ࡱ>  bjbj .{{}+8-</MMccc>>>.......$"13V /E>>>>> /ccR/D&D&D&>cc.D&>.D&D&w((cPJ7$(.h/0/(,4:# 4((4s,`>>D&>>>>> / /D&>>>/>>>>4>>>>>>>>> : STUDENT PRIMARY TEACHERS PERCEPTIONS OF MATHEMATICS Elizabeth Jackson ejackson2 @ myerscough.ac.uk Abstract This paper outlines phenomenographic research carried out at the outset of Initial Teacher Training with a group of UK student primary teachers to determine the range of variation in their perceptions of mathematics. The resulting outcome space indicates four qualitatively differentiated hierarchical categories of ways of perceiving mathematics, forming a potential framework for reflection. It is posited that beliefs about mathematics result from prior experiences which in turn affect subsequent learning and teaching. As such, the framework of mathematical perceptions is intended to provide a means for student primary teachers to make conscious their own experiences and perceptions, through comparison with those of others in terms of resonance with their own relationship with mathematics and to use in setting goals for their future learning in ITT and teaching of mathematics. Key words: primary mathematics; perceptions; student primary teachers; phenomenography; initial teacher training Background Prior research indicated negative perceptions towards mathematics amongst some student primary teachers (Jackson, 2008; Jackson, 2007). As a result of these initial concerns, this study was designed to determine the range of variation of mathematical perceptions amongst a group of student primary teachers at the outset of ITT in a UK university. For students to become the best teachers they can be, awareness and preparation are crucial, arising from an informed and consciously constructed philosophy on which to base their ITT development and future practice. The aim here was to create a means to facilitate awareness of mathematical perceptions which future student primary teachers could use in considering potential effects on learning within ITT and on practice as primary teachers. It is thought that learners prior experiences can influence their subsequent mathematics learning (Briggs, 2014) and as such, this study posits that mathematical perceptions are the result of an individuals prior experiences, which in turn affect the way a student teacher will go on to learn and teach mathematics. Through examination of a group of student primary teachers recounted mathematical experiences, this study set out to ascertain the range of variation in mathematical perceptions across the group, hierarchically categorised to present a framework for reflection suitable for student teachers to use in acknowledging their current relationship with mathematics that is unique to them personally and in considering changes they may wish to make for their future. Theoretical Framework Mathematics education can involve a body of truth taught by instruction, transmission of facts, explanation and practice of procedural method which can lead to recalled and mechanical mathematical knowledge as opposed to relational understanding. In contrast, this study is based on the belief that the key for learning mathematics is the relation between the experienced (mathematics) and the experiencer (the learner). Whilst mathematics may exist as a discipline, created by mathematicians before us as a human construction of agreed knowledge, learning mathematics is wholly dependent on the individuals relationship with experiencing mathematics. The relationality between the mathematics being experienced and the individual experiencing is what leads to mathematical understanding, as opposed to a body of mathematical content being transferred from teacher to learner. A student teachers learning within ITT is therefore dependent on the individuals relationship between themselves as the learner and what is learnt (Marton, 1986): in this case, mathematics. Mathematics is a means created by humans to understand the world, to communicate our understanding and work with what is around us as well as for intrinsic enjoyment and challenge. It has emerged as a social construction of ideas arising from interest, activity and practical need (Thompson, 1992), whereby problems are posed and solutions sought (Szydlik, Szydlik and Benson, 2003) and humans take part in an active process with learners of mathematics engaging in problem-solving to reason, think, apply, discover, invent, communicate, test and critically reflect (Cockcroft, 1982). Mathematics is a human conception, reliant on the way individuals relate to phenomena and is hence a discipline arising from human perception created of understanding as phenomena are interpreted. Learning mathematically involves qualitative experience dependent on interpretations that learners put on their experiences - the internal relationship between the experiencer and the experienced (Marton and Booth, 1997, p113). Student teachers entering initial teacher training are faced with historical difficulties in terms of provision of primary mathematics education. It has been judged a difficult subject both to teach and learn (Cockcroft, 1982, p67) with the suggestion that that something is going wrong for learners in mathematics classes andthis needs remedying (Bibby, Moore, Clark and Haddon, 2007, p16). It is perhaps no wonder, then that student primary teachers insecurities in teaching mathematics are widespread (MacNab and Payne, 2003), although reasons for underlying anxieties about mathematics are not well-known (Jameson and Fusco, 2014). Whilst some theorise that students difficulties with mathematics