Front matter
Students, Human Development Education in South Africa ities, obstacles and outcomes
Melanie Walker Monica McLean Mikateko Mathebula Patience Mukwambo
Low-Income Students, Human Development and Higher Education in South Africa
Contents
Raising ‘learning outcomes’ for inclusive higher education: The Miratho Project
CHAPTER 2 acain einne Eaa E A aN SEN a NNSA 17 Capabilities and functionings: Reconceptualising learning outcomes
CHAPTER Miaon EE E O E E E A 55 The Miratho Capabilitarian Matrix: Evaluating individual achievements and institutional arrangements
Chapter 1
Raising ‘learning outcomes’ for inclusive higher education The Miratho Project
In rural South Africa during times of floods some villages become stranded and children cannot reach schools in other villages. To prevent the disruption of their children’s education, communities build makeshift bridges, known in Tshivenda as ‘Miratho’. These bridges are rickety, therefore it takes courage on the part of parents and students to traverse them when they might collapse at any moment. Over a period of five years, our research project! followed the educational experiences, from leaving school to graduating, of about 60° university students from low-income rural and township households in South Africa. We called the project Miratho because these bridges symbolise the determination of such students and their families to work together to pursue education for a better future for all, in the face of severe obstacles and risks.
Tintswalo is one such student who has pulled through against many odds. His secondary school in a rural village was dilapidated and the only resources were textbooks which he carried with him through the bush to school and back to his home ten kilometres away, so that the goats in the school’s village would not eat them during the night. His teachers and an uncle encouraged him, and he achieved the grades to enter ‘Country University’, a rural historically disadvantaged university, to study for a BEd in agriculture and biology. At university, bursaries were delayed, but he managed to eat enough and pay rent with help from his family. Life was tough in his first two years at Country. Learning in English was difficult and his access to computers was limited, but he enjoyed his course, and his friends were like brothers who kept him going. He worked extremely hard, focused on his dreams for a better life and gained in confidence. Tintswalo is now teaching Life Sciences at his old secondary school and is living at his family home. He would like to obtain a PhD. However, as we shall show, by no means have all the students’ journeys so far have ended with employment or further study.
1 Our project was funded by the Economic and Social Research Council (ESRC) and the Department for International Development (DFID), now known as the Foreign, Commonwealth and Development Office (grant number ES/NO10094/1), with supplementary funding from the National Research Foundation (NRF) (grant number 86540). The project was funded till September 2020, with a no-cost extension to June 2021.
2 A total of 66 students were included for the first interviews in 2017 and 58 by the last in 2020, with an informal follow-up in 2021. Originally, we had planned for 48 interviews across four universities, but the Thusanani Foundation non-governmental organisation (NGO) asked us to include Rural University. In some universities we were able to recruit more than 12 students.
LOW-INCOME STUDENTS, HUMAN DEVELOPMENT AND HIGHER EDUCATION IN SOUTH AFRICA
What the Miratho participants have in common is the battle to get into university, to flourish at university, and to transition to work or further study. As researcher Nic Spaull (in Nxumalo 2021: 1) has pointed out, while degree-entry grade 12 passes have increased by 7% since 2011, university enrolment has grown by just 2.7% since the same year. Spaull (Nxumalo 2021) recounts the 2016 Davis Tax Committee report which gave a stark glimpse into access to higher education: Only 10% of children from the poorest 70% of the population qualify to go to university, compared to 40% of children from the wealthiest 10% of the population. As Spaull (in Nxumalo 2021: 1) explains, ‘The children of the wealthy are likely to get to university because the children of the wealthy are more likely to attend functional schools which give them the passes that they require to gain entry to university’. We can assume that the challenges for the 70% are significant.
The call for funded research proposals in 2015 to which we responded was focused on ‘raising learning outcomes in education systems in challenging contexts’. Miratho had two main aims. First, the project aimed to investigate how complex biographical, socio-economic, policy, and educational factors interact to enable or inhibit pathways for rural and township youth to get into, get on, and get out of higher education with valuable learning outcomes. Second, we aimed to explore a theoretical approach for understanding higher education learning outcomes which considers students from low-income backgrounds who face multi-dimensional challenges when pursuing education. In this book we will discuss what we learned of the students’ lives and how we conceptualised the multi-dimensional benefits that such students value and can accrue from a university education. In parallel, we discuss the limitations on benefitting, resulting from students’ university experiences, their personal circumstances and the broader socio-economic context.
