The current study examines the effects of a mathematics methodology course on the efficacy beliefs of pre-service elementary teachers, with a focus on identifying (1) how the teaching efficacy of these teachers is affected by the course, (2) teachers’ perceptions of their skills, competence, and ability to teach mathematics, and (3) the aspects of the teaching context that affect the self-efficacy beliefs of these teachers upon exposure to the methodology course.
Chapter 2 presents an assessment and synthesis of available research studies surrounding teacher self-efficacy beliefs and the teaching of mathematics. Specifically, the chapter assesses the literature on the following areas: Bandura’s theory of social learning; self-efficacy; sources of self-efficacy; self-efficacy in the pre-service teacher context; teaching efficacy; summary of research studies on teacher self-efficacy; the role of the cognitive domain in mathematics teachers’ performance; and effectiveness in the teaching of mathematics.
Bandura’s Theory of Social Learning
A number of studies (e.g., Berna & Gunhan, 2011; Bleicher, 2004; Cheong, 2010; Czerniak, 1990; Isiksal, 2005) have demonstrated the capacity of Bandura’s theory of social learning in providing an important framework for investigating the dimension of personal science or mathematics teaching self-efficacy from a cognitive science standpoint.
As acknowledged by Bleicher (2004), Bandura’s theory states that individuals “are motivated to perform an action if they believe the action will have a favourable result (outcome expectation), and they are confident that they can perform that action successfully (self-efficacy expectation)” (p. 384). From a widespread appraisal of the literature, Bandura (1997) was of the opinion that the evidence across studies demonstrated reliability in not only showing that “perceived self-efficacy” adds substantially to the intensity of motivation and performance achievements, but also in illuminating how the social influences that affect the performance of individuals are to a large extent dependent on psychological mechanisms.
This view is consistent with the perspective of most social cognitive theorists, that “self-efficacy beliefs strongly influence the choices people make, the effort they expend, and the degree of anxiety they experience” (Isiksal, 2005, p. 8). Consequently, as postulated by Bandura (1977), self-efficacy beliefs and expectations are critical in the decisions made by individuals on whether to engage in a particular task or activity, how much effort they are willing to expend in completing the task, and also how much effort they are willing to display in the face of challenges.
The basis of the theory is predicated upon the assumptions that individuals are creators as well as outcomes of social arrangements and that people exercise self-influence and hence function generatively and proactively rather than merely reactively (Berna & Gunhan, 2011; Isiksal, 2005). Other important elements of the theory include the presuppositions that social structures are developed by effectual human action, and that structural applications inflict restrictions and afford resources and opportunity applications for the individual development and operation of the human agency (Bleicher, 2004; Ediger, 2012).
A strand of existing literature demonstrates that Bandura’s theory of social learning and attendant self-efficacy expectations have been used in studies aimed at investigating why the performance attainment of individuals might differ irrespective of the fact that they may have similar knowledge and skills (Albayrak & Unal, 2011; Enochs, Smith, & Pintrich, 1997; Henson, 2002; Isiksal, 2005; Pajares, 1996).
Self-Efficacy
First introduced in the mainstream psychology literature in the 1970s by Alberta Bandura, the self-efficacy concept forms one of the central tenets of social learning theory (Albayrak & Unal, 2011) and continues to be incorporated in contemporary teacher education programs to increase teaching confidence (Bray-Clark & Bates, 2003).
Simply put, self-efficacy denotes a person’s judgment about how well he or she can organize and execute courses of action necessary to realize certain goals or objectives (Albayrak & Unal, 2011), an individual’s conviction in his or her competence to organize and execute the most probable path of action necessary to manage upcoming and potential circumstances (Bray-Clark & Bates, 2003), or a belief about one’s own capability to reach the necessary levels of learning and behaviour (Isiksal, 2005).
