Teachers and students relationship IN TEACHING and learning
Mathematics and ITS IMPACT in CLASSROOM
AN AUTOETHNOGRAPHIC INQUIRY
A Dissertation Proposal
School of Education
In Partial Fulfillment of the Requirements for the Degree of
Master in Education
Balkumari, Lalitpur, Nepal
31st June, 2012
TABLE OF CONTENT
TABLE OF CONTENT. i
CHAPTER I 1
Purpose of the Study. 6
Research Questions. 7
Significance of the study. 7
CHAPTER II 10
LITERATURE REVIEW… 10
Effective Teaching. 11
What is teaching?. 14
Interpersonal Relationships. 15
The socio-cultural context of classroom meaning. 18
Research Gap. 20
Chapter Summary. 21
CHAPTER III 22
METHODOLOGIES AND METHODS. 22
Methodology and Method of My Research. 22
Methodology and Methods. 22
Narrative Inquiry. 23
Personal Reflections. 23
Critical Research Paradigm.. 24
Ontological Consideration. 24
Epistemological Consideration. 25
Data Sources. 25
Theoretical Referents. 25
Critical Theory. 25
Variation Theory. 27
Transformative Learning. 27
Quality Standards. 29
Critical Reflexivity. 30
Ethical Considerations. 30
‘Some activities primarily affect future well-being; the main impact of others is in the present’ (Becker, 1993, p. 11).
Great teachers are not born, they are made. Beginning teachers become accomplished teachers, and skilled teachers become great teachers, by thinking hard about their teaching and finding ways to improve it. (Artzt, 2002)
Sometime around March 2012…
It’s “Such a lovely evening” I whispered, speaking to myself as I waited for the bus in a on cool March of 2012 evening for my university. As I sat and waited for the bus to come, which was unusually late on that evening and threatened to dampen my mood, my thoughts continued to wander, this time, about what our Professor Bal Chandra Luitel, PhD told us in our Research Methods class: “Start writing your stories…narratives…about yourself…your experiences and keep on writing.” Finally the bus arrived.“An empty seat! Great!” I almost uttered loudly as the bus is always full in the evening. As I sat down, my thoughts continued: “What do stories and narratives have anything to do with research and most especially in accomplishing my Re-entry Action Plan?” my scepticism is trying to win over my good mood. “Well I just have to write my stories and see what comes out of it”, I said to myself trying to sound positive this time. But how and where do I begin my story?
“Who among you here have heard the word “social distance” as teacher and student relationship in your learning or teaching experiences?” Sahara (name changed) asked this question during our first class in Research Methods in University. I raised my hands sensing that nobody was ready to speak about it. But raised I did. I have not only heard about it but had experienced, felt and got overwhelmed by it. Nevertheless, as days went by our discussions towards this subject continued to expand and flourish. As, I slowly began to understand this theory I asked myself “Was I just being too dramatic about my interpretation of social distance (teacher and student realtioship) or is my mediocre understanding of this theory trying to rule over me again?
Now, I know where to begin my story…
As a student’s of mathematics, I have to face different problems in the field of teaching and learning. As a student, it’s hard to understand the mathematical concept in simple and easy ways but on other hand as a teacher of secondary level to facilitate my students it’s hard to show and demonstrate the new concept as well as old concept in simplest form. As I heart from my elder, life start from murder because we are here in this world to kicked old and develop a new approaches on same ways, we must try to change our teaching and learning according to the need of nation and on easy understanding ways to reduce the social distance (teacher and student relationship) in teaching and learning mathematics.
Before joining to Kathmandu University, I’m not doing justice to my student and I’m not satisfies on my own approaches of teaching as well as learning it’s a just increase the high level of gap in teacher and student relationship. But now, my dimensions of teaching and learning have been changed on better ways like a good teacher which may reduce social distance. But now my hope and ability to show my performance is increase and about to satisfy on my own work.
Studying is a long life process, from where we develop our own personal skills knowledge and power to deal on different subject matter, and face different problems among them. To understand why such relationship in mathematics have surfaced in my questioning self, allow me to take you to my beautiful and not so beautiful experiences as I came face to face with this pedagogical approach.