can appear illogical (Aydin, 2011), student teachers anxiety in their ability to teach mathematics is not unfounded, given the responsibility that lies ahead of them, for it is deemed that teachers can and do make huge differences to childrens livesindirectly through theirattitudes (DfES, 2002, p2). If student teachers have negative attitudes towards mathematics it is reasonable to suggest that their future teaching could be affected and there can be strong perceptions and pervasive emotions associated with mathematics. Negative attitudes towards mathematics have been found to exist amongst adults, including dislike (Ernest, 2000), tension (Akinsola, 2008), anxiety (Ernest, 2000), anger (Cherkas, 1992), terror (Buxton, 1981), fear (Akinsola, 2008), lack of confidence (Pound, 2008), feeling foolish (Haylock, 2010), bewilderment (Buxton, 1981), shame (Bibby, 2002), guilt (Cockcroft, 1982), frustration (Haylock, 2010), distress (Akinsola, 2008) and panic (Buxton, 1981). Negative attitudes towards mathematics can potentially affect engagement via physical means including churning stomach (Maxwell, 1989), difficulty breathing (Akinsola, 2008), crying (Ambrose, 2004) and not being able to cope (Akinsola, 2008). Past learning experiences can be a contributing factor to negative attitudes towards mathematics with circumstances described of unsympathetic teachers (Briggs & Crook, 1991), hostile behaviour (Jackson & Leffingwell, 1999), a classroom environment of impatience and insensitivity (Brady & Bowd, 2005), expectations to understand after brief explanations (Brady & Bowd, 2005), feeling a nuisance (Haylock, 2010), being too afraid to ask (Haylock, 2010), low self-esteem (Akinsola, 2008), embarrassment (Brady and Bowd, 2005) and fear of being found out by someone in authority (Buxton, 1981). For some, negative attitudes can lead to avoidance of mathematical situations (Brady & Bowd, 2005) and development of coping strategies (Cockcroft, 1982). Far-reaching consequences have been demonstrated including disaffection (NACCCE, 1999), assumed inability (Metje, Frank and Croft, 2007) and feeling written off (Haylock, 2010). Negative perceptions have been shown to last into adult life (Houssart, 2009), leaving learners of mathematics with emotional baggage and feeling a mathematical failure (Haylock, 2010, p5). Research into teachers negative perceptions of mathematics indicates origins in previous mathematics experience which in turn impact upon teaching (Tatar et al, 2015) and studies suggest a connection between perceived mathematics ability and beliefs linked to development of teaching competency (Rott, Leuders and Stahl, 2015). As Tatar et al (2015, p67) suggest, since it is a frequently encountered condition in every stage of education, it is important to understand and define, and to avoid or reduce mathematics anxiety. There is, however, no assumption made here that only negative attitudes exist towards mathematics amongst student teachers. Through ascertaining the range in variation of mathematical perceptions across a group of student teachers, the aim was for the resulting framework to include positive mathematical perceptions to consider in setting goals for future learning and teaching in addition to any negative connotations to be considered in terms of resonance with personal experience and the potential effect these may have on future practice. Mathematical experiences lead individuals to form beliefs about the subject which in turn can be a contributory factor to mathematical attitudes and understanding as beliefs have been shown to potentially impede learning (Hofer and Pintrich, 2002). According to Andrews (2015, p369), while math anxiety is a result of math-skill related fears, it can have as much to do with the experience of anxiety itself and a student wanting to avoid repeated anxious feelings, especially in public. As such, student teachers embarking on ITT with negative attitudes towards mathematics, are likely to have any mathematics anxiety exacerbated as they enter mathematics classrooms again, both as ITT learners and teachers in primary school. A reflective framework could therefore be useful in students ascertaining their own mathematical perceptions, comparing with those of others, and identifying the relationship with mathematics they would want to have, so that they can prepare and set goals for their ITT experience. There is hence a clear need for student primary teachers to confront the nature of their own mathematical understanding (MacNab and Payne, 2003, p67) due to potential implications of students mathematical perceptions affecting their learning within ITT and their future practice as teachers of primary mathematics. As perceptions are personal and intrinsic, direct learner involvement is needed (Tolhurst, 2007), but this is not straightforward since perceptions are the indirect outcome of a students experience of learning mathematics over a number of years (Ernest, 2000, p7). As perceptions can be unconsciously held (Ambrose, 2004), identification of variation in the range of student teachers mathematical perceptions could facilitate the opportunity for them examine these beliefs and consider their implications (Schuck, 2002, p335). Methodology Exploration of perceptions that are intangible and potentially unconsciously held needed a qualitative approach. Phenomenographic methodology provided a means of focusing on the relational aspect of constructing mathematical understanding through experience and hence was used here as a means of capturing student teachers mathematical experiences