ࡱ> 5@ Kbjbj22 9XX,,,8-LT-vt--....>P.d. ݙߙߙߙߙߙߙ$R<-p...p.p...0L2L2L2p.^..ݙL2p.ݙL2 L2l2~1.- PA,.X<F0vٗXx111pL2p.p.p.%,62,ON METHODOLOGIES OF RESEARCH INTO GENDER AND OTHER EQUITY QUESTIONS Jeff Evans Middlesex University, UK J.Evans(at)mdx.ac.uk This discussion starts from a concept of social justice, embracing both distribution and recognition aspects of social relations (Vincent, 2003). The first aspect considers the way that goods, knowledge, skills, rights, etc. are distributed among social groups; this aspect might suggest researching questions like: How does performance (or provision) differ between girls and boys in school mathematics / science? The second aspect concerns the relations structuring society methods of communication, 'treatment', respect; this might prompt questions like: What are relations like between teachers and students of different language groups in higher education? Here I shall focus on gender, and its inter-relations with social class, and, to a lesser extent, with ethnicity (Arnot, 2002; Gillborn & Mirza, 2000). I argue that researching the questions posed by a social justice agenda, and developing theorisations to begin answering them, will require both 'quantitative' and 'qualitative' methods within any substantial research programme, and even within individual studies. I discuss several examples of fruitfully combining different methods. Finally, I briefly consider some barriers to the sort of fruitful cooperation I am arguing for, currently within the mathematics education community and I question the idea that the distinction between quantitative and qualitative methods can always be neatly drawn. Key Words: social justice, equality, gender, social class, ethnicity, quantitative, qualitative. 1. Introduction There is a range of concepts available, for considering the social arrangements in society, and their relationship to the education system. The title of the paper mentions equity, or fairness across groups. We might also focus on equality after specifying whether we mean equality of opportunity, or of outcomes or on democracy (see below), or social justice. Indeed, social justice is a good place to start, because it is clearly related to the idea of equity or fairness, and because it is currently widely discussed in educational research (e.g. Vincent, 2003; Arnot, 2002; Burton, 2003). It also appears to resonate with contemporary policy-makers' concerns, for example, with the European Union's social agenda. The concept of social justice provides a way of grouping two distinct, but related, aspects: distributive justice and justice in terms of recognition. This paper has several aims: To discuss a dual understanding of social justice in terms of distribution and recognition, in recent work in educational policy studies To discuss several illustrations, both from the sociology of education, and from mathematics education To argue, drawing on these illustrations, that researching the questions posed by a social justice agenda requires both 'quantitative' and 'qualitative' methods To show the problems with any simple distinction between quantitative and qualitative methods To consider the value of extending the analysis to consider three or four aspects of social justice. 2. A dual understanding of social justice The first distributive aspect of social justice emphasises: having (or having available) material goods and services, and symbolic resources, e.g. knowledge or skills having opportunities to get access to, to participate in, or to succeed in, particular spheres, e.g. further and higher education, or certain occupations or grades of work. The overriding concern of policy-makers from the 1960s (in English-speaking countries on both sides of the Atlantic, at least) was 'equality of opportunity' across social groups meaning, at that time, across social classes. This made a distributive view of social justice dominant in social science analysis. However, in recent years, in mathematics education at least, the tendency is for social class not to be talked about directly (Secada, 1992), and perhaps to be presented in educational systems as 'ability differences'. This of course is especially important in situations where educational opportunities may be rationed and distributed according to 'ability', or 'ability to benefit'. Distributive concerns might suggest researching questions like: How are different forms of knowledge (e.g. mathematical, scientific), or certain educational credentials / qualifications distributed among the different social categories of class, gender, ethnic or language groups? How does performance (or provision of resources) differ between different social categories in school mathematics or science? For example, Gillborn & Mirza, in Educational Inequality: Mapping race, class and gender(2000), a study largely concerned with distributive issues, appears to use mostly quantitative methodology based on a moderately large sample of official ethnic monitoring returns from local educational authorities, and a representative national youth survey. However, these researchers also draw on (their own and others') ethnographic research to show that Black pupils receive harsher treatment in discipline terms than others Teachers have lower expectations