I’m not happy at the beginning of the class of mathematics in my childhood because, i feel mathematics is boring subject and behave of mathematics teacher is not good and match able for me since my childhood. Mathematics as im/pure subject to do solve immediately and get solution at once therefore (Luitel, 2003), I don’t care about that so I guess mathematics as hard subject after sometimes my thought have been changed. I knew that the mathematics is not only the solving the problems of the given content but getting the empowerment in future. So at this time I categories mathematics in two ways i.e. one may be pure mathematics and another is mathematics educations. Both of have difference aspects and their own specific ways to define. But both of have their important in their area I supposed to told that both of them have their own importance in related field.
Now, I convinced that mathematics is not only to solve the problems in the context base but also I convince about its’ educational importance likewise why we are reading all mathematics problems just as in solving ways? What are its’ implication in day to day life? Is all knowledge in mathematics are not changeable? Is mathematics is just the transmission of the knowledge from teacher to student? And what are the main issues to create a social distance in mathematics between teacher and students? This sort of question arises in my mind so, i convince that mathematics has not only pure part but it is also having the important of philosophy part.
This is a journal, where I describe my autobiographical beliefs and thought as a student in school level to till now as well as i describe my critical thought( social distance) towards my mathematics teacher as well as subject matter in my childhood to Master level. I forgot the behave of my mathematics teacher more than that I forgot who taught mathematics in my primary level in my childhood but I just remember in mathematics I read about the number like 0, 1, 2, 3, ……, 100, binary, query, base 20 etc. I easily can tell that so my mathematics teacher treats me in next way then my entire friend and there is big gap between teacher and students. In that time, I think mathematics as playing doll and my mathematics teacher as remote controller because he just control us to waste the time, Moreover doll’s can be changed according to our desire and wants, that means if we want to make doll beautiful then we easily make it.
When, I completed class V in government school my father demotion my class and admitted me in private boarding school in class III that time I didn’t have any idea to demotion my class. When I got good percentage in Mathematics my father encouraged me to get better marks in all the subjects and my math teacher was like a symbol of truth for encouraging my further performance but he never encourage my friend who secure less mark then me. In that time I think mathematics is the easy subject because all the term and formulae are just repetition for me so, I got class first that time I think mathematics as easy subject. I continue reading when I was reading in class VI in private school, I found all of my school friends of government school were in class VIII so, I got forestation then I leaved private school and again joined in government school in class VIII at the end of the session at once, I join in final examination sitting with one of my old friend as well as coping his all subject matter except Compulsory English in this stage I don’t know the behave of mathematics teacher in that school. When result was published I got the pass, so I’m happy to upgrade my class.
Now, my secondary level of education started but I don’t know how much I have to face the struggle just being happy and stay in class IX. The mathematics teacher of secondary level of that school seems like frightful man (Dangerous Man). I afraid even look to him which create a big gap between him and me. He came in class and say something and try to understand his language but couldn’t and couldn’t able to solve even any problems that time i think mathematics as dream girl like angel and mathematics teacher as Ghost. Angel may not see so I think mathematics like dreams. When I secure zero marks in examination I feel bored about mathematics and guess how I can secure good marks. And came up question on mind, which factor disturb in my reading? By the time I completed my class IX getting zero marks in mathematics. My father may not pay any attention to upgrade my progress. I was good in the entire remaining subject except Mathematics. So my mum make plan to send me to my sister home, near to my sister home there was one the best mathematics teacher whom is my school mathematics teacher where I’m studying so by according to the plan of them I been sent to my sister home near to my own area and I join with that mathematics teacher. He changed my ways of thinking power and able to get good marks in S.L.C. Those times in my thought towards mathematics teacher have been changed and his behave towards me.
After completing S.L.C. (School leaving Certificate), I became able to continue my study in mathematics that time I think mathematics as interesting subject to make active in learning. But when I was in Bachelor level of second year again I got frustration in mathematics because of a same issue i.e. behaves of a mathematics teacher towards me, But till I continue in search of each mathematics application in real world and why the behave of mathematics teacher to create bad relationship in between teacher and student as well as it impact on the outcomes of the performance of both teacher and student too in mathematics. If I’m able to search that sort of implication I guess I become the good mathematics teacher of Nepal for Nepali people.
