The purpose of this study is to examine the impact of mathematics methodology courses on the self-efficacy and beliefs of pre-service teachers (Ediger, 2012; Hart, Smith, Smith & Swars, 2007), as well as to examine the possible factors responsible for shaping the efficacy beliefs regarding teaching practice among pre-service teachers (Savran–Gencer & Çakiroglu, 2008). This will ascertain the understanding of mathematics teachers about the learning process viewed from the perspective of their instructional beliefs and practices about learning (Ashton, Webb & Doda, 1982a). In this study, instructional themes are explored in their emergence from neuroscience and related theories in the process of learning (Artistico, Pezzuti & Cervone, 2003). The research will examine the effects of a mathematics methodology course on the efficacy beliefs of pre-service elementary teachers, with a focus on identifying:

- how the teaching efficacy of these teachers is affected by the course (Çakiroglu, 2000),
- how teachers perceive their skills, competence, and ability to teach mathematics,
- how the aspects of the teaching context affect the self-efficacy beliefs of these teachers upon exposure to the methodology course (Ball & bass, 2003).

Some researchers have shown that training teachers requires more than just supplying them with knowledge of requirements. Instead, teacher education programs ought to help in preparing pre-service teachers to adopt the approach of lifelong learning (U.S. Department of Education, 2008). As such, there is a need for teacher education to shift the current focus on helping pre-service teachers develop deeper levels of content knowledge (Bandura, 1986; Bandura, 1997). It should also incorporate the strategies for the training of pre-service teachers for engaging in progressive learning of content throughout their teaching careers in varying cultures (Lin, Gorrell, & Taylor, 2002; Stipek, Givvin, Salmon & MacGyvers, 2001). According to the updated standards (National Council of Teachers of Mathematics, 2000), a potential teacher needs at least a thorough grounding in the subject matters that they plan to teach in order to hold up to the standards set by the Department of Education (Musser, Peterson, & Burger, 2008). A Mathematics methodology course, in its turn, will help provide the knowledge and strategies that young teachers would otherwise spend years for locating; consequently, the course in question will help pre-service teachers become proficient in teaching Mathematics to young students even before the instructors start their teaching practice (Swars, 2005).

It would be wrong to assume, though, that the strategies for laying out the course material are the only pieces of information that the application of a mathematic model for teachers will help develop (Cohen, 1988). Quite on the contrary, the training of pre-service teachers will also incorporate a range of disciplinary tools, which will help the instructor locate a unique approach for enhancing the learning process for a specific student or a group of students having issues with understanding the material or finding the learning material engaging. The opportunity to change of the behavioral and attitudinal models that students adopt, therefore, can be viewed as a major breakthrough in teaching pre-service mathematic instructors (Cheong, 2010; Hoffman, 2010).

The effect of methodology courses on pre-service teachers has been examined in various empirical studies; for instance, Huinker and Madison (1997) studied the importance of such programs for preparing teachers working in elementary schools. Additionally, Cone (2009) explored the relations between the training of teachers and their self-efficacy. Such research articles have offered a rather detailed explanation of the challenges faced by these educators. As a rule, teacher-training programs are aimed at achieving several objectives. For instance, they should help an educator understand how various instructional techniques should be used in the classroom. Moreover, they are supposed to enhance the self-efficacy of a teacher, who should not be apprehensive of possible challenges that may arise during classroom activities (Hoy & Spero, 2005). In this case, this concept can be viewed as a person’s perception of his/her skills and the ability to achieve the expected educational goals (Phan, 2012). Research findings have indicated that the level of self-efficacy profoundly affects the behavior of a teacher in the classroom, especially his/her interactions with learners (Smith, 2008). It should be mentioned that a lack of teacher self-efficacy could adversely affect the educational outcomes of students. Therefore, it is vital to show how methodology courses can affect the attitudes and beliefs of future educators. This information can be important in the design of educational programs that are offered to future teachers who need to know how to cope with possible challenges.