As demonstrated by Bray-Clark and Bates (2003), self-efficacy “is a task-specific belief that regulates choice, effort, and persistence in the face of obstacles and in concert with the emotional state of an individual” (p. 14). Inciting the seminal works of Bandura (1977), Albayrak and Unal (2011) argued that “efficacy beliefs govern how people think, feel, motivate themselves and behave, and determine whether coping behaviour is initiated, how much effort is expended, [and] how long the behaviour is sustained [when] faced with obstacles and unfavourable experiences” (p. 183).
Additionally, these authors noted that self-efficacy convictions arbitrate in the correlation involving knowledge and action, implying that individuals must demonstrate the requisite knowledge, skills as well as efficacy beliefs and expectations in order to develop the capability to execute specific actions effectively. Following this elaboration, Berna and Gunhan (2011) acknowledged that individuals who demonstrate firm self-efficacy beliefs are also inclined to show more effort when they face challenges and continue to demonstrate confidentiality and faithfulness to the struggle as they attain the requisite skills needed to surpass the challenges.
Self-efficacy is also generally categorized as a motivational construct, with available literature demonstrating that the beliefs held in this construct not only affect the judgments and perceptions of people but also shape how an individual can perform in a given scenario (Pajares, 2002; Phan, 2012). The present research study attempts to expound on the self-efficacy concept, and its theoretical viewpoints cited comprehensively in available research studies under the theories of expectancy-value and the self-concept (Pajares, 1996). According to the expectancy-value theory, “individuals will be motivated to engage in tasks when they value the outcome expected; they will be less predisposed to perform tasks whose outcomes they do not value” (Pajares, 1996, p. 558).
This implies that self-efficacy beliefs, viewpoints and expectations relate to the expected outcomes of an action taken to demonstrate that one’s beliefs can contribute to the expected outcomes; for instance, if a mathematics teacher is confident that his or her skills in lesson planning are exceptional, it is most likely that the beliefs and expectations of such a teacher will be very firm (Esterly, 2003).
The available self-efficacy scholarship demonstrates that the concept differs from self-concept in that, while the former denotes a context-specific assessment of proficiency to perform a particular task or activity, the latter is assessed at a broader intensity of specificity (Pajares, 1996; Tatar & Buldur, 2013). As observed by Bandura (1986), self-efficacy looks at the relationship created between what an individual perceives as self-efficacy and the functional cognitive development of the individual.
The available literature demonstrates that the self-efficacy concept has two dimensions, namely, outcome expectancy and efficacy expectation (Bray-Clark & Bates, 2003). Efficacy expectancy refers to the belief that an individual has in his or her capability to finish a job successfully, while outcome expectancy refers to the belief of this individual that the accomplished task will result in the desired outcomes (Bandura, 1986).
Most people develop self-efficacy through observational learning, experiences in social settings, and the reciprocal determinism to develop one’s personality (Czerniak & Schriver, 1994). The experiences that people undergo provide them with an opportunity to develop high or low levels of self-efficacy. Abilities, attitudes, and cognitive skills make up a self-system that plays a vital role in people’s perception of situations and responses to these different situations (Bandura, 1986; Kranzler & Pajares, 1997 Swars, 2005; Swars, Hart, Smith, Smith, & Tolar, 2007).
In practice, people who have high self-efficacy believe in their abilities and take chances in accomplishing tasks (Grossman & McDonald, 2008); they trust themselves and believe that they will achieve reasonable results when they focus on doing something (Hall & Ponton, 2005). Conversely, people who possess low self-efficacy have little belief in their abilities and thus often remain doubtful about their ability to achieve positive outcomes (Pendergrast, Garvis, & Keogh, 2011). Accordingly, their efforts and determination will always fall below the standards, forcing them to get undesired results.
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), cited in Charalambous and Philippou (2003), posited that there are four sources of efficacy information, namely mastery experience, vicarious experience, social persuasion, and physiological and emotional arousal. It is evident from the existing literature (e.g., 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
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 disproportionate external assistance or when he or she is exposed to an easy and unimportant task (Bray-Clark & Bates, 2003).
