Chapter
1
Mathematics is in the
unenviable position of being simultaneously one of the most important school
subjects for today’s children to study and one of the least well understood.
Its reputation is awe-inspiring. Everybody knows how important it is and
everybody knows that they have to study it. But few people feel comfortable
with it; so much so that it is socially quite acceptable in many countries to
confess ignorance about it, to brag about one’s competence at doing it, and
even to claim that one is mathophobic!
[Bishop, 1991b, p. xi]
1.1 Introductory Background
With
the setting up of the first-ever
separate Ministry of Higher Education, Science and Technology by the current
Chan-Haiveta government towards the end of 1994, it is evident that
mathematics, in the foreseeable future, will continue to play an important role
in Papua New Guinea’s national development, particularly in the light of two
growing problem areas. The first of these relates to the direction which
mathematics education should take in the face of the increasing presence of
computers and calculator-related technology in society. The second problem area
relates to concerns, particularly among mathematics educators, of the children
whose home and family cultures do not fully resemble that of the school and the
wider society.
Both
of these problems are related and thought provoking with the first one raising
questions about educational values, about the importance attached by society to
different kinds of knowledge, and about the relationship individuals have with
that knowledge. In this respect, it is currently argued within some educational
circles in Papua New Guinea (PNG) that the kind of mathematics provided must
therefore meet the utilitarian needs and the demands of a higher level of
mathematical application. On the other hand however, it is the second problem
area that is of particular concern to this study mainly because it raises
questions about the role of education in society with specific reference to its
stated objectives, the underlying educational assumptions and subsequently the
type of classroom practices it envisages.
Likewise,
for mathematics education in PNG, it is perhaps inevitable that a critical
re-examination of its societal role with respect to its stated objectives
contained in the curriculum and the type classroom practices it advocates
requires an immediate attention of everybody concerned, from policy makers down
through mathematics educators at the teacher education level, to ordinary classroom
teachers. At this point in time of the country’s development, such critical
re-examination is necessary particularly given the fact that the current
curriculum is heavily based on ‘Western’ models of education. The past and
present mathematical learning difficulties experienced by many Papua New
Guinean students in understanding the various formal mathematical knowledge is
also indicative of problems. Moreover, having an education system that is set
in a culturally diverse country of more than 700 distinct languages comprising of rich cultural
heritage, values, belief systems, traditions and kinship systems, it is ironic
that the current mathematics curriculum content and its classroom practices in
PNG are heavily biased on Western ideals, thoughts and teaching models. Because
these classroom practices are often characterised by abstract theorisation of
mathematical ideas based on absolutist view of mathematical knowledge, they
therefore give little attention at all to the historical and cultural context
of mathematical development in PNG. In doing so, they subsequently conflict
with both the underlying educational assumptions of the current PNG Philosophy
of Education and the current Government’s educational goal of providing
accessibility to all levels of the education system for the learners,
particularly its objective of achieving universal primary education by the year
2000.
1.2 Aims of the Study
With the above background in mind, the aim of this
study was to investigate the possibilities for a socio-cultural based
mathematics education in PNG developing from the fact that mathematics is a
product of culturally based human social activities by exploring the notion of
ethnomathematics. Thus, ethnomathematics is a term which refers to all cultural
practices of mathematics found within the everyday activities of a specific
cultural group whose purpose is other than doing mathematics (Nunes, 1992)
which includes their jargons, codes, symbols, myths and specific ways of
inferring and explaining cultural phenomenon.
In short, the investigation in this study by way of
an in-depth literature survey on the notion of ethnomathematics can be seen as
serving five basic objectives:
1. To
reflect on the current practices of mathematics education in PNG with respect
to its underlying educational assumptions, curriculum content and classroom
practices;
2. To
formulate a theoretical base for an ethnomathematical approach to mathematics
education in PNG;
3. To
formulate a proposal for the incorporation of ethnomathematical approach to
teaching and learning of mathematics in PNG;
4. To
identify the implications of ethnomathematical approach to mathematics
education in PNG in terms of the curriculum, teaching-learning process and
teacher education.
For many years mathematics educators and
researchers in mathematics education have focused on the classroom as the
primary setting in which mathematics learning takes place. More recent research
studies have however suggested that much mathematical knowledge is acquired
outside school. The realisation that mathematical knowledge can be acquired
outside school brings new variables into the analysis of mathematics learning
and teaching. A number of research projects have also challenged the widely
held view that mathematics can be learned in school embedded within any
particular learning structures and then taken out of school to be applied to
any situation in the real world. Moreover, the fact that many research
literature have acknowledged greater mathematics learning difficulties
experienced by students from diverse cultural backgrounds citing language, culture, and learning modality as the three key areas
implies that the current mathematics teaching practices in PNG need to be
re-examined. This situation has prompted some Mathematics educators to advocate
the incorporation of multicultural perspectives into the mathematics
curriculum. In emphasising the teaching of mathematics based on socio-cultural
environment of the learners, these educators argue that since mathematics is a
social product it is necessary that it be included in every aspect of the
teaching-learning process.
This is
based on the view that all societies, for thousands of years, have developed
mathematical practices that are most appropriate to their daily lives and
cultures, an area of mathematics defined in this study as ethnomathematics. The benefits of incorporating students’
ethnomathematical background into the mathematics curriculum include the such
things as:
1. Increased
self-esteem on the part of the learners;
2.
Increased interest when
instruction is related to daily life and experiences; and
3. An
appreciation of different ways of thinking.
It
is in the light of the above background that this study explores the
possibilities of an ethnomathematical approach to teaching and learning of
mathematics in Papua New Guinea (PNG). In particular, it aims to identify the
underlying assumptions of such an approach in terms of the curriculum, the
teaching-learning process and teacher education in PNG.
1.2 Brief
Outline of the Study
The second chapter of this study provides the
reader with a condensed background on the historical and cultural context of
education in Papua New Guinea (PNG). Thus, it describes only those significant
developments in education spanning for almost 470 years from its first contact
with the outside world in 1526 to the present-day PNG after gaining
independence from Australia in 1975.
Chapter 3 provides the reader with the background
on the current practices of mathematics education in PNG in terms of its underlying
educational assumptions, the curriculum development activities with their
implicitly stated objectives, and the type of classroom practices employed
within the teaching-learning process. In particular, the analysis of these
practices indicate that they are strongly based on the Old Humanist educational
ideology which sees education as the transmission of pure knowledge and
subsequently views the socio-cultural aspect of the learners as being
irrelevant.
Chapter 4 describes the central theme of this study
namely, the notion of ‘ethnomathematics’ and its associated theme, the process
of ‘mathematical enculturation’. The term ‘ethnomathematics’, refers to
mathematics as found within the everyday cultural practices of a specific
cultural group whose purpose is based on the survival of its members in their
environment. These practices can be classified as having characteristics of one
or more of the six ‘universal’ mathematical activities, namely counting,
locating, measuring, designing, playing and explaining.
The notion of ethnomathematics is further explored
in chapter 5 where two specific ethnomathematical activities namely, ‘counting
and measuring’, and two cultural activities of geometry notably, ‘basket and
blind weaving’ are investigated for their mathematical ideas within the
cultural context of PNG.
The final chapter mainly focuses on the educational
implications of an ethnomathematical approach to mathematics education in PNG
in terms of its underlying educational assumptions, curriculum objectives, teaching-learning
process and teacher education. The key feature of the ethnomathematical
approach is that it is based on the same educational assumptions pursued by the
current philosophy of education in PNG.