Cultural Mathematics and Curriculum Development in Education Reform
Paper Presented at Education
Conference
University of Goroka
23-25th September, 2003
Introduction
This paper was prepared for the conference organised by faculty of Education at the University of Goroka. The theme of the conference was: National Education Reform: Where now, Where to? In line with this theme, the major aim of this paper is to report on curriculum development that occurred in the area of ‘cultural mathematics’ during the current education reform (Where now?) and propose what might be done in the near future in this area (Where to?).
The paper begins by revisiting the education reform policy that directly relates to the inclusion of cultural knowledge, specifically cultural mathematics. This is to say that teaching cultural mathematics is in line with the policy of the current education reform. So far, under the current education reform, official curriculum documents for cultural mathematics has been developed for Elementary sector only. There has not been a similar development for primary and secondary sectors. This paper intends to suggest that curriculum should be developed for all sectors, including primary and secondary sectors in the future.
Education Policy
Education reform policies emphasises that cultural knowledge from student’s background must be used in schools for teaching and learning. In other words, the knowledge that considered important and used by people in the culture in which the school children live should be used for teaching and learning at schools. The particular knowledge concerns this paper is ‘cultural mathematical ideas’. This means that the current education reform policy allows cultural mathematical ideas to be used for teaching and learning. Therefore, such knowledge should be considered in the area of curriculum development.
The policy is already in place for cultural mathematical knowledge to be included in curriculum development for teaching and learning purposes. It has begun with elementary sector and should continue to primary and secondary sectors. The following section describes what kind of curriculum development has taken place due to the current education reform, in relation to cultural mathematics. The section explores curriculum development in Elementary , Primary and Secondary Sector of Education system.
This section will report on the progress made already in curriculum development in the area of cultural mathematics. The description will focus within the three sector of schooling: elementary, primary and secondary sectors.
The Elementary teachers are grade ten drop-outs and are recommended by the community they live in. During their training, they develop their own specific curriculum for each subject area. The national curriculum unit provides a general guideline and using this guide, the trainees prepare their own specific teaching material. This means that from the general guidelines, each trainer produces a specific teaching material for cultural mathematics.
The most recent syllabus produced to provide the general
outline for this sector of schooling is called “Cultural Mathematics”. There
are five strands are listed below with their sub-topic.
·
Space
- Space
- Shape
·
Measurement
- Measuring and Estimating
- Area
- Time
·
Number
- Counting
- Mathematical Language
- Operations
- Money
· Pattern - Patterns
· Chance – Chance and information
Within these recommended strand and its’ sub-topics, teachers are required to prepare appropriate cultural knowledge to be taught.
As far as I know, there was no official ‘cultural mathematics’ curriculum guidelines developed to be used at the Primary and Secondary School Sector. When studying the plans put in place for curriculum development at the Primary and Secondary levels, it is obvious that cultural mathematics is not included. In this paper, I would like to suggest that such documents should be prepared for primary and secondary schools. In the following section, I aim to provide the basis to my suggestion. .
I am personally impressed that a national curriculum guideline has already been put in place to be used for teaching and learning at the Elementary sector, in the area of cultural mathematics. I wish to propose that this should continue for the primary and secondary sectors. To support my suggestion, I provide brief description of what I experienced through my research and teaching.
The research I am referring to is the research I pursued for my Masters degree. This study aimed at identifying counting systems in Mid-Wahgi culture of Western Highland Province. On the other hand, the teaching experience refers to my work at Madang Teachers College. For semester three, I introduced an elective course called Ethnomathematics. Throughout the process of producing a course book, I have learnt a lot. These experiences will be described below.
There is enough evidence from recent studies that all cultures in the world have cultural practices that could be considered mathematical. For instance, longitudinal studies carried out by Bishop (1988), indicated that all cultures in the world are involved in six universal activities and they are; counting, locating, measuring, explaining, playing and designing. Studies done in Papua New Guinea (PNG) have already proven this general view. Studies such as Lean (1992) and Muke (2001), confirm the knowledge of counting systems practiced in more than three quarters of 850+ cultures of PNG. It is my believe that further research will help identify other mathematical ideas found in the different cultures of PNG and the findings should help inform further curriculum development.
Through my research and teaching in this area, it become obvious that cultural mathematical knowledge could be found in different levels. For instance, my study with the counting system of Mid-Wahgi people, illustrated that the people have established sophisticated tally system that helped them count. My study noticed that the Mid-Wahgi people did involve in some important activities that involved items of cultural importance in hundreds and thousands. The number system they established was limited and did not assist them to count items in bigger numbers. To my surprise, it was the tally system that help them quantify successfully.
For instance, a whole person was tallied for one thousand items after ten common parts of the human body was tallied for one hundred each. This means that the people went through the multiplicative system to arrive at this number. In other words, they understood that ten groups of hundreds would give one thousand (100 x 10 = 1000). Such a skill is more complicated for Elementary school children and even the lower primary school children.
Similarly, the Mid-Wahgi way of telling yearly calendar required more thinking, remembering and analysing. The movement of the sun was monitored and different happenings of the nature were remembered and the people were able to foretell the next even. This evens included the telling of weather that helped gardening, different sessions and so on. The following diagram describes such a process. This obviously could not be taught at the Elementary level because it requires a higher level of thinking. Such knowledge could be taught in a secondary school sector.
Observer
The policy obviously requires cultural mathematics to be included in any curriculum document to be taught at schools. Progress has already been made to develop a curriculum document for cultural mathematics for the Elementary sector. The policy does not say that such curriculum development should only be for Elementary schools. The research done so far shows that cultural mathematical ideas used in all 850+ cultures and also comes in all levels. If proper research is done, appropriate level of knowledge could be recommended within the three respective sector of schooling (elementary, primary & secondary). Therefore, cultural mathematics curriculum document should be prepared for all sectors of schooling, which includes elementary, primary and secondary sectors.
The following is a list of suggestions that form my recommendations.
Bishop, A.J. (1988). Mathematical Enculturation. Dordrecht, North Holland: Kluwer.
Lean,
G. (1992). Counting Systems of Papua New
Guinea and Oceana. Unpublished Ph.D. thesis. University of Technology of
Lae, Papua New Guinea.
Muke,
C. (2000). Ethnomathematics: Mid-Wahgi
Counting Practices in Papua New Guinea. (Unpublished Masters thesis).
University of Waikato, New Zealand.