Abstract
Official Papua New Guinea (PNG) Government education policies encourage a “community
oriented and a culturally based” education and curriculum. A perusal
of mathematics curriculum however shows an intended curriculum which is no
different from those found in other countries - curriculum which is assumed
to be culture free and “canonical” (Howson & Wilson, 1986).
The mathematics taught in PNG clearly shows that the intentions of the government
are not being implemented. However, little is known about the beliefs of those
who implement the curriculum - the teachers - especially their beliefs about
the cultural dimension of the mathematics curriculum.
Although there is an abundance of literature on teacher beliefs about mathematics
and its importance to their practices in the classroom, little is known about
PNG teacher beliefs about mathematics or their beliefs about “ethnomathematics”
and their classroom practices. Some research has been done on PNG teacher
practices in the classroom, although the focus of the studies was at the primary
level. The focus of mathematics education research conducted in PNG over the
last twenty years has been on student achievement and the factors influencing
student learning.
This study investigated PNG secondary teacher (as well as student teacher and
student) beliefs about the cultural dimension of the mathematics curriculum.
The primary focus of the study was on teacher beliefs about school mathematics
(SM) and “cultural mathematics” (CM). It was also the aim of this
study to investigate the relationship between these teachers” beliefs
and their practices in the classroom.
Three main methods were used to collect data : questionnaires, interviews and
observations. Teacher questionnaires were mailed to the 114 PNG high schools
early in 1995. One hundred and thirty five national teachers returned the
questionnaire. After the initial analysis, five teachers from three schools
were selected for observations, based primarily on the responses which determined
the position of the teacher on a ‘beliefs” continuum. All the
lessons were audio-taped and each teacher was observed for a week. Twelve
teachers, including those observed, were interviewed. Questionnaires were
also administered to student teachers at the Goroka campus of the University
of Papua New Guinea and to the students taught by the teachers who were observed.
The results showed that the
teachers, student teachers and the students were “culturally aware”
However, there were differences in their beliefs about mathematics teaching,
mathematics content (ie. whether CM should be taught in schools or included
in the secondary mathematics curriculum) and their beliefs about the nature
of mathematics. The teacher sample was more “cultural mathematics”
oriented than the student teachers and the student samples.
An important
finding of this study is the concept of the ‘portrayed curriculum”
It is asserted that there is an intermediate level between the intended and
the implemented curriculum - the interpreted curriculum. How the teacher interprets
the intended curriculum determines how he/she “portrays” the mathematics
in the classroom. The teacher interpretation of the curriculum is influenced
by the teacher’s beliefs about mathematics. Ethnomathematical ideas
(or ideas about mathematics and culture) can help shape teacher beliefs about
the nature of mathematics to be more “cultural mathematics oriented”
It clearly relates to the teaching of beliefs and values, and could be an
important determinant of further changes in culturally aware teaching. There
was also some evidence of the influence of teacher conceptions of mathematics
on student conceptions of mathematics.