Common Sense or Good Sense?

Ethnomathematics and the Prospects for

a Gramscian Politics of Adults' Mathematics Education

Diana Coben

Goldsmiths College, University of London

Abstract

This paper looks at Antonio Gramsci's concepts of 'common sense' and 'good sense' in the light of recent research and practice in adults learning mathematics, focussing particularly on issues around ethnomathematics, and explores the prospects for a Gramscian politics of adults’ mathematics education.

Introduction

Mathematical knowledge is socially powerful: it enjoys high prestige and being 'mathematically knowledgeable' is often treated as an indicator of general intelligence, as evidenced by the widespread use of mathematics in entry tests for employment and employment training; mathematics is precise, rigorous, a powerful discipline in its own right. Common sense, by contrast, is regarded - or rather, it is often disregarded - as a low-level, practical, 'everyday' phenomenon, hardly noticed, except when its absence is suddenly revealed in the actions of an otherwise apparently intelligent, capable adult. What then is the connection between mathematics and common sense and where does Gramsci come into the picture?

For me, the connection between mathematics and common sense has long been a source of interest. As an adult numeracy tutor in the 1970s and 1980s I was aware that there seemed to be a strong connection in students' minds between those elements of mathematics they felt comfortable with and what they called common sense and my later research, with Gillian Thumpston, on adults' mathematics life histories, bore this out (Coben and Thumpston 1995, 1996). We found that some adults consistently undervalue the mathematics they can do, dismissing it as 'just common sense', while regarding as mathematics only that which they cannot do. Mathematics was thus effectively rendered invisible, a phenomenon also noted by Mary Harris (1997).

And Gramsci? Antonio Gramsci and Paulo Freire figure as 'radical heroes' in my research into political theory in relation to adult education (Coben 1998) and I became intrigued by the possibility that the concept of 'common sense' developed by Gramsci in his prison notebooks (Gramsci 1971) and his distinction between 'common sense' and 'good sense', might shed light on adults' learning and practice of mathematics. I began to explore aspects of the complex relationship between adults' mathematical knowledge and understandings and conceptions of common sense (Coben 1997).

In this paper I want to focus on Gramsci's concepts and their relevance to current debates around ethnomathematics, but first, a brief review of recent research and practice in adults learning mathematics may help to set the scene.

Recent research and practice in adults learning mathematics

As a field of practice, adult mathematics (numeracy) education in the UK flourished from the mid-1970s largely without benefit of research and underpinning theory in the wake of the adult literacy campaign of the 1970s, with interest periodically re-fuelled by reports of the parlous state of the nation's numeracy. In January 1997 two reports were published in Britain to coincide with the BBC numeracy campaign, 'Count Me In'. The first was a survey of the numeracy skills of adults in seven countries undertaken by the Opinion Research Business (ORB) (Basic Skills Agency 1997) and the second looked at the impact of poor numeracy on adult life (Bynner and Parsons 1997). In the first report, adults in the UK came bottom of the international league: on questions covering the addition and subtraction of decimals, simple multiplication, the calculation of area, calculating percentages and using fractions, only 20% of people tested completed all twelve tasks accurately. The authors of the second report conclude that the impact of poor numeracy on adult life is profound and severe:

People without numeracy skills suffered worse disadvantage in employment than those with poor literacy skills alone. They left school early, frequently without qualifications, and had more difficulty in getting and maintaining full-time employment. The jobs entered were generally low grade with limited training opportunities and poor pay prospects. Women with numeracy difficulties appeared especially vulnerable to exclusion from the clerical and sales jobs to which they aspired. Men's problems were less clearly differentiated between occupations. (Bynner and Parsons 1997:27)

A series of reports in the 1980s revealed an equally sorry picture (ALBSU 1987; ACACE 1982; Sewell 1981). For example, Brigid Sewell's (1981) enquiry into adults' use of mathematics in daily life, commissioned for the Cockcroft Committee (Department of Education and Science 1982), together with the associated national survey (ACACE 1982) revealed that approximately 30% of those questioned could not handle simple subtraction, multiplication, division or percentages, or understand a simple graph; almost half the adult population could not read a simple timetable and over half did not understand the meaning of the rate of inflation (ACACE 1982). The cost to British industry of poor basic skills was estimated at £4.6 billion a year in 1993 (ALBSU 1993).

