Teacher self-efficacy, content and pedagogical knowledge, and their relationship to student achievement in Algebra I

The purpose of this quantitative study was to explore the relationship between teacher self-efficacy beliefs and the level of student achievement their students obtain as evidenced by the Algebra I Virginia Standards of Learning (SOL) assessment. This study also explored teachers’ mathematics content knowledge, mathematics pedagogical knowledge, and the relationship of each of these to their self-efficacy beliefs as teachers, and to student achievement. Finally, the study explored whether there were significant differences between teachers who teach Algebra I at the middle school level versus those who teach Algebra I at the high school level in each of the four variables under study. A strong correlation was found between teacher self-efficacy and mathematics pedagogical knowledge. The more mathematics pedagogical knowledge a teacher possesses, the higher his or her self-efficacy is likely to be. Teachers with high selfefficacy tend to exhibit behaviors in the classroom that lead to greater student outcomes. While this study did not find a significant statistical relationship between teacher selfefficacy, student achievement or mathematics content knowledge, these may be relationships worthy of future study. This study suggests that school leaders can impact student outcomes by providing high quality, on-going professional development for teachers in die area of mathematics pedagogy. Teaching teachers how to teach math will increase teacher’s self-efficacy which may lead to higher goals and greater effort, persistence, and resilience. These, in turn may ultimately impact the overall achievement of the students. Teacher Self-Efficacy, Content and Pedagogical Knowledge, and Their Relationship to Student Achievement in Algebra I Teacher Self-Efficacy and Student Achievement 2 CHAPTER 1: THE PROBLEM Statement of the Problem Algebra I is a unique course to involve in a research study for several reasons: 1) it is a gateway course a high school diploma cannot be awarded in the state of Virginia without a student taking and passing the Algebra I course and the End-of-Course (EOC) SOL assessment; 2) Algebra I is taught at both the middle school and high school level; and 3) math progress, particularly Algebra I, is an area of concern for researchers and educators nation-wide and within the context of global achievement and preparation. One way to address the concerns about student’s mathematics achievement is to ensure that teachers who believe that they can impact student learning are standing before our students. The purpose of this study is to build upon the research base in the area of teacher self-efficacy and student achievement in the Algebra I classroom, and to determine if there are statistically significant differences in these variables at the high school or middle school level, and in terms of the level of mathematics content and pedagogical knowledge a teacher possess. With this information in hand, school leaders can develop professional development that centers about die specific needs of teachers. Ultimately, this method impacts the achievement of students in Algebra I. Educational administrators, parents, and school leaders want every teacher to be able to say with confidence “As a teacher, I know that I can positively impact the learning of my students. ” Teacher self-efficacy is defined as a teacher’s belief in his or her capability to organize and execute the courses of action required to successfully accomplish specific teaching tasks in a particular context (Bandura, 1997; TschannenTeacher Self-Efficacy and Student Achievement 3 Moran, Hoy & Hoy, 1998). The concept of self-efficacy is an important one to study as it deeply impacts teachers’ behaviors, such as motivation, goals, persistence, and resilience, as well as their performance and attitudes toward their students (Erdem & Demirel, 2007). Teacher content and pedagogical knowledge are also important elements in understanding the complex nature of teaching. Not only do teachers need to believe they can have an impact on the learning of their students, but they must have a thorough understanding of the content they teach, as well as a firm grasp of which pedagogical method would be best utilized to teach a particular concept. Mathematics content knowledge is the knowledge a teacher has of various mathematics concepts and it is acquired through formal education (Cancoy, 2010). Mathematics pedagogical knowledge is the skills the teacher uses to impart specialized knowledge or content related to their subject area. Every student would do well to have a teacher standing before them who believes in their ability to positively affect the outcome of his or her learning and achievement. Teacher Self-Efficacy and Student Achievement 4 Teacher Behaviors Mathematics Content Knowledge Teacher Self-Efficacy for Math Instruction Mathematics Pedagogical Knowledge Student Achievement in Algebra I