According to Albert Bandura, the self-efficacy theory is representative of an individual’s belief in his/her ability to complete a given task successfully (1986). As stated by Murphy and Alexander on the self-efficacy theory, individuals or teachers’ decision about their ability to teach any given task is entirely dependent on their will and confidence to do the particular task. An understanding of this concept can go a long way in helping educators boost teachers’ self-efficacy in mathematics. This is commonly known as the ‘I can’ or ‘I cannot’ belief. However, it is said that teachers can improve their performance and self-efficacy; this can be achieved through some teacher training and later the execution of their knowledge in the classroom. When teachers learn and apply some key strategies, their students’ performance is improved.
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The examination of self-efficacy about pre-service elementary teachers has been the focus of several educational studies, with results suggesting that it is one of the most fundamental aspects affecting teachers’ behaviors, attitudes and effectiveness in the classroom context (Albayrak & Unal, 2011; Haverback & Parault, 2008). A strand of existing literature demonstrates that teachers who are conscious of their self-efficacy and teaching efficacy work more effectively and efficiently (Briley, 2012), endeavor to spend more time on their work and with students to increase their chances of success (Onen & Kaygisiz, 2013), accomplish results with speed (Phelps, 2010), and work more productively and easily when faced with difficulties (Lancaster & Bain, 2010). Research is also consistent that teacher efficacy influences particular classroom behaviors known to stimulate achievement gains, implying that a teacher with high efficacy beliefs can assist students to accomplish more academically (Haverback & Parault, 2008).
Within the mathematics domain, a number of studies have demonstrated that participation in a pre-service mathematics methodology course positively influences the attitudes and self-efficacy of pre-service teachers by boosting their confidence in solving mathematics problems (Briley, 2012; Swars, Hart, & Smith, 2007). Consequently, these programs are thought to increase pre-service teachers’ self-efficacy for teaching mathematics substantially. Despite these positive effects, only a few studies (Albayrak & Unal, 2011) have examined the impact of various training programs on the attitudes and beliefs of future educators. A proper understanding of this training is indispensable if future educators are to make an impact on students’ academic success. Such an understanding will illuminate aspects of the teaching context that affect the self-efficacy beliefs of these teachers upon exposure to the methodology course. More still, there is a need to understand the pre-service teachers’ perceptions of their skills, competence, and ability to teach mathematics with the view to informing policy and future direction on the teaching of mathematics. It is these gaps in knowledge that the present study seeks to fill. As a result, educators must be more aware of the impact of the pre-service self-efficacy belief, hence they can play a more active role in helping their students develop confidence and faith in their abilities to excel in mathematics. The study was carried out to examine the impact of mathematics methodology courses on pre-service teachers’ self-efficacy and beliefs, as well as to examine the possible factors responsible for their teaching-efficacy beliefs.
Bandura’s Theory of Social Learning
Many researchers including, Berna and Gunhan (2011), Bleicher (2004), Isiksal (2005), Cheong (2010) and Czerniak (1990) have focused on demonstrating how the concept of the Bandura’s Theory of Social Learning could offer an imperative model for exploring various aspects of self-efficacy in learning individual science and mathematics from the nature of human mind point of view. Bleicher (2004) observed that Bandura’s theory posits that people are driven to conduct an activity when they hope that the activity would result in a constructive outcome (outcome expectation), and such people are certain that they can do that activity effectively (self-efficacy expectation) (p. 384). Bandura (1997), based on a thorough analysis of available studies, inferred that, “perceived self-efficacy” as constantly demonstrated by many findings from other researchers, led to high-levels of interest and task completion. Further, Bandura (1977) showed that perceived self-efficacy contributed to social controls that influenced a person’s actions and interests by mental processes. Relative to other cognitive theorists, this observation is similar to points of view of other social cognitive theorists who have maintained that self-efficacy beliefs compellingly influenced choices that people make, the attempt they make and the level of apprehension they face (Isiksal, 2005, p. 8). This development led Bandura (1977) to insist that self-efficacy outcomes were imperative in decision-making by a person, particularly over task performance and the subsequent efforts an individual would apply over a given obstacle.
Berna and Gunhan (2011) and Isiksal (2005) noted that this concept is based on the idea that individuals generate and are products of social functions and are recognized to display self-influence to operate effectively and by taking initiatives to act instead of reacting to outcomes. Further, as shown by Bleicher (2004) and Ediger (2012), this theory also infers that social structures are constructed through effectual or efficient individual activity and a combination of activities enforce certain restrictions and offer supports and chances for individual advancement and relations to reflect human action. Researchers such as Albayrak and Unal (2011), Enochs, Smith, and Pintrich (1997), Isiksal (2005) and Pajares (1996) have shown that the Theory of Social Learning and supporting self-efficacy anticipations have been applied in research that strived to evaluate why accomplished outcomes of people could vary even though they tended to show the same levels of awareness and expertise.
Alberta Bandura had initially applied the self-efficacy approach in traditional psychology studies in the 1970s. This approach constitutes one of the fundamental beliefs of the social-learning theory (Albayrak & Unal, 2011) and as a result, it proceeds to be integrated in the present-day teacher-education materials to enhance teaching self-belief (Bray-Clark & Bates, 2003). Albayrak and Unal (2011) believed that self-efficacy simply reflects an individual’s belief regarding how better he or she can systematize and finish courses of action required to achieve specific goals or objectives. Still, Bray-Clark and Bates (2003) consider it as a person’s belief in his or her ability to manage and do a wide range of activities needed to control probable situations. Alternatively, self-efficacy shows a belief about an individual’s own strengths to achieve the essential levels of understanding and performance (Isiksal, 2005).
