Chapter
6
Implications
of an Ethnomathematical Approach to Mathematics Education in PNG
This final chapter will focus on
the implications of the ethnomathematical approach to mathematics education in
PNG advocated by this study and described in chapter 4 and 5. In particular,
these implications directly affect three separate but equally important and
related key features of any formal education system namely, the curriculum, the teaching process and teacher
education. These three key areas, because of their status within the
educational process, have been significantly implicated as a result of this
study’s search for a formulation of mathematical education which represents
children as active learners, engaged in developing their cultural knowledge
through social interaction with other people within the cultural group, who are
the bearers of ideas, norms and values of that culture (Bishop, 1991b;
D’Ambrosio, 1990a; Ernest, 1991). Hence, an ‘Ethnomathematical Approach to
Mathematics Education’ in PNG is proposed. The implications of such an approach
for mathematics education are clear from the detailed discussions provided in
the earlier chapters, that is, it cannot be just process-oriented, nor
should it be just content-oriented
characterised by the performance of ‘technique’ as is the case with the current
approach (Bishop, 1991b; Ernest, 1991). As noted in the introductory section to
chapter 4, educating people
mathematically requires more than just teaching them some mathematics. It
involves educating people about mathematics,
through mathematics and with mathematics (Bishop, 1991b).
With such a view in mind, it has
to be pointed out that both the ‘curriculum’ and the ‘teaching process’ which
are the focus of section 6.1 and 6.2 respectively, are strongly interconnected
and interdependent, with the enculturation ‘process’ being the complementary
aspect of the two sections (Bishop, 1991b). This is the area where the real
challenge lies, that is, to create a conceptualisation of the teaching process
which will eventually operate successfully within the knowledge frame described
in section 6.1.
6.1 Mathematics Curriculum Implications
6.1.1 The Proposed Mathematics and Society (MS)
Curriculum
As noted in the earlier chapters,
it is in the light of the negative educational outcomes of the current
mathematics curriculum in PNG, that this particular study, strongly advocates a
‘Mathematics and Society’ (MS) curriculum (Abraham & Bibby, 1988). Unlike
the current ‘Technique-Oriented’ (TO) curriculum (Bishop, 1991b) noted in
section 3.4.5 which is strongly geared towards the interests of an elite
(Ernest, 1991), the MS curriculum, in using the current PNG Philosophy of
Education, proposes education for Integral
Human Development (Matane, 1986). In other words, the educational goal of
the PNG philosophy of education as noted in section 2.5.1, is to fulfil the
individual learner’s potential within the wider context of society of which he
or she is a part. This means that it aims to empower and liberate the
individual through education to play an active role in making his or her own
destiny (Abraham & Bibby, 1988) and to initiate and participate in social
growth and change through appropriate social relationships with the family, the
local community, as well as with people from other parts of the country and the
world at large (Matane, 1986).
In terms of mathematics
education, the two educational philosophies namely, the Old Humanists (Abraham
& Bibby, 1988; Ernest, 1991) and the PNG Philosophy of Education (Matane,
1986) somewhat provide two contrasting views concerning the role of mathematics
in society. For the Old Humanists as noted in section 3.2.2, mathematics has no
apparent relationship with society at all. Subsequently, it therefore views
mathematics and society as having no interactive relationship (Abraham &
Bibby, 1988). On the other hand, the PNG Philosophy of Education takes a more
interactive approach in that the kind of mathematics which is seen as
appropriate for the curriculum is built on a view of society which takes
account of different constituencies of interests, including the cultural
interests of the learners (Abraham & Bibby, 1988; Matane, 1986). It is
because of the latter view of mathematics education that this study envisages
the adoption of the underlying assumptions of current PNG philosophy of
education as the basis for the MS mathematics curriculum in PNG.
6.1.2 The underlying principles of the Mathematics
and Society (MS) Curriculum
The mathematical culture
described in section 4.4 is the association of the particular symbolic
technology developed as a result of those cultural activities described in
chapter 4 and 5. This combination therefore provides the basis for the analysis
of both the ethnomathematical approach to mathematics education and the five
underlying principles described in the following sections namely, representativeness, formality, accessibility,
explanatory power and broad and elementary (Bishop, 1991b). It
is strongly suggested that these five principles, originally suggested by
Bishop (1991b), should characterise all facets of the proposed Mathematics and
Society (MS) curriculum pursued by this study for mathematics education in PNG.