In my thought my mathematics teacher as frightful man, he always frighten me in various part of his class. He enters in class with stick to beat us. That time I guess he is not teacher but he is like an animal in my school level. I think he only came in our class just for to beat us. I don’t understand his languages of teaching because of his behave towards me. I just want to be escape from him so, that I miss my class sometimes to be escape from him, as well as mathematics as meaningless formulae and useless.
All the critical and reflective though towards mathematics is differing in context for create bad relationship with teacher and student in mathematics. When I secure good marks that time I become happy and my reflective and critical though is positive even though for mathematics teacher too and if I secure less marks in the examination that time opposite. These all situations say about the nature of mathematics and reflective and critical though towards mathematics which may be different for each individual in the present context of Nepal.
Mathematics is a subject which seems to be hard subject in the context of Nepal but I guess in other country also have the same problems in mathematics for creating the high level of relationship with teacher and students. Students feel mathematics as hard and usually they face the mis-concepts on the subject matter which create the distance in mathematics. In my view it is easy to discuss and hard to define which part is creating social distance in mathematics in classroom.
Purpose of the Study
The main purpose of the study will be to explore the problems and challenges incurred in teaching and learning mathematics in classroom. More specifically, the research would enabled me to identify the reasons as to why students feel mathematics as difficult subject, teachers failed to create mathematics as learner-friendly. And this research project had enabled me to suggest the viable pedagogy so as to enrich the present mathematical pedagogy to reduce bad relationship in between students and teacher in classroom.
This study will draw on an autoethnographic tradition. An autoethnographic study allows me to position my life experiences and my role identity, beliefs, knowledge and teaching practice. This study will therefore focus on the following research questions:
- Question 1: What are my beliefs as student and mathematics teacher about mathematics, mathematics learning and mathematics teaching?
- Question 2: What factors have led to teachers’ beliefs about the learning and teaching of mathematics?
a) What biographical factors have led to me?
b) What are inhibiting and enabling factors exist in classrooms in relation to a relationship of teacher and student of mathematics teaching in classroom?
Significance of the study
My study (research) investigating teacher beliefs concerning the nature of mathematics, mathematics learning and mathematics teaching, the usefulness of the study lies in its ability to verify conclusions, and extends the ambit of teacher beliefs in the areas of learning and teaching mathematics. Not only the study provide thematic descriptions of teachers’ beliefs but it also identifies factors, both biographical and contextual, that have had an impact on their beliefs to create social distance in mathematics teaching.
My study proved to be of value to the four teacher-participants who were interviewed and wrote journal entries. Firstly, the study provided these teachers with an opportunity to articulate their beliefs about mathematics, mathematics learning and mathematics teaching and to reflect on their beliefs. This was the first time that each of these teachers explicitly expressed their beliefs on a range of teaching-related issues and the process of so doing appeared to bolster their willingness to consider and commit to a range of teaching strategies they had not previously considered in their classrooms as a main issue to create social distance.
This study has had a personal significance for me. As a researcher, I have learned a great deal about qualitative research methodology, having only dabbled with quantitative methodology (questionnaire analysis). The findings in my study have confirmed, albeit on a limited basis, the results I expected to find initially. My understanding has been considerably extended as to the reasons underlying teaching practice and teachers’ beliefs. I have also realized that beliefs and practice exist in a dialectic relationship, each affecting the other in iterative and incremental ways which may reduce social distance in mathematics teaching.
As a practitioner, I have been made fully aware of the constraints and enabling factors involved in adopting a constructivist approach in the secondary level classroom. As a result of this study I feel freshly committed to developing a (judiciously) eclectic approach to my teaching to replace my purely transmission approach and reduce social distance at the time of mathematics teaching.
There are various factors that restrained in limiting my research project. I would like to expose them as-
i. Since, the time duration to accomplish the project was six months and thus I being a full time working student had difficulties in devoting the full time in studies which might have restrained me in exploration of ideas through far and wide.
ii. My research project tried to find the real problems of Nepalese students and teachers in mathematical pedagogy to create social distance in mathematics teaching in classroom but it was confined within Kathmandu Valley and Some Village area in Dolakha.
iii. Due to time constraint and inadequate financial budget my research project was confined to small samples.
iv. My literature review might have not found suitable rooms to befit in Nepalese context as most of the reviewed literatures were of western cultures.
