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Beliefs, Assumptions, Knowledge (BAK) Research in Teaching

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Published: Mon, 12 Feb 2018

2.1 Belief Research

In the mid-1970s a new body of research began to emerge that worked to describe teachers’ thoughts, judgments and decisions as the cognitive processes that shaped their behaviors (Calderhead, 1996, Clark and Peterson, 1986; Dann, 1990). As a consequence of this, a surge of interest in the area of teacher belief systems has appeared (Pajares, 1992). This research “has helped to identify the nature and complexity of the teacher’s work , and helped to provide ways of thinking about the processes of change and support” (Calderhead, 1996, p.721). Researchers found that teaching could not be characterized simply as behaviors that were linked to thinking done before and during the activity but rather that the thought process of teaching included a much wider and richer mental context. As Shavelson and Stern (1981, p.479) explained, research on teacher cognition made “the basic assumption that teachers’ thoughts, judgments, and decisions guide their teaching behavior”.

Kagan (1990, p. 420) noted that teacher cognition is somewhat ambiguous, because researchers invoke the term to refer to different products, including “teachers’ interactive thoughts during instruction; thought during lesson planning, implicit beliefs about students, classrooms and learning; reflections about their own teaching performance; automized routines and activities that form their instructional repertoire; and self-awareness of procedures they use to solve classrooms problems”.

Currently, there is increasing recognition that the beliefs individuals hold are the best indicators of the decisions they make during the course of everyday life (Bandura, 1986). Pajares (1992, p. 307) argues that the investigation of teachers’ beliefs “should be a focus of educational research and can inform educational practice in ways that prevailing research agendas have not and cannot”. Educational researchers trying to understand the nature of teaching and learning in classrooms have usefully exploited this focus on belief systems. The research of Jakubowski and Tobin (1991) suggests that teachers’ metaphors and beliefs not only influence what teachers do in the classroom, but that changes in these same metaphors and beliefs can result in changes in their practices.

A belief can be defined as a representation of the information someone holds about an object, or a “person’s understanding of himself and his environment” (Fishbein and Ajzen, 1975, p.131). This object can “be a person, a group of people, an institution, a behavior, a policy, an event, etc., and the associated attribute may be any object, trait, property, quality, characteristic, outcome, or event” (Fishbein and Ajzen, 1975, p.12). While Rokeach (1972) defined a belief as “any simple proposition, conscious or unconscious, inferred from what a person says or does, capable of being preceded by the phrase ‘I believe that…’” (p.113), Fishbein and Ajzen (1975) defined a belief system as a hierarchy of beliefs according to the strength about a particular object.

Researchers exploring teachers’ beliefs at the primary and secondary levels have used a number of definitions: “the highly personal ways in which a teacher understands classrooms, students, the nature of learning, the teacher’s role in the classroom, and the goals of education” (Kagan, 1990, p. 423); “psychologically held understandings, premises or propositions about the world that are felt to be true” (Richardson, 1996, p.103); and “generally refer to suppositions, commitments and ideologies” (Calderhead, 1996, p.715).

Beliefs play an important role in many aspects of teaching as well as in life. They are involved in helping individuals make sense of the world, influencing how new information is perceived, and whether it is accepted or rejected. Teachers’ beliefs are a term usually used to refer to pedagogic beliefs or those beliefs of relevance to an individual’s teaching (Borg 2001b). Teacher beliefs have been identified by Kagan (1992a) as tacit, often unconsciously held assumptions about students, about classrooms, and the academic material to be taught.

The literature on teacher knowledge and beliefs from the primary and secondary levels has developed a number of terminological differences. Kagan (1990, p.456) highlighted this problem by noting: “Terms such as teacher cognition, self-reflection, knowledge and belief can be used to refer to different phenomena. Variation in the definition of a term can range from the superficial and idiosyncratic to the profound and theoretical”. The use of these varying terms makes it difficult to investigate in this area of teacher cognition. Pajares (1992) addressed this difficulty:

Defining beliefs is at best a game of player’s choice. They travel in disguise and often under alias-attitudes, values judgments, axioms, opinions, ideology, perceptions, conceptual systems, preconceptions, dispositions, implicit theories, explicit theories, personal theories, internal mental processes, action strategies, rules of practice, practical principals, perspectives, repertories of understanding, and social strategy, to name but a few that can be found in the literature. (p.309)

Defining beliefs is not a very easy task. There is a “bewildering array of terms” as Clandinin and Connelly (1987, p. 487) put forward including teachers’ teaching criteria, principles of practice, personal construct/theories/epistemologies, beliefs, perspectives, teachers’ conceptions, personal knowledge, and practical knowledge.