According to Hoy and Spero (2005), the discernment that an individual has succeeded in accomplishing a particular task or activity raises his or her efficacy beliefs and contributes to the anticipation that performance will be proficient in the future, while the discernment that an individual has failed to accomplish a particular task or activity lowers his or her efficacy beliefs and contributes to the anticipation that future performance will also be inept.
Successful completion of a task strengthens one’s sense of self-efficacy, which allows them 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). In their study, Hackett and Betz (2009) explained that mastery experiences allow pre-service teachers to develop a firm sense of efficacy.
Vicarious experiences
As demonstrated by Hoy and Spero (2005), “vicarious experiences are those in which the skill in question is modelled by someone else” (p. 3). A strand of existing literature demonstrates that vicarious experiences may modify efficacy beliefs, expectations, or judgments about self-competence through comparison with the attainment of others (Berna & Gunhan, 2011), implying that watching admirable 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 that “the degree to which the observer identifies with the model moderates the efficacy effect on the observer” (p. 3). This means that the more closely an observer identifies with admirable and credible people, the stronger the impact on his or her efficacy will be; that is, the efficacy of the observer is undoubtedly enhanced when the admirable or credible person with whom the observer identifies with performs well and is substantially lessened when the person performs poorly.
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 other with whom they have similar characteristics succeed through sustained effort, they raise their beliefs that they have the same capabilities and chances of success.
Verbal or social persuasion
Verbal or social persuasion serves as a further avenue 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) or when encouragement is provided in a more effective and realistic manner and reinforced by real experiences (Berna & Gunhan, 2011; Bursal & Paznokas, 2006).
As acknowledged by Hoy and Spero (2005), verbal or social persuasion may be in the form of a “pep” conversation or an explicit performance response from a superior or a coworker, or it may relate to the common gossip in the staffroom or in the mainstream media outlets about the capacity of teachers to influence and motivate students. These authors further posited 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 source of self-efficacy may be instrumental in countering sporadic setbacks and challenges that may substantially inspire sufficient self-doubt to interrupt persistence; however, as acknowledged by Hoy and Spero (2005), the effectiveness or success of persuasion depends to a large extent on the integrity, dependability, and proficiency of the persuader. In the mainstream teaching occupation, pre-service teachers are routinely exposed to colleagues who succeed effortlessly, which in turn persuades them to raise their game so that they can also do better. For instance, they undergo 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 (Ball & Bass, 2003; Enoch et al., 2000; Hackett & Betz, 2009).
Physiological states
Psychological states denote how thoughts of restfulness, confidence, and positive em*otions indicate self-assurance and the expectancy of upcoming success for the individual concerned (Hoy & Spero, 2005) and how negative feelings such as rapid heartbeat, fatigue, and pain indicate a lack of self-assurance and the expectancy 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 factual concentration 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
A strand of existing 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), in spite of the fact that they understand the significance of mathematics self-efficacy and therefore should show high levels of mathematics teaching efficacy (Ashton, Webb, & Doda, 1982). Indeed, some pre-service teachers have confirmed their dislike for subjects that they are supposed to teach passionately 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).
A study by Albayrak and Unal (2011) acknowledged that teachers with a high efficacy belief have a tendency to behave in some specific ways to influence student motivation and achievement, with the most common forms of efficacy behaviours demonstrated by these teachers outlined as “elevating expectations, valuing, pushing (encouraging), greeting behaviour, opening and closing ritual, equalizing response opportunities, feedback and teacher help, waiting, praising and respecting” (p. 184).
Other studies have underscored a number of characteristics associated with pre-service teachers with high levels of self-efficacy. First, these teachers perceive challenging problems as tasks that must be mastered (Bates et al., 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 a keen 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 dismal results, as exhibited in the performances of their students (Hackett & Betz, 1989).
Third, pre-service teachers with high levels of self-efficacy are likely to develop and form a firm 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 proactive and self-organizing. In most cases, they do not wait to tackle their problems when they arise but work to eliminate or minimize possible challenges.
