Mathematics Teaching Efficacy Belief

Self-efficacy, first introduced in the 1970s by Albert Bandura, is one of the important components of social learning theory and is defined as individuals‟ judgments about how well one can organize and execute courses of action required to accomplish certain goals. Self-efficacy is the belief about one‟s own capacity of reaching the necessary degrees of learning and behaving (Bandura, 1977). According to Bandura (1977) expectations of personal efficacy are derived from four principal sources of information: performance accomplishment, vicarious experience, verbal persuasion, and physiological states. Performance accomplishment, especially past success and failure is the most influential source of efficacy beliefs. Vicarious experiences are the other factor effecting self-efficacy; the performances of other similar people may affect the judgments about self-competence, especially as individuals have little personal experience with the task. The third factor influencing self-efficacy is verbal persuasion. Encouragement may be more effective when it is realistic, reinforced by real experience and given by a credible person. Physiological states such as rapid heart beat, fatigue and pain, are the last factor effecting self-efficacy judgments. Bandura (1977) claimed that efficacy beliefs govern how people think, feel, motivate themselves and behave, and determine whether coping behaviour is initiated, how much effort is expended, how long the behaviour is sustained as faced with obstacles and unfavourable experiences. Further, parts of behaviours are constituted by beliefs (Enochs, Smith, & Huinker, 2000). 

Self-efficacy beliefs mediate the relationship between knowledge and action; even individuals may possess certain skills they may prevent to perform them. In other words, to perform specific actions effectively, knowledge, skills and efficacy beliefs are required (Huinker & Madison, 1997). People, who have high efficacy beliefs, tend to make more effort when they are faced with obstacles and as they attain necessary skills, they are more faithful for struggle (Schunk, 2007, p. 105-129). The examination of self-efficacy in relation to teaching has been the focus of several educational studies (Enochs et. al., 2000; Gibson & Dembo, 1984; Guskey & Passaro, 1994; Huinker & Madison, 1997; Tschannen-Moran & Woolfolk Hoy, 2001). Gibson and Dembo (1984, p. 570) relate self-efficacy belief concept with teacher efficacy belief as 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. 

Teacher efficacy belief is defined as „the extent to which teachers believe they can have a positive effect on student learning, and student achievement‟ (Ashton, Webb, & Doda, 1982a, p. 3) or „teachers' belief or conviction that they can influence how well students learn, even those who may be considered difficult or unmotivated‟ (Guskey & Passaro, 1994, p. 628). Teachers‟ sense of efficacy is related to students outcomes, such as achievement, motivation and their own sense of efficacy (Tschannen-Moran, Woolfolk Hoy, & Hoy, 1998) and approved as one of the most important factors affecting classroom activities implemented by teacher (Isiksal & Cakiroglu, 2005). Teacher efficacy has two dimensions as personal teaching efficacy and teaching outcome expectancy; the first dimension, personal teaching efficacy is defined as the belief in individual‟s own ability to teach effectively (Dembo & Gibson, 1985; Enochs et. al., 2000; Swars, 2005). The second dimension, teacher outcome expectancy is defined as the belief that effective teaching can affect student learning positively (Enochs et. al., 2000), regardless of external factors such as home environment, family background and parental influences (Swars, 2005), school conditions and IQ (Gibson & Dembo, 1984). 

Teacher efficacy influences teacher behaviours such as persistence on a task, risk taking, classroom instructional strategies, effort they invest in teaching, the goals they set, and the use of innovations (Asthon & Webb, 1986; Swars, 2005; Tschannen-Moran & Woolfolk Hoy, 2001). Teachers with high teaching efficacy beliefs, try new teaching strategies which are difficult to implement and involving risks such as sharing control with students (Riggs & Enochs, 1990). Teachers, who have strong sense of efficacy and confidence in teaching, are more likely to have students to improve their basic performances, even though students are coming from difficult home backgrounds or being difficult to motivate (Ashton et. al., 1982a). Further, they are found to be more likely to use inquiry and student centred approaches and to be more effective teachers (Czerniak, 1990; Swars, 2005), and believe that they can control or at least influence student achievement and motivation (Tschannen-Moran et. al., 1998). On the other hand, teachers with low efficacy beliefs have a tendency to use teacher centred approaches like lecturing and reading from the text (Czerniak, 1990; Swars, 2005). 