Bray-Clark and Bates (2003) have shown that self-efficacy is an action-oriented belief that controls option, effort, and determination when face with a challenge and it concurs with the emotional condition of a person (p. 14). By basing their observation on the important contributions of Bandura (1977), Albayrak and Unal (2011) claimed that efficacy beliefs controlled how individual make sense of situations, experience activities, drive themselves and act, and agree on whether adapting act is instigated, efforts used, [and] how long the act is maintained when faced with challenges and adverse situations (p. 183). Moreover, the researchers claimed that self-efficacy beliefs controlled the association between awareness and subsequent action, meaning that a person must show the basic knowledge, expertise, and efficiency beliefs to widen the ability to do certain activities well. With this explanation, Berna and Gunhan (2011) noted that people who display high levels of self-efficacy beliefs are also expected to demonstrate more effort when they experience difficult situations and proceed to sustain self-belief and faithfulness to the fight as they acquire the expertise needed to solve that challenge.
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Researchers such as Pajares (2002) and Phan (2012) have traditionally considered self-efficacy as a component of motive, with studies showing that the beliefs highlighted in a situation not only influence the decision and observations of individuals but also control how a person can act in a possible situation. The available studies aim to associate the self-efficacy concept and its abstract points of view that these research results have elucidated under the theories of expectancy-value and self-concept (Pajares, 1996). According to the Expectancy Value Theory, people will be driven to take part in activities when they understand the importance of the outcome anticipated; they will be less inclined to do activities whose results they do not regard as important (Pajares, 1996, p. 558).
This means that self-efficacy beliefs are connected to the anticipated results of an activity performed to show that one’s beliefs can influence the anticipated results. For example, if a mathematics teacher is convinced that his/her expertise in lesson planning is perfect, it is highly probable that the anticipation of such a teacher will be extremely high (Esterly, 2003). Past studies (Pajares, 1996; Tatar & Buldur, 2013) have shown that the idea of self-efficacy is varied from that of self-concept, as self-efficacy because concentrates on a context-specific or scope-oriented assessment of proficiency to do a certain activity, while self-concept highlight a wider case of preciseness in its evaluation. A study by Bandura (1986) had depicted that self-efficacy portrays the association developed between what a person observes as self-efficacy and the functional mental changes of the person.
Studies (Bray-Clark & Bates, 2003) have shown that the self-efficacy concept consists of two dimensions, namely outcome expectancy and efficacy expectation. About efficacy expectancy, a person believes that he or she possesses the ability to accomplish a given task effectively and on the other hand, outcome expectancy focuses on the perceived outcomes based on the belief system of an individual (Bandura, 1986). Some researchers (Czerniak & Schriver, 1994) have shown observational learning and personal experiences in social setups that make one’s personality could be effective in developing self-efficacy. Various experiences that individuals go through present them with different chances to develop diverse levels of self-efficacy. For instance, different authors such as Bandura (1986), Kranzler and Pajares (1997), Swars (2005) and Swars, Hart, Smith, Smith, and Tolar (2007) have observed that a composition of abilities, attitudes, and cognitive skills create self-efficacy to influences critical aspects of individuals’ perceptions of situations and responses to these different situations.
According to Grossman and McDonald (2008), individuals who possess high-levels of self-efficacy generally believe in their abilities and rely on opportunities to finish a given role, and they trust themselves. Hall and Ponton (2005) further show that such individuals maintain the belief that they can obtain realistic outcomes when they concentrate on performing a given task. On the other hand, other researchers (Pendergrast, Garvis, & Keogh, 2011) have demonstrated that individuals who have low levels of self-efficacy possess limited belief about their abilities and therefore, in most cases, remain uncertain regarding their abilities to attain favorable results. Given such doubts, their inputs and willpower will always fail to achieve the expected standards and therefore, they will achieve unfavorable outcomes.
Sources of Self-Efficacy
Bandura (1977), comprehensively cited in Albayrak and Unal (2011), noted that “the expectations of personal efficacy are derived from four principal sources of information: performance accomplishment, vicarious experience, verbal persuasion, and physiological states” (p. 183). In another study, Bandura (1997), as cited in Charalambous and Philippou (2003), posited that there are four sources of efficacy information, namely “masterly experience, vicarious experience, social persuasion, and physiological and emotional arousal”. It is evident from existing literature (Berna & Gunhan, 2011) that masterly experience is the same as performance accomplishment and that verbal persuasion and social persuasion are also the same.
Performance accomplishment also referred to as masterly experience, is considered the most powerful source of efficacy information, in large part because efficacy beliefs are reinforced considerably when success is attained on difficult tasks with minimal assistance (Charalambous & Philippou, 2003). However, as noted in the literature, not all successful experiences reinforce efficacy; for instance, an individual’s sense of self-efficacy cannot be reinforced when success is attained through unbalanced external assistance or when he or she is exposed to an easy and unimportant task (Bray-Clark & Bates, 2003). The certainty that an individual’s performance in any action has been doing well increases his or her efficacy beliefs and enhances the anticipation that future performances will also be triumphant. Conversely, the view that an individual’s performance in any activity has been a failure lowers his or her efficacy beliefs and contributes to the anticipation that future performances will also be unsuccessful (Hoy & Spero, 2005).
Successful completion of a task strengthens one’s sense of self-efficacy, which allows individuals to believe that they have the prerequisite skills to accomplish every task; however, the failure to deal entirely with a challenge or task will undermine and weaken one’s self-efficacy (Enoch, Smith, & Huinker, 2000). Hackett and Betz (2009) explained that mastery experiences allow pre-service teachers to develop a firm sense of efficacy.