This is because they are not only seen to be consistent with the educational
assumptions of the current PNG Philosophy of Education and the proposed
ethnomathematical approach to mathematics education in PNG, but are also
sufficient in allowing the development of mathematical ideas within the MS
curriculum (Bishop, 1991b). Moreover, they would also enable the development of
critical thinking in mathematics, an important feature of any mathematical
development, through meaningful interaction and reflection between the teacher
and learners which is greatly lacking in the current TO curriculum. These five
principles are briefly described in the following sections.
6.1.2.1 Representativeness
The first important feature of
the proposed MS curriculum is that it should adequately represent the
mathematics culture. In other words, it should not only be concerned with the
symbolic technology of mathematics, as is the case with the current TO
curriculum, but must also attend explicitly and formally to values of the
mathematical culture (Bishop, 1991b; 1991c). This means that the proposed MS
curriculum must take into account the individual, cultural and societal values
in the process of mathematical enculturation including the cultural practices
of mathematics found within the learner’s socio-cultural environment as
highlighted by the two examples from PNG described in section 5.3 and 5.4
respectively. The TO curriculum, because of the explicitness of its content,
usually ignores these values (Bishop, 1991b).
In the context of PNG in
particular, given a cultural base of over 700 different languages, traditions, cultural
values and belief systems, the principle of ‘representativeness’ should enable
the MS curriculum to adequately represent the rich cultural variations found
within the local community of which each individual learner is a part. This
will further enhance the learners to also make comparisons of the differences
and similarities that exist between each of the mathematical practices of the
respective cultural groups thereby further leading them to provide reasons and
explanations for the existence of those contextual differences and
similarities.
6.1.2.2 Formality
Secondly, it is also important
that the proposed MS curriculum should objectify by showing the connections
between the formal and informal level of the mathematics
culture by also offering as one of its objectives, an introduction to the
technical level (Bishop, 1991b). In other words, it should be able to provide
the necessary connections between the formal mathematics and the present-day
society as well as mathematics as a cultural phenomenon (Bishop, 1991a). Thus,
the reflective structure to be adopted in this curriculum should be based on
the six ‘universal’ activities (Bishop, 1991a; 1991b) described in chapter 4.
This would in effect involve investigative work on the part of the learners into
specific societal and cultural mathematical practices such as the traditional
counting and measuring activities and the two geometrical activities of basket
and blind weaving described in section 5.3 and 5.4.
For example, the formalised ideas
of ‘logic’ can be used to connect up with the underlying logic behind the
development of the many traditional numeration systems in PNG in addressing the
problem of memory load. The use of the labels of the body parts by many
traditional counting systems in PNG has to a greater degree enabled members of
these cultural groups to maintain fixed order in the respective numeration
systems in addressing the problem of memory load is a good contextual example
of the notion of logic currently taught in many formalised mathematics
classrooms as an isolated concept divorced from its everyday use. It is obvious
that such an example not only provides the conceptual meaning (Masingila, 1993)
as illustrated by this example, but also provides the relational understanding
(Skemp, 1978) of the concept of logic, more often seen to be very abstract by
many learners in PNG.
6.1.2.3 Accessibility
A third crucial principle which
should characterise the MS curriculum is that it should be accessible to all
children. As discussed in chapter 3, the ‘top-down’ curriculum approach to
content (Ernest, 1991) obviously disadvantages the vast majority of the
learners who either do not wish or are unable to go onto further mathematical
study. Thus, it is of no help to anyone to plan an enculturing curriculum which
will in the end fail the majority of the learners (Bishop, 1991b). While there
should be some flexibility in creating opportunities for those learners who
wish to pursue some mathematical ideas further according to their interests and
background, such provision however should not take precedent over the needs of
the majority of the students, because as soon as this happens it will
immediately negate the underlying principle of accessibility (Bishop, 1991b).
As noted in section 2.5.2, this is
probably one of the important considerations to be taken note of in PNG,
particularly in the light of the recent major educational structural reform
which is aimed at providing the learners access to all levels of the education
system. In this regard, the ethnomathematical approach through the MS
curriculum also fulfils the role of popularising mathematics and at the same
time addresses the above objective of the government in allowing socio-cultural
aspects of the learners to characterise all mathematical activities in the
classroom. This subsequently portrays mathematics as a meaningful, attractive
and reflective subject connected to the learners’ own cultural knowledge,
thereby increasing their participation in the teaching-learning process
(Bishop, 1991b; Ernest, 1991). Another key aspect of this principle is that the
curriculum content must not be beyond the intellectual capabilities of the
learners, nor should it contain material, examples, situations and
phenomena-to-be-explained that are exclusive to any one group in society
(Bishop, 1991b).