2.1.1 Belief Research in English Language Teaching

The concept of belief, which has been a common feature of research papers in education for the past decade, has recently come into favor in ELT. In the field, various terms have been used to refer to the term ‘belief’: pedagogical thoughts (Shavelson and Stern 1981), perspective (Zeichner, Tabachnick, & Densmore, 1987), theoretical orientation (Kinzer, 1988), image (Calderhead, 1996), theoretical belief (Kinzer, 1988; Johnson, 1992; Smith 1996).

Terms used in language teacher cognition research include theories for practice (Burns, 1996) which refer to the thinking and beliefs which are brought to bear on classroom processes; philosophical orientation and personal pedagogical system (Borg, 1998) which corresponds with stores of beliefs, knowledge, theories, assumptions and attitudes which shape teachers’ instructional decisions; maxims (Richards, 1996) to comprise personal working principles which reflect teachers’ individual philosophies of teaching; images (Johnson, 1994) which means general metaphors for thinking about teaching that represent beliefs about teaching and also act as models of action; conceptions of practice (Freeman, 1993) to cover ideas and actions teachers use to organize what they know and to map out what is possible; BAK (Woods, 1996) which includes the concepts beliefs, assumptions, and knowledge, In all those studies the core term on which there is focus is “belief”.

Despite the popularity of the term, there is no consensus on meaning yet. The definition set forth by Rokeach (1968) claims that a belief is any simple proposition, conscious or unconscious, inferred from what a person says or does and knowledge is a component of belief. Rokeach uses the term ‘attitude’ to refer to the beliefs teachers have about constructs.

Richards and Lockhart (1996, p.30) state that “teachers’ beliefs systems are founded on the goals and values that teachers hold in relation to the content and process of teaching, and their understanding of the systems in which they work and their roles within it”. These beliefs and values serve as the background to much of teachers’ decision making action and hence constitute what has been termed the “culture of teaching”. Richards and Lockhart (1996) summarize those teachers’ beliefs systems, which are derived from a number of different sources. They are,

a) their own experience as language learners,

b) their experience of what works best for their learners,

c) established practice,

d) personality factors,

e) educational based or research-based principles,

f) principles derived from an approach or method (pp.30-31).

Borg (2001b) discusses three aspects of the term belief:

  1. The truth element-drawing on research in the philosophy of knowledge, a belief is a mental state which has as its content a proposition that is accepted as true by the individual holding it, although the individual may recognize that alternative beliefs may be held by others. This is one of the key differences between belief and knowledge must actually be true in some external sense.
  2. The relationship between belief and behavior – most definitions of belief propose that beliefs dispose or guide people’s thinking and action.
  3. Conscious versus unconscious beliefs – on this point there is disagreement, with some maintaining that consciousness is inherent in the definition of belief, and others allowing for an individual to be conscious of some beliefs and unconscious of others.

The field of language teaching has been one of tradition and transition since its beginning hundreds, indeed, by some accounts, thousands of years ago (Kelly, 1969; Howatt, 1984; Richards and Rodgers, 1986). Even though a much newer pursuit than the teaching of languages such as Greek and Latin or Chinese, the teaching of the English language has already been through many transitions in methodology. What are now considered traditional methods were once the innovations of their time, characterized by the attitudes and values of their creators, who recommended that other educators abandon one method and choose another, with unquestioning optimism, as though this latter method were the solution to their classroom concerns (Clarke, 1982).