Both the 1997 reports discussed above are based on somewhat restricted notions of numeracy, a concept which is deeply contested and subject to shifts of definition (Baker and Street 1994). The international survey (Basic Skills Agency 1997) is based on a notion of numeracy as a set of computational skills, while Bynner and Parsons' (1997) research employs a functionalist notion of numeracy. Both the computational and the functionalist models of numeracy ignore other important aspects of mathematics, such as its use as a means of communication. Also, as mentioned above, research on adults' mathematics life histories (Coben and Thumpston 1995, 1996) indicates that some adults undervalue the mathematics they can do, dismissing it as 'just common sense', while regarding as mathematics only that which they cannot do. It seems likely that this phenomenon may have a bearing on adults' poor performance in numeracy tests.

Whether or not there is a real crisis of adult innumeracy, there is certainly a perception of one in many countries and it may come as no surprise that research in adults learning mathematics has emerged in recent years as a growing field of international interest after a long period of neglect. It is an exceptionally diverse field which defies precise categorisation. What practitioners and researchers have in common is a serious interest in adults learning mathematics, whoever and wherever they are, however and for whatever purpose they are learning. For example, contributors to the Working Group on 'Adults Returning to Mathematics Education' (WG18) at the eighth International Congress on Mathematics Education (ICME-8) focussed on a wide range of issues, from adults studying mathematics for an engineering degree in the UK to mathematics education and the struggle for land in Brazil (FitzSimons, ed.1997).

The ICME-8 Working Group was one of a series of separate conferences in the 1990s, focussing on different aspects of research and practice in adults learning mathematics. These included the first UNESCO International Seminar on adult numeracy, which was held in France in 1993; UNESCO held a further conference, on literacy, which included adult numeracy, in 1996 in Philadelphia, USA. The third *Political Dimensions of Mathematics Education* (PDME-III) conference took place in 1995 in Norway, and included sessions on the political dimensions of adults' mathematics education (Kjærgård et al., eds, 1996).

Meanwhile, researchers and practitioners have come together to form national, regional and international organisations, such as the Adult Learners Special Interest Group of the Mathematics Education Research Group of Australasia (MERGA), and, in the USA, the Adult Numeracy Network (ANN). Other international groups include the UK-based Philosophy of Mathematics Education Network (POME), the US-based Criticalmathematics Educators Group (CmEG) and the International Study Group on Ethnomathematics (ISGEm) founded in 1985 under the guidance of Ubiratan D'Ambrosio, who coined the term ethnomathematics to indicate the influence of sociocultural factors in the creating, teaching and learning of mathematics.

*Adults Learning Maths *(ALM)1, established in 1994, is an international research forum in which researchers and practitioners come together and share experience. ALM has undoubtedly been an important factor in the worldwide development of interest in this area as a field of research as well as a field of practice and the Forum now has members in Argentina, Australia, Austria, Belgium, Brazil, Canada, Denmark, Finland, Germany, Ireland, The Netherlands, New Zealand, Slovenia, South Africa, Spain, Sweden, Uganda, UK, USA and Zimbabwe. Research topics discussed at the fourth international ALM conference, ALM-4, reflect the diversity of the field, including: mathematics in work, such as the use of calculators by nurses and the development of a 'mathematics profile' of adults undergoing training as crane operators; the assessment of numeracy skills of adults with special needs; adults' independent learning in mathematics; and Paulo Freire's legacy for adults learning mathematics (Coben and O'Donoghue, comps, 1998).

Other relevant research includes that at the Institute of Education, University of London, on adults' mathematising at work (Hoyles, Noss and Pozzi, in press); Mary Harris's research on - and celebration of - the 'invisible' mathematics in women's work (Harris 1997); Juan Carlos Llorente's investigation of ways in which adults constitute knowledge (including mathematical knowledge) in their work (Llorente 1997); work on situated cognition by Jean Lave (1988) and others; and developments in the field of ethnomathematics (Powell and Frankenstein, eds, 1997), discussed below.

Some of the above research engages implicitly (and occasionally explicitly) with notions of adults' common sense in relation to mathematics, including my own (Coben 1997, Coben and Thumpston 1996). Research on common sense *per se* (although not necessarily in relation to adults) is discussed by contributors to 'Mathematics Education and Common Sense' (Keitel *et al., *eds, 1996). On the whole, however, common sense has not been the subject of a great deal of research in relation to adults' mathematics learning and education. This is strange when one considers that, in the West, at least, common sense is one of the features that distinguishes an adult from a child, in that adults are expected to demonstrate common sense whereas children are regarded as in need of adult care and protection at least partly because, paradoxically, they are not expected to have what is also called 'the sense they were born with'.

But first, to return to Gramsci: what are his concepts of 'common sense' and 'good sense' and what distinction does he draw between them?