6.1.2.4 Explanatory
Power
The fourth principle is that the
MS curriculum should explain. As described in detail in chapter 4, being a
cultural phenomenon (Bishop, 1991a), mathematics derives its power from being a
rich source of explanations. In other words, because mathematics has the
capability to explain many of the everyday phenomena there is no reason why
such characterisation cannot be used in the formal classroom environment to
explain both the ‘cultural’ and the ‘formal abstract’ mathematical ideas.
Moreover, such an explanation has to be characterised by a two-way process in
that the informal mathematical ideas should be used to explain the many formal
ideas and concepts of mathematics particularly with respect to their contextual
meanings.
The above proposition means that
the “power of explanation will only be conveyed if the
phenomena-to-be-explained are accessible to all children, are ‘known’ by them,
and as yet are unexplained” (Bishop, 1991b, p. 97). In this respect, the source
of such phenomena should be none other than the learner’s own physical (both
natural and man-made) as well as the social environments (Bishop, 1991b).
However these sources need to be modified accordingly to reflect the local variations
in these cultural practices of mathematics.
6.1.2.5 Broad and Elementary
The fifth principle is in essence
a logical extension of the fourth principle in that rather than being ‘narrow’
and ‘technically demanding’, the MS curriculum should be relatively broad and
elementary in its conception (Bishop, 1991b). Moreover, in order for the power
of explanation to be fully realised, a variety of contexts should be offered
because of mathematics’ ability to connect unlikely groups of phenomena
(Bishop, 1991b). Furthermore, because of the rigid timetable situation found in
many schools in PNG, the mathematical content must be relatively elementary,
particularly if the breadth of explanation and content is to be taken as an
important goal (Bishop, 1991b). This is a crucial point in that if learners do
not have some good basic understanding of elementary mathematical concepts,
they would be unable to understand or even process higher levels of
mathematical knowledge. Though many of its features seem elementary, this is
the level where cultural practices of mathematics can play a very important
role in explaining basic but fundamentally important mathematical ideas.
It has to be pointed out from the
outset that the above five principles somewhat broadly provide the structural
framework for an ethnomathematical approach to mathematics education in PNG.
However, the finer details of this approach are left to individual teachers to
determine and select the type of topics and cultural practices based on local
knowledge and contexts. It is important that the selection made should reflect
as much as possible the cultural differences or similarities that exist within
PNG for possible comparisons and contrasts, thus providing the teacher with
flexibility within the MS curriculum.
One such approach is proposed by
Bishop (1991b) in which he suggested that the MS curriculum should prominently
feature three components namely, the symbolic
component which should be ‘concept-based’, the societal component which should be ‘project-based’ and the cultural component which should be
‘investigation-based’.
6.2 Implications for the Mathematics
Teaching-Learning Process
In this section,
the actual process of mathematical
enculturation, that is, the induction of learners into the mathematics culture
(Bishop, 1991b) noted in section 4.4, and how this should be put into operation
within the knowledge frame (curriculum) described in section 6.1 are
considered. Essentially, the ‘process’ is an interpersonal interaction that
takes place between the teacher and learners in a formalised and
institutionalised setting (Bishop, 1991b). Although there are also other people
who are involved in this process, their roles will however not be considered in
any detail because of space limitations as well as for reasons not to
overparticularise the analysis in this section (Bishop, 1991b).
On the basis of
the discussions provided in earlier chapters and the structural framework
provided by the MS curriculum (Abraham & Bibby, 1988) described in section
6.1, it is clear that an ethnomathematical approach to mathematics education in
PNG implies that the actual mathematics teaching-learning process in PNG be
characterised by the following features, in that it should:
·
be
interpersonal and interactional;
·
take
significant account of its social context;
·
be
formal, institutionalised, intentional, accountable;
·
be
concerned with concepts, meanings, processes and values;
·
be
for all (Bishop, 1991b, p. 124)
The first feature
simply means that the teaching-learning process must be strongly characterised
by a two-way communication between the teacher and learners involving
interpersonal and interactional relationship. The establishment of such
relationship is necessary in that it provides an opportunity for a meaningful and
‘open’ discussions to take place within the classroom environment, thus
developing students’ critical thinking in mathematics. The current teaching
practices, because of their explicit emphasis on the learning of pure knowledge
for its own sake through the performance of established rules and procedures
(Bishop, 1991b) does not allow for the development of such relationships to
occur.
