Exposing The Conscious Self Education Essay

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A growing body of research on mathematics teachers knowledge, beliefs, attitudes, practices, and professional development are framing our conceptualization of what it means to become a mathematics teacher (Brown & McNamara, 2011; Leatham, 2006; Lee, 2004; Wood, Cobb & Yackel, 1991). The impetus of such a corpus of studies is to gain an in depth understanding of the dynamic and complex processes that characterize the daily practice of teaching in the mathematics classroom. Lester (1994) draws attention to the ongoing under-representation of research that specifically explores the affective and emotional predispositions of teachers predominantly while engaged in teaching through problem solving. In particular, he points out that very little of the literature on mathematical problem-solving instruction discusses the specifics of the teacher's role or the teacher's perspective of that role .Equally under-represented in the literature are studies on how teachers frame their identity in the context of teaching. Interestingly, this vacuum in research input is inconsistent with the prominent role problem solving plays in the current reform movement in mathematics education (NCTM, 2008).

Globally, current reform recommendations in mathematics education emphasize a problem solving perspective to teaching mathematics as the principal instructional technique to enhance students' explorations of vital mathematical content (Francisco & Maher, 2005).. This perspective necessitates that teachers understand "authentic" problem solving before guiding their students through the process. However, given the differential training during initial licensure and teaching preparation programs teachers might not have opportunities to experience robust mathematical problem solving adequately as a disciplined topic or as way of thinking and reasoning to make them comfortable enough to adopt in their teaching.

Another factor to consider is the relationship between teacher's beliefs and practice while engaged in the act of teaching a mathematical content. There is ample evidence in the literature that beliefs about mathematics and its teaching play a significant role in shaping their classroom behaviors (Chapman, 1997; Richardson, 2003; Sanger & Osguthorpe, 2011). It has been argued that significant and meaningful teaching reforms are unlikely to take place unless teachers are willing to engage in metacognitive self-dialogue continuously challenging beliefs they deeply hold about practices for mathematics. Implicit in this relationship between teachers' beliefs and practices is a focus on self-understanding vis á vis teachers' thinking and behaviors. Specifically in teacher-centered educational settings where the instruction is predominantly teacher led and where the teacher embodies the main source of information, there is a heightened emphasis on teacher competence in content and pedagogy. As a result, teachers' effectiveness is continuously scrutinized as it is inextricably correlated with student's academic success.

Our charge in this study is to explore the lived experience of a high school teacher while immersed in a problem solving situation in the classroom setting. The main gist of our investigation is to textualize and, thereof, capture the essence of a teacher's encounter of failing to solve a mathematics problem during one of the classroom sessions. To this end, we use personal experience as a lens to reflect on teacher's reconstruction of the situation where personal meanings about problem solving and the problem-solving instruction are concealed.

To unpack the lived experience from a socio-cultural perspective, we envision the teacher's classroom behavior on a past-future spectrum. In relation to this past-future structure, Carr (1986) describes three critical dimensions of human experience: significance, value, and intentions. In general terms, the past conveys significance, the present conveys value, and the future conveys intentions. We argue that as teachers focus and reflect on their lived experience in their classrooms, they will construct their identities by delineating trajectories for their teaching practices terms of the personal meanings they attach to past, present, and future encounters and which shape the behavior they display in the classrooms.

Teaching is embedded in the context of culture, and will therefore vary according to societal views, values, customs and socio-economic status. We conceptualize teaching behavior in terms of personal meanings and epistemologies teachers frame in the context of their teaching practice. (Hammer & Elby, 2002). According to Polanyi (1958), personal meaning is constructed from experience and reflects a dialectic blend of the individual and the social. Personal meaning is also a basis for organizing one's knowledge of the world and one's behavior in it acts as a catalyst to framing one's identity relative to their daily teaching practice. Personal meaning, then, can be used as a basis for considering and modifying the ways in which teachers perceive and execute their professional tasks. A teacher's personal meaning embodies what the teacher feels, thinks, believes, and wants. To expose the essence of this meaning it is necessary to engage in an internal dialogue that scratches deep beneath the surface. Our tacit assumption in this study is that teachers' personal epistemologies can be probed and exposed as teachers are immersed in a state of "mental flow" where they consciously and purposely reflect on past experiences and dispositions.