As demonstrated by Hoy and Spero (2005), “vicarious experiences are those in which the skill in question is modeled by someone else” (p. 3). Research is consistent that vicarious experiences may modify efficacy beliefs, expectations, or judgments about self-competence through comparison with the achievement of others (Berna & Gunhan, 2011), implying that watching competent and convincing individuals with more or less the same capabilities as the observer can influence the observer’s self-efficacy beliefs (Charalambous & Philippou, 2003). Bandura (1977), cited in Hoy and Spero (2005), argued, “the degree to which the observer identifies with the model moderates the efficacy effect on the observer” (p. 3). This implies that the more directly a viewer relates with knowledgeable, driven and believable persons, the favorable the outcome of his or her effectiveness will be. That is, the efficiency of the viewer is unquestionably improved when the talented, motivated and honorable individual recognized by the viewer does well and it is significantly reduced when the individual identified by the viewer does badly. In practice, when pre-service teachers watch other experienced teachers complete their tasks successfully, they will also want to trust their abilities and work hard to achieve tasks. Bandura (cited in Battista, 1994) explained that when people see others with whom they have similar characteristics succeed through sustained effort, they raise their belief that they have the same capabilities and chances of success.
Verbal or social persuasion
Verbal or social persuasion provides a further opportunity for reinforcing the beliefs or expectations of an individual, particularly in the context whereby significant others express confidence and faith in the capabilities demonstrated by the individual (Charalambous & Philippou, 2003). Alternatively, encouragement may be provided more effectively and realistically and reinforced by real experiences (Berna & Gunhan, 2011; Bursal & Paznokas, 2006; Phelps, 2010). As noted by Hoy and Spero (2005), verbal or social persuasion may entail “a pep talk or specific performance feedback from a supervisor or a colleague or it may involve the general chatter in the teachers’ lounge or the media about the ability of teachers to influence students” (p. 3). These authors further acknowledged that “although social persuasion alone may be limited in its power to create enduring increases in self-efficacy, persuasion can contribute to successful performance to the extent that a persuasive boost in self-efficacy leads a person to initiate the task, attempt new strategies, or try hard enough to succeed” (p. 3). Social persuasion as a major source of self-efficacy is not only important in removing past hindrances responsible for encouraging self-doubt and disorder but is also known to depend, to a large extent, on the credibility, trustworthiness, and expertise of the convincing individuals (Hoy & Spero, 2005). In the teaching profession, pre-service teachers are exposed to colleagues who succeed effortlessly, which in turn influences them to raise their game so that they can also do better. For instance, they go through a self-reflection process to identify the weaknesses that undermine their ability to succeed and focus on eliminating these weaknesses so that they can perform like other teachers (Enoch, Smith, & Huinker, 2000; Hackett & Betz, 2009).
Psychological states indicate how feelings of relaxation, confidence, and positive emotions indicate self-assurance and the anticipation of future success for the individual concerned (Hoy & Spero, 2005) and how negative feelings such as faster heartbeat, exhaustion, and pain indicate a lack of self-assurance and the anticipation of immediate or future failure for the individual concerned (Charalambous & Philippou, 2003). Battista (1994) noted that personal emotional reactions and responses to situations influence the development of self-efficacy, implying that emotions, moods, stress, and physical reactions have effects on a person’s perception of his or her abilities during a situation. However, the actual awareness of a physical or emotional reaction is not the most significant aspect of the relationship between psychological responses and the development of self-efficacy; on the contrary, the most significant factor is the perception and interpretation that a person uses to reduce stress and elevate mood during challenging or difficult tasks (Ashton & Webb, 1986; Battista, 1994; Cakiroglu, 2008).
Self-Efficacy in the Pre-Service Teachers’ Context
Available literature demonstrates that most pre-service teachers specializing in mathematics or math-related subjects have low levels of self-efficacy (Swars, Hart, Smith, Smith, &Tolar, 2007), even though they understand the significance of self-efficacy in mathematics and therefore should show high levels of teaching efficacy in mathematics (Ashton, Webb, & Doda, 1982). Indeed, some pre-service teachers have confirmed their enthusiastic dislike for subjects that they are supposed to teach, once they begin their profession (Bates, Latham, & Kim, 2011). Often, the attitudes and judgments of teachers concerning their competence will have a direct impact on the attitudes and outcomes of their students toward the subjects they teach (Hackett & Betz, 1989; Kazmpour, 2008).
A study by Albayrak and Unal (2011) acknowledged that teachers with a high-efficacy belief tend to behave in some specific ways to influence student motivation and achievement, with the most common forms of efficacy behaviors demonstrated by these teachers as “elevating expectations, valuing, pushing (encouraging), greeting behavior, opening and closing ritual, equalizing response opportunities, feedback and teacher help, waiting, praising and respecting” (p. 184). Other studies have underscored several characteristics associated with pre-service teachers with high levels of self-efficacy. First, these teachers view challenging problems as tasks that must be mastered (Bates, Latham, & Kim, 2011; Cone, 2009), implying that high self-efficacy enables teachers to master challenging problems so that they can be solved successfully both at the present moment and in future events (Bray-Clark & Bates, 2003). Accordingly, they develop the prerequisite skills that boost their confidence in related tasks or other challenging problems. Second, high levels of self-efficacy cause pre-service teachers to develop a firm interest in the activities they undertake (Charalambous, Philippou, & Kyriakides, 2008; Grossman & McDonald, 2008). It is a shared belief that an intense interest in something allows an individual to acquire the skills and knowledge that will guarantee positive outcomes. When a mathematics teacher has little interest in the subject, he or she will achieve poor results, as exhibited in the performances of his/her students (Hackett & Betz, 1989).