In the past 50 years alone, English language teaching has gone through a whirlwind of transitions in its methodology, from grammar translation to direct method, to audiolingualism, to cognitive code, and a host of variations in each. In recent years, the most substantive transition in English language teaching has taken place through a collection of practices, materials, and beliefs about teaching and learning that are known by many different names, e.g. communicative methodology, communicative language teaching, and the communicative approach (Richards and Rodgers, 1986). Contemporarily, English teaching methodology is going through yet another transition. This transition, frequently referred to as the `post method’ condition (Kumaravadivelu, 2001),

Research in the area of teacher thinking has grown rapidly particularly since the 1980s, with the consequence that the literature is vast and is often focused on very specific aspects of teaching. Nevertheless, the research concerned with teachers’ implicit theories of teaching and learning, particularly concerned with epistemological and pedagogical beliefs is of considerable relevance to research in language teaching (Kagan, 1992a; Pajares 1992). The reasons are: first, educational beliefs have shown to influence teaching practice (Kagan 1992a) and learning outcomes. Second, methods used to investigate relationship between beliefs and/or conceptions and teaching practice and the ways of analyzing data, are of interest.

By the mid 1980s, a rising view of teaching began to highlight the complex ways in which teachers think about their work as being shaped by their prior experiences as students, their ‘personal practical knowledge’ (Golombek, 1998). More recently the notion of work context has been recognized as central in shaping teachers’ “conceptions of their practices” (Freeman, 1993).

Language teaching is defined as a dynamic process, which arises out of the meeting and interaction of different sets of principles: different rationalities. In this sense, a rationality is the inner logic which shapes the way in which participants perceive a situation and the goals which they will pursue in this situation (Tudor, 1998). Tudor proposes that to understand language teaching, a first step is to explore the different rationalities which are present in each situation in order to discover the reality the participants involved in. There are four different types of rationalities: those of the students and teachers, socio-cultural rationalities and then the rationality of methodology.

While describing teacher rationalities, Tudor (1998) argues that research into subjective needs has led us to appreciate the uniqueness of each learner’s interaction with their language study. More recently something similar about the teachers has been realized. They, too will perceive and interact with methodology they are implementing in the light of their personality, attitudes, and life experience and the set of perceptions and goals which these give rise to. For this reason there is a need to listen to the teachers’ voices in understanding classroom practice. There is a need to understand teachers’ perceptions and the way in which these perceptions influence teachers’ classroom behaviors.
The maxims (Richards, 1996) or the pedagogic principles (Breen et al.2001) teachers use are important in understanding their pedagogical actions. The reality of classroom teaching is how the teachers interpret official curricula or the recommended materials. Teachers are not skilled technicians who dutifully realize a given set of teaching procedures in accordance with the directives of a more or less distant authority. They are active participants in the creation of classroom realities and they do this on the basis of their own attitudes and beliefs, and their personal perceptions of interaction with their teaching situation.

All teachers hold beliefs about their work, their students, their subject matter, and their roles and responsibilities. They are individuals with their personal perceptions and goals, which go to shape the rationality which will guide their actions in the classroom and their interaction with the context in which they are operating (Tudor, 1998, p. 324).

A major goal of research on teachers’ thought processes is to increase our understanding of how teachers think and behave in the classroom. The drive for this area of research comes from the assumption that what teachers do is a reflection of what they know and believe, and that teacher knowledge and teacher thinking provide the underlying framework or schema which guides teacher’s classroom practices (Sutcliffe and Whitfield 1976, Westerman 1991, Flowerdew, Brock & Hsia 1992, Kagan 1992a, Richards and Lockhart 1994, Bailey 1996, Woods 1998, Borg 1998, Richards 1998). Therefore, in order to understand teaching, we must understand how thoughts get carried into actions (Clark and Yinger 1977, Shavelson and Stern 1981, Clark and Peterson 1986, Johnson 1992, Nunan 1992).

Pajares (1992) reviewed research on teacher beliefs and argued that ‘‘teachers’ beliefs can and should become an important focus of educational inquiry” (p. 307). He then sketched numerous facets of beliefs and acknowledged that a variety of conceptions of educational beliefs appear in the literature. Citing Nespor’s (1987) influential work, he suggested that ‘‘beliefs are far more influential than knowledge in determining how individuals organize and define tasks and problems and are stronger predictors of behavior” (p. 311). Studies on teacher beliefs have slowly gained prominence, especially with regard to teacher change issues.

Guskey (1986), for example, examined 52 teachers who participated in teacher development programs and concluded that change in teachers’ beliefs ‘‘is likely to take place only after changes in student learning outcomes are evidenced” (p. 7). In contrast, Richardson, Anders, Tidwell, and Lloyd (1991) found that change in beliefs preceded change in practices. The current view is that relationships between beliefs and practices are interactive and ongoing (Fullan, 1991; Richardson, 1996). Richardson (1996) even states that ‘‘In most current conceptions, the perceived relationship between beliefs and actions is interactive. Beliefs are thought to drive actions; however, experiences and reflection on action may lead to changes in and/or additions to beliefs” (p. 104).