of Black students and less positive assumptions about their motivation / ability (p.17) This suggests that there is also a need to study social justice and inequalities in social interactions. Thus a second aspect of social justice concerns 'recognition of difference', and a concern with status-related inequalities, relating to: manners of communication, 'treatment', respect for difference avoidance of misrepresentation, stereotyping, disrespect. Since the 1980s, there has been increased interest in a 'politics of recognition' (Cribb & Gewirtz, 2002), understandable as a response to a range of 'New Social Movements' concerning gender, ethnicity, disability, sexual preference leading to assertions of / demands for 'women's liberation', 'black is beautiful', 'gay pride', etc. These have important relations to policy concerns such as 'multiculturalism', 'social inclusion' (Tett, 2003), and so on. Recognition concerns might prompt educational research questions like: How are different groups of students treated by teachers in school? What expectations and assumptions do teachers have about different groups in education? To what extent are these sometimes 'stereotypical'? Examples include, besides Gillborn & Mirza (2000), research programmes, and individual studies in the sociology of education on issues of difference and identity, such as: Arnot (2002), Soro (2002) on gender; Gillborn (1995) on ethnicity; Connolly (2003) on ethnicity and religion; Barton (1996) on disability. We can use the discussion so far to suggest a number of provisional directions for further consideration. First, we might distinguish the bases of educational inequality / oppression for different groups. For some, inequality may be rooted primarily in an economic context, requiring redistribution: for example, social class, 'ability' differences, disability. For others, oppression may be generated largely in a cultural context, by lack of recognition/ mis-recognition, e.g. ethnicity, sexual orientation, religion, disability. In this connection, gender inequalities are especially interesting, since they can be seen as 'multiply generated' (Lynch & Lodge, 2002, p3). Nevertheless, there is a complex inter-relation between recognition and redistributive aspects of social justice. One possible criticism might be that social and sociological analyses of social justice or inequality have been too narrow, and have entailed, over the last forty years (in English-speaking countries at least), replacing concerns about social class, with those relating to gender, then with concerns about ethnicity, then disability and so on. This would lead to a proliferation of sub-fields, of 'experts', and so on. However, the discussion so far (of the duality) and the first example below suggest that, with each new form of inequality, we have not simply a replacement, but an enriching of the idea of social justice / equality. 3. An example Arnot (2002) provides a critique of social (class) reproduction theory (Bowles and Gintis, 1976), itself based on a 'correspondence principle' between schooling and the economy. This is the idea that the social structure 'works' through ensuring broadly that 'working class kids get working class jobs', and similarly for middle class kids. Arnot and others have criticised a notion of social class defined only in economic (or occupational) terms, and argued for inclusion of 'dynamic aspects of identity', and the role of patterns of consumption (spending), community and family values (Arnot, 2002, p. 205). Thus the family, with its influence on gender relations, becomes crucial in processes of social class formation, through its role in forming identity, authority relations, perceptions of / resistance to schooling, mediation of differences in material circumstances. (Thus the 'long shadow of the family' also influences the 'expressive [affective] order of school' (Bernstein, 1977).) Youth cultures now soften and cross social class boundaries, and their class cultures are formed by young people acting during schooling as mediators between family class cultures and work cultures; that is, not formed only by the latter. Social class inequality may be affected by the differing opportunities of middle class professional and working class young women. The former now take responsibility for perpetuating their own class position (rather than aiming to do so via marriage), while also making different demands on family life (e.g. sharing of childcare), and different contributions to building up the family's capital (cultural and economic); the latter (working class women), despite little if any improvement in the real opportunities available to them, paradoxically seem to overcome the contradictions by using the discourse of individualisation and choice (Arnot, 2002, p. 212-14). Black women have emphasised education and exam qualifications as a way of crossing class and breaking out of traditional gender and race classifications, and gaining an advantage in securing scarce local jobs (Mirza, 2005). Nevertheless, in the national study discussed above of overall school attainment at age 16+, Gillborn & Mirza (2000), find that social class differences have remained over the previous ten years, and, when social class differences are controlled for, there remain significant ethnic group differences. Gender differences are small overall. The research discussed by Arnot illustrates the importance of theoretical development (illustrated here by 1.), findings based at least partly on ethnographic (qualitative) work (2. to 5.) and findings based on survey (quantitative) work (illustrated here by 6.). Drawing on Arnot's account for illustration, I argue that researching the questions posed by a social justice agenda, and developing theorisations to begin to address them, will require both 'quantitative' and 'qualitative' methods within any substantial research programme. Below I show further examples of individual studies, each of which combines the two types of method. 