Third, pre-service teachers with high levels of self-efficacy are likely to develop and form a strong sense of commitment in their activities, which in turn allows them to acquire new skills since they are often ready to learn new approaches and strategies for tackling math problems and the challenges that their students face (Czerniak & Schriver, 1994; Esterly, 2003; Riggs & Enochs, 1990). Fourth, pre-service teachers with high levels of self-efficacy are hands-on and self-organizing. In most cases, they do not wait to tackle their problems when they occur but work to eliminate or minimize possible challenges. Similarly, problems that occur are tackled in an organized manner without any delays (Battista, 1994). Finally, preservice teachers with high levels of self-efficacy have an excellent ability not only to recover from disappointments and impediments very quickly but also to work toward the next success (Huinker & Madison, 1997; Kagan, 1992). For example, these teachers do not see failure as the end of their success or inability to achieve positive outcomes (Enoch, Smith, & Huinker, 2000); rather, a negative outcome is regarded as a one-time occurrence that allows them to work harder or acquire better skills required to solve future challenges (Hall & Ponton, 2005).
In a study aimed at measuring the self-efficacy of in-service teachers in Slovakia, Gavora (2011) cited other research studies to demonstrate that teachers with high levels of self-efficacy (1) frequently experiment with fresh teaching procedures; (2) demonstrate a tendency to be minimally critical of their learners; (3) are usually more sympathetic to their learners, both instructional and emotionally; (4) demonstrate a capacity to work longer with problematic or challenged pupils; (5) are frequently more enthusiastic; (6) are usually more devoted to their profession than other teachers; (7) demonstrate a sufficient capability to deal with the needs and expectations of low-ability or challenged students; (8) exhibit greater levels of planning; (9) tend to be more open to new concepts and ideas; (10) demonstrate the capacity to employ less teacher-directed, whole-class instruction; and (11) adopt a more people-oriented strategy to classroom instruction and management. These observations are consistent with the assertion purported by most social-learning perspectives that the self-efficacies demonstrated by teachers are of huge importance in determining how they approach various tasks, challenges, and goals related to student learning (Lampert, 1990) and normally correlate positively with effective teachers’ action in the classroom context (Gavora, 2011).
Conversely, pre-service teachers who have a weak sense of self-efficacy display characteristics that function to disrupt or negatively affect student educational outcomes and achievement. Indeed, Gavora (2011) cited Tschannen-Moran and Hoy (2007) to demonstrate the following:
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According to social-cognitive theory, “teachers who do not expect to be successful with certain pupils are likely to put forth less effort in preparation and delivery of instruction and to give up easily at the first sign of difficulty, even if they know of strategies that could assist these pupils if applied. Self-efficacy beliefs can, therefore, become self-fulfilling prophesies and therefore validate beliefs either of capability or incapacity” (p. 80).
First, teachers with a weak or poorly developed sense of self-efficacy often tend to keep away from demanding and difficult tasks. In most cases, they believe that challenging situations and tasks are beyond their abilities. The practice becomes routine among teachers who avoid difficult tasks and hence undermines their ability to acquire the skills required to solve various challenges. Second, these teachers tend to concentrate on their limitations, failures, and negative outcomes (Bates, Latham, & Kim, 2011; Charalambous, Philippou, & Kyriakides, 2008). Third, these teachers cannot come back and start planning for future success. Finally, they lose confidence in their abilities and stop working on tasks that they think they will not manage. Some of the common behaviors demonstrated by teacher professionals with low self-efficacy beliefs and expectations include “lowering expectations, categorization, lessening, short-gunning, as well as questioning and distancing” (Albayrak & Unal, 2011). In realization that efficacy beliefs are shaped by an individual’s previous performance, encounters and experiences within the social environment (Bandura, 1997), it is highly probable that past experiences of pre-service teachers (e.g., failure with mathematics in school or negative students’ attitudes toward mathematics lessons) may form the underlying reasons as to why teachers develop a low-efficacy belief and internalize some of the negative behaviors indicated above (Cone, 2009).
Self-efficacy enables teachers to create strategies that enhance performance and provide the desired feedback for positive results (Cone, 2009). Teachers who possess a high level of self-efficacy often can create a number of strategies that they use to approach different class problems (Ashton, Webb, & Doda, 1982). Accordingly, they have several alternatives that allow them to develop a strong sense of success. In teaching practice, the best results are often attributable to the sourcing and utilization of several strategies. Accordingly, it is rare or impossible to find a teacher who uses only one strategy and remains successful (Charalambous, Philippou, & Kyriakides, 2008).
The performance of various students in mathematics may depend on various factors, but teachers with high self-efficacy believe that performance is mainly influenced by the experiences obtained from classrooms (Cone, 2009; Hart, 2002; Phelps, 2010). Accordingly, teachers will use their self-efficacy to ensure that all children perform well in mathematics regardless of their backgrounds and histories (Bursal, 2007). For example, teachers who understand self-efficacy will stress its significance to the learners and maintain it during the learning process (Ipek & Camadan, 2012). Bandura (1986), cited in Bursal and Paznokas (2006), stated that self-efficacy allows teachers to achieve the desired outcomes for students’ learning and engagement even among students who may be difficult or unmotivated to perform. In this case, a teacher believes that external factors such as parents, background, intelligence quotient (IQ), school conditions, and environment do not affect the outcomes of learning as long as the teacher uses the best and most appropriate strategies to deliver different units of the course (Battista, 1994; Charalambous, Philippou, & Kyriakides, 2008). Therefore, these teachers will adopt different inclusive strategies that allow students to learn, develop interest, and work hard to pass the subject.
