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Mathematics Methodology Classroom Effect on Efficacy of Elementary Teachers Analytical Essay

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Updated: Jun 12th, 2019

Background of the Study

The theoretical concept of this research is teacher efficacy and belief, which originated from Bandura’s self-efficacy in social cognitive theory (Bandura, 1986). It has two elements, which include “efficacy expectations and outcome expectancies” (Bandura, 1986). The author is also quite categorical that efficacy among individuals has been demonstrated in various ways. For example, individuals can undertake self reflection in order to boost their levels of self efficacy.

In addition, they are excellent self-regulators especially if they are allowed to monitor themselves. Other similar characteristics of self efficacy include being proactive, and self-organizing. Bandura notes that human beings usually contribute to the circumstances facing their lives besides the fact that they are products of the same circumstances.

Kazempour also shares a similar sentiment about the relationship between the ideas of self-efficacy and teacher efficacy by asserting that they relate to each other (Kazempour, 2008). He noted that teachers who demonstrated confidence in mathematics teaching strategies had the ability to influence their students. In this context, the teacher’s belief has a direct influence on potential student outcomes in mathematics.

It is also imperative to mention that teachers can use various strategies to enhance student outcomes and provide appropriate feedback that encourages positive results. As a matter of fact, teachers with high levels of efficacy have the ability to put in place and utilize various types of strategies. It is not possible to deliver the best results and claim efficacies if myriad types of strategies are not sourced and utilized.

The role of an elementary teacher should be to improve student outcomes through different teaching strategies. Based on this observation, Kazempour (2008) concluded that learners’ performances in mathematics depended on their teacher’s efficacy, because teacher efficacy as dictated by the use of various strategies had a significant influence on the outcome of students. When multiple and efficient strategies are used, learners are easily motivated and therefore are expected to perform exceptionally well.

On the same note, Bursal (2007 also noted that the use of self-efficacy in improving mathematics literacy allowed teachers to enhance student outcomes regardless of their social backgrounds or other challenges (Bursal, 2007).

Teachers who were aware of self-efficacy stressed the importance of learners in the teaching and learning process. Such teachers made students believe they were a part of the learning process. In this model, learners may feel that their contributions are also important to the class and develop interest in the subject (Bursal, 2007).

With reference to Bandura’s theoretical framework and other studies on personal efficacy and teacher self-efficacy, teacher efficacy may be defined as the teacher’s “judgment of his or her capabilities to bring about desired outcomes of student engagement and learning, even among those students who may be difficult or unmotivated” (Bandura, 1986; Ashton, Webb, & Doda, 1982a; Ashton, & Webb, 1986). It is important to understand the two aspects of teacher efficacy.

Teachers also have personal beliefs through which they view the effectiveness of their teaching strategies. In addition, teaching outcome expectancy consists of teachers’ beliefs that effective teaching can effective teaching can create “positive student learning outcomes regardless of external factors” (Bandura, 1986; Ashton, Webb & Doda, 1982b).

Teachers who hold this view believe that external factors such as family background, parental influence, IQ, school conditions, and home environment do not influence a student’s performance in mathematics once the teacher uses the appropriate strategy to enhance the student’s ability to learn and grasp new information.

The above is among the strategies that have been employed to boost the efficacy of teachers when handling mathematics at the elementary level. This strategy is indeed an effective mathematics methodology for improving the efficacy of teachers (Cone, 2009).

In yet another assertion, the author made it clear that community-based service learning “significantly influenced pre-service elementary teachers’ outcome expectancy toward equitable science teaching and learning” (Cone 2009, p.26). Cone’s study aimed to establish why pre-service teachers had low levels of teaching efficacy beliefs despite the improvement in science and other education courses.

Problems may occur when the teacher is not certain about his or her skills or ability to ensure effective teaching. Teacher efficacy accounts for learners’ achievement, teacher behavior, and motivation, but it tends to be specific to certain contexts (Little, 2003).

Within the context of mathematics, teaching efficacy focuses on two fundamental areas that relate to two aspects of teacher efficacy: mathematics teaching efficacy and teaching outcome expectancy. Few studies regarding mathematics teaching efficacy among elementary pre-service teachers exist.

However, available studies have shown “a statistically significant increase in mathematics teaching efficacy after completion of one methods course or a sequence of methods courses” (Huinker & Madison, 1997; Cakiroglu, 2000). Moreover, such improvements were also evident after completing content in mathematics courses.

According to Lee (2010), studies have concentrated on teacher efficacy and correlated its significance to factors like classroom instructional strategies and eagerness to use new approaches in teaching. Both pre-service and in-service teachers who demonstrated high standards of teacher efficacy often used various approaches during their classroom lessons.

