Methodology and Method of My Research (SOCIAL DISTANCE IN TEACHING AND LEARNING MATHEMATICS AND ITS IMPACT IN CLASSROOM, AN AUTO-ETHNOGRAPHIC INQUIRY)

Methodology and Method of My Research

This chapter shows overall framework of my research so I am trying to show my research according to my research methodology. This chapter presents my research methodology, research method, quality standards of my research, my ontology of research, epistemology, axiology, ethical issues, and different theoretical referents together with data sources of my research.

Methodology and Methods

It is an auto-ethnography that enters into my own lived experience as a mathematics learner and teacher in the term of creating social distance in classroom. Auto-ethnography comprises three words- auto, ethno and graphy which signify the textual representations of one’s personal experiences in his/her cultural contexts (Luitel, 2009, p. 35). Auto-ethnography provides opportunities to the development of learner and teacher as well and to understand the very possibility of the method that arises from the embodied nature of researcher’s experiences. An auto-ethnographic methodology that centers on my own lived experiences as a learner of mathematics and as a classroom teacher of mathematics will be adopted as a framework to answer my research questions. Creswell (2008, p. 475) defines auto-ethnography as “a reflective self-examination by an individual set within his or her cultural setting (context). According to Ellis (2004, p. 37), it “refers to writing about the personal and its relationship to culture. It is an autobiographical genre of writing and research that displays multiple layers of consciousness”. Using auto-ethnography, therefore, allows me to critically reconstruct and deconstruct my held beliefs that will define the real meaning of my lived experiences. My approach to auto-ethnography in this research design focuses on investigating my lived experiences of teaching and learning, as both child and adult (Afonso & Taylor, 2009). However, according to Taylor (in Afonso & Taylor, 2009 p. 4) “auto-ethnography is not simply an autobiographical study of idiosyncratic self who has been separated out somehow from her own culture…”  It will help me understand how I may explore my culture which may have always influenced the belief I hold towards social distance in teaching and learning mathematics in classroom. Autobiographical research refers to a family of related forms of self study, including auto-ethnography (Ellis, as cited in Belbase, 2006).

An auto-ethnography, perhaps, seems to be one of the appropriate methods of study my own practice as I am the primary source of data. This auto-ethnographic research is also very much useful tool for improvement of my personal and professional practice. The notion of the dialectic becomes important only within a commitment to emancipation, one that seeks to liberate … in both subjective and objective terms (Taylor, 2007).

Narrative Inquiry

            In an effort to relate my lived experiences as a learner of mathematics and a classroom teacher of mathematics, I believe that a narrative inquiry is the appropriate method to be used in this study. Stories and conversations shall be my way of unfolding and finding meaning in my lived experiences (Cohen et al., 2000). Creswell (2008, p. 512) asserts that a narrative research design “focuses on studying a single person, gathering data through collection of stories, reporting individual experiences, and discussing the meaning of those experiences for the individual”. Using narrative inquiry in this study allows me to reflect on my own pedagogical experiences and uncover the construction and reconstruction of my personal and social stories in a more meaningful way (Pinnegar and Daynes 2007).

Personal Reflections

            I shall engage myself in critical reflection about the meaning of my past, present and future possible experiences as I come face to face with what truly are my beliefs and assumptions towards social distance teaching and learning practices in mathematics in classroom and improvement in my teaching praxis.

Critical Research Paradigm

            Ontological, epistemological and methodological considerations of critical research paradigm are ‘historical realism’, ‘transactional and subjectivist’ and ‘dialogic and dialectical’ (Guba & Lincoln, 1989). The present contour of reality is taken as the transactional and subjective reality. The main role of critical researcher is to be changing agent of society. Positivistic paradigm offers no space for articulating the researcher’s unfolding ‘self’ during the research process (Luitel, et. al., 2012). So, I have chosen critical research paradigm as my research paradigm. The paradigm of criticalism uses a transformative ontology of critical selfhood (Kincheloe, 2003) and enables me to critically examine assumptions, values and beliefs invisibly embedded in my thinking and action (Kincheloe, 2010).

Interpretivism

            I used interpretivism as a supportive research paradigm. It has emerged in the social sciences to break out of the constraints imposed by positivism. Interpretivism, as Taylor, Settelmaier, and Luitel (2012, p.) claim, “is concerned primarily with generating context-based understanding of people’s thoughts, beliefs, values, and associated social actions”. As an interpretive researcher, I have attempted to seek for clarification, understanding, and extrapolation to similar situations of the status of reflective writings in my research.