The literature review chapter opens with the thematic review of the related literature and ends with conceptual framework of the study. In this chapter, I attempt to review related literature categorically in three levels: the thematic information, the theoretical reviews and the earlier related research work followed by a conceptual framework for analyzing teachers’, student’s relationship with their behaviors that emerge as outcomes from influence dissatisfaction. To this end, I collected the contextual themes in the literature that I needed for the research, and explored the existing information on my topic areas. The collected authentic pieces of information about teachers and student’s relationship and its impact in mathematics teaching, support the findings, and show the relation with the research themes.
Further, the literature review provides the background and contexts for the research problems. Wiersma (1995) observed, “It establishes the need for the research and indicates that the writer is knowledgeable about the area” (p.406). It presents various ideas and opinions of the various renowned scholars on relationship between teacher and student in Mathematics teaching and elements of behaviors as a backup for the themes of the case study.
The main purpose of review of literature was to enhance the present level of personal understanding of the related concepts and practices governing level of relationship between teacher and students and its impact in Mathematics teaching. For this, the total task has been performed from two perspectives – review of theoretical perspectives, and review of related studies. Accordingly, this chapter has been developed in two sections comprising of these two aspects respectively.
One of the primary concerns for educators is effective teaching. However, effective teaching is an elusive concept and it is not easy to identify the specific teaching characteristics that are considered as effective (Harris, 1998). Ingersoll (2001, p.42) noted that “there is surprisingly little consensus on how to define a qualified teacher”. Although there is not a common definition for effective teacher, there are vast numbers of researchers who attempted to define characteristics of effective teachers (Harris, 1998). Centra (1993) characterizes effective teaching as; good organization of subject matter and course, effective communication, knowledge of and enthusiasm for the subject matter and teaching, positive attitude toward students, fairness in examinations and grading and flexibility to approach teaching. Sherman (1987) identifies following characteristics, some of which are similar to those were mentioned by Centra:
1) Enthusiasm (pleasure in teaching; love of and interest in the subject)
2) Clarity (clear explanation of concepts; systematic presentation of materials)
3) Preparation and organization (detailed course outlines; established course objectives; good definition of evaluation procedures)
4) Stimulation (stimulation of interest; ability to motivate students)
5) Knowledge (grasp of subject matter)
Sheffield (1974), in his book “Teaching in Universities: No one way”, summarizes the most often mentioned effective teacher characteristics as follows:
Master of his/her subject, competent
Well prepared for the lesson
Relates subject to real life, practical
Encourage students’ questions and opinions
Enthusiastic about his/her subject
Approachable, friendly, available
Concerned for students progress
Has a sense of humor, amusing
Warm, kind, sympathetic
Uses teaching aids effectively
According to Darling-Hammound, Wise and Pease (1983), the effective teacher must have mastered the ability to teach. This ability includes the skills needed to transmit knowledge, skills, and attitudes from teacher to student. The ability to develop an atmosphere that encourages student learning can also be considered within this category. Knox and Mogan (1985, p.26) defines characteristics of effective teaching by categorizing behaviors identified as effective into five broad categories:
a) Teaching ability: The process of transmission of knowledge, skills and attitudes, and the creation of an atmosphere in which this is done.
b) Professional competence: The teacher’s theoretical and practical knowledge used in teaching as well as the teacher’s attitude toward the profession.
c) Evaluation of students: The type and amount of feedback the student receives from the teacher.
d) Interpersonal relationships: A state of reciprocal interest or communication between two or more people.
e) Personality traits: The totality of individual’s attitudes, emotional tendencies and character traits, which are not specifically related to teaching or interpersonal relationships but may affect both.
These five categories are determined as a result of a broad review of the literature and they encompass all aspects of teaching characteristics (Knox and Mogan, 1985). Therefore these five categories are used as the organizing framework for the following discussion of effective teaching.