In the rest of this chapter, we first locate our research within a commitment to human development defined as expanding people’s freedoms and opportunities towards improving their well-being. In this definition, higher education is one of society’s public goods. Next, we outline our research methodology and methods and introduce the capability domains which are the product of the research. Finally, we sketch the main argument of the book as it unfolds chapter by chapter.
Rationale for pursuing the human development capability approach (CA)
The United Nations Development Programme (UNDP 2020) defines human development simply:
The human development approach is about expanding the richness of human life, rather than simply the richness of the economy in which human beings live. It is an approach that is focused on creating fair opportunities and choices for all people.
Human development focuses on human flourishing and freedom from poverty and other deprivations. Having followed our South African students from low-income backgrounds through tribulations and some triumphs as they tenaciously pursued a university education for six years or more, our commitment to human development ye principles and goals has been strengthened. The Miratho students’ experience of poverty is a legacy of colonialism and apartheid, not least in the historical imposition of rural ‘bantustans’ or ‘homelands’ set aside for Africans and segregated urban townships (see Ross 1999), which are the sites of the home communities of these students. We aim to produce evidence and an argument for proposing that South African universities’ contribution in social transformation and human development should have a dual focus: on mitigating the effects of material deprivations and redistributing material resources more justly, which we understand as integral to the decolonisation project; and, on a wider set of opportunities and freedoms for students from low-income households. In turn, the expansion of such freedoms can have a positive impact on social development and the public good.
The capability approach is grounded in human development. It was developed with a focus on poverty reduction by the welfare economist Amartya Sen (1985, 1999) who is committed to human development and social justice. Later, Martha Nussbaum (1997, 2000, 2003, 2010, 2011) took up Sen’s ideas, bringing in a philosophical perspective to the capability approach and producing her own set of ten ‘universal’ capability dimensions. Since then, the approach has been applied in many social fields, including education.
The capability lens has the power to illuminate both the conscious and deliberative aspects of human agency (the decisions and choices that students make) and how structural inequalities present barriers to students’ success. In the terminology of the approach, ‘capability’ is the opportunity and freedom to make choices in life, while ‘functioning’ is an achieved being or doing. We employ this approach because it enables us to investigate and evaluate the fair distribution of what matters to people in the form of capabilities and functionings.
As Mahbub ul Haq (2003: 17) elucidates, ‘the basic purposes of [human] development is to enlarge people’s choices’. While a definition of human development might be simple, the actualisation of such a vision is complex and requires demanding transformations across multiple economic and social arenas. In this book, we argue that the mainstream discourse of learning outcomes in education does not offer sufficiently expansive conceptual and theoretical purchase on the highly complex problem of educational success, which should encompass economic, social, historical-colonial, political, cultural, and psychological aspects of human life. Rather than restricting focus to pre-specified ends of curricula and pedagogy, our conceptualisation is grounded in human development applied to all aspects of a university education, linking opportunities, processes, and outcomes.
The Miratho students are human individuals trying to set themselves apart from a crisis of poverty and inequality in the world, exacerbated now by Covid-19. In 2018 the World Bank? declared that it had set itself the goal of ending extreme poverty by 2030 by reducing the share of the global population living on less than USD 1.90 a day (about ZAR 30), and by increasing the incomes of the poorest 40% of people in every country. Even such modest goals are in serious jeopardy. After 15 years of progress in eradicating poverty, Covid-19 pushed approximately 124 million more people below the poverty line in 2020 (Van Trotsenburg 2021). Calculations indicate that the pandemic’s potential impact on multi-dimensional poverty reduction is between 3.6 and 9.9 years
3 https://openknowledge.worldbank.org/handle/10986/30326 a3
LOW-INCOME STUDENTS, HUMAN DEVELOPMENT AND HIGHER EDUCATION IN SOUTH AFRICA
(Alkire et al. 2021). All over the world, health, educational and social inequalities have been both exposed and worsened, including in South Africa.
