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.