and perceptions as they were enabled to describe an aspect of the world as it appears to the individual (Marton, 1986, p33). Through pooling collective meaning, a hierarchical range of mathematical perceptions was presented via a phenomenographic outcome space formed of categories of description of student teachers mathematical perceptions. This determination of the range of variation of qualitatively different ways of experiencing (Linder and Marshall, 2003, p272) mathematics across this group of student teachers, subsequently provided a useful tool (Speer, 2005, p224) in terms of a framework for reflection by others. Semi-structured open-ended interviews, designed to be diagnostic, to reveal the different ways of understanding the phenomenon (Bowden, 2000, p8), were carried out with thirty-seven student primary teachers at outset of ITT. Phenomenography seeks to capture the range of views present within a group, collectively, not the range of views of individuals within a group (kerlind, 2005b, p118) and so responses were not analysed individually. Instead, transcribed interview data was amalgamated with perceptions interpreted to provide pools of meaning across individuals (Green, 2005, p39) and hence determine the variation in the range of experience across the whole set (Bradbeer, Healey and Kneale, 2004, p19). Categories of description forming the phenomenographic outcome space incorporated key elements from the statements of a number of people (Cherry, 2005, p57) and hence do not correspond to any individual (Bowden, 2000) and no individual student would expect their perceptions to match a single category (Barnacle, 2005). In analysis of the outcome space, researcher knowledge was bracketed in terms of the interview process and interpretation of data was conducted without preconceptions of what interviewees might contribute (Patrick, 2000), with a focus maintained on what they said (kerlind, 2005b) and no pre-existing themes (Barnacle, 2005). Results Four qualitatively different ways of describing perceptions of mathematics by student primary teachers at the outset of initial teacher training were constituted in the analysis of the interviews: Category Of Description 1: Mathematics - Knowledge Learned From An External Relationship Student primary teachers descriptions of their mathematical experiences within this category were consistent with mathematics being externally imposed, by transference to passive learners. The perception was that learners were taught with little evidence of gaining mathematical knowledge beyond recall of memorised numeric facts and that mathematics was an entity to be feared and avoided wherever possible. Mathematics was described as a secret code that I dont understand and mathematicians as swotty, clever, weird and geeky. Alarming instances were recollected of being frightened of mathematics lessons: the maths teacher was horrid you got shouted at if you didnt understand and we were terrified of asking any questions. One guy I remember would throw the board duster at you really hard and bang his fist on the desk in front of you it was just awful, I hated maths lessons. Recalled experiences of learning mathematics were described as all about getting the right answer, a series of numbers that didnt always seem to make sense and I wasnt sure why I was studying it; You just had to do it. Perceptions of mathematical ability included its almost shaming that Im not as good at it as Id like to beits like a big black cloud. Mathematics was described as something to avoid if possible: its just so scary to be faced with having to do anything to do with maths it freaks me out, actually makes me shake and I just want to cry; its like freezing in the headlights, so Ill just avoid it and not tell anyone Im not very good whereas actual engagement with mathematics left learners exposed: what switches me offyou have nowhere to hide with maths...you can either do it or you cant thats the big scary thing with maths - you either have to get it right or everybodys looking at you. Feelings towards ITT included: it actually really frightens me, going in to college in September and not being able to answer a question in maths or feeling like everybody is looking at me if I got asked a question or I couldnt answer it Category Of Description 2: Mathematics - Knowledge Learned From An Internal Relationship Within this category of description, as in the previous, student primary teachers experiences were of gaining mathematical knowledge, with a qualitative difference of attempts at forming some internal relationship with mathematics through individual practice involving teacher-given methods and working individually through schemes. As such, mathematical knowledge was demonstrated sufficient to know how to follow a given method to reach required answers, alongside learners awareness of the limitations of their learning which lacked depth of understanding. As in the previous category, mathematics was perceived as an entity separate to the learner, qualitatively differentiated by the inclusion of given methods and rules as well as facts to be memorised, alongside some individual and internal relational learning. Rather than giving up in the face of mathematical adversity, frustration was described of the apparent inability to understand mathematics, although there was a desire to achieve and it was not avoided. Perceptions of mathematics included that the teachers methods had to be followed: you have to do it their way or its wrong, you know with experience of being taught recalled as being shown how its