Gramsci's concepts of 'common sense' and 'good sense'2

Common sense

For Gramsci, common sense comprises the "diffuse, unco-ordinated features of a general form of thought common to a particular period and a particular popular environment" (Gramsci 1971:330n). It contains "a healthy nucleus of good sense" which, he argues, "deserves to be made more unitary and coherent" (Gramsci 1971:328). Gramsci states that:

Its most fundamental characteristic is that it is a conception which, even in the brain of one individual, is fragmentary, incoherent and inconsequential, in conformity with the social and cultural position of those masses whose philosophy it is. At those times when a homogeneous social group is brought into being, there comes into being also, in opposition to common sense, a homogeneous - in other words coherent and systematic - philosophy. (Gramsci 1971:419)

He emphasises the chaotic and contradictory nature of 'common sense', describing it as "a chaotic aggregate of disparate conceptions, and one can find there anything one likes" (Gramsci 1971:422). It is "an ambiguous, contradictory and multiform concept". Nonetheless, although it is "crudely neophobe and conservative" (Gramsci 1971:423), it contains truths.

Gramsci insists that both 'common sense' and 'good sense' are historically and socially situated: "Every social stratum has its own 'common sense' and its own 'good sense', which are basically the most widespread conception of life and of man" (Gramsci 1971:326, n5).

Good sense

For Gramsci, 'good sense' is exemplified by the 'philosophy of praxis' (a term he uses throughout the notebooks for Marxism, partly as camouflage to deceive the prison censor). 'Good sense' is analogous to 'philosophy', in that it is inherently coherent and critical. As he says, "Philosophy is criticism and the superseding of religion and 'common sense'. In this sense it coincides with 'good' as opposed to 'common' sense" (Gramsci 1971:326). Good sense is thus an "intellectual unity and an ethic in conformity with a conception of reality that has gone beyond common sense and become, if only within narrow limits, a critical conception" (Gramsci 1971:333). In order for 'common sense' to be to be renewed, i.e., to become 'good sense', one must start with

a philosophy which already enjoys, or could enjoy, a certain diffusion, because it is connected to and implicit in practical life, and elaborating it so that it becomes a renewed common sense possessing the coherence and sinew of individual philosophies. But this can only happen if the demands of cultural contact with the "simple" are continually felt. (Gramsci 1971:330n)

Good sense, for Gramsci, may be created out of common sense through an educative Marxist politics. This process does not entail "introducing from scratch a scientific form of thought into everyone's individual life, but of renovating and making 'critical' an already existing activity" (Gramsci 1971:331). So how do Gramsci's concepts of 'common sense' and 'good sense' relate to issues in adults' mathematics education, and in particular, to ethnomathematics?

Ethnomathematics3

Ethnomathematics seems to me to offer several parallels to Gramsci's concepts. Ethnomathematics problematizes dichotomies between different 'knowledges', formal and informal, academic and popular, and questions the allocation of power to preferred forms of knowledge, in ways that find parallels in Gramsci's concepts. Gramsci's broad conception of culture encompasses mathematics as a cultural phenomenon, a core conception for ethnomathematicians. Gramsci, crucially, regarded common sense as something to be worked with and transcended rather than rejected. This implies an educative process rooted in, and respectful of, people's lived experience. It is the nature of people's experience in relation to mathematics that Gillian Thumpston and I sought to explore in our mathematics life history research, and the exploration of the nature of people's mathematical experience lies at the heart of the ethnomathematics enterprise.

Thus far, it seems that a Gramscian and an ethnomathematics approach may have significant elements of congruency, at least in terms of method and approach, though not necessarily in terms of political purpose. Gramsci was, after all, a major figure in twentieth century Marxism; I am not suggesting that all ethnomathematicians share his political perspective and commitment. Ethnomathematics is a diverse movement, bringing together researchers with different political perspectives, as is evident in Arthur B.Powell's and Marilyn Frankenstein's edited collection, __Ethnomathematics__ (Powell and Frankenstein, eds, 1997). Such diversity is not only historically inevitable in these postmodern times but probably also essential for the intellectual health of the movement. Instead of a shared political commitment, it seems to me there is in ethnomathematics a shared ethical commitment: most ethnomathematicians would presumably echo Ubiratan D'Ambrosio's humanitarian concern with "an ethics of respect, solidarity, and co-operation" (D'Ambrosio 1997:xx).

But there is another problem in assuming congruency between a Gramscian conception of good sense and common sense and ethnomathematics, and it is a problem that strikes at the heart of the ethnomathematics project, as I understand it. This is the question of whether Gramsci's distinction between good sense and common sense is predicated on an irredeemably hierarchical conception of knowledge, as Gelsa Knijnik has argued (Knijnik 1996).