Of direct relevance to us is that, within these circumstances, tertiary education is in crisis (World Bank 2021) and students or new graduates who come from low-income households are most vulnerable to the adverse effects of the pandemic and reduced graduate employment opportunities. According to Unesco (2020), during 2020, 166 countries had closed universities, affecting 87% of the world’s student population, a staggering 1.52 billion students. Inevitably, the lower the income of a student’s background, the more disadvantaged they will be by being unable to attend university. Most obviously, benefitting from digitalised education relies on resources, time and space, even for those who make it into university. So, it has become more urgent to think about economic, social and educational arrangements to support under-represented students to work towards their futures and to challenge the deficit position they are viewed from.
Universities can serve both economic development and social justice and are, therefore, significant for human development (Boni & Walker 2016). Yet, globally, the discourse of human capital dominates; that is, the measure of skills, capacity and attributes of labour which emphasise peoples’ productive capacity and earning potential (Becker 1964). Despite challenges to human capital revealing how its analyses recognise neither diversity nor a lack of good jobs (Brown et al. 2020), higher education continues to be portrayed as a vehicle for producing human capital for national and international wealth creation in a world becoming increasingly characterised by technology-dependent knowledge economies (Castells 2017a). A recent study of low- and middle-income countries (Howell et al. 2020) found that universities contribute to sustainable economic development locally and nationally, but do less well on social development and inclusion. Yet the study found that graduates make demands for equality, human rights, health, education and peacebuilding. In low- and middle-income countries there is evidence of wider social and individual benefits. Compared with non-graduates, graduates enjoy social mobility, better health, more stable employment, more autonomous work, higher lifetime earnings, and more engagement in civic affairs (Oketch et al. 2014).
Since the end of apartheid, South Africa has been concerned with expanding higher education for social transformation.’ In line with development agendas across the world and on the African continent, higher education in South Africa is seen as playing a significant role in growing skills and a knowledge economy (National Planning Commission 2012). However, the transition in 1994 from a racially segregated system has generated equity and quality imperatives. Consequently, while human-capital higher education goals have been prioritised in most countries, in South Africa, universities have been closely associated with redressing apartheid’s racial inequalities, thereby contributing to social transformation by offering social mobility. According to Cloete and Van Schalkwyk (2017: 4), this preoccupation resulted in the National Commission for Higher Education’s (NCHE 1996) framework which focuses on equity and democratisation, while paying virtually no attention to development, research and
4 See Van Schalkwyk et al. (2021) for a recent critique of the muddiness of the transformation discourse notwithstanding real quantitative gains in equity.
5 See, for example, the African Union’s Agenda 2063: The Africa We Want (https://au.int/en/agenda2063/ overview; and, Continental Education Strategy for Africa 2016-2025 (https://au.int/en/file/33863-doccesajournalvol2finalpdf )
innovation. Be that as it may, the goal of higher education for socio-economic redress has not yet been achieved. Most students from low-income households in South Africa leave school at grade 10 or earlier and do not go to university (Walker 2018b). The benefits, quality and outcomes of higher education continue to be inequitably distributed (Lewin & Mawoyo 2014). Underpinning our research has been the question of what kind of university educational aims, policies and practices might promote both economic growth and individual prosperity and a broader conception of equality and human flourishing.
Until now there has not been a systematic, integrated, longitudinal mixed-methods South African investigation of the multi-dimensional dynamics or factors shaping and/ or inhibiting low-income students’ capabilities to access, participate and succeed in a variety of higher education institutions, and to move on to work or further study. Nor do we have much research on rural students or rural universities (although see Mgqwashu et al. 2020; Naidoo et al. 2020; Timmis et al. 2019; Trahar et al. 2020). The Miratho Project for the first time offers fine-grained detail derived from talking to students about how they understand and experience disadvantage, equity and educational quality and about how higher education can foster or frustrate the agency and decision-making processes that empower them to change their own lives and those of others.
While statistics tell of the broad trend of inequalities in South African higher education, our research fills a lacuna about the past experiences and day-to-day realities of undergraduates from low-income households. We offer a rich and nuanced account of how these students grew up, how they made the decision to go to university, and got in; how they survived and studied and nourished their aspirations; and, how they are now sustaining or trying to sustain their aspirations for a better life, including social mobility.
Methodology and methods of data generation
The Miratho Project was designed to investigate the complexities of how higher education opportunities and achievements are distributed among students from challenging low-income households. It also aimed to generate data which illuminate, from a capabilities perspective, what students do gain from a university education that is of value to them and what they should gain. In this sense our research is ‘phronetic’ (Flyvbjerg 2001) in that we aim both to develop knowledge that has explanatory power in relation to equity in higher education access, participation and outcomes, and to suggest practical action to address the challenges.