Theoretical framework

We adopt Bendixen and Rule's (2004) Integrated Model of Personal Epistemology as the primary theoretical framework for this study. ***** NEED FURTHER STUDY

The Study Context

Across its nine provinces, South Africans speak a total of 11 official languages (S. J. Howie & Blignaut, 2009). These languages are implemented as the languages of instruction in the first three years of formal primary education, and of the 12 million students currently in school, over 90% of children attend school during the compulsory phase in the 26,592 schools, which have an average class size of 49-50 students at secondary school level and 42 at primary school level (S. J. Howie & Blignaut, 2009).

In South Africa apartheid left large inequalities in the schools and many educational

challenges. Like any country with a centralized educational system, most decisions on education in the KwaZulu Natal area are managed by the Ministry of Education. Despite the establishment of School Governing Bodies (SGB) by the MoE, the provincial Member of the Executive Council (MEC) for Education determines election procedures within the framework created by the South African Schools Act (SASA). These governing body stands in a position of trust towards the school (Department of Education, 2005). Throughout the KwaZulu Natal province the Ministry of Education, has developed and enacted policies in the education sector to the grassroots. These include the hiring of teachers in more than 27,000 schools and all matters pertaining to curriculum are still centrally controlled by the Ministry of Education and its agencies. Obviously, in such a scenario, teachers feel left out. Their voice is seldom heard since their participation in the whole process is superficial. The teachers' role is narrowed to implementation of curriculum.

The study was conducted during a 10-day trip the author took to KwaZulu Natal in South Africa, in preparation for launching a study abroad program for graduate mathematics education students and teachers from an Urban South East University in the U.S.A .The purpose of the trip was to visit schools and meet with teachers to explore the daily practice of teaching mathematics in a South African school context. Prior to leaving the U.S., ethics approval for the research, was granted from the University of Research Ethics Board where the participant was assured of anonymity in every aspect of the research study including written reports and audiotaped records.

Research questions

In this study we examine the following question: what is the nature of experience of a mathematics teacher not being able to solve a mathematics problem in front of her students? To answer this question, we employ a hermeneutic phenomenological approach centered on personal interpretations of lived experiences captured through interviews and extracted from interviews (De Gagne & Walters, 2010). The data source for this study is a single actual life-text description of the experience of one participant. Through a face-to-face interview with a mathematics teacher, we give the interviewee an opportunity to elaborate on her lived experience with careful probes and minimum distractions as completely as she cared to. An important aspect of the interview process is to provide a temporal space where the fine-grained descriptions of the lived experience facilitate the discovery of meaning and essence of the phenomenon. The interview was tape recorded, transcribed, and then reflectively and interpretively articulated in terms of inherent hidden meanings. Interview transcripts were subjected to fine-grained analysis to identify recurring themes of how the participant viewed herself in the context of teaching a particular topic. In the course of narrating her experience, the teacher embraced a more realistic view of mathematical problem solving that exposed a plethora of past nuances of the obstacles she encountered in the solution process and the resulting frustrations as integral features in the problem solving act and not as situations she created because something went wrong.

Method

We adopt a phenomenological methodology as a systematic attempt to uncover and describe the internal meaning structures of a teacher's lived experience of a teacher immersed in a problem solving act (van Manen, 2003). A phenomenological approach seeks to understand and describe the meaning of a phenomenon that is experienced by several individuals (Creswell, 2007). This approach deals well with human issues, including human occupation, by adding broad, new perspectives. It seeks the essence of the human experience by searching beyond the reductionist sciences, and brings value to the study of human occupation (Gray, 1997; Sadala and Adorno, 2002; Creswell, 2007). We argue that to do phenomenology is to construct a full interpretive description of some aspect of the lifeworld, and yet to remain aware that lived life is always more complex than any explication of meaning can reveal. (See appendix A). Van Manen (2003) explains that a good description that constitutes the essence of something is construed so that the structure of a lived experience is revealed in a way that permits full grasp of the nature and significance of this experience in an unseen way.