74Similarly, 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 admirable ability not only to recover from disappointments and setbacks 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 investigating the self-efficacy beliefs of in-service teachers in Slovakia, Gavora (2011) cited other research studies to demonstrate that teachers with elevated intensities of self-efficacy beliefs (1) regularly experiment with new teaching approaches, (2) demonstrate a propensity to be less critical of their students, (3) are generally more helpful to their students both instructional and expressively, (4) demonstrate a propensity to guide challenged students, (5) are generally more passionate, (6) demonstrate more dedication to their career than other teachers, (7) demonstrate sufficient capacity to deal with the needs and expectations of low-ability students, (8) demonstrate elevated levels planning intensities, (9) are generally inclined to new ideas, (10) demonstrate a propensity to work with student-centered approaches, and (11) implement a more humanistic orientation to classroom management.
These observations are consistent with the view held by most social learning perspectives that the self-efficacies demonstrated by teachers are of immense importance in determining how they approach various tasks, challenges, and goals related to student learning (Lampert, 1990) and that a strong sense of self-efficacy normally correlates positively with effective teacher action in the classroom context (Gavora, 2011).
Conversely, pre-service teachers who have a weak sense of self-efficacy exhibit characteristics that function to derail or adversely affect student educational outcomes and achievement. Indeed, Gavora (2011) cited Tschannen-Moran and Hoy (2007) to demonstrate the following:
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 actually know of strategies that could assist these pupils if applied. Self-efficacy beliefs can therefore become self-fulfilling prophesies, validating beliefs either of capability or of 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 habitual 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 dwell on their shortcomings, failures, and negative outcomes (Bates, Latham, & Kim, 2011; Charalambous, Philippou, & Kyriakides, 2008). Third, these teachers lack the ability to bounce back and start planning for future success. Finally, they lose confidence in their personal abilities and stop working on tasks that they think they will not manage. Some of the common behaviors demonstrated by teachers with low self-efficacy include low or deficient expectations, sorting, undervaluing, excommunicating, using a high rate of speed to teach, questioning, and estrangement (Albayrak & Unal, 2011).
Owing to the fact that efficacy beliefs are to a large extent shaped by an individual’s previous performance and experiences (Bandura, 1997), it is exceedingly feasible that previous experiences of pre-service teachers (e.g., disappointment with mathematics in school or pessimistic 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 formulate strategies that enhance performance and provide the desired feedback for positive results (Cone, 2009). Teachers who possess a high level of self-efficacy often have the ability to formulate a number of strategies that they use to approach different class problems (Ashton, Webb, & Doda, 1982). Accordingly, they have a number of 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 a myriad of 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). 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 uphold 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 experiencing learning difficulties and with minimal motivation 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 stipulate 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 & Widman, 1997).
This may not be appropriate for teachers who are not flexible and dynamic because they have already predetermined their abilities and inabilities (Enochs, Smith, & Huinker, 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, Webb, & Doda, 1982; Bandura, 1977; Bursal, 2007). The development of strong self-efficacy allows teachers to develop appropriate teaching efficacies, as discussed below.
Teacher Efficacy
Tschannen-Moran and Hoy (2001) explained that the concept of teacher efficacy refers to the judgment and belief of a teacher that his or her abilities and strategies will bring the desired results for students’ learning and engagement for all students. Teacher efficacy belief is an adaptive dynamic contract (Kim, Sihn, & Mitchell, 2014), defined in the literature as the extent to which teachers believe that they can have a positive impact on students’ learning outcomes and achievement (Albayrak & Unal, 2011), the 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 teachers’ belief or personal conviction that they can positively influence how well students are able to 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 own sense of self-efficacy (Bray-Clark & Bates, 2003; Isiksal, 2005). Consequently, a strand of existing literature demonstrates that the concept of teacher efficacy has two foremost aspects, namely (1) personal teaching efficacy, or the conviction in the individual’s own capability and aptitude to teach, and (2) teaching outcome expectancy, or the conviction that effective teaching can affect student learning positively in spite of existing conditions such as the home environment, family settings, parental influences, school conditions, 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, yet the teacher is uncertain about the 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 instructions, class management, reflective teaching, student motivation and engagement, and stakeholder engagement in the educational process (Kazempour, 2008).