Ontological Consideration

The notion of reality about this research may not single. Different learning and teaching strategies are my assumptions (constraint). Ontology of change/motion rather than ontology of rest/statics is my preference thus my assumption of reality is related to science. Ontological assumptions concern the very nature or essence of the social phenomena being investigated (Cohen, et al., 2002).

Epistemological Consideration

The notion of epistemological considerations is the very basis of knowledge, its nature and forms, how it can be acquired and how it can be communicated to other human beings (Cohen, et.al, 2002). I try to use stories, poems and different art-based writing of my experiences as a mathematics learner/teacher and try to reflect it critically in my own learning experiences.

Data Sources

This research is an auto-ethnography. So I am the primary source of data. My data sources are narrative writing, diary, reflections, my different historical images, story and some semi-factual writings and pictures.

Theoretical Referents

            Using the interpretive paradigm as a perspective on how I view my lived experiences that will re-examine the underpinning beliefs I hold towards social distance of mathematics in classroom teaching and learning practices, for making my theoretical standpoint clear i have used some theory as my theoretical referents. From the help of some theories and literature i tried to make my narratives clear. Those theories are as below;

Critical Theory

            Critical theory offers a multidisciplinary approach to society which combines perspective drawn from political economy, sociology, cultural theory, philosophy, anthropology, and history (Bronner & Kellner, 1989). Thus critical theory can emancipate people from different disciplinary boundaries and critical theory is concerned with creating societies free from dehumanizing policies and practices that perpetuate social injustice, cultural exclusion, social inequity, racism, sexism, ageism, scientism and many other forms of repression (Taylor, 2012). It is a meaning making process through reflexive voice of practitioners.

Constructivism

Constructivism, though it began as a theory of learning, has been used as framework of much research to improve teaching practices, particularly those of science and math (von Glasersfield 1995). This pedagogical framework has made an impact in education particularly on learning theories and teaching methods in science and mathematics (Treagust, Duit & Fraser, 1996). A constructivist view of learning emphasizes that students construct their own knowledge using their own prior knowledge and experiences (Gunstone 1995). As a referent in doing this study, I shall embrace the four essential criteria to characterize my constructivist teaching practices to reduce social distance in teaching mathematics in classroom: eliciting prior knowledge, creating cognitive dissonance, application of the knowledge with feedback and reflection on learning. Using these criteria, I believe, allows me to recognize whether or not my pedagogical practices. As an interpretive researcher and writing as self-inquiry, the activities I will be involved in (forming research questions, making sense of my experiences, writing the research report) are framed. As I make sense of the beliefs I hold towards teaching and learning classroom practices I call on my lived experiences and the continuous learning process I am engaged in while doing this self-study. In doing so I will constantly ask myself whether the knowledge I produce is useful and viable as I try to find the answers to my questioning self. According to Taylor (1996), the quality of knowledge I may produce in embracing this theoretical referents depends on: (1) my ability to sustain and resolve my perplexity, (2) the quality of my communicative relationships with others while trying to understand their understanding; and (3) my ability to engage in critical self-reflective thinking about the quality of my knowledge construction process.

 Variation Theory

Variation theory has its roots in phenomenographic research which accounts for how the same things or same situation can be seen, experienced and understood in a number of qualitatively different ways (Runes son, 2005). Some ways of experiencing are more powerful than others. So the way something is experienced is fundamental to learning. Variation theory seeks to account for differences in learning and describes the conditions necessary for learning. From a variation theory position, learning is defined as a way something is seen, experienced or understood. Central to this theoretical position is that the learner, in one way or the other, experiences that which is learned. Education aims at developing the learners’ capability to handle various situations; to solve different problems and to act effectively according to one’s purpose and the conditions of the situation.

Transformative Learning

Transformation comes from understanding the system of profound knowledge (Daszko & Sheinberg, 2005). The transformed individual perceives new meaning to his/her life, to events, to numbers, to interactions between people. Once the individual understands the system of profound knowledge, he/she will apply its principles in every kind of relationship with other people. Transformation is not for the other person to do, but for every individual to take personal responsibility to help create new futures, to ask questions, to take risks, and to make a difference. According to Daszko and Sheinberg (2005), transformation occurs when people create a vision for transformation and a system to continually question and challenge beliefs, assumptions, patterns, habits and paradigms with an aim of continually developing and applying management theory, through the lens of the system of profound knowledge.