As originator of phenomenology, Husserl methodology was to begin with the "phenomenological reduction" or "epoche" which involved the attempt to put all of one's assumptions about the matter being studied into halt, to "bracket" them. As Giorgi(1981) pointed out, to proceed without this step when reflecting upon personal experience leaves one open to the "psychological fallacy", namely, the likelihood that one's judgments about such experiences will be biased by various preconceptions, wishes, desires, motive, values and other influences. Husserl (1962) augmented the process of bracketing with the procedure of free imaginative variation in which different constituents of the experience were altered in imagination in order to test the limits within which it retains its identity. With a thoroughgoing and deep reaching imaginary variation, I tried as much as possible to delimit the essence of the phenomenon of not being able to solve a math problem by analyzing concrete descriptions of the lived experience.

In order to capture the experiential dimension of being unable to solve a mathematical problem, I interviewed a math teacher to describe the phenomenon. Throughout this time, I adopted the following stance while conducting the interview:

Concentrating on the described situation

Slowing down and patiently dwelling with the interviewee on the details of the description

Magnification of the details

Turning from objects to meanings

Being highly open, suspending belief and employing intense interest

Participant

The participant was chosen after an informal visit to a high school in Durban in the KwaZulu Natal province. After meeting with the teachers and having informal conversations the participant was selected based on her willingness to share a lived experience she encountered in teaching mathematics early in her professional career.

Protocol Analysis

Analysis was initiated by uncovering essential themes which were either stated explicitly and directly by the participant's words or hinted at directly, or only present implicitly but is supported by the overall structure of the lived text. Because of the richness of the data, we took extra care during the data analysis stage to not lose any of the essence in the process of interpretation as we moved from the raw data successively toward the essential constituents. Embedded in this process was a mindfulness to allow the process to unfold naturally and slowly with a systematic intention to further clarify and articulate the essential meaning as was influenced by my pre-understandings and reflections as a math teacher. We employed Lichtman(2006) 3 Cs for textual data analysis : Coding fragments of ideas, clustering relevant ideas under meaningful categories, abstracting concepts and themes from categories.

The protocol analysis was partially adapted from Colaizzi (1973) and was conducted d as follows:

The protocol from the interview was carefully read through in order to acquire a feeling for its characteristic, meaning, and intent.

Significant statements were then identified as directly pertaining to the experience being investigated

The protocol was reread several times until the significant statements began to emerge or suggest themselves as categories of themes. The protocol was read slowly to discern natural breaks in the meaning pertinent to the experience as a whole. According to Giorgi (1997), meaning units do not exist as such, but are instead perceived transitions relative to the sensitivity of the researcher. The significant statements were sorted into theme clusters within the protocol

The theme clusters were then condensed to form constituent themes. The protocol is reread again with the categories in mind to check for the comprehensiveness of the constituent themes.

The essence of the phenomenon was then derived from the final comprehensive constituent themes.

Heidegger (1962) states that in seeking to understand a phenomenon, "the phenomenologist thinks meditatively about its meaning". I was mainly concerned with the meaning of the experience with the way things are experienced by the "experiencer", and with how events are integrated into a dynamic meaningful experience. Hermeneutical- phenomenological research focuses on the works of great literature, on myths, autobiography, and works of art including film, theater, and television to widen the understanding of the meaning of life-texts. Fictional and creative accounts were included as acceptable data for reflective-interpretive work (Gadamer, 1975). To reflect on the verbatim transcribed notes, we tried to extrapolate inherent meaning beyond the textual data in order to conceptualize insights extracted from the experience. . We kept the following fundamental questions in mind while analyzing the scribed notes: What does each utterance mean? What does it say? What is concealed in it? What can be revealed through dwelling" with it patiently? What insight lies hidden therein? In answering these questions, we were permissive of fluid manifold interpretations to decipher and distillate insights from what the text is narrating, trying to bring conveyance of meaning to as full and accurate an articulation as possible. By focusing on the essential meaning-constituents or what Giorgi (1997) calls "meaning units", we tried to capture essential nuances of the phenomenon by aligning valid and plausible descriptions of the experience as depicted by the participant. . . In so doing, we intended to grope for expressions that maintained the integrity, complexity and essential being of the phenomenon under investigation. .

