Teacher Efficacy in Secondary Mathematics: Fostering Confidence and Fluency
Introduction
In these days of better, faster, more, it is all about the numbers. Where are we ranked as a nation in mathematics prowess in regards to other economically developed countries? How many students are preparing to study science and other technical fields? What measures are being taken to focus teachers on these goals? The setting of this research was in progressive secondary mathematics classrooms focused on project-based learning with an emphasis on open-ended problems. The hypothesis was there would be higher than average state test scores because the methods used in these schools were focused on deeper learning. Deeper learning, as defined by the Hewlett Foundation (2013), states student learning should contain the following aspects: mastering content, thinking critically, collaborating, communicating effectively, and developing a growth mindset. Hence the anticipated results of using deeper learning techniques would equate with a deeper grasp of the concepts and procedures, which would translate into higher test scores. However, Figure 1 shows the percentage of students and their proficiency in Algebra II topics on the 2013 California STAR test (California Department of Education). The comparison between the setting school and the state averages was concerning due to the high percentage (74%) of students falling into the Below Basic and Far Below Basic categories. Though the setting school follows an integrated math approach, students in traditional or integrated series should be reaching equivalency in knowledge upon the completion of Math 3 or Algebra II.
Other areas of concern existed about mathematics instruction at the setting. There were parent meetings with the setting school director which focused on the mathematics program and its ability to prepare students for both college entrance exams and college mathematics courses. Students wishing to pursue a higher level of mathematics were supplementing their school learning with community college classes. Additionally, initial conversations with several math instructors revealed a lack of understanding of the vision of the mathematics program and feeling unprepared to provide curriculum to the wide breadth of learners in their classroom. The above factors led to an inquiry process surrounding the teaching and learning of mathematics in the setting of a progressive secondary school.
Many questions surround the challenges and goals of learning mathematics. There are pedagogical questions surrounding teacher and classroom practices. Do students need to be drilled in the basics before being able to apply them to higher level concepts? How can students discover mathematical formulas without knowing the “language” of mathematics? Mathematical fluency, or the state of being able to understand and transfer knowledge, may also be impacted by institutional practices or the ways in which schools define structures like student and teacher schedules, inclusion decisions, daily schedules and other factors. It is also important to identify and understand the goals and design principles of a school in relation to the structures it has developed.
In an attempt to influence the content of what high school graduates should know, state leaders in government and education united to create standards or a listing of academic goals for students. However, these standards do not address the institutional structures or pedagogy which should be in place to ensure their successful attainment. These new standards are also linked to student outcomes (yes, back to numbers) in the form of new standardized tests created by the Smarter Balanced Assessment Consortium (SBAC) and Partnership for Assessment of Readiness for College and Careers (PARCC), along with upcoming changes to the current college entrance exams created by the College Board (SAT) and ACT organizations. Whether individual teachers or schools view these assessments as a valid predictor of college success or preparedness, they both will be judged by student performance on these exams from rating boards, colleges/universities and probably their harshest critics, parents. This paper will not discuss the merits or inferiority of the standards and related tests, but it does hold the belief learning outcomes need to be measurable and attainable.
This research reviewed current theories in the pedagogy and the learning of mathematical knowledge. From there it examined teacher preparedness and analyzed reasons why teachers may have a gap in their sense of efficacy in the classroom. As per long term self-efficacy researcher Albert Bandura, “People’s beliefs about their capabilities affect what they choose to do, how much effort they mobilize, how long they will persevere in the face of difficulties” (Bandura, 1994, p.1). The research investigated the practices and data of a progressive, constructivist school who incorporate a project-based learning (PBL) pedagogy. The goal was to determine whether the practices being employed contributed to a sense of efficacy in teachers based on the current strategies provided by past and present experts. Examples of effective practices and recommendations for possible areas of improvement were provided with the intent of boosting the numbers: the numbers of students prepared for college and careers, along with the number teachers who feel prepared to teach them.
Research Question: What practices and school structures create a sense of efficacy in secondary mathematics teachers in order to develop mathematical fluency in students?
Other areas of concern existed about mathematics instruction at the setting. There were parent meetings with the setting school director which focused on the mathematics program and its ability to prepare students for both college entrance exams and college mathematics courses. Students wishing to pursue a higher level of mathematics were supplementing their school learning with community college classes. Additionally, initial conversations with several math instructors revealed a lack of understanding of the vision of the mathematics program and feeling unprepared to provide curriculum to the wide breadth of learners in their classroom. The above factors led to an inquiry process surrounding the teaching and learning of mathematics in the setting of a progressive secondary school.
Many questions surround the challenges and goals of learning mathematics. There are pedagogical questions surrounding teacher and classroom practices. Do students need to be drilled in the basics before being able to apply them to higher level concepts? How can students discover mathematical formulas without knowing the “language” of mathematics? Mathematical fluency, or the state of being able to understand and transfer knowledge, may also be impacted by institutional practices or the ways in which schools define structures like student and teacher schedules, inclusion decisions, daily schedules and other factors. It is also important to identify and understand the goals and design principles of a school in relation to the structures it has developed.
In an attempt to influence the content of what high school graduates should know, state leaders in government and education united to create standards or a listing of academic goals for students. However, these standards do not address the institutional structures or pedagogy which should be in place to ensure their successful attainment. These new standards are also linked to student outcomes (yes, back to numbers) in the form of new standardized tests created by the Smarter Balanced Assessment Consortium (SBAC) and Partnership for Assessment of Readiness for College and Careers (PARCC), along with upcoming changes to the current college entrance exams created by the College Board (SAT) and ACT organizations. Whether individual teachers or schools view these assessments as a valid predictor of college success or preparedness, they both will be judged by student performance on these exams from rating boards, colleges/universities and probably their harshest critics, parents. This paper will not discuss the merits or inferiority of the standards and related tests, but it does hold the belief learning outcomes need to be measurable and attainable.
This research reviewed current theories in the pedagogy and the learning of mathematical knowledge. From there it examined teacher preparedness and analyzed reasons why teachers may have a gap in their sense of efficacy in the classroom. As per long term self-efficacy researcher Albert Bandura, “People’s beliefs about their capabilities affect what they choose to do, how much effort they mobilize, how long they will persevere in the face of difficulties” (Bandura, 1994, p.1). The research investigated the practices and data of a progressive, constructivist school who incorporate a project-based learning (PBL) pedagogy. The goal was to determine whether the practices being employed contributed to a sense of efficacy in teachers based on the current strategies provided by past and present experts. Examples of effective practices and recommendations for possible areas of improvement were provided with the intent of boosting the numbers: the numbers of students prepared for college and careers, along with the number teachers who feel prepared to teach them.
Research Question: What practices and school structures create a sense of efficacy in secondary mathematics teachers in order to develop mathematical fluency in students?