4. Quantitative and qualitative methods We need to begin to clarify the basis, or more precisely, the possible bases of the Quantitative / Qualitative distinction; see Table 1. Table 1 Facets of the Quantitative / Qualitative Distinction QuantitativeQualitativeForm of datanumerical ?textual ?Degree of structuring (by the researcher) of interaction in the fieldsubstantial? (in standardised, and coded, tests, interviews or questionnaires) relatively little? (in semi-structured interviews and participant observation) Methods of analysis of the datastatistical ?semiotic ? Perhaps the simplest way to try to distinguish the two types of method is to look at the form of the data: numerical data indicates quantitative methods, and textual data indicates qualitative. However, this simple position ignores the fact that much 'quantitative' data is originally produced as text (as in an interview response) before being coded into categories (often not really into numbers), and also that repeated instances of 'qualitative' text that are similarly categorised can be counted. Perhaps the difference can be clearly related to the degree of structuring of the verbal social interaction (by the researcher) during the data production and coding stages? Thus quantitative methods would use standardised tests, interviews, questionnaires or official statistical returns, and standardised coding of responses, while qualitative research would use semi-structured interviews participant observation, and a range of types of documents. But again this is too neat: case studies may use questionnaires or test results, and exploratory interviews in surveys, or experimental de-briefings, may be semi-structured. For methods of data analysis, quantitative research seems to use statistical methods and qualitative to employ semiotics. But how would we classify a cross-tabulation of counts of qualitative material that has been 'read semiotically' and then coded into categories? See the 'hybrid' example given below in the discussion of Evans (2000). 5. A consideration of further examples To explore the use of, and the distinction between, types of methods in practice, I now discuss two studies in mathematics education, Jo Boaler's Experiencing School Mathematics: Teaching styles, sex and setting (1997), and my own Adults' Mathematical Thinking and Emotions (Evans, 2000). 5.1 Experiencing School Mathematics: Teaching styles, sex and setting (1997) Jo Boaler studied the school mathematics experiences of secondary students in the context of two secondary schools: one traditional ('AH') and one progressive ('PP'). In school AH, traditional policies included procedures for setting, or dividing students into 'ability groupings' for maths, and whole class teaching, working at the same pace. In PP, the students were encouraged to work on problem-solving in mixed ability groups, at their own pace. Boaler's methodology was a comparative and longitudinal case study: she followed 300 students in the two schools, over 3 years. She produced or gained access to many sources of quantitative and qualitative information. She considered gender differences and social class differences. Related to both, she has much information on distributional differences: national exams results and school records. She also negotiated access to the archive of examination scripts held by the Examination Boards. First, on gender differences, Boaler compared the two cohorts on the percentage of 'good passes' (grades A-C) in GCSE Mathematics: in the traditional school, AH, 20% of the boys attained such passes, compared with 9% for the girls. In school PP, the two groups were about equal, at 13%. These differences were explained by data from: questionnaires: gender differences in rating of importance of different areas of mathematics semi-structured interviews: at AH, girls emphasising importance of 'understanding', boys emphasising performance (completing questions quickly and getting the right answer) classroom observation Thus to research the distributional questions, she uses both quantitative and qualitative methods. But she also considers lack of recognition. Here she focuses on top set girls, since gender differences in maths performance at the highest levels of ability are considered to be the hardest to eradicate in the English-speaking countries. Now certain 'attribution' theories blame these girls for 'maladaptive' motivational patterns towards school mathematics. However, Boaler argues that girls' responses should be considered in relation