To an extent, this must remain an open question, since the distinction between good sense and common sense is not fully worked out in the prison notebooks. Certainly, it may be interpreted as a distinction between true and counterfeit knowledge; between order (unified knowledge), and chaos (fragmented knowledge); between higher and lower forms of knowledge. If so, it would seem perverse and irrational to prefer the counterfeit to the true, to celebrate people's inchoate lived experience and practice of mathematics, whether effective and accurate in mathematical terms or not. In educational terms, such a view of common sense would imply that it should be rejected in favour of academic rigour. If ethnomathematics were aligned with common sense conceived in this way, that would be to relegate ethnomathematics to the status of a non-academic practice and an anti-science theory, connotations which it already holds for many observers, as D'Ambrosio points out (D'Ambrosio 1997:xxi). It would also be to align Gramsci's concept of good sense, in this context, with academic mathematics, privileging what Gramsci would call the 'traditional intellectual' and the traditional intellectual's knowledge over the simple. It would be tantamount to accusing Gramsci of educational conservatism (as Harold Entwistle does in his 1979 book) and acknowledging that ethnomathematics sacrifices concern about issues of accuracy and effectiveness in mathematics on the altar of a sentimental relativism.

I believe to make such an alignment would be to misread Gramsci and to distort ethnomathematics. On the question of misreading Gramsci, as I argue in my book,

__Radical Heroes__,

Gramsci's distinction between good sense and common sense is both epistemological and sociological: both a distinction between different forms of knowledge and a distinction between the 'knowledges' characteristic of different social groups. But the distinctions are not mutually exclusive in either case. In epistemological terms, common sense includes elements of good sense. In sociological terms, good sense is not the preserve of an elite, and common sense is common to us all. (Coben 1998:213-4)

Gramsci problematizes both common sense and good sense. He makes a conceptual rather than an empirical distinction between common sense and good sense, since the categories are not mutually exclusive.

On the question of distorting ethnomathematics, I defer to D'Ambrosio (1997:xx-xxi) who insists that ethnomathematics is "an holistic and transdisciplinary view of knowledge", "a research program", "a comparative study of the techniques, modes, arts, and styles of explaining, understanding, learning about, and coping with the reality in different natural and cultural environments" and "an analysis of the generation of knowledge, of its social organization, and of its diffusion". If it is all these things, then the question is not whether ethnomathematics should be equated with a Gramscian conception of mathematical 'common sense' but instead how ethnomathematics might contribute to our understanding of common sense and good sense and deepen and enrich our conception of mathematics and our commitment to radical democratic principles of adult mathematics education.

If mathematics life histories research tells us that adults tend to dismiss the mathematics they can do as "just common sense", and if ethnomathematics helps us to engage with adults' chaotic, fragmented 'common sense' in an educational context, and to understand better the relationship between adult students' - and our own - 'common sense' and 'good sense', then we have the beginnings of some fruitful lines of research and practice in adult mathematics education. We have the possibility of research into 'adult numeracy' that makes better sense of adults' mathematical strengths as well as their weaknesses and we have the prospect of more effective and socially and politically sensitive practice in adults' mathematics education. In terms of the development of a radical, democratic politics of adults learning mathematics, it seems to make 'good sense' to start with adults' 'common sense'.

Notes

- For details of
*Adults Learning Maths - A Research Forum*(ALM), please contact me in my role as ALM Secretary, address below. - I explore Gramsci's concepts of 'common sense' and 'good sense' in greater depth my book,
__Radical Heroes__(Coben 1998) and especially in my chapter in a forthcoming book on Gramsci and education in preparation under the auspices of the International Gramsci Society (IGS). For details of IGS, contact the International Gramsci Society, Secretary: Joseph A. Buttigieg, Department of English, University of Notre Dame, Notre Dame, Indiana 46556, USA. - This section draws on a paper I presented at the International Study Group on the Relations between History and Pedagogy of Mathematics and the International Study Group on Ethnomathematics Conference in Honor of the 65th Birthday of Ubiratan D'Ambrosio, in Baltimore, USA, 6 January 1998.