The investigation of self-efficacy in relation to teaching has been a foremost concern of several educational studies (e.g., Bray-Clark & Bates, 2003; Esterly, 2003; Hoy & Spero, 2005), with many of these studies relating the self-efficacy belief concept with 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 available literature demonstrates that teacher efficacy influences teacher behavioral orientations in core areas such as persistence on a task, risk taking, classroom instructional strategies, investment in teaching effort, goal setting, and the use of innovations (Albayrak & Unal, 2011; Hoy & Spero, 2005), implying that teachers with optimal teaching efficacy beliefs and confidence attempt new teaching approaches that are difficult to implement (Bray-Clark & Bates, 2003), engage in risk-taking behaviors such as sharing control with students (Berna & Gunhan, 2011), invest much effort in teaching with a view to enhancing the basic performance of students despite the difficulties that may arise (Arslan & Yavuz, 2012), employ inquiry and student-centered approaches to be more effective (Ashton & Webb, 1986), and demonstrate a personal conviction that they have the capacity to control or at least influence student achievement and motivation (Savran-Gencer & Cakiroglu, 2007).
This elaboration is 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 efficacious teachers have a positive effect on student learning outcomes because efficacy influences the teachers’ persistence on a task, willingness to take risks, and employment of innovations in their teaching.
Teacher efficacy is exhibited through the use of various instructional approaches 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 day; rather, he or she formulates various strategies that can effectively allow him or her to deliver the syllabus or curriculum (Riggs & Enochs, 1990).
With respect to student-centered learning, the teacher refrains from 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, a 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 is counted among forms of self-efficacy focusing on views held by individuals and their beliefs. In teaching, this affects their ability to teach and manage learning activities effectively in the classroom. It can also be considered as a belief demonstrated by teachers 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 also 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 influencing the behaviors, attitudes, and effectiveness of teachers (Albayrak & Unal, 2011).
Drawing from social learning theory, it is evident that the importance of teacher efficacy in contemporary teacher education is embedded in its role of enhancing the development of specific beliefs that reinforce the capacity of teachers to deal with modifications and perform desired behaviors (Kim, Sihn, & Mitchell, 2014). This section appraises literature on existing teacher efficacy research with a focus on pre-service teachers and the teaching of mathematics and/or science.
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 with a view to expanding 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 (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 may have long-term effects in maximizing students’ confidence intensity and achievement in mathematics.
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 novice teacher to teach science or mathematics successfully in the classroom context and that such confidence can only be embedded in a healthy science or mathematics teaching self-efficacy belief.
This particular study concluded that the underlying objective of self-efficacy studies in the contemporary education field should be nested in developing approaches to better inform teacher educators, as such research-oriented information enables educators not only to afford an opportunity for pre-service elementary teachers to nurture and expand self-efficacy and outcome expectancy beliefs but also to transform these beliefs into heightened teaching confidence that is instrumental in the future teaching of the pre-service teachers.
Another study conducted by Isiksal (2005) to examine the consequences of gender and year in program variables on the performance and mathematical self-efficacy convictions of 145 pre-service mathematics teachers enrolled in a Turkish institution found that there were considerable statistical consequences arising from the two variables and impacting both pre-service teachers’ performance and self-efficacy outcomes. Specifically, the study found that the performance outcomes of female pre-service teachers were considerably higher than those of their male counterparts although no noteworthy variation was discovered between the two in reference to mathematics self-efficacy outcomes, and that senior pre-service teachers scored highly on performance as well as mathematics self-efficacy outcomes compared to newer students enrolled in the same education curriculum.