As education researchers we have long been committed to contributing to justice and equality. As the project progressed, we realised the need for increased sensitivity to a decolonial ethic which challenges West-centric knowledge practices. We see this book as a contribution to Africa-centred Southern scholarship. It was important that the original research proposal came from the University of the Free State and that the funded project was led by a South-based scholar as principal investigator (unlike the majority of the projects in the research programme on raising learning outcomes referred to earlier). During the time of the project, South African students were also involved in protests about access to university (#FeesMustFall) and the need to decolonise the discursive practices of universities (HRhodesMustFall). All over the world, educators
LOW-INCOME STUDENTS, HUMAN DEVELOPMENT AND HIGHER EDUCATION IN SOUTH AFRICA and researchers were urged to scrutinise their own discursive practices, while recently there has been a plethora of webinars, blogs and conferences (mostly initiated by the global North) about decolonisation and decoloniality (Mignolo & Walsh 2018).°
Writing about decolonising methodology, Tuhiwai Smith (2012: 2) warns that ‘belief in the ideal that benefitting mankind is indeed a primary outcome of scientific research is as much a reflection of ideology as it is of academic training’. Similarly, we should be wary of our version of ‘development’. We should cease to take for granted that we are representatives of communities which are disadvantaged and of those who are stereotyped as lacking epistemic material to contribute to shared knowledge and development outcomes they value. Well-meaning higher education research will carry and represent the residual cultural presence of colonisation (Maldonado-Torres 2007). We understand that our research practices, as well as the substantive focus of our research, should be grounded in advancing ‘authentic humanity’ (Smith 2012: 24). As Tuhiwai Smith (2012: 41) puts it, as researchers we ought to be committed to producing knowledge ‘that helps create spaces for the voices of the silenced to be expressed and “listened to,” and that challenge racism, colonialism and oppression’. Research need not privilege the interests and power of the (academic) researcher but rather reposition those who have been objects of research into ‘questioners, critics, theorists, knowers, and communicators’ (Ndlovu-Gatsheni 2017: 1). Thus, Goetze’s (2018) ‘epistemic humility’ highlights the need to admit the gaps in one’s own interpretive tools as a (decolonial) researcher of the lives of others, primarily referring to those that have experienced epistemic marginalisation.
In particular, a participatory element to the research allowed us to acknowledge low-income students from rural and township areas in South Africa as legitimate producers of higher education knowledge based on how they experienced, understood, learned and talked about exclusions and inclusions at university. Thus, in Miratho, we sought to address misrecognition and research exclusions by contextually understanding the experiences and perceptions of students through their own eyes and with their own voices and by forming and sustaining meaningful relationships with the group over more than four years. Nor was this outsider ‘parachute’ research. Most of the research team are deeply embedded in the context and committed to working for real transformation in higher education in South Africa over time.
Complex datasets were required because the distribution of capabilities is revealed in biographical detail about families and schools; in the students’ lived experience of university educational and social arrangements and of preparing for working life; and in their values and commitments. Insights gained by exploring student pathways, experiences, aspirations and future plans were contextualised by statistical information of trends in university access, participation and outcomes, and by keeping up with the policy context. The multi-method, longitudinal approach generated the following datasets combining fine-grained individual qualitative data, surveys and existing large datasets.
6 For a perspective on global South and global North knowledge and research relations see Walker and Martinez Vargas (2020). Also, while post- and decolonial viewpoints are on the development agenda, there are also criticisms of a co-opted approach in the North which fails to challenge underlying unjust structures.
he
Table 1.1 Summary of Miratho datasets
246 transcribed life-history interviews with between 58—66 students interviewed four times between 2017 and 2021. There were between 12 and 15 in each of 5 universities, with an overall attrition of 8 students (one of whom died) by 2020.
Participatory research generated three photobooks containing the ‘photovoice’ stories of 19 students and one Common Book, field notes and transcribed recordings of workshops.
Recordings of three ‘Identity Wheel’ and ‘Imagined Futures’ workshops for life-history participants.
Thirty-nine Miratho students completed a pilot survey and 472 students in one university completed the revised student survey.