General self-efficacy theories acknowledge that self-efficacy beliefs determine the behaviors of people through the development of attitudes toward their capabilities (Bates, Latham, & Kim, 2011; Cone, 2009). Accordingly, when teachers develop an attitude toward their abilities, they tend to determine what they can do or not do with their knowledge and skills (Lampert, 1990; Steele &Wildman, 1997). This may not be appropriate for teachers who are not flexible and dynamic, because they have already predetermined their abilities and inabilities (Enoch et al., 2000). Therefore, skills and knowledge should be assumed to be powerful tools that can be used to solve any problem, regardless of the situation. Self-efficacy is a fundamental factor in human competence since it mediates between beliefs and behaviors concerning abilities (Ashton et al., 1982a; Bandura, 1977; Bursal, 2007).
Tschannen-Moran and Hoy (2001) explained that teacher efficacy refers to the judgment and belief of a teacher that his abilities and strategies will bring the preferred results for all students’ learning and involvement. Teachers’ efficacy belief is an adaptive, forceful contract (Kim, Sihn, & Mitchell, 2014) defined in literature as the extent to which teachers believe that they can have a positive impact on students’ learning outcomes and achievement (Albayrak & Unal, 2011), teachers’ individual beliefs in their competence to perform specific teaching tasks at a specified level of quality in a school context (Kim, Sihn, & Mitchell, 2014), or their belief or personal conviction that they can positively influence how well students can learn and cope with various learning challenges (Hoy & Spero, 2005). The concept of teacher efficacy is different from teacher self-efficacy, as the former focuses on successfully influencing the performance of students in a classroom context, while the latter focuses on the capacity of teachers to perform particular teaching tasks successfully in their current teaching conditions (Kim, Sihn, & Mitchell, 2014).
In teacher efficacy research, it is evident that classroom activities implemented by a teacher are responsible for influencing students’ learning outcomes in key areas of achievement, motivation, and their sense of self-efficacy (Bray-Clark & Bates, 2003; Isiksal, 2005). Consequently, the concept of teacher efficacy as documented in various teacher-education studies has two dimensions, which are (1) personal teaching efficacy, or the belief in the individual’s own ability to teach, and (2) teaching outcome expectancy, or the belief that effective teaching can positively affect student learning and grade achievement, despite external conditions such as the home setting, family background, parental influences, school circumstances, and IQ (Albayrak & Unal, 2011; Cohen, 1988; Esterly, 2003; Lee, 2010). Bandura (1986), cited in Guskey and Passaro (1994), called for a distinction between these two dimensions of teaching efficacies, because a teacher may assume that student learning originates from effective teaching while yet being uncertain of his/her essential capabilities for the successful delivery of lessons. The concept of teacher efficacy focuses on the factors that enhance teachers’ confidence and enable them to achieve the goals and objectives associated with class instruction, class management, reflective teaching, student motivation and engagement, and stakeholder engagement in the educational process (Kazempour, 2008).
The investigation of self-efficacy about teaching has been a leading concern of several educational studies (Bray-Clark & Bates, 2003; Esterly, 2003; Hoy & Spero, 2005), with many of these studies relating the concept of self-efficacy belief with the teacher-efficacy belief in an attempt to demonstrate how teacher-efficacy beliefs enhance student-learning outcomes in school. One such study conducted by Gibson and Dembo (1984) and comprehensively cited in Albayrak and Unal (2011) acknowledged the following:
“…teachers who believe student learning can be influenced by effective teaching outcomes expectancy beliefs and who also have confidence in their own teaching abilities self-efficacy beliefs should persist longer, provide a greater academic focus in the classroom, and exhibit different types of feedback than teachers who have lower expectations concerning their ability to influence student learning” (p. 184).
The benefits of high teaching efficacy are well documented in the literature, with several teacher-education and efficacy studies concluding that teacher efficacy influences teacher behavioral orientations in important areas such as perseverance on a task or activity, confidence-building, risk-taking, classroom instructional approaches, investment in teaching effort, tendency to solve new challenges, goal-setting as well as the use of innovations (Albayrak & Unal, 2011; Bray-Clark & Bates, 2003; Hoy & Spero, 2005). Other studies have found that teachers with high teaching-efficacy beliefs not only engage in risk-taking behaviors such as sharing classroom control with students but also invest a lot of time and resources into teaching to enhance the basic performance of students despite the difficulties faced (Arslan & Yavuz, 2012; Berna & Gunhan, 2011). Several researchers have found that teachers with high teaching efficacy employ inquiry and student-centered strategies for efficiency and effectiveness, not to mention that they demonstrate a personal belief of having the capacity to control or at least influence student achievement and motivation (Ashton & Webb, 1986; Savran-Gencer & Cakiroglu, 2007). These findings are supported by Kim, Sihn and Mitchell (2014), who not only acknowledged that students’ development of mathematical proficiency is related to teachers’ efficacy in teaching mathematics but also proposed that highly effective teachers have a positive effect on student learning outcomes because effectiveness influences the teachers’ determination for a task, willingness to take risks, and utilization of innovations in their teaching.