The second feature
in essence implies that mathematics, being socio-cultural product (Bishop,
1991a), cannot simply ignore its historical and social context which throughout
history have made it possible for the development of many of the significant
mathematical ideas. Such a consideration in the long run has the potential to
provide not only a rich source of learning experience for the learners, but
also the necessary contextual meaning to many of the abstract mathematical
ideas.
The third feature
is somewhat an extension of the second feature in that many of the informal
mathematical ideas found in socio-cultural practices such as the traditional
counting and measuring activities and the traditional geometrical activities
noted in section 5.3 and 5.4 respectively, should be formally
institutionalised. The intention of this is to accommodate and to explain the
formal mathematical ideas and likewise, the formal mathematical ideas can be
used in explaining informal mathematical ideas. In other words, it should be an
intentional process of shaping ideas (Bishop, 1991b).
The fourth feature
in effect means that the teaching-learning process should address all aspects
of mathematical knowledge starting from the basic mathematical concepts, the
meanings associated with those concepts, their processes as well as values. In
other words, it must not only be concerned with performance of procedures and
techniques as is the case with the current teaching practices, but must attend
explicitly and formally to those concepts in explaining their associated
meanings, processes and values (Bishop, 1991b).
The fifth feature
implies that teaching-learning process should ensure that mathematical
knowledge be made accessible to all learners and not be limited to few
individuals or interested groups which is so often the case with the current
teaching practices. One way to ensure that this becomes a reality is to use
examples from the learners’ own social and cultural environment which are
familiar to them but are yet to be explained (Bishop, 1991b). This can be seen
as one way in which to popularise mathematics in PNG which is often viewed by
both the learners and many ordinary people as somewhat comprising of foreign
abstract ideas and concepts.
6.3 Implications for Mathematics Teacher
Education
If there is to be
any one single factor that would determine the way in which mathematics is
characterised in the classroom teaching, then it has to be the basic beliefs
teachers hold about the nature and the role of mathematics (Dossey, 1992). The
subtle messages communicated to the learners about mathematics and its nature
may, in the long run, affect the way these learners grow to view mathematics
and its role in society. In terms of mathematics instruction, Cooney (cited in
Dossey, 1992) has argued that in order for any proposed changes in mathematics
teaching to have any significant impact in the actual classroom teaching, a
change in teachers’ beliefs is a necessity. In this respect, Cooney noted that
the most prevalent verb used by preservice teachers to describe their teaching
is present (Dossey, 1992). This is not surprising for the fact
that such conception of teaching embodies the notion of authority in that there
is a ‘presenter’ with a ‘fixed message’ to send (Bishop, 1991b; Dossey, 1992;
Ernest, 1991). As noted in the preceding chapters, such a position is based on
the assumption that there is in external existence, a body of mathematical
knowledge to be transmitted to the learners (Bishop, 1991b; Boaler, 1993b;
Ernest, 1991). Thus, when such a conception is extended into the process of how
mathematics relates to education and its practices, it has far reaching
implications for both the teaching-learning process, and in particular, the
views about the role and nature of mathematics developed by the learners
(Dossey, 1992; Ernest, 1991).
In view of the
above background and in the light of the ethnomathematical approach to
mathematics education advocated by this study, the implication for teacher
education is that such an approach necessarily requires a change in view of
mathematics as an external body of knowledge to the one based on socio-cultural
environment of the learners (Abraham & Bibby, 1988; Ascher &
D’Ambrosio, 1994; Bishop, 1991a; 1991b; Ernest, 1991). Thus, there are three
key areas of teacher education activities in PNG which require some
re-examination and redirection to accommodate the underlying assumptions of
such an approach. These three areas are the role of a teacher, teacher beliefs
and values, and teacher background subject knowledge.
Before proceeding
any further, it has to be however pointed out from the outset that although the
teacher education activities take place at a much higher educational level,
this does not in itself mean that its classroom practices should be any
different from what is being proposed for the lower levels of education noted
in the previous section under the teaching-learning process. In other words, it
is strongly suggested that its classroom practices should feature all of the
five key areas of the ethnomathematical approach to mathematics education noted
in section 6.1. However, these features should involve discussion,
investigative work and reflective interactions (Ascher & D’Ambrosio;
Bishop, 1991b) in mathematics at a much higher level to reflect the particular
level of education of the learners. Furthermore, because their subsequent role
will be one of ‘enculturing’ the learners into the mathematics culture (Bishop,
1991b) as noted in section 4.4, it is essentially important that these features
form the underlying basis of all teacher education activities in PNG in terms
of its programs and the classroom practices. With such background in mind the
three key areas noted earlier are therefore briefly described in the following sections.
