1. The personal journey
In some sense this talk is a reflection and critique of a personal journey. Like many who conduct research in mathematics education, I come to this conference with a background in mathematics, mathematics education, and the psychology of mathematics education. In 1985 I started what became the Social Psychology of Mathematics Education Working Group within PME because of my concerns and those of others about the way that the social aspects of learning mathematics were being ignored in research. Following on the ‘Mathematics for all’ sessions and D’Ambrosio’s plenary lecture on ethnomathematics at the ICME conference in Adelaide in 1984, and after much lobbying, we were finally able to persuade the ICME organisers for 1988 to put some focus on social aspects and they agreed to have a special day on Mathematics, Education, and Society (Keitel, et al.,1988).
That day, and that experience, not only met a need, it also created others. As a result of the understandable frustrations which several people felt with that compromise of a day, a conference was held on the Political Dimension of Mathematical Education (Noss et al., 1990) Since that time we have seen other significant developments, particularly in relation to ethnomathematics, technology, and critical mathematics education.
My own journey since that day in 1988 has been one of exploring further the cultural terrain and of developing my knowledge and critique of the anthropological perspective. I explored mathematical enculturation as a metaphor for mathematics education (eg. Bishop, 1988), provoking some challenging but helpful critiques from Connors (1990) and Chevallard (1990). For various reasons however, I decided for that book to just focus on the enculturation metaphor, but since that time I have been drawn more and more into exploring the ideas of acculturation, mainly through working with some interesting colleagues in challenging situations in their countries.
A first excursion was with an article in 1994 which tested the idea of a research agenda in relation to cultural conflicts (Bishop, 1994). Several papers, several projects, several PhD students, and several readings later, I am hoping that this conference gives me, and all of us who attend, an opportunity to discuss our journeys and through our papers to develop some new perspectives in research with which to confront the meaningless and oppressive mathematics education which many students still have to suffer today around the world.
The cultural metaphor
Interrogating the cultural metaphor has revealed for me some insights as well as some challenging gaps. As a first example, the metaphor of enculturation assumes that there is a cultural consonance between the culture of school and the culture of home, that enculturation is somehow a natural process, and that home and school experiences are symbiotic. However detailed research on the notion of ‘home culture’ challenges those assumptions (eg. Abreu, Bishop and Pompeu, 1997) and shows that in certain situations the home culture and the school mathematics culture can be conceptualised as mutually exclusive.
The research literature generally indicates that some members of all the following groups have suffered in some way from conflicts with what I have called the Mathematico-Technological Culture (MTC) (Bishop, 1988):
For many learners around the world the educative experience within schools and other institutions is clearly not consonant with their home, or outside, experience. The situation is one of cultural dissonance and the process is an acculturative one.
Conflict is a construct referring to affective aspects of a particular situation, which involves antagonists. My observations have led me to suggest that conflict fits within the following table of emotional and affective states in mathematics classrooms, which can vary from time to time:
|Large change, accommodation|
Further it is likely that a student will experience greater conflict in their MTC classrooms if s/he:
I have been working with the construct of ‘cultural conflict’. I will argue that a young person’s mathematics education is necessarily an acculturation experience, with its accompanying emotional states and cultural conflicts which need to be understood and tolerated.
I intend to interrogate this acculturation metaphor further. For example, if education is considered to be an intentional process on the part of society, and carried out by the teachers, what then can be understood by ‘intentional acculturation’?
The period of school education can be a time of turmoil for both learners and parents. In relation to mathematics education it can arguably be even more of a turmoil. Some parents, and other people also, despite (or perhaps because of) their limited understanding of the role of mathematics in formatting modern society, hold onto the myth that mathematical knowledge is crucial for gaining ‘success’ in that society.
Often their children undergo various forms of mental and personal anguish in order to gain this knowledge, and of course many reject it, or are excluded by ‘official’ methods. The irony is that having been through this experience themselves, and presumably having seen the myth exposed, they then seem to even more vehemently exhort their own offspring to go through the same anguish!
But there are good psychological and sociological reasons why these parents and their teachers cannot deny or expose the myth, of course, including the fact that the mathematical qualifications which are obtained through examinations, selection mechanisms, streaming in school etc. are the gates and hurdles on the way to ‘nirvana’ in this technocratic society.
5. The culture of Mathematicians
Another crucial question concerns into what culture are these young people presently being acculturated?
The critical perspective makes us look beyond the reified nature of Mathematics and ask: where does this "culture of Mathematics" come from; who owns and sustains it; who is empowered by it, and who has the most to lose if it is attacked? The answer to all these questions is simply ‘Mathematicians’, but it is also necessary to unpack that construct further. (I am using the capital ‘M’ where I feel the words refer to the Western hegemonic mathematical tradition, which underlies the MTC above.)