Czernaik noted that teachers who possessed high standards of self-efficacy were most likely to use inquiry and student-centered teaching and learning methods (Czerniak, 1990). On the other hand, teachers who had low-levels of self-efficacy were likely to apply teacher-centered approaches in the classroom.

In addition, teachers who had high standards of teaching efficacy were likely to apply new methods in their classrooms. This could be a difficult method to implement, “involved risks and would require sharing control with learners” (Czerniak, 1990, p.120). Such teachers attempt to match reforms proposed by the NCTM of 2000.

Pre-service teachers often have preconceived beliefs concerning mathematics and their teaching and learning abilities in this subject (Cakiroglu, 2008). Most of these beliefs originate from their experiences as students. A number of these pre-service teachers have different views about mathematics. According to Cakiroglu, pre-service teachers also noted that exposure to “reform strategies in mathematics methods courses affected their level of mathematics teacher efficacy” (Cakiroglu, 2000).

Hoffman studied the role of “self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency; i.e., the ratio of problem-solving accuracy to response time (Hoffman, 2010). He noted that there were differences in “self-efficacy role on efficiency and response time, and a possible compensatory association between self-efficacy and mathematics anxiety in relation to efficiency outcomes” (Hoffman, 2010).

Some past studies have noted that pre-service teachers with high standards of mathematics teacher efficacy often used manipulative instructional strategies. When manipulative strategies are used, misconceptions that may arise from poor instructional methods are avoided. For example, when mathematical teachers offer instructions to learners, it is vital for them to diagnose the common errors that individual learners often face when carrying out calculations.

It may be possible that a learner persistently fails a particular mathematical problem due to misconceived ideas. If such misconceptions are not dealt with out rightly, the affected learner may continue facing the same mathematical challenge. It is against this backdrop that the mathematical teacher is supposed to make use of instructional exercises that cannot just diagnose the problem, but also assist the learner to solve the mathematical challenge as quickly and effectively as possible.

It is inevitable that learners may sometimes experience difficulties when handling mathematical problems. While some of these difficulties may be occasioned by ineffective instructional methods in a classroom environment, it is also possible that students may individually acquire erroneous procedures and misconceptions when they are practicing how to carry out mathematical computations.

Perhaps, mathematical instructions should take the form of paper and pencil guideline especially when teachers are introducing new concepts to young learners

Therefore, pre-service teachers who demonstrated high standards of mathematics teacher efficacy were favorable toward reforms in teaching and learning mathematics. On the other hand, pre-service teachers who demonstrated low standards of mathematics teacher efficacy required improvement in their manipulative strategies in order to facilitate teaching mathematics in classrooms. Such outcomes are persistent with some past studies (Battista,1994;Czerniak, 1990).

Cakiroglu (2000) is of the opinion that pre-service teachers must understand the importance of classroom instructional approaches and teacher efficacy besides showing their eagerness for adopting reforms in teaching and learning mathematics at the elementary level. The author has used a theoretical model to expound this phenomenon.

Cakiroglu noted that it was important for elementary pre-service teachers to take part in “a mathematics methods course in order to increase mathematics teacher efficacy” (Cakiroglu, 2000, p.92). In addition, elementary pre-service teachers also require encouragement and outstanding experiences when teaching mathematics method courses.

This will allow such teachers to work toward achieving the efficaciousness required by mathematics reforms. It is also vital for pre-service teachers to gain and utilize the much needed teaching experience bearing in mind that long term exposure to different levels of complexities often enhances teacher efficacy and high level delivery of lesson content.

To ensure that all these factors are considered, this study will seek to answer the following questions:

  1. What are the main impacts of the teachers’ training course on the self-efficacy levels of pre-service teachers?
  2. Do self-efficacy and beliefs towards mathematics affect the behavior of pre-service teachers in classrooms and their teaching practices?
  3. How do the participants view mathematics, and what is the relationship between their perception of mathematics and their classroom practices?
  4. What are pre-service teachers’ perceptions of their understanding of the subject of mathematics and their ability to teach the subject?

Characteristics of the Subject Population

Age range. The age range for research participants will be 20 years and above. This will account for diversity among pre-service teachers in the United States.

Gender. Research participants will consist of both female and male pre-service teachers in the ratio of 1:1 respectively.

Number of participants. Approximately 14 to 18 pre-service teachers in Indiana university of Pennsylvania

Sample. The researcher will determine the appropriate sample based on the population of pre-service teachers in the region of the study. This sample will consist of pre-service teachers enrolled in a method class.

Inclusion criteria. The study will include only Indiana University of Pennsylvania students who are majoring in education (pre-service) and are training as mathematics teachers at the elementary level.

Vulnerable subjects

No vulnerable subjects will be included in the study. The participants are adult and volunteers. They can withdraw at any time in the study.