Teacher efficacy is shown through the use of various instructional and student-centered approaches. A diversity of instructional approaches means that the teacher does not use the same teaching methods from the first day to the last. Instead, the teacher formulates various strategies that can effectively allow him or her to deliver the syllabus or curriculum (Riggs &Enochs, 1990). Concerning student-centered learning, the teacher avoids acting as the sole source of knowledge and information and instead plays the role of a supervisor and mentor who trains students in how to acquire information and use it as knowledge (Cady & Rearden, 2007; Charalambous, Philippou & Kyriakides, 2008). Accordingly, students tend to work in groups to acquire and synthesize knowledge, and they approach the teacher only when they experience a significant setback or challenge (Czerniak & Schriver, 1994). In contrast, teacher-centered learning entails a situation whereby the teacher controls all class activities and allows little room for student contribution (Hoffman, 2010).
Teacher self-efficacy focuses on the views, perceptions, and beliefs held by individuals. In teaching, this affects educators’ ability to teach and manage learning activities effectively in the classroom. It can also be considered a demonstrated belief that they can indeed make a difference in the learning process of a student. To some extent, it also affects the achievement of students (Guskey & Passaro, 1994) and is related to the behavior of teachers in the classroom in what Tschannen-Moran and Hoy (2001) noted as “their openness to new ideas and their attitudes towards teaching” (p. 215). Research has also indicated that teacher efficacy tends to influence how a student eventually performs in course work, the attitude of the student toward what is being taught, and the eventual social, mental, and cultural growth of the student. The bottom line of the significance of positive teacher efficacy is that the beliefs of teachers about the self and what they are teaching affect not just their profession but how they influence the children they teach.
Summary of Research Studies on Teacher Self-Efficacy
The available scholarship on teacher self-efficacy demonstrates that the concept has been studied from many perspectives (Alsup, 2004; Bleicher, 2004) and has been at the core of teacher-education studies for several decades as one of the most fundamental aspects for influencing the behaviors, attitudes, and effectiveness of teachers (Albayrak & Unal, 2011). Drawing from the social learning theory, it is evident that teacher efficacy in contemporary teacher education is important in its role of enhancing the development of specific beliefs that reinforce the capacity of teachers to deal with modifications and promote desired behaviors (Kim, Sihn, & Mitchell, 2014).
In an unpublished thesis, Esterly (2003) used both quantitative and qualitative research methodologies to investigate the mathematics teaching efficacy and epistemological beliefs of elementary pre-service and novice teachers to expand knowledge on the concept and how it influences student performance outcomes. The study found that teachers demonstrating a low efficacy score tend to employ teacher-directed approaches to teach mathematics in classrooms, with two of the foremost outcomes associated with these approaches being low student performance in mathematics and diminished student participation. The study also found that (1) teachers’ sense of efficacy for effectively using instructional strategies is influenced, to a large extent, by instructional time-management and teacher-related skills in effectively addressing students’ different mathematics performance levels and that (2) teachers’ beliefs about their capabilities in core areas of student engagement, classroom management, and the use of instructional strategies influence their evaluation of their competence to teach. Consequently, the study concluded that designing interventions to enhance teacher efficacy in teaching mathematics might have long-term effects on maximizing students’ confidence and achievement.
In a study aimed at re-examining the internal validity and reliability of an instrument used in measuring self-efficacy in pre-service elementary teachers, Bleicher (2004) found that confidence is important in enhancing the capability of a pre-service or student teachers to teach science or mathematics successfully in the classroom context and that such confidence can only be based on a healthy self-efficacy belief in teaching science or mathematics. This particular study concluded that the underlying objective of self-efficacy studies in the contemporary education field should be based on developing approaches to better inform teacher educators, as such research-oriented information enables the educators not only to allow pre-service elementary teachers to nurture and expand self-efficacy and outcome-expectancy beliefs but also to transform these beliefs into a superior teaching confidence, which is instrumental in the future teaching of pre-service teachers.
Another study conducted by Isiksal (2005) to examine the influences of gender and program year on the performance and mathematical self-efficacy beliefs of 145 pre-service mathematics teachers in Turkey found that there were “significant statistical or quantifiable results of gender and program year on both pre-service teachers’ performance and self-efficacy scores” (p. 12). Specifically, the study found that female pre-service teachers scored noticeably higher than their male counterparts did on performance, although no observable variations were noted between the two considering mathematics self-efficacy scores (Isiksal, 2005). Furthermore, senior pre-service teachers recorded high performance and high mathematics self-efficacy scores relative to newly enrolled students in the education program (Isiksal, 2005).
In a study conducted by Savran-Gencer and Cakiroglu (2007) to investigate Turkish pre-service science teachers’ science teaching efficacy and classroom management beliefs, it was found that “pre-service science teachers usually expressed positive efficacy beliefs relating to science teaching” (p. 183). They found that the most important factor that affected their teaching efficacy is their teaching practices. In another quantitative study aimed at exploring the effect of a mathematics methodology course on elementary, pre-service teachers’ mathematics teaching-efficacy beliefs in Turkey, Albayrak and Unal (2011) found that (1) elementary, pre-service mathematics teachers demonstrate high mathematics teaching-efficacy beliefs and that (2) attending a mathematics methodology course changes the mathematics teaching-efficacy beliefs of elementary pre-service teachers positively.
Arslan and Yavuz (2012) conducted a study at Istanbul University in Turkey with a view not only to establish prospective (pre-service) teachers’ self-efficacy beliefs about mathematical literacy but also to investigate these beliefs against a set of variables that included teaching department and gender. Their study found that (1) the mathematical literacy self-efficacy beliefs of prospective mathematics and physics teachers were below average, that (2) prospective teachers’ mathematics literacy self-efficacy beliefs did not differ according to the department, and that (3) gender did not influence the mathematical literacy self-efficacy beliefs of prospective mathematics and physics teachers. In another research study, Charalambous and Philippou (2008) enrolled eight interviewees from a larger group of 89 four-year students who registered for a teaching practice program (TPP) to “investigate the factors that influence the development of pre-service teachers’ efficacy beliefs in mathematics during fieldwork” (p. 3). Their influential study found that (1) pre-service teachers’ teaching efficacy beliefs gradually improved while they were participating in a TPP, that (2) the main source of the development of their efficacy beliefs was “masterly experience” or actual experiences in a certain domain, and that (3) teaching tasks and personal capabilities interacted with cognitive processing to result in different levels of teacher-efficacy beliefs, even though individuals may have similar experiences.