In a study conducted by Savran-Gencer and Cakiroglu (2007) to investigate science teaching efficacy/conviction and classroom management approaches exhibited by pre-service science teachers in Turkey, a key finding demonstrated that these participants generally articulate optimistic efficacy convictions regarding science teaching and also implement an interventionist strategy in the instructional management aspect, highlighting the importance of teacher efficacy behaviors in the teaching of science.
In another quantitative study aimed at investigating 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 exhibit elevated mathematics teaching efficacy convictions and expectations, and (2) enrolling in a mathematics methodology course changes the mathematics teaching efficacy convictions and expectations of elementary pre-service teachers in a constructive way.
In a study that used narrative interviews to investigate the sources that pre-service teachers use in developing their self-efficacy beliefs and learning goals, Phelps (2010) found that pre-service elementary teachers rely on manifold sources to develop “their efficacy beliefs and goals, including past performance, vicarious experiences, verbal persuasions, career goals, and the fit between participants’ views of mathematics and the nature of mathematics in their classes” (p. 293).
It is important to note that, in career goals, most participants in the study acknowledged that their awareness of their career goals and objectives led them to hold more masterly goals, implying that focusing on career goals can be a source of self-efficacy by virtue of developing a more productive motivational profile. Citing previous research, the author concluded that the same set of factors are responsible for influencing the development of both learning goals and self-efficacy, hence the possibility that the two constructs (self-efficacy beliefs and learning goals) develop similarly despite a number of researchers showing in their research studies that they develop separately.
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) mathematical literacy self-efficacy convictions of upcoming mathematics and science teachers were beneath the standard, that (2) prospective teachers’ mathematics literacy self-efficacy beliefs did not differ according to the department, and that (3) gender did not mediate or influence the mathematical literacy self-efficacy beliefs of prospective mathematics and physics teachers.
In another research study, Charalambous and Philippou (2003) used eight interviewees from a larger cluster of 89 fourth-year students taking part in a teaching practice program (TPP), with the view to investigating the factors that influence the development of pre-service teachers’ efficacy beliefs and expectations in mathematics during the practice program. Their influential study found that (1) pre-service teachers’ teaching efficacy beliefs and expectations gradually improve while participating in the practice program, that (2) the foremost source of the development of efficacy beliefs and expectations is “masterly experience” or actual experiences in a certain domain, and that (3) teaching activities and individual capabilities interact with cognitive processing to result in different levels of teacher efficacy beliefs and expectations irrespective of the fact that individuals may have had similar experiences.
Bilari (2013) used a sample of 243 student teachers enrolled in two programs (elementary teacher and preschool teacher) in the Faculty of Education, Elbasan, Albania, not only to investigate the level of sense of efficacy among these participants, but also to explain the relationship between the level of sense of efficacy noted in the participants and other variables such as gender and type of diploma.
The study found that many of the students in the two teaching programs demonstrate a high level of teaching efficacy during pedagogical practice, and that these participants are more efficient in instructional strategies and less efficient in student engagement. The study reinforces Arslan and Yavuz (2012) finding that gender do not mediate or influence the self-efficacy beliefs of prospective teachers, as it demonstrated no substantial differences in teacher efficacy level between male and female teachers. Additionally, no substantial differences were found between the level of teacher efficacy in the sampled participants and the type of diploma course undertaken.
Boyd, Foster, Smith, and Boyd (2014) sampled 223 students enrolled in a first-year mathematics unit in the Bachelor of Education of Early Childhood and Primary Education Program in an attempt to develop the knowledge on the particular characteristics of pre-service teachers that make them to experience high levels of mathematics anxiety about both the learning of mathematics and the teaching of the mathematics curriculum.
Their study found that (1) student teachers who were positive about mathematics recalled quality teaching interventions of mathematics such as engaging students, student centered learning, supporting the students’ learning by giving time, assistance, and assurance about mathematics skills, and that (2) student teachers who had struggled with mathematics identified that their former teachers had employed poor teaching practices, such as inadequate explanation of concepts, working from the textbook, worksheets, and poor teaching management practices.