Results

Participant's perception of problems and problem solving

The participant construed a mathematical problem as any situation that had barriers to a solution. Such situations could occur in a variety of forms. Consistent with this view of problems, the teacher's thinking of problem solving reflected a more flexible process. The teacher viewed mathematical problem solving as an open-ended process in which the problem solver had to be in control in terms of interpreting the problem and deciding on how to overcome barriers to a solution. The process could be unpredictable in terms of what might or might not work. Thus, problem solving was viewed as involving a cycle of failure and success. Both positive and negative emotions were natural consequences of the process. In particular, it has to do with thinking and knowing what to do to get out of being stuck.

Constituent Themes

The epistemological framing of the structure of the phenomenon arouse from pondering, wondering and reflecting about our own classroom experiences as teachers, the choices we have made as well as the conversation with the participant. Questioning the meaning of the lived experience led to the widening of the "horizon" of what is meant by not being able to solve a mathematics problem in front of the students. By means of "explication" we come to discover what the essential constituents of the phenomenon under study. Van Kaam (1966) defined explication as making explicit implicit awareness of a complex phenomenon (p. 305). Through "explication", we tried to screen out those "imaginative variations" to arrive to an understanding of what the phenomenon essentially embodies as a lived human experience. Through the process of selecting, focusing, simplifying, and transforming ten constituent themes emerged from the single participant narrative account. These identified themes encompass every meaning statement we found significant in our analysis of the protocol and illustrated a South African teacher recollection of a lived problem solving experience.

Losing control

A wide range of mathematics education research on problem solving has advanced the thesis that the tangible cognitive actions involved in solving a mathematics problem are often the result of consciously or unconsciously held beliefs about the task at hand, the social environment within which the tasks takes place, and the individual problem solver's perception of self and his or her relation to the task and the environment. In his "Beyond the Purely Cognitive" article, Alan Schoenfeld (1983) proposed that in addition to seeking cognitive explanations of problem solving behavior, other factors need to be considered. Specifically, he suggested that any problem solving situation should be analyzed with respect to three qualitatively different categories of knowledge and behavior: resources (or knowledge base), control, and belief systems. The bulk of research on problem solving has focused on how one has control of how to store and retrieve information. Losing control, physically and mentally, seemed to be an essential instance of the lived experience. In her words, the teacher explained:

I felt the unassailable truth…I am the worst teacher…the lesson is flopping and everything is out of control…

Also, when she said:

After a while… with a feeble…so low-pitched voice, I moved on to something I have prepared and which I am most comfortable with-Something I have control on- I wasn't in control… that was the main thing…

There is a great value attached to being in control, losing this sense is a sign of failure, of weakness and disintegration.

Not being prepared

It was something I didn't prepare for…A student asked the question on the spot… It was a homework problem…

Being put on the spot, surprisingly, not being prepared intellectually and emotionally are perhaps among many instances that put teachers under stress. In our preparation as mathematics teachers, we are always instructed to plan and prepare ahead of time on how to best deliver the lessons with maximum efficiency and accuracy. Failing to do so, represent a major violation to the rules and professional code of the profession.

Continual questioning

And a raging stream of thoughts kept flowing in my mind….how can I face the students after this disappointment?

There is considerable agreement that people are moved to learn when they ask themselves questions - questions that demand answers if restlessness or hunger or unhappiness is to be dispelled. This provoking of learning is perhaps a major necessity for teachers to question their performance in the classroom and reflect on their practices as problem solvers. It has also been discovered that, when- teachers are given the opportunity to articulate, or to give some kind of shape to their lived experience, all kind of questions arise. Through continual questioning, the teacher tried to make visible an awareness of lacks and deficiencies and highlight the dark times, the fears, and the felt failures.

Feeling the need to physically and mentally escape the experiential space

Blocking everything out… not wanting anybody else to be with me- trying to ignore the whole thing -just looking at it very quickly not wanting any one to engage me… not looking at them…wishing I can just evaporate…get away from their sight…remove from myself and from everybody else..