Methods and Procedures

Method of Subject Selection

In order to conduct the study, a list of pre-service teachers in Indiana University of Pennsylvania will be obtained from the coordinators of the mathematics departments. Each of the mathematics department will be requested to avail 3 male and 3 female participants in order to balance the number of participants in the survey.

Study Site

The study site for each interview will be in University settings. However, she will also respect the wishes of respondents. Therefore, respondents are free to choose a location for the interview.

Methods and Procedures Applied to Human Subjects

Firstly, I will send the survey to everyone by the email n the beginning of the semester then at the end of the semester I will ask the class to participate in the interview. In the end of the semester the one who agree to participate will sign the consent and put it in the box. I will then interview them individually in a university sitting

The study will engage respondents in a face-to-face interview. This will provide the opportunity to gather the in-depth information necessary for the study question. The preferred place for the interview is a school environment. This is necessary to ensure professional tone during the process.

The study will use survey questionnaires to gather data. The study will involve the use of tape recorders. The researcher will transcribe all collected data and draw his conclusions. This is a preliminary stage of collecting data for the main study. Collected data will help the researcher to identify common themes and formulate appropriate study questions.

Risks or Benefits

Potential Risks

This study does not pose any form of risk to research participants. There is no form of intervention in the study.

Protection against Risks

The study does not pose risks to participants. Therefore, no protection against potential risk is necessary.

Potential Benefits

  1. This study will assess the pre-service teachers’ attitudes, beliefs, and efficacy toward mathematics. From the results of the study, the relationship between self-efficacy and teaching practices will be determined. Finally, the study will discuss measures that can be taken to ensure that teachers’ training processes are effective and lead to the development of professionals who are effective and efficient in performing their duties.
  2. Compensation for participation: Participants for the study will not be compensated, as their involvement will be voluntary.
  3. Alternatives to participation: There will be no alternatives to participation.
  4. Information withheld: All the information provided by the participants will be confidential.
  5. Debriefing – A summary of the procedures and results of the study will be made available to any participant at the end of the study.

Privacy or Confidentiality


Prior to the interview process, the confidentiality of the respondents will be guaranteed. The information gathered from the study will not be accessed by any unauthorized individuals except in the event of an investigation where a warrant has been issued. The researcher will store personal information as well as the data generated from the study in a secure location.

Consequently, the confidentiality of the respondents will be maintained during the data analysis and interpretation phases. In the event a participant wishes not to be included or continue with the process, the questionnaires that have been administered to him/her will be destroyed immediately.


Ashton, P. T., Webb, R. B., & Doda, N. (1982a). A study of teacher sense of efficacy, Final Report Volume 1. Florida: Foundation of Education University of Florida.

Ashton, P. T., Webb, R. B., & Doda, N. (1982b). A study of teachers’ sense of efficacy, Final Report Volume 2. Florida: Foundation of Education University of Florida.

Ashton, P.T., & Webb, R.B. (1986). Making a difference: Teachers’ sense of efficacy and student achievement. New York: Longman.

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 34, 191-215.

Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory.Englewood Cliffs, NJ: Prentice Hall.

Battista, M. T. (1994). Teacher beliefs and the reform movement of mathematics education. Phi Delta Kappan, 75, 462-470.

Bursal, M. (2007). Turkish preservice elementary teachers’ self- efficacy beliefs regarding mathematics and science teaching. International Journal of science and Mathematics Education, 8(4), 649-666.

Cakiroglu, E. (2000). Preservice elementary teachers’ sense of efficacy in reform oriented mathematics. Indiana: Indiana University.

Cakiroglu, E. (2008). The teaching efficacy beliefs of pre-service teachers in the USA and Turkey. Journal of Education for Teaching, 34(1), 33-44.

Cone, N. (2009). Pre-service elementary teachers’ self-efficacy beliefs about equitable science teaching: Does service learning make a difference? Journal of Elementary Science Education, 21(2), 25-34.

Czerniak, C. M. (1990). A study of self-efficacy, anxiety, and science knowledge in preservice elementary teachers. Atlanta, GA: the National Association for Research in Science Teaching.

Hoffman, B. (2010). “I think I can, but I’m afraid to try”: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and Individual Differences, 20(3), 276–283.

Huinker, D., & Madison, S. K. (1997). Preparing efficacious elementary teachers in science and mathematics: The influence of methods courses. Journal of Science Teacher Education, 8(2), 107-126.

Kazempour, M. (2008). Exploring attitudes, beliefs, and self efficacy of pre-service elementary teachers enrolled in a science methods course and factors responsible for possible changes. Ann Arbor: UMI Dissertations Publishing.

Lee, T. (2010). Teaching mathematics creatively, New York, NY: Taylor & Francis.

Little, M. E. (2003). Successfully teaching mathematics, Educational Forum, 67(3-6).

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