Use of secondary data: (1) Existing large datasets, specifically South African Higher Education Management and Information System (HEMIS) 2006-2013 and 2007-2013; (2) Statistics in the public domain: Census (2011) and Community Household Survey (2017).
Note on data analysis
Interview transcriptions, participatory research and survey data were analysed as discrete entities. Ethnographic field notes from field trips to interview students and to facilitate participatory research, along with field notes and materials from workshops and secondary quantitative data, were drawn on only to supplement the primary analysis as the processes of analysis and interpretation proceeded. The combined data were further informed by textual data including national development and education policies, media reports, university mission and vision statements, and relevant websites. By contextualising qualitative data within a socio-economic, quantitatively informed understanding, there emerged both a macro view of the educational pathways of the selected student population and fine-grained micro accounts of students’ lives. The combined data have been iteratively interrogated, analysed and theorised, and these processes have resulted in the creation of the South African multi-dimensional, intersectional capability-based Miratho Matrix which is a key outcome of the research (see Chapter 4). There now follows a more detailed account of the elements of the research.
The longitudinal life-history interviews
Life-history interviews with students at five different universities took place four times, starting in 2016 with second-year students (third-year at Rural) to allow for the high drop-out rate in the first year and for students to have completed at least one year of university to reflect on. The last interview was in 2020, six years after they had first registered at university. In 2021 we followed up with nearly all the students using WhatsApp. All of these interviews are the centrepiece of the Miratho research project and constitute the main material for the book. They comprise 246 longitudinal life-history interviews whereby we were privileged to capture the life stories of students told in their own distinctive voices. Fine-grained annual life-history data served as a micro lens on well-being, revealing over time the intersections between biographical and material circumstances and social and educational experiences. The data allowed us to chart the complex interactions of agency and conversion factors, including structural constraints or enablers.
Participating students Access to university students for research purposes is difficult unless the research team aye
LOW-INCOME STUDENTS, HUMAN DEVELOPMENT AND HIGHER EDUCATION IN SOUTH AFRICA also composed of university staff who teach undergraduates themselves and conduct research at the university. For this reason, the project worked with the youth-led non-profit Thusanani Foundation’ which supports students from rural areas and townships to apply for and — to some extent — succeed at university. So, the student research participants were those who had gained access to higher education through the support of the Foundation. Two of the staff joined us for the first round of fieldwork to explain the Miratho Project to students they knew and to help organise the first two years of interviews. The students whom the Foundation was supporting came from rural KwaZulu-Natal (KZN), Limpopo, the Eastern Cape, and some Gauteng townships. The table below offers key information about the students.
Table 1.2 Profile of life-history students
Gender Female 28 Male 38 Community Rural 56 Township 10 School quintile 1-3 60 4-2 6 First in extended Yes 35 family to attend No 31 university Level of university Three-year diploma 12 study Undergraduate degree (three or four years) 54 Broad field of study Accounting 11 Education 13 Commerce and marketing 4 Construction 4 Engineering: mechanical, civil, mining 5 Governance and management: public, tourism 4 Law 1 Maths, logistics and computing 8 Nursing 1 Natural sciences: biochemistry, chemistry, soil science, genetics 7 Pharmacy 1 Social sciences: politics, indigenous knowledge systems, language 7 Award status in Completed with transcript 38 2020-2021: six to Completed but transcript withheld due to debt oF SEVEn ieee arier Not completed 13 registration Dropped out of studies 2 Work/further study: | Employed 14 2020-2021 Continuing undergraduate study 13 Further study 8 Internship, training, community service 7 Unemployed 16>
N=66 for the first interviews in 2017 and 58 by the last in 2020 and for the 2021 contact.
# Students do not receive their transcripts if they owe the university money. Without a transcript a graduate cannot be employed as a graduate or enrol for further study.
* 7 in permanent, full-time employment and 7 with contracts and part-time employment.
~ 14 were graduates and two non-graduates who had dropped out of their studies.
7 https://thusananifoundation.org/ Thusanani means ‘helping each other’.
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After six years of registration (seven for Rural students), 36 of our original Miratho 66 had successfully completed their course. This is consistent with the national average of 58.1% (a combined aggregate of 61.6% for degrees and 47.8% for three-year diplomas) (Jeynes 2016). For now, we draw attention to most students’ being from rural communities and most going to schools with limited resources. Over half have a relative who has entered (but may not have completed) higher education before them in their families.