Throughout the lived text, there was a wide range of intense, at times overwhelming, emotions, anger, guilt, helplessness, fear, and an ever present panic. During these times, there was often a need to escape, to get out, a feeling of not being able to stay a minute there. At times, there was not just the desire to leave physically but a sense of leaving one's body, of putting up a wall and distancing oneself from the surrounding.

Inability to act

...I felt I am going to fall down…something kept pulling down as if wanting to sit, I felt my body slipping…pushed… I felt a bit faint

Many studies have highlighted the immediacy of much that occurs in the activity of teaching. (Moore, Masterson, Christophel & Shea, 2008)

it is believed that such immediacy makes it very difficult for teachers to weigh in a detached fashion each and every word or act in the classroom. Baker (2003) argues that "teacher immediacy" or as Garrison (2007) defines "teacher presence" is a necessary prerequisite for teaching effectiveness and students' attentiveness. By the same token, Garrison & Anderson (2003) propose a 3-tier conceptualization of teacher presence: a) social presence; b) cognitive presence; and c) teaching presence. Inability to act seemed to be one restraining moments that the mathematics teacher lived when not being able to solve a mathematics problem posed by a student.

Van Manen (1997) focuses on the concept of "tact" as an important aspect that illuminates further the moral relevance of who is the teacher. Tact has been defined as the "immediate ruler of practice" having to do with making "instant judgments" and being "attuned to the uniqueness of the situation". "Tactful actions" being immediate involvement in situations where one must instantaneously respond, as a whole person, to unexpected and unpredictable situations. Van Manen suggests that tact is related phenomenologically to "pedagogical moments". The process is so immediate, requiring teacher to act instantly and thoughtfully. In Van Manen's perspective, tact becomes a lens through which the moral meaning in teaching is highlighted.

Awakening of the self to the other

That made me think about how we, as teachers, should accept the idea that we are vulnerable and be sensitive to how we evaluate our students…

As human beings, we always feel the space between what we expected and has not yet taken place, between what we hoped for and what may fulfill that hope, and between an answer we seek and an answer found. The encounter may manifest itself as a sense of lack, of deficiency, or of something suddenly seen as in need of repair. This moment of sudden almost unwilling awakening has been and still is being dramatized in literature, particularly, in novels. The Plague (Camus, 1948) begins in such a moment, with the citizens of Oran submerged in habit; everyone is bored, and few have any expectation of the coming unusual, unfamiliar events. When the pestilence arrives, they deny it or resign themselves; only when Tarrou comes and organizes sanitary squads does some kind of action seem possible, and the plague becomes the concern of all. The power of this figure for me is in the way it makes me think of the connection between shared experience or intersubjectivity and learning to understand. Also, in The myth of Sisyphus, Camus (1955) offers a metaphor for those of us reflecting on the act of teaching. He describes the deadly rhythm of daily labor and daily activities.

"But one day the "why" arises and everything begins in that weariness tinged with amazement. "Begins"-this is important. Weariness comes at the end of the acts of mechanical life, but at the same time it inaugurates the impulse of consciousness. It awakens consciousness and provokes what follows. What follows is the gradual return into the chain or it is the definitive awakening ….for everything begins with consciousness and nothing is worth anything except through it" (p.13)

To speak of consciousness, perhaps is to hold in mind that the conscious being is always becoming, projecting, or striving towards what is not yet achieved. Even as many of us as math teachers cling to the familiar or to forms that seem to confirm to what we already know, we are, on the same level, rejecting stagnation and objectness. We always hope for achieving something, something we expect. And perhaps part of teaching is to come in contact with that sense of incompleteness.

Developing ways of coping with things one can't change

I wasted a lot of time-in denial-trying to talk about it… trying to pretend that it is a learning experience for them…unconsciously lecturing that it is not just knowing the answer that matters… and eventually… said it is not working out

At some point, the realization hits that there is an only one thing teacher have to give, and that is themselves. Experiencing what is real often involves a more direct coming to terms with what could or could not be done. As human beings, we always search for ways to pull back from any dissonant situation, trying to defend our position and free ourselves from chains of embarrassment or sufferings.