to their goals, in this case of understanding the content, rather than merely getting the right answers. Thus her aim as researcher is to 'give voice to' the top set AH girls' concerns (1997, pp118-23). I now turn to Boaler's discussion of social class. In UK schools, social class differences are often considered as 'ability' differences (as indicated above), and influence the ability grouping the student is put in; see Figure 1. Figure 1 Social Class, Setting and Performance ! ! ! Student's Initial 'ability' ! Set individual put ! achievement Social Class ! in exam ! ! ! results This is no longer a simple model, so the research needs to be able to examine the relationship between two factors, while holding constant a third. This needs the idea of partial correlation. For example, to assess the claims above, we need to try to disentangle the 'effects' of social class and ability groupings on the placement of students into 'sets' for mathematics. Let us suppose this were done solely on the basis of ability (as measured, say, by an ability test after one year at secondary school), without social class being involved. Then we would expect the correlations of social class with the set into which each student was placed, after ability differences were taken account of, to be zero, or very close to zero. In fact, at school AH, this ' partial' correlation was positive and statistically significant, indicating that after controlling for initial ability score, there was a tendency for students of a 'low' social class to be placed in a low set. At school PP, the ' partial' correlation of social class with set into which students were placed for the last six months of exam preparation was found to be negative (and statistically significant): this showed that 'at the end of their mixed-ability teaching experiences, there was a small tendency for students of a "lower" social class to be placed in a higher examination group [], than middle-class students of similar initial attainment' (Boaler, 1997, p138). So she concludes that social class has some effect on the placing of students into sets, over and above that of ability (as measured) in the traditional school (AH). So far, the analysis appears to include quantitative methods only. Now we would like to examine some correlation or association between social class and attainment. But what we find, in the description of the schools, and from the rules of the 16+ examination, is that students are registered for different levels of examination, depending on their teachers' expectations of their likely results. This will depend on the set they are in at the AH school and other factors, including social class. But once in a certain exam group, in the English system, there is a ceiling on the grade the student can get: the lower the exam group, the lower the ceiling. So there is no point in a quantitative analysis of correlations, here since the variability of the data is constrained by the social regulation of the examination process. What Boaler did was to assess the reactions of the students to this situation. Using evidence from semi-structured interviews, she found the students 'don't like maths any more', because they disliked needing to keep up with the (supposedly common) pace, and the feeling of being judged against their (supposed) peers. This led to pressure and anxiety, and a feeling by students that they were not learning or understanding as well as they could. Thus Boaler's highly-regarded study of secondary school mathematics includes a concern with social justice issues. In her consideration of social class differences, she begins from a focus on distributional aspects, and a use of quantitative methods (in the several senses of Table 1 above). But she shows how to move back and forth between quantitative and qualitative methods, and to broaden the social justice concerns to include 'recognition' aspects. 5.2 Adults' Mathematical Thinking and Performance: a study of numerate practices (2000) Evans (2000) studied adults' mathematical thinking and performance in a higher education (polytechnic) institution. He produced several types of data on three cohorts of students studying mathematics, as part of their main study of a social science subject. Evans studied distributional issues e.g. gender differences in performance by asking students to complete a questionnaire including some performance items, and by building a mathematical (statistical) model. He found that the size of gender differences was initially quite substantial. But they decreased (and were no longer statistically significant for school leavers in the 18-20 age range), once the model controlled for a range of competing explanations such as social class, age, level of qualification in school maths, and affective variables, especially confidence and mathematics anxiety. Besides these quantitative methods, the research also used semi-structured interviews (life history / clinical) to observe student problem solving and affective reactions. This allowed the problematising of categories and scales from the questionnaire, and more flexible and rich description of several concepts: performance, in a context-specific more precisely, a practice-specific way, as in how to understand a student's