Informed by the need to explain ways through which teacher efficacy can be enhanced, Kim, Sihn, and Mitchell (2014) conducted a study to investigate South Korean elementary teachers’ mathematics teaching-efficacy beliefs and the factors that come into play to increase the efficacy beliefs demonstrated by teachers. According to these authors, it is evident that teachers who believe that effective teaching can influence student learning (teacher efficacy) and who demonstrate confidence in their teaching capabilities (self-efficacy) may provide “a greater academic focus in the classroom and offer diverse feedback according to the students’ academic backgrounds more than teachers who have [a] low mathematics teaching efficacy belief” (p. 3). Their study found that (1) the years of teaching experience achieved by teachers enhanced their mathematics teaching-efficacy beliefs, (2) the participation of elementary teachers in professional development programs and other certification courses enhanced their mathematics teaching-efficacy beliefs, and (3) their mathematics teaching-efficacy beliefs increased as they attained a higher academic degree in mathematics education.
Role of Cognitive Domain in Math Teacher Performance
Teachers’ efficacy beliefs form very strong determinants of the extent to which they can accomplish various tasks (Pajares, 1996). Most of the cognitive domains are significantly related to how individuals perceive their self-efficacy (Artistico, Cervone, & Pezzuti, 2003). For example, as observed by Harrison, Rainer, Hochwarter, and Thompson (1997), and comprehensively cited in Broadbent, Boyle, and Brady (2009), “Increased performance with computer-related tasks was found to be significantly related to higher levels of computer self-efficacy” (p. 102). On the other hand, performance tends to decrease as the individual’s level of perceived self-efficacy drops. Studies have revealed contrasts in cognitive task performance but have also shown that the results are similar; for example, Artistico, Pezzuti, and Cervone (2003) revealed that an individual’s perceived self-efficacy can be used to predict how well he or she can accomplish problem-solving tasks, regardless of whether the individual is a younger or older adult. This particular study also showed that participants with higher self-efficacy levels were able to outperform those with lower levels of self-efficacy, giving credibility to what Bandura (1993) had earlier noted: depending on variations in the self-efficacy perception, an individual with the same level of knowledge and skills can still have a performance that is poor, satisfactory, or highly satisfactory.
According to Turner, Cruz, and Papakonstantinou (2004), teacher self-efficacy has a positive association with the willingness or eagerness of a teacher to start new teaching ideas and to use them as variations in teaching strategies. This is consistent with SearsSears’ (2005) observation that teachers with a high perception of teacher self-efficacy “are more likely to use inquiry and student-centered teaching strategies, while teachers with a low sense of self-efficacy are more likely to use teacher-directed strategies such as lecture and reading from the text” (p. 2). As such, it is common to find teachers with a low perception of self-efficacy in classroom contexts using a traditional or teacher-directed method and technique, which is different to highly effective teachers who tend to build confidence among students, use student groups, and generously allow the learners to navigate through their learning process for optimal comprehension. As proposed by Swars (2005), such teachers will also try a wide range of new approaches without giving much attention to the fact that these strategies may be risky or challenging to implement in the learning environment.
Beyond instructional strategies, the available literature demonstrates that, if teachers have developed a high perception of their self-efficacy, they have minimal chances of becoming inflexible, rigid, and strict in how they approach the teaching of mathematics as a content with discipline (Alsup, 2004; Kazemi, Lampert, & Ghousseini, 2007; Rimm-Kaufman & Sawyer, 2004). Research further reveals that if teachers have high self-efficacy perception, they will be more competent in exerting influences over the conduct of their learners and therefore control decisions made by school heads (Ericsson, 2002). These factors are indicative of the teacher’s effectiveness in controlling the classroom and in making important decisions about the school in general.
Even though research links the efficacy beliefs of teachers to how they behave in the classroom setting, their investment in teaching, the goals they set for students, and their persistence in ensuring that learning occurs, it is not clear where these teachers’ self-efficacy beliefs come from (Tschannen-Moran & Hoy, 2007). As suggested by Bandura (1998, 1986), it is possible that the theory of social cognition could offer a better explanation of the sources of such self-efficacy beliefs in teachers, which include teachers’ mastery experiences, their verbal or social persuasions, the vicarious experiences they go through, and their psychological arousal. It has been argued in the mainstream psychology and education scholarship that the mastery experiences of the teacher are indeed the single most important factor in developing or building a high perception of self-efficacy in teachers (Arslan & Yavuz, 2012; Bandura, 1998; Hoffman, 2010). While mastery experiences were initially thought to be derived from the training programs that teachers go through in colleges, it has been noted that the actual teaching experience reinforces this mastery experience, which in turn leads to the teachers’ sense of high self-efficacy (Hoy & Spero, 2005; Kazemi et al., 2007). Pajeras (2002) observed that the social persuasions of an individual can be formed in the mind of the person as he or she develops the beliefs of self-efficacy based on the signals and impulses received from the external environment. Concerning psychological states or stimulation, the available scholarship has noted that a positive correlation exists between the feelings of satisfaction developed by the teacher in his or her teaching experiences on the one hand and the satisfaction derived from the achievement of actual teaching on the other (Tschannen-Moran & Hoy, 2007). These factors are known to influence the self-efficacy of teachers remarkably and their beliefs in a manner that largely affects their capability to accomplish their desired tasks or objectives; hence, they are described in the mainstream psychological and educational literature as the foremost foundations of self-efficacy.