Experiencing an altered, unreal reality

The things that I used to imagine are not actually true. I had blown the situation in my mind and exaggerated…it is not really true.

The common notion of expertise in teaching among in-service teachers spotlights what teachers know with respect to a particular domain of knowledge and application. In the early years of teaching, math teachers are held accountable in the extent to which they are competent in mathematics as a subject matter. As mathematics teachers, we are always expected to fully provide accurate answers to every mathematical question posed. While we extensively emphasize comprehensive knowledge of mathematics as a subject matter in our teacher preparation program, we are rarely exposed to notions of moral knowledge. The idea of moral knowledge points neither to a specific body of facts and theories nor to a predefined content of any kind. Rather, it signifies an appreciation of how difficult it is to know something well, of how little in fact we know, and of how much we will always want and need to know to live flourishing lives and contribute the best way we can to others. This what the math teacher discovered as an altered reality after several years of experience in teaching math.

Being transformed

In a second I felt I am bathed with cold sweat…the adrenalin rushing through my veins… I was angry…

Suggestions of how awareness and reflections on lived instances in the classroom may imply can be found in Virginia's Woolf's memories of her own youth, in her remembered feelings of the ground giving way and old assurances being destroyed. Ordinary life, she wrote, contained a large amount of what she called "cotton wool" meaning nonbeing, life not lived consciously (1976, pp.71-72). Then Woolf talked about examples of "shocks" that aroused and transformed her: one when her brother continued to beat her after she dropped her fists in a fight with him, and she felt the foolishness of trying to hurt another person. For a teacher willing to pay heed, what is significant is perhaps the sense of powerlessness Woolf associated with not understanding. Of the exceptional moments she remembered, therefore, certain ones brought a kind of horror with them: "they seemed dominant, myself passive". (p.72).

Teacher as the sole authority: knows everything

I felt I should know everything because I was the teacher so I should not do mistakes…

The resilience of the common patterns of mathematics instruction reflects what has been called the "mimetic" tradition, which is at odds with the more ambitious instruction that is advocated by reformers. Knowledge is seen as fixed; teachers give knowledge to pupils who store and remember it. Also, Cohen(1989) writes that, as many as 300 years ago,

"Most teaching proceeded as though learning was a passive process of assimilation. Students were expected to follow their teachers' directions rigorously. To study was to imitate: to copy a passage, to repeat a teacher's words, or to memorize some sentences or numbers. Students may have posed questions in formal discourse, and perhaps even embroidered the answers. But school learning seems to have been a matter of imitative assimilation" ( pp.42-43)

The view that knowledge is fixed, that teaching is achieved through transmission, and that teachers are authorities run deeply in the participant's consciousness of the teaching and learning of mathematics. It is quite obvious the pressure that the teacher feels to make sure that all the pupils master the required content. The common maxim that has long been prevailed in schools is that the more mathematical knowledge teachers have, the more mathematical knowledge their students will have. Being the source of knowledge dissemination, it has been of utmost importance for the teacher to provide a proper answer to the question posed by the student.

Paulo Freire is perhaps one of the most significant figures in education in the last half of the century who addressed the issue of power and authority in education. His insightful theories represent an important alternative to the "banking model" of education that has and still is generating failure in many school systems today. He proposed an antimethod pedagogy that refuses the rigidity of instructional models and rejects mechanization of teaching. In Teachers as Cultural workers (1997), Freire addresses teachers:

We must dare, in the full sense of the word, to speak of love without the fear of being called ridiculous, mawkish, or unscientific, if not antiscientific. We must dare in order to say scientifically that we study, we learn, we teach, we know with our entire body. We do all of these things with feeling, with emotion, with wishes, with fear , with doubt, with passion, and also with critical reasoning. However, we never study, learn, teach, or know with the last only. We must dare so as not to dichotomize cognition and emotions. We must dare so as to continue to teach for a longtime under conditions that we know well: low salaries, lack of respect, and the ever-present risk of becoming prey to cynicism. We must dare to learn how to dare in order to say no to the bureaucratization of the mind to which we are exposed to every day. We must dare so that we can continue to do so even when it is so much more materially advantageous to stop daring ( Freire, 1997, p.3).