Figure 1. Conceptual Framework: Teacher Self-Efficacy, Content Knowledge, Pedagogical Knowledge and Student Achievement in Algebra I Mathematics Achievement In this era of educational accountability, schools and educational leaders are continually looking for better ways to assist students in meeting these various learning outcomes, as well as how to discover ways to meet the ever-increasing demands of the No Child Left Behind Act of 2001 (NCLB). NCLB has strict measures by which schools are judged each year. Many of these measures are based on achievement tests that students are required to pass to demonstrate mastery of state-approved curricula. The problem addressed in this study relates to recent reports from the Trends in International Mathematics and Science Study (TIMSS) which have highlighted the fact that American students perform more poorly than their peers in the rest of the world on Teacher Self-Efficacy and Student Achievement 5 mathematics assessments. The most recent T1MSS study ranked the United States tenth in math achievement, as compared to other developed countries (National Center for Educational Statistics, 2011). Educators are pondering how to move America’s students back into the forefront of mathematics achievement. One recommendation that came from a 2002 Southern Regional Education Board (SREB) study was to challenge students at a higher level prior to entering the ninth grade (Bottoms, 2002). Taking Algebra in the middle grades leads to enrollment in higherlevel math courses in high school and has not been found to increase failure rates (Bottoms, 2002). In the state of Virginia, there has been a strong push to have all students complete their study of Algebra I by eighth grade, the end of middle school for most students. This has placed formidable anxiety on middle school educators as they have had to find teachers who are not only certified, but are skilled enough to teach Algebra I to middle school students. Unfortunately, not every student meets the benchmark of completing Algebra I by the end of middle school, so Algebra I is one of the few courses in Virginia taught at both the middle and high school level. Additionally, Algebra I is a course which is required for all students to pass with a grade of D or better, and receive a passing score on the End-of-Course (EOC) Standards of Learning (SOL) assessment in order to receive a standard or advanced diploma. Thus failure in either the coursework or the assessment of Algebra I prohibits graduation. Given the importance of having students be successful in Algebra I, the mandates of NCLB, and the renewed push to have students be competitive in a global market, it is imperative to have teachers who are motivated by the belief that they can reach every Teacher Self-Efficacy and Student Achievement 6 student in these Algebra classes. This study will investigate the extent to which a teacher who stands before students with the belief that he or she can get even the most unmotivated of students to pass Algebra I has an impact on the achievement of students. The Role of Teachers In recent years, the accountability movement has intensified the attention given to the impact teachers have on the students in America’s classrooms. Bandura (1997) asserted that “the task of creating learning environments conducive to the development of cognitive competencies rests heavily on the talents and self-efficacy of teachers” (p. 240). Teachers’ talents are expressed in many different ways; from the style of teaching they employ, to the effort they devote to their craft, the depth of their content knowledge, or to the manner in which they interact with students. However, what remains consistently true about teachers is the key role they play in student outcomes. The research evidence that supports the important role of the teacher to student learning is plentiful. Wright, Horn, and Sanders (1997) found that the single most dominant factor affecting student academic gain is the teacher. Evaluation of numerous empirical studies found that the teacher made up 30% of die variance of determining what influences learning the most (Hattie, 2008). If a student has a high performing teacher for just one year, the student will attain an advantage over his or her peers that will last for several years (Stronge, Ward, Tucker, & Hindman, 2008). Haycock (1998) wrote “the difference between a good and a bad teacher can be as much as a full level of achievement in a single school year” (p. 3). Meanwhile, students who are assigned to several ineffective teachers in a row have significandy lower gains in achievement than those who are assigned to several Teacher Self-Efficacy and Student Achievement 7 highly effective teachers in sequence (Sanders & Rivers, 1996). Strong teachers appear to be effective with students of all achievement levels, regardless of the level of heterogeneity in their classrooms (Wright, Horn, & Sanders, 1997). Teachers are crucial to students’ opportunities to learn and substantial differences in math