The instrumental and technical aspects of teaching and teacher education are well documented in the research literature. In the last century, significant emphasis has been put on studying causal relationships between teaching and learning. The focus of many educational researchers appeared to have been on the designing of teaching and learning aids. Comprehensive and ingeniously designed experimental research methods were developed to gauge almost every ‘measurable’ aspect of the classroom practice. However, not until the last couple of decades of the last century, almost no attention was paid to studying the subjective aspects of teaching and learning. The influence of the scientific method on educational research might have caused many to believe that the subjective aspects of teaching and learning are unresearchable. This literature review aims to assist us to take a second look at teaching, in a global context, and the crucial role it plays in every phase of human development. In particular, this review explores three main concepts, or theories, that make up the theoretical framework of this study. Firstly, I will try to gain a thorough insight into the concept of teaching with better relationship with student. Starting with a brief chronological overview of the development of teaching as an art, Secondly, I will have a brief look at the notion of constructivist teaching with regard to its role in helping teachers and students achieve the best out of their practices in the classroom. In the last part of, I will take a brief look at hermeneutic phenomenology in an attempt to give us an appreciable degree of understanding of the extent in which this method is being employed in researching the lived experiences of teachers.
What is teaching?
Teaching: A Historical Overview
Education is a product of human Cultural Revolution. It was only able to develop among human beings after the invention of some sort of spoken language during prehistoric times. It began at the primitive camping sites of early Homo sapiens where parents and adults taught the young basic survival skills such as making simple tools and weaponry. The act of teaching was the paramount means that transformed these hunting and gathering life forms into the more sophisticated human forms that we know today. Before the evolution of writing, teaching was an informal practice. Parents and adults had to repeat orally what was to be learned until the young had memorized it. The invention of different systems of writing by the Sumerians and the Egyptians between 4000 – 3000 B.C. (World Book, 1999) marked an era of knowledge explosion, the beginning of formal education.
The early form of formal education, apparently, had been inseparable from religion. Most of the early teachers were priests, prophets and scribes, and their task was mainly to teach religious sacred writings to sons of high-class families. From the Sumerians and the Egyptians, the act of teaching spread civilization to Greece and Rome. By 400 B.C. the education of the Greeks had advanced to produce subjects such as logic, mathematics, science, history, and public speaking (World Book, 1999). Athens produced famous philosophers and teachers such as Plato, Aristotle, and Socrates who laid the foundations of western philosophy (Castle, 1970). Based on the old Greek system of education, the Romans had built an extensive education system in which they excelled in other fields such as law, agriculture, and engineering. By 200 A.D. (World Book, 1999), the Roman culture of education had covered much of the Western world. During the 1100s, teachers’ guilds in cathedral schools led to the establishment of modern universities in Europe (World Book, 1999). By the arrival of the Renaissance in the 1300s, the people of Western Europe showed a renewed interest in democracy and independence. Classical humanist scholars such as Desideratum, Erasmus emphasized the idea that the main purpose of education was to train well-rounded, cultured citizens (World Book, 1999), or the education for wholeness (Castle, 1970). In the 1500s, the work of great teachers such as Galileo Galilee resulted in increasing demands for the teaching of physical and natural sciences in schools and universities. At the same time, John Locke and other great teachers from the behavioral sciences pursued further into understanding human behaviors. The resulting Industrial Revolution realized even greater demands for teachers and better schools. The 1700s and 1800s saw an increase in state-owned education systems in Europe. Teachers were now well trained. Famous teachers and renowned scholars such as Isaac Newton, Jean Piaget, and John Dewey continued to mould the human understanding of themselves and the world. We, teachers of today, learn from the writings of these pioneers. Their shrewdness and ingenuity had left us with a rich history of human achievement and feats. From their writings, we learn of their ideas and accomplishments. Surprisingly, though, we do not know much about their lives as teachers and their experiences in their classrooms. Perhaps it is our part, our contribution to this educational journey, to probe further into our own lived experiences in order to understand the human qualities that make us teachers. By so doing, we will lay open the reality of teaching to be understood and refined by generations to come.
