Purpose, Research Variables, and Population

Purpose of Study

According to Bilim (2009), self-efficacy is the extent in which an individual achieves set goals and objectives. On the other hand, Hackett (1985) defined self-efficacy as the attitude and beliefs of an individual that determine the level of achievement he/she will attain with regards to the set goals and objectives. From these definitions, it is evident that success of an individual is highly determined by the self-belief that he/she has. It is as a result of this fact that psychologists always perceive self-confidence as an essential factor in determining the success of an individual (Borko et al, 1992). The level of efficacy within an individual plays a critical role in determining the effort he/she will put to achieve specific goals and objectives and the persistence such an individual will have on a given task. As Plourde (2002) asserts, individuals with self-efficacy view difficult tasks in life as challenges that need to be tackled rather than problems that should be avoided. In the process, therefore, such individuals come up with effective plans and strategies that they will use to achieve desirable goals and objectives given the challenges that they might be facing. On the other hand, people with low levels of efficacy usually shy away from the difficulties that they may face in life. Such individuals usually have low levels of aspiration. They also have low efficacy levels. Therefore, in an event where they are faced with challenges, such individuals will develop the belief that they do not possess the required skills and techniques to overcome such problems to become successful in the long run.

From this analysis, it is evident that self-efficacy plays a critical role in determining the confidence as well as the strategies that an individual will develop to overcome the challenges that they may face in a given situation. Self-efficacy also determines the choices that an individual will make, the effort that he/she will put to achieve specific goals and objectives, and the extent to which the individual will extend these efforts to achieve the set goals and objectives. In his study, Bandura (1997) formulated four sources of efficacy within individuals. These were:

1. Mastery of experiences – The skills and experiences possessed by an individual.
2. Psychological and emotional states – The effects that the emotions and psychological background of an individual have on his/her decision making process.
3. Vicarious experiences – The impacts that the success and/or failure of others have on an individual.
4. Social persuasion – The social interaction of an individual.

Several studies have been conducted to determine the impacts of self-efficacy in various academic fields including mathematics. Smith (1996) defined mathematics self-efficacy as the ability or the confidence that an individual has in accomplishing specific tasks or goals in mathematics. Mathematics self-efficacy is highly related to other academic constructs such as the teaching methods, practices employed, the performance in mathematics, and the attitudes, beliefs, and perceptions that individuals develop towards mathematics. Despite the detailed studies that have been conducted on these constructs, Swars (2005) asserts that only a few of these studies focused on pre-service teachers. Thus, to increase the knowledge available in this field, this study will focus on the correlations that exist between self-efficacy beliefs towards mathematics in pre-service teachers with their teaching practices. The results of this study will attempt to explain the teaching practices that pre-service teachers develop as a result of their levels of efficacy and beliefs that they have towards teaching mathematics. To achieve this, a quantitative study will be undertaken to determine the relationship that exists between the efficacy levels of pre-service teachers and the teaching practices that they employ. Consequently, the study will also focus on the impacts that these teaching practices have in teaching mathematics to elementary students.

Background of the Study

Teaching has always been a complex process. Thus, to ensure that this process is effective and efficient, several models, methods, and strategies have been advanced. For instance, it has been identified that learning mathematics is a lifelong process (Hart, 2002). The learning process can take place inside or outside a classroom. The learning process does not consider the age, sex, or background of an individual and most importantly, it increases the precision, and efficiency of an individual. Due to this fact, it is the role of elementary school teachers to ensure that their students have a strong foundation in mathematics in order to enable them to achieve these goals (Bilim, 2009).

To ensure the teaching process is effective, rigorous mathematics instructions need to be developed and implemented all through the learning process. However, the development of these instructions and the success that will be achieved through them highly relies on the attitudes and beliefs of the teachers. The attitude and belief that a teacher has determines the strategies that he/she will implement, the motivation that he/she will have to teach, the relationship that he/she will develop to his/her students and finally, the success that will be achieved (Bilim, 2009). It is with regards to these facts that curricula related to mathematics and its teaching has been reformed on several occasions in the United States of America as well as other nations in the world to ensure that pre-service teachers develop a positive attitude with regards to teaching and learning mathematics (Pajares, 1992).

Hiebert (2003) asserts that many pre-service teachers in the United States have developed the beliefs and attitudes with regards to the process of teaching and learning mathematics that go against the procedures that have been set by the National Council of Teachers of Mathematics (NCTM). According to the results of his study, Haser (2006) found that pre-service teachers have the perception that the process of teaching mathematics involves stringent rules, steps and procedures that have to be mastered to ensure that the teaching process is successful, effective, and efficient. Consequently, pre-service teachers view themselves as a bridge between the instructions contained in the teaching curriculum and materials and the process of acquiring mathematics by the students (Swars, 2010). Therefore, pre-service teachers tend to develop the attitude and belief that they need to possess a high level of knowledge authority for them to be successful in imparting knowledge to their students. As a result, such teachers tend to employ traditional methods while teaching their students. In accordance to the traditional methods, students are expected to learn mathematics by following direct instructions and using the concepts learnt to solve problems. This method has been criticized due to its emphasis on memorization and repetition that limits the chances of conceptual understanding of the concepts taught (Sikula, 2002). As a result, students fail to apply the concepts learned in solving problems in real life situations due to lack of creativity.