Pre-service training is important for the professional growth of educators. The experiences of pre-service teachers have been explored in a variety of studies. For example, Del Prado et al. (Schaffer, Gleich-Bope & Copich, 2014) focused on the apprehensions and misgivings of pre-service teachers. Additionally, Walter Fajet et al. (2004) investigated the beliefs of teachers who did not have any practical experience. Such studies can be important in improving the educational programs designed for the teachers willing to upgrade their knowledge and skills, therefore, contributing the development of student–teacher relationships.

The discoveries of the efficacy of pre-service teachers have attracted close attention of many educators and psychologists. Researchers have noted that a teacher’s efficacy has specific dimensions that are related to the context of the learning environment as well as the subject matter (Bandura, 1977; Tschannen-Moran, Woolfolk, & Hoy, 1998). It is one of the variables that is used to predict the ability of a teacher to promote students’ learning and cognitive development. In particular (Harrison, Rainer, Hochwarter & Thompson, 1997), self-efficacy influences a teacher’s choice of instructional methods and his/her willingness to empower students and promote their creativity (Smith, 2008). Overall, this concept is widely used by people who design mathematics methodology courses since it is a critical element that influences the behavior of a teacher in the classroom (Cady & Rearden, 2007). In particular, the teachers adopting the aforementioned strategy as their manner of communicating with students should be sufficiently confident in their ability to achieve the educational objectives. Therefore, one should determine whether existing educational programs can help a teacher become more self-efficacious (Boud, 2012).

## Statement of the Problem

Though in the education environment, the emphasis is legitimately put on the methods and techniques of enhancing student knowledge, the significance of teachers’ professional evolution is not to be underestimated, either. Because of the necessity to condone with the existing standards and at the same time work on an original and compelling teaching method, a teacher often encounters a range of problems when starting to work on their professional competency when reaching a mature age. Herein the significance of teaching instructors to locate the most efficient strategies of approaching students at the earliest stages of teachers’ professional development; specifically, the need for teachers to acquire the necessary skills before they are capable of shaping their strategy for addressing the students should be mentioned.

Unfortunately, in the present-day environment, the importance of preparing teachers for handling specific issues related to motivating the students with the help of transformative leadership approach and being capable of serving as a role model for the learners in terms of personal and academic growth seems to have been abandoned. More to the point, the significance of enhancing teachers’ sense of self-efficacy at the pre-service stage of their career needs to be proven and reminded of. As a result, the urgency of the research in question is predetermined by the failure of the education authorities to create the environment that will facilitate the evolution of both teachers and students, thus, spurring the need for self-education in both and galvanizing each of the stakeholders for accomplishing more in the designated field.

More to the point, the significance of pre-service teachers education and further training is essential to the learning outcomes for students. Studies have shown that the learners, whose instructors have been adopting a homogenously encouraging model of teaching throughout the course and have been promoting certain behavior by using their own example as a model to follow (Hill, Phelps & Friedland, 2007), have shown better scores than the students, whose teachers chose a standard teaching approach (Smith, 2008).

## Purpose of the Study

The study in question aims at proving the significance of mathematic methodology courses for both pre-service teachers and their young learners. Particularly, the research will revolve around the analysis of the teaching strategies, in general and the reasonability behind the choice of specific teaching patterns and methods in particular adopted by pre-service teachers that have attended the aforementioned mathematic courses and those that are unaware of the mathematic model as one of the major tools in analyzing the learners’ progress and enhancing young students’ motivation (Henson, 2002).

On a more general scale, the goal of the study is to determine the importance of the mathematic model under analysis and promote its use as a perfect tool for developing proper teaching skills in general (Charalambous & Philippou, 2003). The fact that a teacher needs to seek a specific strategy for each class and even for each single student is incontrovertible; therefore, an instructor needs to be capable of locating a unique solution to each educational situation (Charalambous, Philippou & Kyriakides, 2008). Nevertheless, it is essential that a single problem solving model should provide the basis for the choice of a specific teaching approach. Herein the above-mentioned mathematic model factors in, allowing to create the basis for motivating the students of diverse backgrounds and with different learning abilities to excel in their academic endeavors, at the same tie spurring the professional evolution of instructors (Kazempour, 2008). The purpose of the study, therefore, is to prove that teaching pre-service instructors the given mathematical model as a basic tool for teaching young students is indispensable for the academic progress of the latter and the professional growth of the former (Lee, 2010).