The available literature demonstrates that teacher efficacy is a concept with the potential to influence the learning outcomes, motivation, and attitudes of students toward the learning of different subjects and that it is responsible for adjusting student beliefs, attitudes, and learning priorities toward their projected behavior in the classroom (Rimm-Kaufman, 2004). Most social-learning theories support this concept and observe that “understanding the belief structures of teachers and teacher candidates is essential to improving their professional preparation and teaching practices” (Pajares, 1992, p. 307), implying that it is important for researchers in education to consider further how these factors specifically influence the efficacy of a teacher, to determine what is needed to assist teachers (especially teachers of mathematics) to gain a greater sense of teacher efficacy.
Effectiveness in Teaching Mathematics
The debate on the various methodology courses provided at teacher-training institutions is gaining importance as educators and other relevant stakeholders increasingly realize that teacher quality is tied to the educational outcomes demonstrated by students (Arslan & Yavuz, 2012; Esterly, 2003; Haverback & Parault, 2008; Isiksal, 2005; Kim, Sihn, & Mitchell, 2014; Lancaster & Bain, 2010). Arslan and Yavuz (2012) cited previous research to demonstrate that “the most effective way to raise educational quality is to modify initial teacher education and recruitment and to develop the means to train teachers that are already in-service” (p. 5622). Teacher-education programs form an important component in the development of pre-service teachers’ self-efficacy beliefs, which are in turn perceived as critical to education because of their ability to influence teaching experiments as well as teacher-student interaction (Bray-Clark & Bates, 2003; Kim, Sihn, & Mitchell, 2014). Charalambous and Philippou (2003) found evidence for the assumption that carefully designed intervention programs (e.g., teaching practice programs or fieldwork) could result in positive shifts in the components of the affective domain, and that it is possible to modify student teachers’ efficacy beliefs since they are not as stable as they are with experienced in-service teachers.
Hackett and Betz (1989), comprehensively cited in Isiksal (2005), defined mathematics self-efficacy in terms of “a situational or problem-specific assessment of an individual’s confidence in her or his ability to successfully perform or accomplish a particular mathematical task or problem” (p. 8). For three decades now, scholars and practitioners in the field of education have continued to examine how the concept of teacher self-efficacy influences their effectiveness; however, Albayrac and Unal (2011); Arslan and Yavuz (2012); Briley (2012); Esterly (2003); Isiksal (2005); and Kim, Sihn, and Mitchell (2014) have focused on examining the impact of teacher efficacy on the math teacher. As discussed elsewhere in this literature review, teacher self-efficacy implies a function of the level of comfort that an individual has with the content that he or she is teaching in a classroom environment, the grade of the students, and–in extremely specific situations–the particular topic area that the individual is handling in the classroom context. A teacher who demonstrates a high level of self-efficacy while handling a reading lesson, for example, may show low teacher efficacy in teaching mathematics (Arslan & Yavuz, 2012; Brown, 2012; Kim, Sihn, & Mitchell, 2014). This means that studying the impact of the efficacy of math teachers should be done with the factors affecting mathematics performance in mind. Some of the factors identified previously include the external environment, the behavior of pre-service teachers and students during a class session, support from school administration, and the influence of senior teachers, among many other factors (Albayrac & Unal, 2011; Briley, 2012; Cakiroglu, 2000; Gresham, 2008; Ipek & Camadan, 2012).
Teachers’ beliefs and attitudes towards mathematics are just a few of the major points that researchers must target in determining their role in raising teacher-effectiveness levels in the handling of mathematics as a subject. Wilkins (2008) noted that the expertise of the teacher, along with the attitudes, expectations, and beliefs that he or she may hold, plays an important role in influencing the teacher’s instructional practice. Studies have also indicated that teachers with low opinions or negative attitudes about math end up using traditional instructional methods that are essentially teacher-directed teacher-directed (Brown, 2012; Swars, 2005). In such a case, if these teachers handle math lessons while having a low sense of self-efficacy, they may end up refusing to use any innovation in technological support or other exploratory-based practices of instruction. This is in opposition to instructors who have a positive attitude toward mathematics and who at all times feel certain teaching the subject matter, are extremely effectual in their teaching activities, and are even prepared to use innovative methods and ingenuity by an inquiry-based method to teaching models in mathematics.
The most powerful indicator that can be used in the evaluation of teacher effectiveness, in general, is teacher self-efficacy. Self-efficacy for mathematics teachers remains very critical to the overall success and well-being of the global economy because of its contribution to nation-building and global safety. Therefore, math teachers must be efficiently prepared to handle classroom challenges that will eventually enhance the performance of learners. At a national level, teachers of mathematics are at the center of the implementation of instructional practices that are not only effective but also good professional practices that are impacted by the high and positive self-efficacy of math teachers. As such, the importance of the self-efficacy construct cannot be overemphasized if the success of mathematics teachers and students is to be maintained. In this study, the source of motivation has notably been the teaching environment and the motivation derived from the actual teaching experience and the success of the students. This means that the teacher evaluators and motivators should shift their focus from judging teachers’ efficacy solely by their academic and training achievements to considering the success indicators derived from the actual teaching experience of the teacher. These have also been explained through theoretical studies of cognitive psychology and social cognition. In these theories, self-efficacy has been directly related to teacher efficacy as an important educational research element.