Using this model, pre-service teachers tend to develop a negative attitude towards mathematics as well as teaching. This in turn reduces their level of efficacy. As a result, such teachers will have neither the motivation nor the persistence to become effective in their profession. Developing such an attitude is detrimental, as it usually results in the application of rudimentary teaching strategies that usually result in the development of a poor relationship between the teacher and his/her students hence reducing the success of the overall teaching process (Swars, 2010). The deficiencies of the traditional method of teaching mathematics have always prompted NCTM to come up with effective teaching methods and practices. After a careful analysis of the problems encountered with the traditional methods of teaching, the proposed amendments by NCTM to develop new teaching models advocate for a constructive view of teaching and learning. Application of the new models increase the level of students’ participation in the learning. At the same time, the new teaching methods emphasize on the teaching of mathematical concepts using simple techniques to increase the level of understanding among students (Szabo, 2005). From the studies that have been conducted, teaching students using modern techniques and practices that follow the modern approach has proved to be more effective and efficient as compared to the traditional approach.

With these challenges, the results of several studies assert that the training programs for mathematics teachers need to be reformed. As Swars (2010) states, the length of pre-service courses is not enough to ensure that all the units of the course are taught to ensure that the students become effective and efficient professionals. Due to the limited length of the course, pre-service teachers usually graduate without developing the required skills and experience that is required to build strong efficacy levels within them. On the other hand, Krows (1999) stated that changing the beliefs of an individual is a difficult process since self-efficacy highly relies on the past experiences. Therefore, the beliefs, attitudes, and perceptions of many pre-service teachers are based upon the traditional teaching approaches and practices instead to the modern practices that focus mainly on imparting knowledge to the students in a comprehensible, effective, and efficient manner (Francis, 1996).

Therefore, from the research that has been conducted, it is evident that the level of self-efficacy and beliefs that an individual has towards teaching and learning mathematics plays a critical role in his/her professional development. Highly qualified and successful teachers usually have high levels of self-efficacy (Bandura, 1997). Such teachers therefore have positive beliefs and attitudes towards teaching and learning mathematics. As a result, they tend to have a positive impact on their students’ learning process. This increases their levels of learning and acquiring mathematical concepts (Sikula, 2002). Wilkins and Brand (2004) went on further to state that the role of teachers, irrespective of the grades that they teach, is not only to ensure that their students develop positive attitudes and perceptions towards mathematics, but also to ensure that they are taught in the most effective and efficient manner. Therefore, through high levels of self-efficacy, teachers are expected to utilize the knowledge that they have acquired together with their creativity to come up with reliable practices and methods that can be used to achieve these goals.

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

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

Characteristics of the Subject Population

1. Age – The age of the respondents for the study will range between 18-60 years. This age difference will ensure that the efficacy, beliefs, and attitudes of individuals of different age groups are collected. This will increase the ease at which the results of the study will be generalized to reflect trends within the general population.
2. Sex – The respondents for the study will be both males and females. Despite the fact that random sampling techniques will be utilized to collect quantitative data, considerations will be put in place to ensure that a balance between male and female respondents is achieved.
3. Number – The sample size of the study will comprise of 260 individuals. The study will use many respondents to increase the validity and reliability of its results by eliminating any errors that may arise in the process of data collection.
4. Inclusion Criteria – The study will include only the students who are majoring in education (pre-service) who are training as mathematics teachers at the elementary level.
5. Exclusion Criteria – The study will exclude any respondent who is not a student of Indiana University. Students who are not majoring in education (specifically mathematics) will also not be included. Finally, in-service teachers will also not take part in this study.
6. Vulnerable Subjects – This study will not include any vulnerable subjects, as all the participants will be adults who are of sound body and mind.

Methods and Procedures

To gain quantitative data, three different questionnaires will be administered to the target group through random sampling. The first questionnaire will aim at identifying the factors that determine efficacy levels in pre-service teachers (see appendix A). The second questionnaire will be used to determine the impacts of the teaching curriculum on the efficacy levels of pre-service teachers (see appendix B). The final questionnaire will be used to determine the impacts of efficacy on teaching practices of pre-service teachers (see appendix C). The interviews will be conducted with the help of a moderator. This will ensure that all requirements of the study have been precisely covered. The questionnaires for the study will be designed using the data and results from the qualitative study (literature review). This information will ensure that the resultant questionnaires are powerful tools for collecting quantitative data for the study. This information will help in designing the questionnaires. The resulting questionnaires therefore will be precise, flexible, and capable of collecting the relevant data that will be required for the research study. Consequently, the questionnaires will be structured in such a way to minimize the occurrence of errors Careful measures will be taken to avoid this. Prior to the study, the validity of the questionnaires will be tested so that they can be approved for use.