## Definition of Terms

Several terms are important for this study. First, self-efficacy can be described as a person’s belief about his/her capacity to reach certain objectives or standards (Aemi, 2008, p. 32; Bandura, 1993). Therefore, this term can be applied to different areas of human activity (Creswell, 2007). This concept is associated with certain specific examples, such as teacher self-efficacy, which can be described as the degree, to which an educator believes in his/her ability to promote students’ learning or the development of their cognitive skills (Creswell, 2009). This attribute is important for instructors, who may represent different fields of education. Additionally, this term can be applied to a particular task or subject, such as mathematics (Steele & Widman, 1997). For instance, mathematics self-efficacy can be viewed as an individual’s belief about his/her capacity to solve mathematical problems (Marshall, 2007, p. 180). Finally, it is important to mention mathematics teaching self-efficacy, which can be regarded as a teacher’s perception of his/her ability to promote learners’ acquisition of mathematical knowledge or skills (Creswell & Clark, 2011; McClain & Cobb, 2001). These terms are vital for examining the main research questions of the study.

## Research Questions

Three research questions that guide this study:

- How do the teaching efficacy beliefs of elementary pre-service mathematics teachers differ between the beginning and end of a mathematics methodology course?
- What are the pre-service teachers’ perceptions of their skills, competence, and ability to teach mathematics?
- What aspects of teaching context affect the self-efficacy beliefs of pre-service educators?

These questions are related to both qualitative and quantitative research designs. One of them is aimed at discussing the relations between variables, whereas the other question is important for understanding the experiences of pre-service teachers.

## Theoretical Position

The concept of teachers’ self-efficacy is derived from the social cognitive theory developed by Albert Bandrura (1986) and other psychologists who examined the factors shaping human behavior. The term “efficacy expectation” can be described as the belief of an individual about his/her capacity to perform a certain task successfully. In its turn, outcome expectancy can be viewed as a person’s beliefs about the effects of his/her actions (Bandura, 1993; Hall & Goetz, 2013, p. 68). As a rule, a person’s outcome expectancy determines the performance standards that he/she tries to reach (Ashton & Webb, 1986).

This theoretical framework can be applied in defining a teacher’s self-efficacy as a person’s views on his/her ability to achieve the expected educational outcomes, such as learners’ acquisition of relevant knowledge and skills (Ashton, Webb & Doda, 1982b). Traditionally, two key components of a teacher’s efficacy: personal belief about one’s effectiveness and outcome expectancy are distinguished. This perception can contribute to the learning outcomes of students and their ability to acquire mathematical knowledge and skills (Bamdura, 1986).

The components of efficacy should be addressed because they shape the ways, in which educators interact with students. In particular, teachers should believe that they have the necessary skills or competences to promote students’ learning activities (Isiksal, 2005). Various scholars have noted that a teacher’s self-efficacy influences the learning outcomes of students as well as the instructional strategies used by the educators (Smith, 2008; Aemi, 2008). Overall, the study aims to examine the relations between the self-efficacy of a mathematics teacher and his/her behavior in the classroom. In particular, it is important to understand how educators can implement student-centered instructional strategies, which are critical for effective student performance (Bray–Clark & Bates, 2003). At this point, the possibility for students to perform without the student-centered approach implemented by the instructor should be considered (Brown, 2012). One may aver that the academic success of a student does not depend on whether the teacher adopts an ordinary or a student centered strategy in their teaching approach (Bursal & Paznokas, 2006; Granger, Bevis, Saka, Southerland, Sampson & Tate, 2012). Indeed, on a range of occasions, the learner only requires the basic instructions so that the learner could grasp the course material and succeed at learning the basic information concerning the subject matter (Brusal, 2007; Gresham, 2008). However, researches show that the lack of student centered strategies limits the application of other techniques for boosting learners’ performance (Bates, Latham & Kim, 2011). In other words, without a student centered approach, the use of information technology related tools, as well as any tools for better information retrieval in general, is pointless (Gavora, 2011). One might argue that the use of purely student centered strategies may lead to learners having an intermittent success in studying, with little to no opportunities for practicing their skills on their own and, therefore, gaining independence in learning. Fu (2013), however, points at the significance of combining the student-centered and the self-directed learning strategies (Fu, 2013) so that the incorporation of information technologies into the learning process (Hall & Ponton, 2005), though still remaining appurtenant to the overall learning process, could assist learners in acquiring knowledge and training new skills: “Based on learning through ICT, students are more capable of using information and data from various sources, and critically assessing the quality of the learning materials” (Fu, 2013, p. 113).