calculation of a restaurant tip as '37.2p' (Evans, 2000, p162ff) social class, elaborated to include not only an economic, work-based aspect, but also cultural and identity-based aspects (see e.g. pp230-1, and also the discussion of Arnot's elaborations above) anxiety expressed, distinguished from anxiety 'exhibited', using insights from psychoanalysis (pp171-2). These elaborated categorisations were used to examine the main relationships in a richer way (though for a smaller sample), in what I called 'qualitative cross-sectional' (or could have called 'quantitative semiotic') analyses. These 'hybrid' analyses combine an interpretive reading of textual material with a basic statistical analysis; see Table 2 below, where the categorisation of an interviewee as having 'expressed anxiety' or as 'likely to have exhibited anxiety, but not to have expressed it' depends on a careful reading of the entire interview transcript, drawing on psychoanalytic insights about the way that anxiety can be 'exhibited', even if it is not expressed (Evans, 2000, pp144-5). When the results of the categorisation on the latter anxiety variable are cross-tabulated with gender, the resulting 'qualitative cross-sectional' analysis in principle allows a comparison across genders, etc.; see Table 2. Table 2 Expressing and Exhibiting Anxiety in Semi-structured Interviews: cross-Tabulation of Numbers with Gender (n = 25) Coding MalesFemalesTotalAnxiety expressed  9 13  22Likely to have exhibited anxiety, but not to have expressed it 3 -- 3Total 12  13 25 Source: Evans (2000), Table 9.7 However, virtually all students (22 of 25) took the opportunity to express anxiety during the interview, so any gender differences are small and not very reliable (because of the small sample size). Another way that quantitative and qualitative methods might be brought together is in indicating which students might be 'over-achievers' or 'under-achievers'. This is done by calculating the residual, or the difference between the students observed performance score and their performance score that would be expected, given their gender, social class, age, level of mathematics anxiety, etc., and using statistical modelling (see Evans, 2000, note 8, chapter 10, pp270-1, and also Boaler, 1997, pp138-9). Such 'over-achieving' and 'under-achieving' individuals could then be selected for invitation for semi-structured interviews, on the grounds that they might possibly be more interesting for the analysis. Thus both quantitative and qualitative methods are used for distributive analyses of social difference / social justice. The semi-structured life history interviews provided material on subjectivity / identity, and therefore, allowed for the recognition of students from various social groups. In these interviews, the student related earlier experiences where they were 'recognised', or not, as a learner of mathematics. The interviews gave students space to express anxiety and other feelings about mathematics to the interviewer, as illustrated above. The interview also allowed several students to describe and to celebrate their 'recovery' of confidence and competence in mathematics during the first year of their college course (Evans, 2000, p239). These two studies together show the use both of quantitative and qualitative methods to study distributional and recognition aspects of social justice in mathematics education. In Evans's study, the 'qualitative cross-sectional' method (illustrated in Table 2) appears to be a hybrid, both quantitative and qualitative. 6. Extending the analysis of social justice to further aspects Other views of social justice comprise not only a 'double aspect' of social justice or equality, but a further aspect. This leads us to consider 'distribution', 'recognition', and 'representation' aspects of social relations (Lynch & Lodge, 2002; Bernstein, 1996, pp5ff). Here Lynch & Lodge focus on 'equality'; Bernstein on 'conditions for democracy'. As an indication of the meaning and the importance of this third dimension, we can examine the following summing up of the position of sociology of education at the turn of the century: Sociology (over the last 50 years) has been formed by four sets of questions: Who gets taught what, how, by whom, and under what circumstances, conditions, contexts and resources? How, by whom and through what structures, institutions and processes are these matters defined, governed, organised and managed? What is the relationship of education as a social institution to other social institutions of the state, economy and civil society? and In whose interests are these things determined and what are their social and individual consequences? (Dale, 2001, p. 27) It can be seen that, while the first point relates to distributional issues, the last three points relate to issues concerning politics and power. The latter are not covered by the distributional and recognition aspects of social justice, but require a third dimension to be conceptualised. Thus the third aspect of social justice or equality concerns power and the 'representation of interests': power relations at macro-levels of state and related institutions; micro-level power relations between teachers and students (or 'age-related status'). Overall, this