Analysis of data will involve three major steps:

1. Data preparation – The organization of the data that will be collected in this study for easy analysis.
2. Descriptive statistics – The description and interpretation of the data that will be collected. This will be conducted using charts and bar graphs to explain the trends that have been observed.
3. Inferential statistics that will be conducted to test whether the data that will be collected is consistent with the hypothesis of the study. This is where either the null hypothesis or alternative hypothesis is proved to be true.

For accurate analysis of the statistical data, SPSS 16.0 will be used for descriptive data analysis. The data will be explored using descriptive statistics and histogram plots to determine the shape of the distribution for each sample variable. The name given to each variable in the data analysis will be provided in a table.Data analysis will be carried out using parametric tests where the data will follow a normal distribution and where the sample number will be equal to or greater statistical power. Where the data will not follow a normal distribution or where the data will be split into groups of less than the sample size (n), non-parametric test will be used.

Risks and Benefits

1. Potential risks – This study has not been associated with any risks whatsoever.
2. Protection against risks – Since no risks are likely to arise, protection against risks will not be applicable in this study.
3. Potential benefits – This study is beneficial, as it will bring about a clear understanding of the attitudes, beliefs, and efficacy that pre-service teachers have towards mathematics. From the results of the study, the relationship between self-efficacy and teaching practices will be arrived at. Finally, the study will expound on measures that are to be taken to ensure that teachers’ training process is rigorous leading to the development of professionals who are effective and efficient in performing their duties.
4. Compensation for participation – Participants for the study will not be compensated, as their involvement will be voluntary.
5. Alternatives to participation – There will be no alternatives to participation
6. Information withheld – All the information provided by the participants will be confidential.
7. Debriefing – A summary covering the procedures and results of the study will be made available to any participant at the end of the study.

Confidentiality

Prior to being interviewed, the confidentiality of the respondents will be guaranteed. The information that will be gathered from the study will not be accessed by any unauthorized individuals unless in the event of an investigation where a warrant has been issued. The researcher will store personal information as well as the data that will be 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 an event where a participant wishes not to be included continue with the process, the questionnaires that have been administered to him/her will be destroyed immediately.

References

Bandura, A. (1997). Self-efficacy: The Exercise of Control. New York: W. H. Freeman and Company.

Bilim, E. (2009). Preservice Elementary Teachers’ Attitudes and Self-efficacy Beliefs toward Mathematics. Journal of Education and Science, 34 (151), 132-139

Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., &Agard, P. C. (1992). Learning to Teach Hard Mathematics: Do Novice Teachers and their Instructors Give Up too Easily? Journal for Research in Mathematics Education, 23 (1), 194-222.

Francis, R. W. (1996). Connecting the Curriculum through the National Mathematics and Science Standards. Journal of Science Teacher Education, 7(1), 75-81.

Hackett, G. (1985). Role of Mathematics Self-Efficacy in the Choice of Math-Related Majors of College Women and Men: A Path Analysis. Journal of Counseling Psychology, 32(1), 47-56.

Hart, L. (2002). Preservice Teachers’ Beliefs and Practice after Participating in an Integrated Content/Methods Courses.School Science and Mathematics, 102 (1), 4-14.

Haser, C. (2006). Investigation of Preservice and Inservice Teachers’ Mathematics Related Beliefs in Turkey and the Perceived Effect of Middle School Mathematics Education Program and the School Context on These Beliefs.Unpublished Doctoral Dissertation: Michigan State University.

Hiebert, J. (2003). What Research says about the NCTM Standards. Reston, VA: National Council of Teachers of Mathematics.

Krows, A. J. (1999). Pre-Service Teachers’ Belief Systems and Attitudes toward Mathematics in the Context of a Progressive Elementary Teacher Preparation Program. Unpublished Doctoral Dissertation: The University of Oklahoma.

Pajares, M. F. (1992). Teachers’ Beliefs and Educational Research: Cleaning up a Messy Construct.Review of Educational Research, 62(1), 307-332.

Plourde, L. A. (2002). The Influence of Student Teaching on Preservice Elementary Teachers’ Science Self-Efficacy and Outcome Expectancy Beliefs.Journal of Instructional Psychology, 29 (1), 245-253.

Sikula, T. (2002).Handbook on Research on Teacher Education: A Project of the Association of Teacher Educators.New York: Macmillan.

Smith, J. P. (1996). Efficacy and Teaching Mathematics by Telling: A Challenge for Reform.Journal for Research in Mathematics Education, 27(1),387-402.

Swars, S. L. (2005). Examining Perceptions of Mathematics Teaching Effectiveness among Elementary Preservice Teachers with Differing Levels of Mathematics Teacher Efficacy. Journal of Instructional Psychology, 32(2), 139-147.

Swars, S. (2010). The Development of Mathematics Beliefs of Elementary School Teachers. Web.

Szabo, Z. (2005). Efficacy Sources for Preservice Teachers.Academic Exchange Quarterly, 9(4), 166-171.

Wilkins, J. and Brand, B. (2004). Change in Preservice Teachers Beliefs: An Evaluation of a Mathematics Methods Course.Schools Science and Mathematics, 104 (1), 226-233.