged (Matthews et al., 2003). Meaningful
curricula have to be developed “if for no other reason than we need to break the cycle of
school being a place of failure for young Indigenous people” (Buckskin, 2001, p. 10).
Conclusion
Teachers need to regularly and systematically critique their mathematics teaching in
order to appreciate the particular learning needs of their students, including Aboriginal
children. The teacher voices in this study indicate their struggle in dealing with the range of
abilities in their class, differing learning needs, management issues and mathematics
curriculum demands. There appears to be a lack of awareness of the Aboriginality of the
children in their mathematics classes and the impact it can have on their mathematics
teaching. It is clear that these teachers require focussed professional development and
reflection time to continually address the issue of the presence of Aboriginal students in
their classrooms and what implications such presence has on the development of relevant
learning activities and the adoption of appropriate pedagogical strategies. There needs to be
a greater appreciation of teacher beliefs about mathematics teaching and the impact upon
Aboriginal learners to help lessen the cultural conflicts in the classroom and to enhance the
mathematical learning outcomes for Aboriginal students. Teachers require continual
professional and Aboriginal community support in developing their awareness of the
context of the lives of the Aboriginal learners and implementation of appropriate teaching
strategies to enhance Aboriginal children’s mathematical learning outcomes. It is important
to reform school environments where Aboriginal students learn, “… [for without reform]
methodology will tend to reproduce social inequalities of achievement and subordinate
individual development to social domination” (Teese 2000, p. 8).
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