Interpersonal relationships can be defined as interactions between/among groups and individuals. Good interpersonal relationships include empathy, honesty, trust, tolerance, awareness, and the setting aside of self (Collinson, 1999). Some of the researchers investigated the opinions of students and teachers to find factor of effective teaching and found that teacher’s interpersonal relationships play a role in the teachers’ effectiveness (Collinson, 1999; Walsh & Maffei, 1994; Witty, 1947 (cited in Bossing)). In addition to this, there are researchers who investigated the correlation between students’ perception of teachers’ interpersonal relationships and their evaluation of teacher effectiveness (Teven & McCroskey, 1997). Collinson (1999) interviewed with a group of teachers who identified as excellent. They stated that effective teachers can maintain good interpersonal relationships with the students, other teachers, and the community (Collinson, 1999). According to Walsh and Maffei (1994) the relationship between the student and the teacher is an important factor for teaching effectiveness. The relationship can affect education in three ways. First, a good student-teacher relationship makes education more enjoying experience for both teachers and students. Second, a good relationship improves student evaluations of teachers. Finally, a good relationship enhances student learning. Walsh and Maffei(1994) developed an instrument of 46 items in order to identify behaviors that affect the student-teacher relationship according to students’ and teachers’ perceptions. Most rated five behaviors that students identified as enhancing the student-teacher relationship include treating students equally regardless of race and sex, learning the students’ names quickly, showing patience in explaining points to students, treating students as equals, and smiling and displaying friendly demeanor (Walsh & Maffei, 1994). For each behavior that was identified as enhancing student-teacher relationship, female students ranked the behavior as more important then male students did. As cited in Bossing (1952, p.524), another study of interest about this dimension is conducted by Witty (1947). From nearly 12000 letters written by children on “The Teacher Who Helped Me Most” the following traits are listed in descending order of mention
1) Cooperative democratic attitude
2) Kindliness and patience
3) Wide variety of interest
4) Good appearance and pleasing manner
5) Fairness and impartiality
6) Sense of humor
7) Good disposition
8) Interest in pupils problems
10) Use of recognition and praise
11) Superior teaching efficiency.
Caring is another behavior that influences the student-teacher relationship. According to Teven & McCroskey (1997), caring may be defined as “good will” or “intent toward the receiver”. They designed a study to correlate student perception of teacher caring with teacher evaluations, course content evaluations, and learning. They asked a sample of 235 university students to complete a series of questionnaires. Results indicated that students who perceive their teachers as caring gave higher evaluation scores to those teachers, the course content, and amount of learning as a result of his study which is designed to find the effects of physics teachers’ characteristics on students’ attitudes, motivation and achievement, concluded that teachers should; Be enthusiastic in teaching because students can easily notice whether the teachers are willing to teach or not. Have a smile in their face, Take care of students’ gender, age, current achievement, motivation and attitude. The studies mentioned above revealed that behaving students in a friendly way, showing interest in their problems, showing enthusiasm in teaching, fairness and impartiality, learning their names quickly and treating students equally are examples to effective characteristics related to interpersonal relationships dimension.
The socio-cultural context of classroom meaning
In order to consider meaning-making in mathematics classrooms for participants, both individually and collectively, we have to recognize its dependence on individual experience and socio-cultural practices. This is the subject of an area of study known as Activity Theory, originated by Russian psychologists in the Vygotskian tradition, and developed with rather different emphases by socio-cultural theorists in the United States and Europe. Referring to Leont’ev (1981), Crawford (1991) suggests that Activity Theory “describes the process through which knowledge is constructed as a result of personal (and subjective) experience of an activity. Leont’ev stresses the inseparability of human mental reflection from those aspects of human activity that engenders it.”
The relationship between a constructivist approach to mathematics teaching and social and cultural norms in mathematics classrooms is explored by Cobb et al. (1991). Their paper offers a critique of Activity-Theory, both in its Russian and American manifestations, and in particular the related socio-cultural movement currently exciting educational interest in the United States. They address the work of Ilyenkov, in the Russian school, who suggests that ‘objects as cultural tools serve as carriers of meaning’ i.e. carrying meaning for their use in a practice. These objects include formal mathematical symbols, and so ‘these symbols are for him cultural tools that carry meaning’. A consequence of this is the view that ‘children’s development of abstract mathematical thought is supported by instruction designed to engage them in the social practice of using formal symbols’.
This reminds me of the classroom work of David Hewitt (Open University, 1991) involving his ‘rulers’ activity to influence students’ perceptions of algebra and their familiarity with formal symbols. It is well known that pupils have difficulty with the abstract use of symbols and their manipulation. Hewitt’s very stylized approach is designed specifically to overcome such difficulty by creating a social practice in which symbol manipulation is logical and meaningful and in which attention is attracted away from the symbols and their use, rather than towards them.
