Teacher Efficacy in Secondary Mathematics: Fostering Confidence and Fluency
Research Methods
My original research question was to determine what school structures and teaching practices led students to obtain mathematical fluency, or learning the language of math and to use it effectively and transformatively. This question was formed through preliminary conversations with parents, teachers, students and looking at numerical data, such as SAT and state test scores. There seemed to be questions regarding the college preparedness of some students, specifically in mathematics. After initial rounds of data gathering, the research question evolved to one focused on school practices and structures which promote a sense of teacher efficacy in the teaching of secondary mathematics. Efficacy in teaching is the ability of teachers to produce the desired results they wish to see in their students. Practices and structures are the methods schools use to develop and support their teachers; examples include professional development opportunities, instructional coaching, daily schedules, and prep periods, etc.
Data collection tools included: surveys, interviews, focus groups, exit cards, journal entries/field notes and math discipline meeting notes. Though some quantitative data was extracted from the teacher survey results, the remainder was gathered by analyzing the school’s student survey data (YouthTruth), and standardized test scores, including both state and college entrance exams.
In order to provide context and uncover areas of strengths and challenges, I surveyed secondary math teachers across the organization. The questions began with information on professional background/history and current teaching assignments. There were perception questions on various mathematical teaching beliefs and practices via a scaled ranking system. Finally, there were open-ended questions ranging from the definition of math projects to how an all-inclusive model affects their teaching (see Appendix A).
Next, I interviewed school directors (principals). The interviews gathered background and context information as to what roles and how long they had been associated with the community. From there, the interview transitioned to how and why they created the structures and supports for the mathematics program at their site. I used a semi-structured interview process with the school directors to understand their vision and allow for unknown developments to evolve (Appendix B). The goal was to understand what practices school directors employed with the aim of being able to corroborate certain areas where teachers were feeling supported and/or areas to further examine concerns.
Meanwhile, I sent college advisors a short survey (Appendix C) to gain their perceptions of college preparedness, successes or challenges in the application process, and the rigor regarding course offerings, all in respect to mathematics. As college advisors, they are aware of challenges surrounding students in applying to and choosing colleges. The advisors also work with students and colleges through the Early Assessment Programs (EAP) which determines college placement for many students. My focus was on college mathematics course placement and percentages of students requiring remedial courses. As teacher efficacy and student success has been found to have a correlation (Hoy & Spero, 2005; Bandura, 1997), this data helps provide context to the problem.
The remainder of my qualitative data collection was focused on the work done with a math discipline (department) group. Data gathering techniques included: meeting notes, journal entries, exit cards and individual interviews of team members. The interviews focused on their background and preparation for teaching, challenges and rewards surrounding their current work, and identified needs for support/growth as an educator.
The quantitative data collected included an analysis of YouthTruth (student survey data) to analyze student perception of the mathematics instruction and structures, and their feelings of college preparedness. Test scores, with a focus on the college entrance exams of SAT and ACT, were gathered and compared to state and national averages. The goal of gathering and analyzing all of this data is to provide school communities with a picture of what structures and practices help facilitate a sense of efficacy for secondary mathematics teachers.
Data Collection
Surveys (December, January)
The surveys provided a means for capturing teacher and college advisor perceptions of the work surrounding the instruction and preparedness of students in mathematics. They provided both qualitative and quantitative data with the hope of developing key concepts and themes around the highlights and areas for improvement. The respective surveys were sent to thirty teachers and five college advisors across five campuses. The data for perception questions was quantified in tables and graphs to determine trends. The open-ended questions were coded to capture keywords and trends supplementing baseline interview questions.
YouthTruth, a service which collects student perceptions on schools and their learning, surveyed the students of the setting schools. The results were analyzed for trends in student satisfaction surrounding the mathematics program and their perceptions of teacher efficacy.
Interviews (January, March)
The interviews provided more in depth reporting and analysis of director, instructional coach and teacher thoughts regarding mathematics instruction. Four director interviews were focused on the reasoning for certain school structures, like daily schedule, course definition and support personnel. Two instructional coach interviews were focused on what practices they felt supported teachers and areas for continued teacher/instructional growth. Five individual teacher interviews were focused on their preparation for teaching mathematics, perceptions and reasoning for issues surrounding mathematics instruction and student learning, and areas for support. Partial transcripts of the interviews were coded and triangulated with results from the surveys and theory to create findings.
Inquiry Journal, Field Notes (Ongoing December - March)
These notes were a compilation of my observations and participation in meetings, conversations and teacher and student interactions. They provided insights into the methods employed and other perceptions of the work of teaching and learning mathematics. These notes were reviewed and coded with keywords to supplement earlier research.
Math Discipline Meeting Notes (Bi-Weekly December - March)
These notes were a collection of participant activities and discussions surrounding the investigation and defining of mathematical practices at one of the school sites. Teachers worked together to brainstorm, rank and further define and reflect on these practices. These notes were analyzed for trends and real life examples of teachers creating both individual and collective senses of efficacy.
Timeline
November 2014
- IRB submission
- IRB approval
- Teacher survey sent (with online consent question)
- Ongoing journal/field notes
- Math discipline meeting notes commence (with participants providing consent via online form)
- College advisor survey sent (with online consent question)
- Director interviews (with signed consent forms)
- Instructional coach interview (with signed consent forms)
- Ongoing journal/field notes
- Ongoing math discipline meeting notes
- Exit card following math discipline meeting
- Ongoing journal/field notes
- Ongoing math discipline meeting notes
- Ongoing journal/field notes
- Gathered test score and YouthTruth data
- Individual teacher interviews