Bibliography

ACACE (1982) __Adults' Mathematical Ability and Performance__. Leicester: Advisory Council for Adult and Continuing Education

ALBSU (1993) __The Cost to Industry: Basic Skills and the UK Workforce__. London: Adult Literacy and Basic Skills Unit

ALBSU (1987) __Literacy, Numeracy and Adults: evidence from the National Child Development Study.__ London: Adult Literacy and Basic Skills Unit

D'Ambrosio, U. (1997) 'Foreword' in A. Powell and M. Frankenstein (eds) __Ethnomathematics: Challenging Eurocentrism in Mathematics Education__. Albany, NY: State University of New York Press

Baker, D. A. and Street, B. V. (1994) 'Literacy and Numeracy Concepts and Definitions' __International Encyclopædia of Education.__ Oxford: Pergamon Press

Basic Skills Agency (1997) __International Numeracy Survey: a comparison of the basic skills of adults 16-60 in seven countries__. London: The Basic Skills Agency

Bynner, J. and Parsons, S. (1997) __Does Numeracy Matter? Evidence from the National Child Development Study on the impact of poor numeracy on adult life__. London: The Basic Skills Agency

Coben, D. (1998) __Radical Heroes: Gramsci, Freire and the Politics of Adult Education__. New York and London: Garland Publishing/Taylor and

Francis

Coben, D. (1997) 'Mathematics or Common Sense? Some Reflections on Research into Adults' Mathematics Life Histories' in G.E.FitzSimons (ed.) __Adults (returning to) study mathematics: Papers from the 8th International Congress on Mathematics Education (ICME 8) Working Group 18__ [ICME-8 1996]. Adelaide, SA: Australian Association of Mathematics Teachers

Coben, D. and O'Donoghue, J. (comps) (1998) __Adults Learning Maths-4: Proceedings of ALM-4, the Fourth International Conference of Adults Learning Maths - A Research Forum held at University of Limerick, Ireland, July 4-6 1997__. London: Goldsmiths College, University of London in association with

Coben, D. and Thumpston, G. (1996) 'Common Sense, Good Sense and Invisible Mathematics' in T.Kjærgård, A.Kvamme, N.Lindén (eds), __PDME III Proceedings: Numeracy, Race, Gender and Class__, Proceedings of the Third International Conference of Political Dimensions of Mathematics Education (PDME) III, Bergen, Norway, July 24-27 1995. Landås, Norway: Caspar, pp284-298

Coben, D. and Thumpston, G. (1995) 'Researching Mathematics Life Histories: A Case Study' in D.Coben (comp.) __Mathematics with a Human Face: Proceedings of ALM-2, the Second International Conference of Adults Learning Maths - A Research Forum 7-9 July 1995__. London: Goldsmiths College, University of London in association with

Department of Education and Science (1982) __Mathematics Counts__, Report of the Committee of Inquiry into Mathematics in Schools under the Chairmanship of W.H. Cockcroft, 'The Cockcroft Report'. London: Her Majesty's Stationery Office (HMSO)

Entwistle, H. (1979) __Antonio Gramsci: Conservative Schooling for Radical Politics__. London: Routledge and Kegan Paul

FitzSimons, G. E.(ed.) __Adults (Returning to) Study Mathematics: Papers from the 8th International Congress on Mathematics Education (ICME 8) Working Group 18__ [ICME-8 1996]. Adelaide, SA: Australian Association of Mathematics Teachers

Gramsci, A. (1971) __Selections from the Prison Notebooks of Antonio Gramsci__, edited and translated by Q.Hoare and G.Nowell Smith. London: Lawrence and Wishart

Harris, M. (1997) __Common Threads: Women, Mathematics and Work__. Stoke-on-Trent: Trentham Books.

Keitel, C., Gellert, U., Jablonka, E. and Müller, M. (eds) (1996) __Mathematics Education and Common Sense: the Challenge of Social Change and Technological Development__. International Commission for the Study and Improvement of Mathematics Teaching ICSIMT 47. Berlin: Freie Universität Berlin

Kjærgård, T., Kvamme, A., and Lindén, N. (eds) (1996) __PDME III Proceedings: Numeracy, Race, Gender and Class__, Proceedings of the Third International Conference of Political Dimensions of Mathematics Education (PDME) III, Bergen, Norway, July 24-27 1995. Landås, Norway: Caspar

Knijnik, G. (1996) 'Intellectuals and Social Movements: Examining Power Relations' in T.Kjærgård, A.Kvamme, N.Lindén, (eds), __PDME III Proceedings: Numeracy Gender Class Race__. Landås, Norway: Caspar Publishing Company, 90-113

Powell, A.B. and Frankenstein, M. (eds) (1997) __Ethnomathematics: Challenging Eurocentrism in Mathematics Education__. Albany, NY: State

University of New York Press

Sewell, B. (1981) __Use of Mathematics by Adults in Daily Life.__ Leicester: Advisory Council for Adult and Continuing Education (ACACE)