Socio-cultural theorists view learning as integration into a community of practice in which social actions are identified and classroom activities designed. Cobb et al suggest that “the teacher’s role in this activity is to fashion the last link in the chain by ensuring that children execute the specified social actions that make it possible for them to isolate ideal mathematical forms when they solve tasks”. Social actions are seen to be more broadly based than social interactions. Thus the interactions of children in classroom activities are a small part of their enculturation into the required social actions. This is reminiscent of Bruner’s work on scaffolding, with the teacher performing the role of ‘consciousness for two’ (to do for students what they cannot yet do for themselves) in relation to Vygotsky’s Zone of Proximal Development which also make a better relationship of teacher and student in mathematics classroom.
Constructivist theorists, in general, believe in construction of knowledge by participants being engaged in the activities. They believe that children are not like the black box as behaviorists assume but they come with some prior knowledge constructed by them. “Constructivism is founded on Piaget’s belief that learning is an active process, where new information is accommodated into previously understood meanings or mental images” (Chambers, 2010, p. 101). On the other hand “Behaviorist theories of learning emphasize the effect of punishment and rewards in learning and assume that students are like black box” (Chambers, 2010, p. 99).
When I went through an article ‘A Synthesis of Different Psychological Learning Theories by Dahl (n.d.), I came to know the difference between Piaget’s and Vygotsky’s constructivism. I tried to understand Vygotsky’s constructivism because according to my research purpose I tried to focus more on social-cultural dimensions and its influence on relationship between teacher and students in mathematics classroom and teaching. Vygotsky’s constructivism also called social constructivism focuses on social and cultural environment of learning which has a vital role on the learning process.
In this research study, I am trying to be a qualitative-interpretive researcher. As such, I tried to make my research study rich in description and try to give more emphasis on relative truth, participants’ context and understanding. Ernest (1991) argues, “Social constructivism views mathematics as a social construction” (p. 42) and “identify mathematics as a social institution, resulting from human problem posing and solving” (Ernest, 1991, p. 281). My research study has focused on socio-cultural dimension. I believe that every educational institution is a part of society. So, every member of the society is guided by social norms and values. According to them, an individual creates knowledge according to their understanding and social activities. Constructivist theory of learning in qualitative research believes that there is not a single truth; rather all truth is relative and constructed by the individual or society. So, as a researcher, I engaged in interaction with participants to get the ideas on my research topic. Similarly, participants generated the knowledge and meaning from their experiences and their ideas regarding the research topic.
I went through many related materials and theses for literature review regarding relationship between students and teacher and its impact in classroom. I found rarely studies regarding this issue. My research study tried to explore the ideas on how socio-cultural and pedagogical factors influence relationship of teacher and student in mathematics education. Further, it tries to explore the ideas on how policies and programs are helpful for their better participation in mathematics education. So, my research will contribute to fill the gap between teacher and student distance in mathematics education exploring the ideas on socio-cultural and pedagogical dimensions.
In this chapter, I reviewed different literatures related to my research issues. I went through different literatures regarding socio-cultural dimension on relationship of students and teachers, its impact in teaching mathematics. Similarly, I went through the literatures concerning school mathematics pedagogy and educational programs and policies.
METHODOLOGIES AND METHODS
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 teaching. 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 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 high level of bad/good relationship with teacher and student in teaching and learning mathematics in classroom
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.
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 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 ways.
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. So, I have chosen critical research paradigm as my research paradigm. The paradigm of criticalism uses a transformative ontology of critical selfhood and enables me to critically examine assumptions, values and beliefs invisibly embedded in my thinking and action.
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 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.
The notion of reality about this research may not be 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.
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. I try to use stories and poems writing of my experiences as a mathematics learner/teacher and try to reflect it critically in my own learning experiences.
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.
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 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 offers a multidisciplinary approach to society which combines perspective drawn from political economy, sociology, cultural theory, philosophy, anthropology, and history. 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, 2009). It is a meaning making process through reflexive voice of practitioners.
Constructivism, though it began as a theory of learning, has been used as framework of 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 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 to reduce the social distance in class room teaching in mathematics.
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. 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.
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.
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:
The degree by which the reader can tell how true and realistic the stories I am unfolding is defined by this quality standard. 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.
Bryman (2004), transferability is how the research findings are applicable and similar to others across educational settings. Hence, in this research, using stories and 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.
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. 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.
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 social distance in mathematics 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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