A practical application of this study is that “the resources and pedagogical approaches used by teachers in classrooms need to be appropriate and respectful: teachers need to have a range of strategies to engage students in learning about mathematics in an enjoyable manner” (Boyd, Foster, Smith, & Boyd, 2014). This implies that pre-service teachers’ anxiety about mathematics can be successfully addressed by developing appropriate teaching strategies and interventions for use in the university education classroom context, with the view to ensuring that students become capable and proficient teachers of mathematics upon completing their Bachelor of Education’s degree program.
Lastly, informed by the need to delineate ways through which teacher efficacy can be enhanced, Kim, Sihn, and Mitchell (2014) set out 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 demonstrated by these authors, evidence has been generated to the effect that teachers who believe effective teaching can manipulate student learning (teacher efficacy) and who display confidence in their own teaching capabilities (self-efficacy) may avail “a greater academic focus in the classroom and offer diverse feedback according to the students’ academic backgrounds more than teachers who have low mathematics teaching efficacy belief” (p. 3).
Their study found that (1) the years of teaching experience achieved by teachers enhance their mathematics teaching efficacy beliefs, (2) the participation of elementary teachers in professional development programs and other certification courses enhances their mathematics teaching efficacy beliefs, and (3) teachers’ mathematics teaching efficacy beliefs increase as teachers attain higher academic degree in mathematics education.
Role of Cognitive Domain in Math Teacher Performance
Teacher efficacy beliefs form very strong determinants of the extent to which the teacher can accomplish various tasks (Pajares, 1996), with the available literature demonstrating that most of the cognitive domains are appreciably related to how individuals perceive their own self-efficacy and expectations (Artistico, Cervone, & Pezzuti, 2003). For example, as observed by Harrison, Rainer, Hochwarter, and Thompson (1997), an activity incorporating computer-related tasks tends to be performed well as individuals attain higher levels of perceived self-efficacy.
On the other hand, performance tends to decrease as the individuals’ level of perceived self-efficacy drop. Studies have also 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 are able to outperform those with lower levels of self-efficacy, giving credence 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 perform poorly, satisfactorily, or even extraordinarily.
According to Turner, Cruz, and Papakonstantinou (2004), teacher self-efficacy has a positive association with the willingness or readiness of a teacher to initiate new teaching ideas and to use them as variations in teaching strategies. This is consistent with Swars’ (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 traditional or teacher-directed methods and techniques, which is in sharp contrast to highly efficacious teachers who tend to build confidence among students, use student groups, and generously allow the learners to navigate through their own learning process for optimal comprehension. As postulated by Swars (2005), such teachers will also attempt to use a multiplicity of new strategies and methodologies without giving much attention to the fact that it may actually be a risky or challenging affair to implement the concepts in the learning environment.
Beyond instructional strategies, the available literature demonstrates that, if teachers have developed a high perception of their self-efficacy, they are highly unlikely to show flexible or rigid behaviors in the teaching of mathematics to students (Alsup, 2004; Franke, Kazemi, Kelley-Petersen, Hintz, Lampert, Ghousseini, & Chan, 2007; Rimm-Kaufman & Sawyer, 2004). Research further reveals that, if teachers demonstrate higher levels of self-efficacy perceptions, beliefs and expectations, they will undoubtedly demonstrate more capability in achieving control over the behavior of their classroom and consequently exercise a certain level of influence over the decisions made by school administrators (Ericsson, 2002). These factors are indicative of the teachers’ effectiveness in controlling the classroom and in making important decisions about the school in general.
In as much as 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 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 at teacher training colleges, it has been noted that the actual teaching experience of the teachers reinforces this mastery experience, which in turn leads to the teachers’ sense of high self-efficacy (Hoy & Spero, 2005; Franke, Kazemi, Kelley-Petersen, Hintz, Lampert, Ghousseini, & Chan, 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 on the basis of the signals and impulses received from the external environment.