The effectiveness of pre-service teachers can be improved significantly if these professionals apply best practices that have already been tested in different settings (Hackett & Betz, 1989). These methods can help a teacher better anticipate and cope with possible challenges. In their turn, these strategies can be properly adopted if a teacher believes that he/she can successfully attain various educational goals (Berna & Gunhan, 2011; Kagan, 1992). Finally, methodology courses should strengthen the confidence of future teachers since this component can be important for improving the learning experiences of students (Lampert, 2001; Pendergast, Garvis & Keogh, 2011).

## Significance of the Study

Overall, the results of this study can show how the self-efficacy of pre-service teachers can change after their participation in a mathematics methodology course (Hammerness, Darling–Hammond, Bransford, Berliner, Cochran–Smith, McDonald, & Zeichner, 2005). The methodology course can be viewed as the independent variable that shapes the beliefs of teachers about their competence, skills, and ability to improve the learning of children (Alsup, 2004). Previous studies have already demonstrated the importance of self-efficacy as one of the factors that influences the behavior of a teacher. In turn, this study may prove the existence of the connection between methodology courses and self-efficacy levels. In particular, it is important to show how participation in this educational program influences pre-service teachers’ perceptions of their skills (Tschannen–Moran & Hoy, 2001).

The challenges that pre-service mathematics encounter can be partly explained by lack of confidence in their skills (McGregor & Lesley, 2011). Therefore, recommendations should be made about the design of methodology courses that should raise the level of pre-service teachers’ confidence (Tschannen–Moran & Hoy, 2007). The changes in teachers’ self-efficacy after participation in a methodology course can be viewed as one of the criteria according to which the specified educational program can be evaluated (Lampert, 1990). The study will highlight the need to provide sufficient support to future teachers, who should not be afraid of possible challenges (Tatar & Buldur, 2013; Kazemi, Lampert & Ghousseini, 2007).

## Delimitations of the Study

The sample of this study will include only college students attending Indiana University. In particular, it is necessary to focus on the experiences of participants studying early childhood and special education and currently taking a methodology course (Fajet, Bello, Leftwich, Mesler & Shaver, 2004). The study examines the self-efficacy of educators when they need to teach mathematics. The self-efficacy of teachers in other subjects will not be assessed (Esterly, 2003).

## Limitations of the Study

### The self report theory

A self report study is a survey where participants read and respond to questions without interferences from the researcher. The respondent is required to provide honest responses (Tracy, Robins & Tangney, 2007; Hofer & Pintrich, 1997). The key focus of the survey is on the study of individuals’ beliefs, feelings, and attitudes towards a specific object or phenomenon. The most commonly used assessment tools in this kind of study include interviews and questionnaires (Albayrak & Unal, 2011).