The students attended five diverse universities for which we use pseudonyms and give a short description below to convey the diversity but maintain anonymity.
Table 1.3 The Miratho universities
Pseudonym Description Number of
of university students retained for interview in 2020
Country University Comprehensive, rural, formerly disadvantaged 12
City University Comprehensive, urban, large, formerly advantaged 13
Metro University Traditional, urban, elite, formerly advantaged 13
Provincial University | Traditional, urban, mid-ranking, formerly advantaged 15
Rural University Comprehensive, rural, formerly disadvantaged 13
Two of the universities (Country and Rural) have lower national status and lower status with employers (Walker & Fongwa 2017). They are also at a distance from major metropolitan centres, have large numbers of low-income students, and are less well-resourced overall. On our fieldwork visits we found the differences to be visible, with Rural being by far the least advantaged of the five universities with the main campus and buildings looking rundown, the residences unattractive, and the campus unsafe. Country and Rural are historically disadvantaged universities. Thus, it is clear that apartheid and colonialism constitute key background factors, shaping the universities as they do today, shaping geographical resources and distribution, and influencing individual lives so that being black® means you are more likely to be from a low-income household.
The conduct of the life-history interviews The first three interviews (2017, 2018, 2019) were conducted by members of the research team in venues that were accessible to the students near or at their universities. Due to Covid-19 the final interview in 2020 was by telephone and in 2021 we used our Miratho WhatsApp group. Although the geographical distance was great in the case of some universities, most team members visited all universities some time during the project. Such visits were regarded as ethnographic, enriching our understanding of the environment that the students were living and studying in.
For the first and second years of interviews, the Thusanani Foundation encouraged the students to attend the interview, sometimes transporting them. After that, members
8 We would prefer to eschew racial categorisation altogether but it continues to dominate official statistics and daily discourse in South Africa, where ‘black’ is taken to mean African.
LOW-INCOME STUDENTS, HUMAN DEVELOPMENT AND HIGHER EDUCATION IN SOUTH AFRICA of the research team developed a relationship with the students such that they remained in contact between interviews and arranged for interviews directly with the students. Interviews lasted between an hour and two hours. To signal the value of the time students were giving and the effort they were making, they were offered vouchers for shopping and airtime, as well as refreshments during the interview. Some students travelled significant distances to talk to us and were reimbursed for travel costs.
Each year the research team agreed upon the interview schedule. The first year involved asking students for a good deal of autobiographical information about family, school and community; about their experiences of getting into university; and, about their experiences of leaving home and being at university for a year (or two years in the case of Rural), including all aspects of studying and social and material living (e.g. food and accommodation). In subsequent years we would update information about economic circumstances and how they were progressing with their studies. We also reviewed the questions to probe further as we learned about what students valued about university and about what they were gaining or not gaining from the experience. For example, in 2018 we made a special effort to discuss what knowledge and understanding they were acquiring and how they were acquiring it. The final telephone interview focused on future plans, while the informal follow-up in 2021 focused briefly on who was employed or in further study.
Analysing the life-history data
All life-history interviews were transcribed, and the life-history data were analysed in four different ways:
1. The data were analysed thematically in NVivo qualitative data analysis software. This process began with the research team reading through selected first-year transcripts individually and then discussing these reflectively for emerging themes and agreeing on codes to create a code book as the basis for disaggregating data in NVivo. The code book was revised after the second round of interviews and then sustained for the rest of the project.
2. Theidentification codes were informed by adopting an inductive approach to prevent over-imposing our own framework onto the findings (Thomas 2006). All interviews were coded using grounded descriptive codes, for example, ‘family’, ‘community’, ‘school’, ‘significant others’, and so on, and then clustered into themes. The themes were categorised in various ways: as capabilities, as agency, and so on.
3. At this stage, we still maintained the distinction between what Bernstein (2000) calls the internal language of description, which is the language of the conceptual model (in our case, capabilities) and the external language of description, which are the empirical descriptions that students offered in their own words. Adherence to this distinction made us more open to the opportunities and freedoms that were emerging as central to students’ well-being, and we made constant modifications to our list in the light of empirical findings. The analysed thematic data lend weight to the Miratho Matrix discussed in Chapter 4.
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