Not being able to live up to others expectations

I should understand everything and that's what I think they expect. What we say and do as teachers, matters…It matters a lot.

Scheffler (1968) argues that the practice of teaching embodies a "restriction of manner" on how teachers can conduct themselves. "To teach", Scheffler argues, "…is, at some points at least, to submit oneself to the understanding and independent judgment of the pupil, to his demand for reasons, to his sense of what constitutes an adequate explanation. Teaching …requires us to reveal our reasons to the student and, by so doing, to submit them to his evaluation and criticism" (p.17)

The idea that teachers are moral role models may be as old as formal education itself. According to numerous commentators, figures such as Socrates, Buddha, Christ and Prophet Mohammad- all of whom helped give rise to the practice of teaching -embodied or "modeled" what they stood for. Many educators today continue to give the idea of being a role model an explicit, normative meaning. Teachers need not be able to walk on water , they suggest, but they should model excellence both in their academic work and their personal manner. They should do so because, like it or not, students look to them for models of how to regard education and how to treat other people. From this perspective, being a role model - or being perceived as one-comes with the territory. Teachers cannot prevent themselves from being perceived in this way, any more than they can prevent themselves from expressing moral messages through what they say and do.

Several researches have tackled the idea that teachers feel compelled to enact qualities that they believe their students both want and need to see in them: poise, commitment, hopefulness, consistency, being knowledgeable, and being organized. Needless to say, these self-expectations place a burden on the teachers to be at their best when in the presence of students. Such self-expectations may lead teachers into moral dilemmas if not into actual conflicts with themselves and with their students.

Examining Validity

An important consideration in all hermeneutic work is the problem of the validity of the findings. The validation of interpretation is a difficult issue. Polkinghorne (2003) regarded hermeneutics as an argumentative discipline where validation "….is a process of convincing audiences through evidence and explanation that a claim is likely for action to be based on it"( p. 29) . For Gadamer (1975) the "hermeneutical experience" is one of becoming involved in a dialogue of question and answer between the author/researcher and the reader and where shared language is the medium of understanding and disclosure.

I tried to present the essential meanings of the lived experience of not being able to solve a math problem in front of students by presenting a sound argument to validate and defend my interpretive claim. Supporting my arguments using relevant research and by using direct quotations from the transcribed life text and relating it to the essential extracted constituent units, I endeavored to offer a chain of evidence to make the interpretation of the meaning as appropriate and plausible as possible.

Implications

In his seminal chapter entitled Schools as places of unselving: An educational pathology? Bonnett (2009) explicate the role of different situations and places in determining the

### Exploring education through phenomenology

The themes emerged from the study are germane to understanding the lived experience of a teacher in a problem solving situation. Its implications are personal as well as allude to revising common conceptions concerning teachers' pedagogical content knowledge. Affected as I have been by John Dewey's explorations of experience and by the existential phenomenologist view of consciousness and being in the world, my notions of teaching mathematics are much involved with notions of human relations, intersubjectivity, the pursuit of various kinds s of meanings. As math teachers, we feel a great drive to focus on communicating certain procedures, methods, and processes that would enable students to teach themselves, because as experience showed me, on some level, learners had to choose to learn. I probably was beginning to see what Martin Heidegger meant when he asked why teaching is more difficult than learning.

Not because the teacher must have a larger store of information, and have it always ready. Teaching is more difficult than learning because what teaching calls for is this: to let learn. The real teacher, in fact, lets nothing else be learning than-learning. His conduct, therefore, often produces the impression that we properly learn nothing from him, if by "learning" we now suddenly understand the procurement of useful information. (1972, p.15)

For Heidegger, (and for me, after a while), the teacher has to learn what it is to learn to let others learn. Perhaps, teachers ought to learn what being open to the world signifies and to move from the "natural attitude" where everything, including the objective world around, is taken as given, normal, and the same to everybody. Holding on to the natural attitude, teachers don't reach beyond themselves in a quest for meaning.