The current study aims at examining the sense of self-efficacy in relation to teaching mathematics among pre-service elementary teachers. Interviews and MTEBI will be used to carry out the self assessment of the respondents. The self report theory assumes that the respondent will provide truthful information with regards to their abilities as teachers (Bleicher, 2004; Rimm–Kaufman & Sawyer, 2004). However, this is not always the case, especially due to the willingness of the respondents to be represented in a favorable light with responses. Respondents may feel obligated to impress the interviewer (Hart, 2002). As such, they tend to provide wrong information that may be full of exaggerations. Since there is no way that the researcher can determine the validity of the information provided, the study may be compromised (Tracy et al., 2007). The current researcher acknowledges the shortcomings associated with the self report study and the possibility of respondents giving misleading responses. To address the issue, the participants will be informed that their names and information provided will be treated with confidentiality.

### Unrepresentative sample

To increase the validity of a given study, the sample size should be representative of the general population targeted by the researcher. The researcher may come up with a large sample, yet this sample may still fail to represent the population adequately (Voss, 2012). In addition, a small population makes it hard for the researcher to put into consideration all its qualities during sampling. To ensure that the right sample size is gathered, a sampling frame should be used. The practice ensures that the element of bias is eliminated (Battista, 1994).

In the proposed study, all students attending mathematics methodology course will be requested to participate in the survey. As a result, the sample is expected to be diverse and representative of all types of students to be assessed. However, the sample size will be definite. The respondents have the right to withdraw from the survey at any stage without prior notification. The provision may lead to under-representation of some of the student groups (Tschannen–Moran, Hoy & Hoy, 1998). The interview is also optional to the participants. As such, the researcher will have no option but to work with those willing to take part in the survey.

### Focusing on the Methodology Course Factor Rather than on Self-Efficacy

The aim of the proposed study is to determine the self-efficacy beliefs of pre-service instructors teaching mathematics. However, the research puts a lot of emphasis on methodology course. The two assessment tools that will be used in the study, which are the MTEBI and the interview (Enochs, Smith & Huinker, 2000), will focus mainly on the performance of the teachers taking the methodology course (Czerniak & Schriver, 1994). The tools tend to ignore the self-reported efficacy of the instructors in teaching mathematics. As a result, one may be led to believe that the study is meant to test the comprehension of the students in relation to the concepts taught in the methodology course (Grossman & McDonald, 2008). However, this is not the case. The research focuses on pre-service teachers and their self-assessment in relation to their current abilities. It would have been better if the researcher had taken a broader approach and assessed all pre-service mathematics teachers (Czerniak, 1990). The approach would address the problem of perceptions indicating that the study is focusing solely on the course. As such, the research may lack objectivity (Turner, 2010; Kim, Sihn, & Mitchell, 2014).

### One Semester may not be long enough to show a change in outcome measures

The success of the given research is directly related to the amount of time and other resources invested in it. Most studies, especially those involving a large number of participants, take a considerably long duration compared to those involving a small population (Guskey & Passaro, 1994). The amount of time dedicated to the research also determines how well the researcher is prepared to deal with issues that may arise during the process of collecting information. Researchers that have to work with tight schedules are often ill-prepared and in a haste to complete the undertaking, making it hard for them to get accurate results (Aerni, 2008).

The proposed research will be carried out in a single semester. A large population of pre-service teachers from a number of faculties at the Indiana University is to be studied. The investigation will also be carried out in two phases, before and after the methodology course. In addition, different tools will be used to collect and analyze data. Some of the instruments, such as interviews, are time consuming (Kranzler & Pajares, 1997; Pajares, 1992; Pajares, 2002). They require the researcher to engage personally with the respondents (Gay & Airasian, 2000). Hence, it is clear that there is not enough time to conduct a thorough investigation.

### The study does not address long term adherence

Most studies are carried out with the aim of examining a population to determine what needs to be done to improve on their skills and behavior (Bandura, 1977). As such, the researcher must strive to positively impact the population by coming up with a list of recommendations on what needs to be done to improve their welfare. In the proposed research, the investigator aims at examining pre-service elementary teachers’ sense of self-efficacy in relation to teaching mathematics (Arslan & Yavuz, 2012). The assessment will be carried out after the respondents have completed the methodology course (Wilkins, 2008). Once data is collected and analyzed, the findings will be documented. The researcher has not put in place follow up measures to ensure that the findings are used to improve the wellbeing of those students whose self-efficacy was below average. In addition, no steps are taken to ensure that those with high efficacy scores maintain their exemplary performance.