done on the board and then work through the books and its not particularly engaging, its basically watching somebody do it and not doing it yourself. Described experiences included a focus on getting correct answers: youve always got to get an answer and the answers always got to be right to be good at it. How you got there was irrelevant in the school then, you just had to get the right answer; It was all about getting ticks, getting to the end of the book; passing exams. Descriptions included perceived mathematical inability alongside the expectation of being better: If youre put on the spot to do it, I think, as an adult, that I should be able to do it. Mathematics was associated with frustration: I dont think Ive ever had to do anything with maths that hasnt resulted in tears, because I find it so frustrating it gets on top of me, I feel like theres always going to be something that Im never going to get. Thoughts of impending ITT included anxiety: the one thing that worries the most, is that if I understand how to do something, I will show a child how to do it, but then if they dont understand, then Im not sure I can think of another way of getting the same point across. Category Of Description 3: Mathematics - Understanding Learned From An Internal Relationship This category describes a focus on learners internal relationship with mathematics, but is qualitatively different from Category 2 in that student primary teachers descriptions in this category are focused on experiences of development of mathematical understanding through various methods, including playing, experimenting, handling apparatus, asking questions, solving problems, using and applying mathematics in life and focusing on process. However, some confusion was expressed in terms of mathematics seeming elusive to those with creative minds due its perceived structured, scientific nature. Varying degrees of confidence and a desire for improvement through ITT learning were described, with a qualitatively differentiated view of mathematics constituting a mixture of a scientific and structured entity constituted in given curriculum content to be learnt and an internal relative understanding constructed through social, active engagement. Recollections of being taught mathematics included varied approaches: he used to show us all different ways and then say use whichever one was the besthe always used to say look I dont mind how you get the answer as long I can see how and learning mathematics was described as encompassing different strategies: realising that there are different ways of doing things and that theres nothing wrong with being completely different to how someone else would do it. Mathematical relevance was posited as really important you use it all the time for all sorts of things. Personal perceptions included that mathematics was something to be worked on: I think I learn better doing a problem and like, you know, trying to work it out rather than just writing it out and memorising alongside the notion that mathematics can be worked out if structures are followed: there are some people who are, kind of, a lot more creative brains and struggle to understand the processes, the mechanical processes behind maths maths tends to be very structured and very kind of stage orientated. Category Of Description 4: Mathematics - Understanding Taught Through Perspective Of An Internal Relationship This category also constitutes student primary teachers understanding mathematics through an internal relationship, but is qualitatively different in descriptions of aspirational intentions for future teaching. Development of mathematical understanding was described with interest and excitement in terms of an internal relative experience facilitated via an active learning approach through creative means based on mathematical process. Although there was awareness of curriculum requirements, the approach to learning was qualitatively different in that mathematics was perceived as a way of thinking, essential for understanding and shaping the world and intrinsically a source of stimulation and sense of mystery. Within this category mathematics was described as developmental: dont sort of shut it off and think it is prescribed and that there is just one end resultits getting yourself into that mindset if youve not been used to that and how youve learnt and how you see maths to be with a range of methods advocated when teaching as the approach might be different for every child with intentions for teaching including encouraging an active mind, proactive thinking, rather than just sitting back and being told how to do things. Mathematics was described as essential: if you didnt have maths everything would collapse, everything is based on maths and people just dont realise. As such, an holistic approach was described: it needs to be like the early years for everythingall over the placego with the flow thats the way the world is. Not limited to a discipline to be taught, mathematics was described as a way of thinking with acknowledgement that its weird isnt it that most of our great philosophers were mathematicians as well? Mathematics was perceived as something to be welcomed: I want the children to find it exciting and a challengeit can be a joy with the intended sharing of a sense of wonder about maths and ITT anticipated with excitement - Im counting down the days, literally. Discussion Determination of the range of variation of mathematical perceptions amongst a group of student primary teachers provides substantiation for the notion that teaching and learning