Pajares (1992) promoted 16 ‘‘fundamental assumptions that may reasonably be made when initiating a study of teacher’s education beliefs” (1992, p. 324). These assumptions include among others, the notions that (a) beliefs are formed early and tend to self perpetuate, persevering even against contradictions caused by reason, time, schooling, or experience; (b) individuals develop a belief system that houses all the beliefs acquired through the process of cultural transmission; (c) beliefs are instrumental in defining tasks and selecting the cognitive tools with which to interpret, plan, and make decisions regarding such tasks; (d) individuals’ beliefs strongly affect their behavior; and (e) knowledge and beliefs are inextricably intertwined (for complete discussion of all 16 assumptions, see Pajares, 1992, pp. 324-326).

2.2 Teacher Knowledge Research

Meanwhile doubts arose also from the scientific community about a conception of professionalism that asked professionals (such as teachers) to just apply the theories and insights provided by others. Schön (1983, 1987) analyzed the work of various groups of professionals and concluded that they applied a certain amount of theoretical knowledge in their work, but that their behavior was not at all ‘‘rule governed’ and that they had no straightforward way to determine which behavior was adequate in specific circumstances. Schön contrasted this principle of ‘‘technical rationality” to the principle of ‘‘reflection-in-action”, which pertained to the thinking of the professional during professional activity and implied a continuing dialogue with the permanently changing situation. This situation does not present itself as a well-defined problem situation. On the contrary, defining the problem is itself one of the most difficult tasks of the professional.

This recognition of the centrality of the teacher and the teacher’s knowledge and beliefs regarding each educational process, including educational innovations, is relatively recent (Calderhead, 1996). Birman, Desimone, Porter, & Garet (2000), for example, searched for key features of effective professional development and, based on their research, reported that professional development should focus on deepening teacher knowledge in order to foster teacher learning and changes in practice. Similarly, Hawley and Valli (1999) considered the expansion and elaboration of teachers’ professional knowledge base as essential for their professional development.

In the literature about teacher knowledge, various labels have been used, each indicating a relevant aspect of teacher knowledge. The labels illustrate mainly which aspect is considered the most important by the respective authors. Together, these labels give an overview of the way in which teacher knowledge has been studied to date. The most commonly used labels are ‘‘personal knowledge” (Conelly and Clandinin, 1985; Elbaz, 1991), indicating that this knowledge is unique; ‘‘the wisdom of practice” (Schwab, 1971), and in more recent publications, ‘‘professional craft knowledge” (e.g., Brown and McIntyre, 1993; Shimahara, 1998), referring to a specific component of knowledge that is mainly the product of the teacher’s practical experience; ‘‘action oriented knowledge”, indicating that this knowledge is for immediate use in teaching practice (Carter, 1990); ‘‘content and context related knowledge” (Cochran, DeRuiter, & King, 1993; Van Driel, Verloop, & De Vos, 1998); knowledge that is to a great extent ‘tacit’ (Calderhead and Robson, 1991); and knowledge that is based on reflection on experiences (Grimmet and MacKinnon, 1992).

It is important to realize that in the label ‘teacher knowledge’, the concept ‘knowledge’ is used as an overarching, inclusive concept, summarizing a large variety of cognitions, from conscious and well-balanced opinions to unconscious and unreflected intuitions. This is related to the fact that, in the mind of the teacher, components of knowledge, beliefs, conceptions, and intuitions are inextricably intertwined. As Alexander, Schallert, and Hare (1991) noted, the term ‘knowledge’ is mostly used to encompass ‘‘all that a person knows or believes to be true, whether or not it is verified as true in some sort of objective or external way” (p. 317). This is particularly relevant with respect to research on teacher knowledge. In investigating teacher knowledge, the main focus of attention is on the complex totality of cognitions, the ways this develops, and the way this interacts with teacher behavior in the classroom.

Following Pajares (1992), knowledge and beliefs are seen as inseparable, although beliefs are seen roughly as referring to personal values, attitudes, and ideologies, and knowledge to a teacher’s more factual propositions (Meijer, Verloop, & Beijaard, 2001).