aspect is less developed within educational research than redistribution and recognition. And, within this aspect, the macro level is better researched than the micro level to date. This might prompt research questions such as: What are the views of teachers on power and authority relations in their schools? What kinds of changes would pupils like to see, in order to make school a fairer place? Here we can consider the analysis of Lynch & Lodge, in Equality and Power in Schools: Redistribution, recognition and representation (2002). The methods used included questionnaires distributed to teachers in eight schools; and content analysis of pupils' essays on the above 'would like to see' topic. In developing their work Lynch & Lodge also point to the way that the organisation of interpersonal relations in school also leads to a fourth dimension of social justice. This fourth aspect focuses on equality in the affective domain, on the fact that teachers and learners are not merely rational actors, nor simply cognitive beings but rather 'have an emotional history, as well as a social class, gender, or [and] ethnic history', which relate to the dependence and interdependence that are 'an integral part of the human condition', and the 'emotional dimensions of the learning process' (2002, p11). This is a promising emerging area for further research, though it cannot be discussed further here (see, however, Nurmi et al., 2003; Evans, 2006; Hannula, 2006; Evans, Hannula, Zan & Brown, 2006). 7. Summary and Conclusions A perspective on social justice and equality is fundamental for many important research topics in educational research today. It is also central to many policy concerns. A commonsense view might attempt to align aspects of inequality with methodologies to study them, as follows: Distributive issues (e.g. school performance, access to higher education), to be studied using largely quantitative methods. Inequalities in social interactions (e.g. how students treated, stereotypes held of different groups), to be studied using mostly qualitative methods. But, as we have seen, these neither of these simple linkages work; see for example the discussion of Gillborn & Mirza (2000), and Arnot (2002) above. Indeed, research into social justice and equality requires the use both of quantitative and qualitative methods, as illustrated here. These may sometimes be used together in one particular study (e.g. Boaler's and Evans's above), or sometimes woven together in a developing research programme (Gillborn & Mirza, or Arnot). There is a complex inter-relation between the two / three / four dimensions of social justice / equality which are interpenetrating. The different aspects are inseparable for many groups (Fraser, 2000). Theoretical analysis is important to underpin empirical work of either a qualitative or quantitative kind. Sociological research programmes provide an essential basis for this research, richer than that provided by most policy discourses : Theory [ ] offers a language for challenge, and modes of thought other than those articulated for us by dominant others. It provides a language of rigour and irony rather than contingency. The purpose of such theory is to de-familiarize present practices and categories, to make them seem less self-evident and necessary, and to open up spaces for the invention of new forms of experience. Ball (1998) For example, Madeleine Arnot's (2002) critique (see above) of social (class) reproduction theories which emphasise the economic aspects of inequality, requiring redistribution, highlights the differences in 'cultural capital', which lead to questions of recognition and representation. The richness of this multi-dimensional approach must be grasped theoretically. In closing, I briefly wonder about what possibly might be barriers to a multi-method approach. I sense, within some parts of the contemporary international mathematics education community, and in educational research generally, an apparently 'always switched on' preference for using qualitative, rather than quantitative methods seemingly independent of any consideration of the nature of the problem; see, for example, Delamonts (1997) claim that Quantitative methods have largely disappeared among younger scholars [in sociology of education] (p601). Possible reasons for this may include: a linking of 'positivism' and quantitative research which are then sometimes treated to 'ritual dismissal' but not all 'positivist' research is quantitative, and not all quantitative research is positivist; see Halfpenny (2001) and the examples above. a linking of feminist and qualitative research methods, e.g. Ann Oakley's (1981) article entitled 'Interviewing women a contradiction in terms' but this linkage is softening: see for example Arnot's programme above, and Oakley's (2000) emphasis on the use of quantitative fieldwork methods, given her more recent concerns with 'evidence-based practice'. the idea that the quantitative - qualitative distinction can be easily drawn but some idea of the difficulty of distinguishing simply between the two has been given here; see for example Evans's (2000) hybrid approaches illustrated above and Creswells (2003) mixed methods. 5. 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