6.3.1 Role
of a Teacher
Defining the role of
a teacher is probably one of the most difficult tasks but also one of the most
crucial factors in the implementation of any curriculum innovation activities.
The reasons for such a situation are many and varied. However, in the light of
the proposed ethnomathematical approach pursued by this study, this factor is
seen to be a fundamental issue in that the implications of such an approach to
mathematics education means a change in the view and subsequently a redefining
of the role of the teacher within the classroom context (Dossey, 1992). Thus,
unlike the current role of a mathematics teacher which is somewhat
characterised by ‘authority’ and ‘presenter’ (Bishop, 1991b; Ernest, 1991) in
transmitting mathematical knowledge, the ethnomathematical approach envisages
the role of a teacher to be of a facilitator
(Ascher & D’Ambrosio, 1994; Bishop, 1991b; Borba, 1990) of the
teaching-learning process. In this context, the role of a teacher is more than
just a presenter of knowledge because it involves careful planning and one’s
insight into the value of such a role
(Julie, 1993; Boaler, 1993a). Moreover, such a role also means that the teacher
has to be flexible in accommodating the views of the learners but at the same
time mindful of the knowledge frame defined by the MS curriculum noted in
section 6.1 as well as the culture of mathematics described in section 4.4.
6.3.2 Teacher
beliefs and Values
Teacher beliefs and
values concerning the nature of mathematical knowledge are also important
factors (Clarkson & Kaleva, 1993; Dossey, 1992). In order for the proposed
ethnomathematical approach to mathematics education to become a reality in PNG,
a change in the views held by mathematics teachers concerning the role of
mathematics in society is essential (Conney, cited in Dossey, 1992). The
current approach, with its emphasis on mathematics learning as that of the
acquisition of skills (Bishop, 1991b; Boaler, 1993a; Julie, 1993), has
subsequently led many teachers to employ the expository teaching methods
(Clarkson & Kaleva, 1993; Ernest, 1991) in many of the classrooms in PNG.
On the other hand, because the ethnomathematical approach emphasises the
socio-cultural aspect of mathematics education in the learning of mathematics,
it therefore envisages reflective social interactions between the teacher and
learners within the classroom context (Bishop, 1991a; D’Ambrosio, 1990a). In
other words, in order for the teachers to eventually use the reflective
interactions in the actual classroom situations the underlying principles of
the MS curriculum should feature prominently in all teacher education courses,
particularly during the initial teacher training programs.
6.3.3 Teacher Background knowledge
The final key area in teacher
education concerns the teacher’s background knowledge in mathematics. On the
face of it, this area may appear to be not consistent with the underlying
assumptions of the ethnomathematical approach advocated by this study. However,
if teachers are to be effective in employing the reflective mathematics
teaching practices described in the earlier sections of this chapter, it is
necessary that they be provided with an in-depth investigation of mathematical
content knowledge characterised also by reflective interactions during their
initial training. This means that the teacher training programs must also be
characterised by the five underlying principles, namely ‘representativeness’,
‘formality’, accessibility’, ‘explanatory power’ and ‘broad and elementary’
(Bishop, 1991b) of the MS curriculum (Abraham & Bibby, 1988) noted in
section 6.1. In particular, if teachers are to be effective enculturers in
developing critical thinking in mathematics among their students (Bishop,
1991b), then it is strongly suggested that many of the mathematics teacher
training programs should emphasise critical analysis of mathematical knowledge
through the use of projects and critical investigative work (Bishop, 1991b)
with the results analysed and presented in a form of reports. This view in
essence also suggests that mathematics educators in PNG, particularly at the
teacher education level, need to change their current views of mathematical
knowledge which are strongly based on the absolutist view of mathematics
(Ernest, 1991) described in chapter 3. It is only then that mathematics
education in PNG will be seen to be not only fulfilling its educational
obligation to the learners, but also achieve the objective of producing a
mathematically literate PNG society.
6.4 Conclusion
The focus of this chapter has
been on describing the implications of an ethnomathematical approach to
mathematics education in PNG advocated by this particular study in terms of the
current practices in three key areas namely, the curriculum, the teaching
process and the teacher education.