Concerning psychological states or arousal, the available scholarship has noted that a positive correlation exists between the feelings of contentment developed by the teacher in his or her teaching experiences on the one hand and the contentment derived from the achievement of actual teaching on the other (Tschannen-Moran & Hoy, 2007). These factors are known to influence impressively the self-efficacy of teachers and their beliefs in a manner that substantially affects their capability to accomplish their desired tasks or objectives and hence 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 student learning outcomes, student motivation and attitudes toward the learning of different subjects, and that it is responsible for orienting 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 in improving their professional preparation and teaching practices” (Pajares, 1992, p. 307), hence the need for researchers in education to consider further how these factors specifically influence the efficacy of a teacher with the view to determining what is needed to assist teachers (especially teachers of mathematics) to gain a greater sense of teacher efficacy.
Effectiveness in Teaching of Mathematics
The debate on the various methodology courses provided at teacher training institutions is gaining prominence as educators and other relevant stakeholders increasingly realize that teacher quality is decisively tied to the educational outcomes demonstrated by students (Bray-Clark & Bates, 2003; Kim, Sihn, & Mitchell, 2014). 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 teaching because of their capacity to influence teachers’ teaching experiments as well as teacher-student interaction (Bray-Clark & Bates, 2003; Kim, Sihn, & Mitchell, 2014). Charalambous and Philippou (2003) found evidence for the supposition that carefully designed intervention programs (e.g., teaching practice programs or fieldwork) could result in positive shifts in dimensions of the affective domain and that it is possible to modify student teachers’ teacher efficacy beliefs since these beliefs 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 the effectiveness of teachers; however, only a few of these researchers (e.g. Arslan & Yavuz, 2012; Esterly, 2003; Isiksal, 2005; Kim, Sihn, & 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 basically 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, is likely to show a low teacher efficacy in teaching mathematics (Arslan & Yavuz, 2012; Brown, 2012; Kim, Sihn, & Mitchell, 2014).
This means that studying the impact of teacher efficacy on 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 (Cakiroglu, 2000; Gresham, 2008; Ipek & Camadan, 2012).
The beliefs of the teacher and the attitude of the teacher toward 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 content subject. Wilkins (2008) noted that the knowledge of the teacher, along with the attitudes, expectations and beliefs that he or she may hold, play a significant function in influencing the teacher’s instructional practice. Studies have also indicated that teachers with low opinion of and negative attitudes about math end up using traditional instructional methods that are essentially 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 refraining from the use of any innovation in technological support or other exploratory-based practices of instruction. This is in contrast to teachers demonstrating a positive attitude toward mathematics, who are described in the literature as always feeling confident in teaching the subject, as being very effective in their instructional practices, and as prepared to employ innovative techniques and creativity via an inquiry-based approach to successfully teach concepts in mathematics (Wilkins, 2008).
Conclusion
The review and appraisal of relevant literature in this chapter has demonstrated that the most powerful indicator that can be used in the evaluation of teacher effectiveness in general is teacher self-efficacy. It is of immense importance for pre-service mathematics teachers to be effectively prepared in the teaching of the subject, in influencing student outcomes, and in the handling of classroom dynamics if they are to succeed in improving the achievement of students within the school context. At the national and international levels, teachers of mathematics are at the core of the implementation of instructional and professional practices perceived as effective in influencing these teachers to achieve high and motivated levels of self-efficacy.
As such, the importance of the self-efficacy concept cannot be overemphasized if the success of mathematics teachers and mathematics students will be achieved and maintained in classroom contexts. In this study, the source of motivation has notably been the environment in which the teacher is operating from, the motivation derived from actual teaching experience, and the success of the students. This means that teacher educators and motivators should shift their focus from judging teacher efficacy by their academic and training achievements toward considering the success indicators derived from the actual teaching experience of the teacher. These have also been explained through theoretical studies of cognitive psychology as well as in social cognition. In these theories, self-efficacy has been directly related to teacher efficacy as an important educational research element.
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