Abraham and Bibby (1988) already showed one way by considering how the ‘certified Mathematicians’ at university level become what they called "the industrial trainers" who lobby for a certain kind of Mathematical acculturation via their work in industry, government research establishments, defence industries, businesses etc. These plus of course Mathematicians in university departments of Mathematics, would be one way of identifying the group of Mathematicians who together sustain "the culture of Mathematics". Restivo’s (1993) ‘mathematical workers and mathematicians’ are very similar to these constructs.
What the learners come into conflict with in the classroom then is the whole Mathematical knowledge and affective environment which is:
6. Values in mathematics education
To what extent do the teacher/acculturators share the values and knowledge of the culture into which they are acculturating the young? Do mathematics teachers consider themselves part of the MTC cultural group? Perhaps this depends on whether they consider that they are mathematics teachers, or teachers of Mathematics? I assume that society in any event thinks that they are part of the dominant cultural group. But in my experience there are few teachers of Mathematics, and even fewer mathematics teachers, who consider that they are themselves Mathematicians, or that they ‘know’ Mathematics in the same way that Mathematicians do, or that they teach the Mathematicians’ values, or even that the Mathematics which they teach has any particular values.
I am not of course saying that they think that the Mathematics they teach has no value. They may not think it has any value in fact, but that it has value is one of the values that they are actually teaching, by merely teaching the subject! There are others also; rationalism, objectism, control, etc.(see Bishop, 1988, 1991) They could be acculturating their students into believing that they are learning Mathematics for its benefits as applicable knowledge, or to have pleasure in its finest or most intriguing discoveries or inventions, "for its own sake", or even to train their minds.
For me understanding more about values is the key to generating more possibilities for mathematics education. I am very sympathetic to the ideas of critical mathematics education, and would align myself with its goals (Skovsmose, 1994).
Sadly very little is known about the values which teachers think they are imparting, nor about how successfully they are imparting them, although the evidence from students’ opinions suggests that they are certainly imparting values. Moreover little is known about how teachers and others change the values they are teaching, or even if they are able to consciously do that.
Why do mathematics educators know so little about values in this context? Is it because we/they too are part of the acculturator group, and as such have been fostering the same myths and the same ignorance?
7. Social change
What then is the role of mathematics education in social change? How does any of the above analysis help with facing this challenge? Here then is the key problem. Mathematics is such a strong formatter of society that it should be a key area to focus on if one is seeking to change the social order. However, the fact that the MTC is so entrenched, and accepted in modern society makes it so difficult to affect.
In my view ‘Mathematics educators’ is the group whose views need to change to make the wider change happen. But to what extent can this group bring about change in the Mathematicians’ culture from within mathematics education? (See Breen, 1993)
Are there other sources of resistance? What about the learners themselves?
So how could we all proceed? Here are some questions which I hope will provoke some discussion at the conference towards achieving social change.
Abreu, G. de, Bishop, A.J. & Pompeu, G. (1997) What children and teachers count as mathematics. In T.Nunes & P.Bryant (Eds) Learning and teaching mathematics: and international perspective. (233-264) Hove, UK: Psychology Press.
Bishop, A.J.(1988) Mathematical enculturation: a cultural perspective on mathematics education. Dordrecht, Holland: Kluwer
Bishop, A.J.(1991) Mathematical values in the teaching process. In A.J.Bishop, S.Mellin-Olsen, & J. van Dormolen (Eds) Mathematical knowledge: its growth through teaching. Dordrecht, Holland: Kluwer.
Bishop, A.J.(1994) Cultural conflicts in mathematics education: developing a research agenda. For the learning of mathematics. 14(2), 15-18
Breen, C.(1993) Transforming the culture of learning mathematics: academics as catalysts or intruders? In C.Julie, D.Angelis & Z. Davis (Eds) Political dimension of mathematics education 2. Cape Town, RSA: Maskew Miller Longman
Chevallard, Y.(1990) On mathematics education and culture: critical afterthoughts. Educational studies in mathematics. 21(1), 3-27
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Davis, P.J. & Hersh, R. (1981) The mathematical experience. Boston: Birkhauser
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Noss, R. et al. (Eds) (1990) Political dimensions of mathematics education: action and critique. Proceedings of the first international conference. London: Institute of Education, University of London.
Restivo, S. (1993) The social life of mathematics. In S.Restivo, J.P.van Bendegem & R. Fischer (Eds) Math worlds: philosophical and social studies of mathematics and mathematics education.(p 247-278) Albany, USA: SUNY Press.
Roberts, C. & Sarangi, S.(1995) ‘But are they one of us?’: managing and evaluating identities in work-related contexts. Multilingua. 14(4), 341-362
Skovsmose, O. (1994) Towards a philosophy of critical mathematics education. Dordrecht, Holland: Kluwer