Taken broadly, the curriculum can be defined as an objectified representation
of mathematical culture for the purposes of educational process. Thus, in an
attempt to define a ‘culturally-oriented’ curriculum that will allow for both
the personality to flourish and social interaction to take place, this study
advocates a ‘Mathematics and Society’ (MS) curriculum. In doing this, it
subsequently adopts the underlying educational assumptions of the current PNG
philosophy of education which strongly emphasises education for ‘Integral Human
Development’ based on the principles of ‘socialisation’, ‘participation’,
‘liberation’ and ‘equality’. Thus, in terms of mathematics education in PNG,
this subsequently means that the MS mathematics curriculum must be based on a
view of society which takes account of different constituencies of interests
including the socio-cultural interests of the learners. Moreover, in an effort
to enable the learners to develop critical thinking in mathematics, the
ethnomathematical approach envisages five basic principles which should
characterise all curriculum activities in mathematics in that it should:
·
represent
the mathematical culture in terms of both symbolic technology and values;
·
objectify
the formal level of that culture;
·
be
accessible to all learners;
·
emphasise
mathematics as explanation and
·
be
relatively broad and elementary rather than narrow and demanding in its
conception (Bishop, 1991b, p. 98)
The finer details on the basis of the above
principles, though not explicitly defined in this study, are left to individual
teachers to determine. This is based on the understanding that such an approach
will provide the flexibility and the scope within the MS curriculum for
teachers to use appropriate examples or illustrations found within the
learners’ own socio-cultural environment in explaining the formal mathematical
ideas which in turn can be used to also explain cultural mathematical ideas.
Moreover, such illustrations as much as possible should reflect the cultural
variations of the learners.
As a guide, one such approach
initially suggested by Bishop (1991) which can be adapted for classroom use by
the teachers involves structuring the appropriate topics under three components
namely, the symbolic component which
should be concept-oriented, the societal component
which should be project-oriented and the cultural
component which should be investigation-based. These components subsequently
provide the knowledge frame which will not only exemplify the cultural approach
to mathematics education, but also form the basis for structuring their
analysis further. Moreover, apart from educating the learners, it will also
preserve and stimulate the mathematical culture through their education. The
historical and developmental aspects as offered in the societal and cultural
components will ensure the preservation of the cultural heritage of
mathematics. The attention given to environmental activities, to the societal
uses in the present and hypothetical future, as well as to the creative aspects
of investigation, should do much to stimulate mathematical development in
future generations.
The second section
briefly looked at the implications of ethnomathematical approach in relation to
the actual process of teaching and learning mathematics within the classroom
environment. Thus, consistent with the underlying assumptions of mathematics
education, the ethnomathematical approach strongly envisages the mathematics
classroom practices to: (1) be interpersonal and interactional; (2) take
significant account of the learners’ socio-cultural environment; (3) be formal,
institutionalised, intentional and
accountable; (4) be concerned with concepts, meanings processes and
values; and (5) be made accessible to all learners. The underlying key feature
of the teaching-learning process in the light of such an approach is that it is
an intentional process of shaping ideas, that is, transforming from a ‘way of
doing’ (technique) to a ‘way of knowing’ (meaning).
In terms of the
teacher education activities in PNG, the implications of an ethnomathematical
approach is seen to be significant in three key areas namely, the role of the
teacher, teacher beliefs and values concerning the nature and role of
mathematics, and the teacher’s background knowledge of the subject. These three
key areas are crucial in that they have the potential to enhance any efforts to
incorporate the type of classroom practices advocated by this study into the
actual teaching-learning situations. In this respect, it is anticipated that
the type of teaching practices to be employed at this level of education should
not be any different to those proposed for other lower levels of education. In
other words, the reflective classroom practices involving teacher-learner
interactions should be the underlying feature of all teaching-learning process
in developing critical thinking in mathematics which is clearly lacking in the
current approach to mathematics education in PNG. Moreover, such an approach
also requires that the mathematics educators in the teacher education sector
need to change their views of mathematics education, particularly in the light
of the current difficulties experienced by many learners in PNG in
understanding many formal concepts of mathematics. This situation therefore
calls for a thorough re-examination of the current classroom practices in
mathematics education in terms of its curriculum content, teaching practices
and teacher education programs. It is only through such a critical examination
that worthwhile mathematics classroom practices can be developed, providing an
opportunity to see mathematics fulfilling its educational role as well as
its societal role in PNG.
The ethnomathematical approach to mathematics education is of considerable relevance not only in reducing the many socio-cultural factors that provide barriers to basic conceptual understanding of mathematical knowledge by learners in PNG, but also in providing the necessary contextual meaning to those abstract mathematical ideas. In this context, what has been discussed in this study should be seriously considered for a worthwhile mathematics education in PNG.