Quality Standards

To represent the quality standards of my research, I suggest that the rigor of this narrative inquiry shall be judged and evaluated on the following criteria:

Verisimilitude

The degree by which the reader can tell how true and realistic the stories I am unfolding is defined by this quality standard (Ellis and Bochner 2000). Using my own experiences as the primary data in this study challenges me with the degree of connectedness I may evoke with the readers. Self-study, according to Bullough and Pinnegar (2001) should ring true and enable connections. Therefore, the need to provide vivid descriptions of my own experiences and detailed information of the places and people involved in my stories and conversations is highly essential.

Transferability

Bryman (2004), transferability is how the research findings are applicable and similar to others across educational settings. Hence, in this research, using stories nand conversations I shall take the readers – which could be pre-service teachers, in-service teachers, teacher educators or even researchers – as I recount the lived experiences that I have had in my teaching praxis – experiences which they can identify with and eventually. However, in order for me to establish transferability in this self-inquiry, I should be able to provide extensive and careful descriptions of the time, the place, the context, and the culture which bring my experiences together and weave these into narratives that invoke the reader’s pedagogical thoughtfulness . That is, to engage the reader’s my stories should be able to establish a degree of similarities between my situations and the reader’s situations.

Critical Reflexivity

Being able to critically reflect my own beliefs and practices engages me into the act of pedagogical thoughtfulness in the hopes that students, teachers and teacher educators will come to realize the importance of being reflective in one’s own belief and practices. Therefore in this self-inquiry, understanding the relationship of my constructivist belief and classroom practices plays a vital role in encouraging the readers to think about the educational issues underpinning their pedagogical practices. According to Brookfield (2000 p. 33), “critical reflection focuses on adult educators as inquirers into their own, and others, practice.” Hence, engaging in this process will allow me to critically examine and ask questions the classroom beliefs and practices that I was exposed to as a learner, as well as beliefs and practices which I may have promoted in my classroom as a teacher and a teacher educator. The notions of ideology critique and pragmatist constructivism are amongst the traditions emphasized in the process of critical reflection (Brookfield, 2000). The former allows me to challenge the dominant and hidden ideologies, beliefs and assumptions, such as the issues of language and traditional science classroom practices, embedded in my culture as a learner and as a teacher. The latter emphasizes the role I play as I construct and deconstruct my experiences and meanings (Brookfield, 2000).

Ethical Considerations

      Anderson (1998) emphasize that all studies which involve people should consider ethical issues and responsibility of the individual researcher to see to it that any risk which may affect the community or the individual involved in the study is minimized. Ethical issues in educational research, according to Burns (2000) may come from various sources. They can be from be the nature of the study itself, the procedures to be adopted, the methods that will be used to collect the data, the type of data to be collected, what is done with the data and how these all data will be presented. Researchers should also be aware that each stage of the research sequence may be a potential source of ethical problems (Cohen, Manion et al. 2000). Therefore, in this research, we shall be aware of the ethical responsibilities involved in this research. As researchers, according to Denzin (1997) (as cited in Ellis 2004 p. 149), “ethnographers should operate under an ethic of care, solidarity, community, mutuality, and civic transformation.” Doing self-studies in education may reveal the problems and issues that make someone an educator (Bullough and Pinnegar 2001). In an attempt to investigate the sources of my held belief towards constructivist teaching and learning practices, we may have to examine and contest the curriculum and programs offered by my institutions. In doing so, sensitive issues may be revealed and confronted. Yet, I claim the full responsibility for whatever I write and disclose. On the other hand, Josselson (2007, p. 537) asserts that “narrative researchers have an ethical duty to protect the privacy and dignity of those whose lives we study to contribute to knowledge in our scholarly fields.” Hence, in this study, I shall take extra effort to ensure that the anonymity and privacy of these individual are upheld. This shall be done in order to maintain the confidentiality and privacy throughout the research (Josselson 2007).In writing my negative experiences I may have to change some details around, such as the names of the people, places and institutions. I also concede that in trying to examine my beliefs and understanding of my realities places me at a risk of being subjective. For example, I may choose to reveal only those experiences which have relevance and meaning in study. I am also aware that retelling my personal stories and exposing my beliefs, it can also be the source of my professional growth (Ellis and Bochner 2000).

I shall also consider the integrity of this self-study to be of high importance. I shall try to be unbiased, accurate and honest as I try to narrate my lived experiences. Allowing my stories and conversations to be read by my colleagues will be considered so as to add to the credibility and authenticity of this study. Doing this also gives me the opportunity to acquire their views, suggestions and truthfulness of the situation presented. Their suggestions shall be properly noted and will be incorporated wherever possible and necessary. All the individuals and institutions which will be involved in this self-study shall be properly acknowledged.

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