### The main outcome measures are limited to participant’s self-report and recall

A researcher must gather information from credible sources to enhance the success of a study. Hence, the researcher should support the approaches used for collecting and analyzing data in the study (Gay & Airasian, 2000; Pajares, 1996). Factual data is recommended since it can be easily tested for accuracy. In the proposed study, the researcher will depend on the respondents’ self-assessment. As a result, the outcomes of the study will be limited to the participants’ self-report and ability to recall past events. Consequently, it is difficult to assess the validity of the information provided by the participants. Cases of exaggeration may also arise. In addition, the respondents may not be able to recall all the information required for the study, increasing its limitations. Human beings are prone to making errors. As such, the data collected for the study cannot be considered to be completely reliable (Turner, Cruz & Papakonstantinou, 2004).

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## Appendix A

### Interview for Pre-service Teachers

- What are the differences between your instructional skills during the entry and at the end of the methodology course?
- Do you love mathematics as a subject yourself?
- Have you tutored mathematics before? If yes, for how long? How would you rate your performance at the time?
- Which elements of the course did you find the most helpful? Between peer interaction, presentation, and lectures, which element is commonly used by teachers in assessing their efficacy?
- Did you feel more or less self-efficacious about teaching mathematics when the class started? Please summarize your experiences. Explain why you used to have no impact on your self-efficacy?
- Do you think that a teacher is entirely responsible for the performance of the student? Justify your answer.
- Are you familiar with models that can be used to help children improve their understanding of the concepts taught in the methodology course? If so, what added advantage do you think you have over your peers? If not, what techniques do you use to help the students understand mathematical concepts?
- What is your reflection about tutoring students in the public school for one day? What the benefit of teaching students with the professor observation? What is your reflection about collaborative learning? What is the benefit from practicing the teaching strategies with your peers?
- How do you feel when you are unable to make all students fully understand a point that you are trying to convey? Which steps do you take to deal with this problem? Is the step effective in promoting understanding among the students? Do you think that you will use the new strategy you have learned in the course? Do you think that you can deal with the low-ability students? Are you open to new ideas? How often do you use directed whole-class instruction in your class? Does the students’ environment affect students’ motivation to learn?

## Appendix B

### Interview Questions

- What are the differences between your instructional skills during entry and at the end of the methodology course?
- Do you love mathematics as a subject yourself?
- Have you tutored mathematics before? If yes, for how long? How would you rate your performance at the time?
- Which elements of the course did you find the most helpful? Between peer interaction, presentation, and lectures, which element is commonly used by teachers in assessing their efficacy?
- Did you feel more or less self-efficacious about teaching mathematics when the class started? Please summarize your experiences. Explain why you have had no impact on your self-efficacy?
- Do you think that a teacher is entirely responsible for the performance of the student? Justify your answer.
- Are you familiar with models that can be used to help children improve their understanding of the concepts taught in the methodology course? If so, what added advantage do you think you have over your peers? If not, what techniques do you use to help the students understand mathematical concepts?
- What is your reflection about tutoring students in the public school for one day? What the benefit of teaching students with the professor observation? What is your reflection about collaborative learning? What is the benefit from practicing the teaching strategies with your peers?
- How do you feel when you are unable to make all students fully understand a point you are trying to convey? Which steps do you take to deal with this problem? Is the step effective in promoting understanding among the students? Do you think that you will use the new strategy you have learned in the course? Do you think that you can deal with the low-ability students? Are you open to new ideas? How often do you use directed whole-class instruction in your class? Does the students’ environment affect students’ motivation to learn?

### Mathematics Teaching Efficacy Belief Instrument (MTEBI)

Developed by Larry G. Enochs and Iris M. Riggs (Riggs & Enochs, 1990), used with permission.

Please indicate the degree to which you agree or disagree with each statement below by circling the appropriate numbers to the right of each statement (Enochs, Smith & Huinker, 2000).