Appendix B

Theme statement

Shared theme

Variations

I felt the unassailable truth…I am the worst teacher…the lesson is flopping and everything is out of control…

Losing control

Not being in charge endanger my authority as a teacher

After a while… with a feeble…so low-pitched voice, I moved on to something I have prepared and which I am most comfortable with-Something I have control on- I wasn't in control… that was the main thing…

How can I be sure I won't let other students down when so much is beyond my control?

what am I supposed to do…

I guess…I was just sedated

my body numbed and anesthetized

struggling to keep my imagination under control

I … kept feeling like a temporary paralysis sort of thing

You know as if there was unquiet silence allover…in the room…everyone is looking and …all not sure what to do…

It was something I didn't prepare for…A student asked the question on the spot… It was a homework problem…

Not being prepared

Planning, preparation and practice help the teacher be on the right track

I would like to be prepared… I don't like to be put in the spot in a situation I am not expecting …

I should have known it…I've been always hard on myself and having these unrealistic standards… I should have been prepared… anybody else would have been.

I know what to do now, I have a lesson I practice it

the thing that irritated me was that it was somehow… accidental…just came out of a sudden

And a raging stream of thoughts kept flowing in my mind….how can I face the students after this disappointment?

continual questioning

And said to myself: oh God…. how can I direct them away from blaming me?

kept asking myself: why?...

….what am I supposed to do…

In that situation I tried to pretend that I understood the problem… trying to buy time…

Developing ways of coping with things one can't change.

I wasted a lot of time-in denial-trying to talk about it… trying to pretend that it is a learning experience for them…unconsciously lecturing that it is not just knowing the answer that matters… and eventually… said it is not working out

searching for a way out, thinking fast about how to solve it trying to remember other problems, navigating my thoughts-searching for a road block to where I want to be…

I made less eye contact with students…I looked over their heads rather than at them…

Feeling the need to physically and mentally escape the experiential space

Getting out of the situation

My main concern is how to get out of the situation without admitting that I don't know…

Blocking everything out… not wanting anybody else to be with me- trying to ignore the whole thing -just looking at it very quickly not wanting any one to engage me… not looking at them…wishing I can just evaporate…get away from their sight…remove from myself and from everybody else…

I tried to pull myself together trying to accept my ignorance and face the whole class…

surrender to the inevitable

Admitting that I can't solve the problem

and eventually… said it is not working out…

I felt the unassailable truth…I am the worst teacher…

...I felt I am going to fall down…something kept pulling down as if wanting to sit, I felt my body slipping…pushed… I felt a bit faint…

inability to act

I can't find the right words

talking to myself and reminding myself where am I

awakening of the self to the other

and my animated faces reflected on them as if they were mirrors in front of me

That made me think about how we, as teachers, should accept the idea that we are vulnerable and be sensitive to how we evaluate our students

Perhaps most people become math phobic because they have bad experiences in school when they were young.

We- as adults- may get stuck in our own reactions and actually reinforce negative behavior in children.

The things that I used to imagine are not actually true. I had blown the situation in my mind and exaggerated…it is not really true….

Experiencing an altered, unreal reality

Imagination mixed with reality

I imagined many crying out loud at me-some bursting out in anger-others asking me, "Isn't there anything you can do?"…

In a second I felt I am bathed with cold sweat…the adrenalin rushing through my veins… I was angry…

Being transformed

Emotionally and physically changing from one state to another

I was insulted and I felt the urge to rebuke in return…

Ever since that incidence, I sometimes notice myself looking around as to find some type of reassurance that I was doing the right thing…

I just couldn't think clearly again…

I felt I should know everything because I was the teacher so I should not do mistakes…

Teacher as the sole authority: knows everything

Teacher is empowered

I am supposed to know more than what they do…every teacher should know or else how can we help our students….

The class is sitting waiting for me to explain it

One of my biggest fears of being a teacher is showing that fear to my students…

Actually, I didn't want to admit that I did not know…(Pause) I'll surely lose their respect …I just didn't want to admit it….You see, my biggest fear is looking stupid in front of students…

Not being able to Live up to others expectations

I should understand everything and that's what I think they expect. What we say and do as teachers, matters…It matters a lot.

I was more nervous with letting them down, sad and upset,… sad for them to have to ask somebody else…

I felt I let my students down…

…they thought I am stupid…

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