mathematics is not without its difficulties (Cockcroft, 1982; Bibby, Moore, Clark and Haddon, 2007). Student primary teachers recounted experiences constituting the first and second categories of the framework describe instrumental learning with a lack of mathematical understanding. Descriptions of their feelings about mathematics in the first category mirror the extreme negative emotions that have been identified in literature over recent years (Akinsola, 2008; Bibby, 2002; Buxton, 1981) and in the second category the frustration and anxiety determined amongst adults through prior research (Ernest, 2000; Akinsola, 2008; Ernest, 2000; Pound, 2008; Haylock, 2010) is evident. For such student teachers, entering a mathematics classroom again as an ITT learner and future teacher of mathematics is a brave step, and an even braver one for them to make conscious and confront strong negative associations with mathematics in order to set about overcoming personal difficulties. Student primary teachers descriptions in the first and second categories of the framework matched the negative experiences presented in existing research of peoples emotional and physical reactions to mathematics (Ambrose, 2004; Akinsola, 2008). Their experiences of being taught mathematics also resonated with the negative encounters presented in existing literature (Jackson & Leffingwell, 1999; Brady & Bowd, 2005; Haylock, 2010), anxiety and lack of confidence (Akinsola, 2008; Buxton, 1981; Metje, Frank and Croft, 2007; MacNab and Payne, 2003) and avoidance (Brady & Bowd, 2005; Cockcroft, 1982). Effects were seen to have lasted into students adult lives, as also indicated in previous research with adults (Houssart, 2009), yet despite the extremes of negative mathematical perceptions, the descriptions of the student primary teachers constituting these negative associations with mathematics did not correspond to disaffection or defeat (NACCCE, 1999) since choosing ITT meant mathematical engagement both for their own learning and their future teaching. Hence, all were prepared to overcome any emotional baggage (Haylock, 2010, p5) brought with them to their ITT courses. The first category constituted mathematics being described as something which had to be done in school, in the second a necessity to meet teacher expectations and pass exams and in the third a useful tool for using and applying to everyday life. There was associated relationality described with varying degrees of personal perceptions of themselves as mathematicians and certainly reticence in describing themselves as competent or confident mathematicians. However, in the fourth category of the framework mathematics constituted a way in which we think, meaning that everyone is a mathematician by default the key to student teachers future practice being to recognise this and development their personal relationship with mathematics accordingly. Whilst the range of variation in mathematical perceptions amongst this group of student primary teachers extends to those confident in various aspects of mathematics and excited about their ITT learning and future teaching, the existence of negative mathematical perceptions is of concern given that prior experiences have been shown to affect attitudes (Briggs & Crook, 1991) and that beliefs and attitudes can affect learning and teaching (DfES, 2002; Hofer and Pintrich, 2002). Responsibility for learning lies initially with the learner (Tolhurst, 2007) and as such the framework provides a range of mathematical perceptions to reflect upon extending to the development of mathematical understanding through various pedagogical means in the third category of the framework and aspirations for teaching in the fourth category. The framework also provides a means of reflection on the need for balance between what was seen in the third category as a structured body of knowledge presented by curriculum content and the desire for autonomy in the fourth category to teach creatively to meet learners needs, since mathematics was described here as a way of thinking and therefore wholly creative, being based on the individuals experience and relationship with what was being learnt. Student teachers descriptions constituting the fourth category hence presented a ubiquitous relevance to mathematics as part of our thinking, as opposed to being limited to knowledge to be absorbed without understanding. The determination of the range of variation in mathematical perceptions amongst the group of student primary teachers serves to acknowledge that problems with mathematics education continue, but also provides a means of reflection for student primary teachers to know that they are not alone if they have any prior negative experiences of mathematics. Reflection on the range within the framework can facilitate making conscious their perceptions (Ernest, 2000; Ambrose, 2004) based on their prior mathematical experiences which up until now may have been unconsciously held and for them to analyse their mathematical perceptions in terms of the potential implications for their learning and practice (Schuck, 2002) in order to plan to bring about changes that may be necessary to be able to relate to mathematics positively for their future contribution to educational improvement. Reflective tool Different perceptions of mathematics will exist for different learners under different circumstances, but this studys phenomenographic outcome space provides information for engagement by all student primary teachers since it provides an holistic perspective on collective experience, and the