2.2.1 Teachers’ Knowledge and Beliefs About Teaching

In his extensive review of the literature, Calderhead (1996) found that many different kinds of knowledge have been described as underpinning effective teaching. The main forms are those related to the subject being taught, to teaching methods, and to the ways in which students develop and learn. The extent to which teachers have conscious access to this knowledge is, however, far from clear. Some researchers argue that much of this knowledge is implicit or tacit, derived from experience rather than from any conceptual framework.

The research concerned with teachers’ implicit theories of teaching and learning, particularly work concerned with epistemological and pedagogical beliefs, which reflect their experiences, is of considerable relevance to research in language teaching (Kagan, 1992a; Pajares 1992). First, educational beliefs have shown to influence teaching practice (Kagan 1992a) and learning outcomes. Second, methods used to investigate relationship between beliefs and/or conceptions and teaching practice and the ways of analyzing data, are of interest.

Pajares (1992) attempts to clarify the confusion with the distinction between knowledge and belief. However, as many researchers have found, it is not so much that knowledge differs from beliefs, but that beliefs themselves constitute a form of knowledge. In his attempts to characterize beliefs, Nespor (1987) provides some distinctions between beliefs and knowledge. He singles out four features of the construct previously identified by Abelson (1979) and considers them in relation to teachers:

Existential presumptions or personal truths are generally unaffected by persuasion and are perceived by the teacher as being beyond his/her control or influence.
Alternativity is a feature of beliefs that would include situations such as when teachers attempt to establish an instructional format of which they have no direct experience but which they might consider ideal.
Belief systems can be said to rely much more heavily on affective and evaluative components than knowledge systems. Teachers’ values and feelings often affect what and how they teach and may conflict with their knowledge.
Belief systems are composed mainly of episodically stored material which is derived from personal experience, episodes or events which continue to influence the comprehension of events at a later time. Whereas beliefs reside in episodic memory, knowledge is semantically stored.

A further distinction between beliefs and knowledge, notes Nespor (1987, p.313), is that, while knowledge often changes, beliefs are “static”. As well, whereas knowledge can be evaluated or judged, such is not the case with beliefs as there is usually a lack of consensus about how they are to be evaluated. Furthermore, there do not appear to be any clear rules for determining the relevance of beliefs to real world events. While there is no doubt other distinctions can be made between the two constructs, a better understanding may be gained by exploring the relationship between the two and by considering beliefs as a form of knowledge. This form of knowledge could be referred to as personal knowledge.

Kagan (1992a) refers to beliefs as a “particularly provocative form of personal knowledge” and argues that most of a teacher’s professional knowledge can be regarded more accurately as belief. According to Kagan, this knowledge grows richer and more coherent as a teacher’s experience in classrooms grows and thus forms a highly personalized pedagogy or belief system that actually constrains the teacher’s perception, judgment, and behavior. In terms of beliefs being personal knowledge, Kagan explains: “A teacher’s knowledge of his or her profession is situated in three important ways: in context (it is related to specific groups of students), in content (it is related to particular academic material to be taught), and in person (it is embedded within the teacher’s unique belief system)” (p.74). Like Clark (1988) who equates ‘implicit theories’ with beliefs, Nespor (1987) explains how beliefs become personal pedagogies or theories to guide teachers’ practices:

Teachers’ beliefs play a major role in defining teaching tasks and organizing the knowledge and information relevant to those tasks. But why should this be so? Why wouldn’t research-based knowledge or academic theory serve this purpose just as well? The answer suggested here is that the contexts and environments within which teachers work, and many of the problems they encounter, are ill-defined and deeply entangled, and that beliefs are peculiarly suited for making sense of such contexts. (p.324)

Munby (1982) also equates implicit theories with teachers’ beliefs. Clark and Peterson (1986) in their review of the literature on teachers’ thought processes, argue that teachers’ theories and beliefs represent a rich store of knowledge. Teachers make sense of their complex world and respond to it by forming a complex system of personal and professional knowledge and theories which, as Kagan (1992a) describes, are often tacit and unconsciously held assumptions about students, classrooms and the material to be taught.