According to Ashton, Webb, and Doda (1982b) teachers who have high or low sense of efficacy have a tendency to behave in some specific ways to affect student motivation and achievement. Efficacy behaviours are listed as elevating expectations, valuing, pushing (encouraging), greeting behaviour, opening and closing ritual, equalizing response opportunities, feedback and teacher help, waiting, praising and respecting. In contrast, there are some inefficacy behaviours stated in the report such as lowering expectations, sorting, devaluing, and excommunication, shot-gunning, questioning and distancing. 

In recent years, the concepts of self-efficacy and teacher efficacy are becoming more popular in educational research regarding both students, pre-service teachers and in-service teachers, and there are many studies related with those in many countries. Isiksal and Cakiroglu (2006) conducted a study to investigate pre-service teachers‟ mathematics and mathematics teacher efficacy, and found that universities attended and grade levels have not affected mathematics teacher efficacy, but affected efficacy beliefs toward mathematics. In order to explore Turkish pre-service science teachers‟ science teaching efficacy and classroom management beliefs a study was carried out by Savran-Gencer and Cakiroglu (2007). Findings indicated that pre-service science teachers generally expressed positive efficacy beliefs regarding science teaching and they were interventionist on the instructional management dimension, whereas they favoured non-interventionist style on the people management dimension. Cakiroglu (2008) compared pre-service elementary teachers‟ sense of mathematics teaching efficacy beliefs in a Turkish university and in a major American university. Results revealed that pre-service teachers in the Turkish sample tended to have a stronger belief that teaching can influence student learning when compared with pre-service teachers in the US. Dede (2008) examined elementary and secondary mathematics teachers‟ self-efficacy beliefs, and found that the beliefs of the two groups about teaching effectively and efficacy in teaching are higher that the beliefs about helping the students and motivating them towards mathematics. Aksu (2008) and, Yenilmez and Kakmacı (2008) investigated relationship between the level of self-efficacy beliefs of pre-service elementary mathematics teachers, and pre-service teachers‟ gender, type of high school graduated, grade level and degree of achievement. It was found to be no differences in self-efficacy levels with respect to these variables.

The roles of self-efficacy beliefs, mathematics anxiety and working memory capacity in problem-solving accuracy, response time and efficiency were investigated by Hoffman (2010) and it was found that self-efficacy has a positive effect on problem-solving response time and problem-solving efficiency of pre-service teachers. The effects of community-based service learning (Cone, 2009), scaffolded, student-directed inquiry science course (Liang & Richardson, 2009), integrated science and mathematics content-based course (Moseley &Utley, 2006) and two-part, inquiry-based mathematics and science course (Richardson & Liang, 2008) on pre-service teachers efficacy beliefs were investigated, then results have shown that attending these type of courses increased the pre-service teachers efficacy beliefs. Woolfok Hoy and Spero (2005) investigated changes in teacher efficacy during the teacher preparation program and in the early years of teaching experience. Findings indicated that pre-service teachers‟ efficacy belief inclined during teacher preparation and student teaching, but fell with actual experience as a teacher during the first year of teaching and efficacy beliefs of teachers are difficult to change as they are attained. Since the positive impact on pre-service teachers‟ efficacy during teacher preparation program increases, then these individuals will engage in more effective teaching behaviours in future (Huinker & Madison, 1997). Woolfolk Hoy explained the importance of investigations carried out to examine teachers‟ sense of efficacy beliefs as following (Shaughnessy, 2004): 

Student learning is affected most directly by the hours they spend on appropriate tasks in classrooms… We will never have the perfect curriculum or teaching strategy, but teachers who set high goals, who persist, who try another strategy when one approach is found waiting- in other words, teachers who have a high sense of efficacy and act on it- are more likely to have students to learn. So the question of how to support and not to undermine teachers‟ sense of efficacy is critical.

The research studies related with teaching efficacy beliefs are important because they can help us understand better how to create learning environments that support teachers in their work (Shaughnessy, 2004). Teacher efficacy belief is an important factor influencing teachers‟ professional development and bringing about effective, self-confident, innovative teachers for attaining a better, improving, and impact education system to achieve higher order educational goals. Moreover, Hoy states that teaching efficacy beliefs are more open to changes in the early phases of learning to teach (as cited in Cakiroglu, 2008), for this reason attempts to increase the level of pre-service teachers‟ efficacy beliefs are crucial for teacher education programs. As a consequence, the concept of teacher efficacy beliefs with other dimensions of effective teaching practices will be investigated and findings will lead the ways for enhancing teacher education programs.