presentation of categories constructed through the phenomenographic process could act as a powerful trigger for such meta-reflection (Cherry, 2005, p59) by facilitating them to engage in thinking about their mathematical philosophy. As such, the qualitatively varied categories of description can be reflected upon so that awareness can be raised of the range of variation of mathematical perceptions held by student primary teachers at the outset of ITT. Their own perceptions can be made conscious and considered in terms of their aspirations for their own ITT learning and future teaching for as kerlind (2005a, p72) suggests, the aim is to describe variation in experience in a way that is useful and meaningful, providing insight into what would be required for individuals to move from less powerful to more powerful ways of understanding a phenomenon. Potential implications for student primary teachers ITT development are to identify where the framework resonates with their own experience and to begin to form their personal philosophy for learning and teaching mathematics by considering their own experiences as learners, alongside their aspirations for teaching, and to consider their thoughts on the relevance of mathematics, different approaches to teaching and learning, how a prescribed statutory curriculum could be implemented creatively, how mathematical understanding can be developed, the extent to which learners engage in mathematical activity, how negative mathematical emotion can be overcome, what they believe to be the nature of mathematics, how their confidence as a mathematician could be improved and their expectations for ITT. Whilst student primary teachers may feel secure with mathematics and see no need to change, it is nevertheless worthwhile to expand awareness and gain understanding of potential perspectives of colleagues they will work alongside. However, those who do identify a need for change, could use the framework as a starting point for personally challenging assumptions and beliefs. Confronting mathematical perceptions may be challenging but necessary in order to examine perceptions and consider potential implications (Schuck, 2002). Changing perceptions is difficult, particularly with regard to mathematics, but in raising awareness, this study provides a starting point for potential change (Cherry, 2005) in making conscious and explicit perceptions that might otherwise lay dormant (Ambrose, 2004), in order for student primary teachers to take control of their own mathematical learning (Tolhurst, 2007) and be in a position to set goals for learning prior to ITT. Conclusion This study supports the notion that historical difficulties with learning and teaching mathematics continue. Determination of the range of variation of mathematical perceptions amongst a group of student teachers embarking on ITT provides evidence of some of the difficulties student primary teachers may face based on their prior experience that has led to varied mathematical perceptions, and of potential aspirations for future practice. No assumption was made at the outset of this study that negative mathematical perceptions are prevalent in all student primary teachers, but the phenomenographic outcome space of four hierarchical categories of description illustrates a range of variation from the extremely negative to the extremely positive, providing a framework which can be used reflectively for students seeking to improve their relationship with mathematics, starting with ascertaining awareness of their own mathematical perceptions by comparing and contrasting their own with those of others. Through reflection on prior experiences, making conscious mathematical perceptions and considering the potential impact these could have on learning within ITT and future practice as teachers of primary mathematics, use of the framework could help student teachers to ascertain the relationship they have with mathematics and to form a personal philosophy for future learning and teaching primary mathematics. This research hinges on the valuable insight provided by the participants of the study and must culminate with an interview transcript excerpt that sums up the essence of its enquiry and findings that mathematics holds that sense of mystery to me I dont really understand it all. The phenomena of life are a mystery and nobody can claim to understand it all. If only mathematics could be universally accepted as the means by which we attempt to understand according to our own conceptualisation and relationality, without pressure or expectation, instead of the imposition of others ways of understanding, the mysterious nature of mathematics might be more widely recognised as synonymous with the mysterious nature of the phenomena that surround us and embraced as a source of enjoyment, stimulation and challenge its undoubted frustrations, complexities and sometimes sheer impossibility welcomed with confident wonder. References kerlind, G (2005a). 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Educational Technology & Society, 18 (1), 6776. Thompson, A.G. (1992). Teachers Beliefs And Conceptions: A Synthesis Of The Research. In Grouws, D.A. (Ed.). Handbook Of Research On Mathematics Teaching And Learning. pp127-146, New York: Macmillan. Tolhurst, D. (2007). The Influence Of Learning Environments On Students Epistemological Beliefs And Learning Outcomes. Teaching in Higher Education Vol. 12, No. 2, April 2007, pp. 219-233.      PAGE \* MERGEFORMAT 1 $da$gdq$a$ dgd" hqh,GbCJOJQJaJh4h^g%h",1h. 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