2.2.1.1 Beliefs, Assumptions, Knowledge

Throughout this study the term BAK is used as an inclusive term to refer to beliefs, assumptions, and knowledge. Therefore, the following section describes the rationale behind using this term. In the discussion so far, approaches which divide aspects of teacher cognition were examined in separate categories. A more recent strand of research, however, challenges the categorical distinctions outlined above.

Woods (1996) suggests that these dichotomies do not accurately reflect the relationship between Teachers’ beliefs, assumptions and knowledge and their practices in the classroom. In order to take appropriate action, people need to understand; and to understand they need knowledge about the world and specifically about the situation they are in (Woods, 1996, p. 59). Woods (1996) develops a multidimensional cycle of planning and decision making within teaching. He describes three phases of assessment, planning and implementation which operate recursively to inform different hierarchical levels of the teaching process going from the most local level of discrete events in the lesson plan to the most global level of whole course planning (p. 139).

Woods’s analysis of interview data suggests that knowledge structures and belief systems ‘‘are not composed of independent elements, but [are] rather structured, with certain aspects implying or presupposing others” (p. 200). Woods proposes a model to signify the evolving system of beliefs, assumptions and knowledge (BAK) that recursively informs or is informed by the context of teaching: the BAK was part of the perceiving and organizing of the decisions. Woods has demonstrated that language teachers create and maintain background networks of beliefs, assumptions and knowledge which constitute a valid theory of teaching and learning. These background theoretical networks are grounded in every level of routine classroom practice in much the same way that educational theory is grounded in the systematic collection of empirical data. This construct (BAK) is supported by MacDonaldo, Badger and White (2001). They also suggest that while there is some support for a categorical distinction between theory and practice in language education, it is suggested that the beliefs, assumptions and knowledge of teachers are in fact inextricably bound up with what goes on in the classroom.

2.3 Research on the Relationship between Teachers’ Beliefs, Instructional decisions, and Practices

Beliefs are manifested in teaching practices because teachers’ instruction tends to reflect their beliefs. Pajares (1992) and Richardson (1996) investigated the relationship between teachers’ beliefs and their teaching practices, concluding that teachers’ beliefs were reflected in their actions, decisions and classroom practices. Kagan (1992a) also supported Pajares and Richardson’s claim that teachers’ beliefs served as a vital role in influencing the nature of the instruction.

In her study, Johnson (1992) examined the relationship between ESL teachers’ defined, theoretical beliefs about second language learning as well as teaching and instructional practices during literacy instruction for non-native speakers of English. Three tasks, such as an ideal instructional protocol, a lesson plan analysis, and a beliefs inventory were used to determine how much ESL teachers’ beliefs were reflected in skill-based, rule-based, and function-based orientations. The findings in Johnson’s study showed that ESL teachers’ defined beliefs were congruent with their theoretical orientations, and teachers with different theoretical orientations gave quite different instruction for ESL students. Therefore, her study concluded that overall, teachers had different teaching approaches, selections of teaching materials, and images of teachers and students according to their beliefs about learning and teaching. For example, a teacher whose dominant theoretical orientation was function-based focused generally on comprehending the main idea, following a pattern of pre-reading as well as post-reading questions, and discussion as usual reading activities in her instruction.

In addition, Smith’s (1996) study explored the relationship between nine experienced ESL teachers’ beliefs and their decision-making in classroom practices. The result of her study showed that teachers’ articulated theoretical beliefs were consistent with their instructional planning and decisions. For example, those teachers who believed in communication of meaning as a primary goal in learning a language designed and implemented tasks which promoted student-interaction and meaningful communication, such as small-group or pair activities.

Golombek (1998) examined how two in-service ESL teachers’ personal practical knowledge informed their practice through a description of a tension each teacher faced in the classroom. The teachers’ personal practical knowledge informed their practice by serving as a kind of interpretive framework through which they made sense of their classrooms as they recounted their experiences and made this knowledge explicit. The results of this study suggested that L2 teacher educators should recognize that L2 teachers’ personal practical knowledge is embodied in individuals. For this reason, personal practical knowledge is important to acknowledge in L2 teacher education practice and research.

Similarly, in his article Borg (2001a) presents two cases which illustrate the extent to which teachers’ perceptions of their knowledge about grammar emerged as one of the factors which influences teachers’ instructional decisions in teaching grammar. The two case studies suggested clearly that teachers’ self-perceptions of their knowledge about grammar had an impact on their work. Two conclusions emergi


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