*Teacher Efficacy in Secondary Mathematics: Fostering Confidence and Fluency*

*Findings*

Over the course of six months, I observed, participated, and recorded events in math classrooms and schools across the setting. I began my research by surveying math teachers to gauge their background and experiences with progressive math education in an inclusive setting. All students in a given grade level are placed into the math course for their grade level with the vision the teacher will provide access and challenge to all students in the room. Only secondary math instructors were polled with a response rate of 33% of the population across five sites. In combination with this activity, results from a student perception survey, YouthTruth, was analyzed to help determine students’ view of the mathematics program. The results used were from one of the five secondary schools with 87% of the students responding. These results then assisted in the collecting of information from school directors, teachers and instructional coaches via interviews.

In trying to understand the mindsets of teachers, questions surrounding the purpose of mathematics were posed. As per the indicated research (Harel, 2008; Polya, 1954), teachers understood the importance of thinking critically and providing a foundation of math skills. However the teacher responses to the purpose of these skills varied; with eight of the ten responses focused more on college and exam preparation, “

While teacher passion and commitment to their students was evident in their responses, there was confusion, and sometimes disagreement, as to what the purpose of mathematics education is across the respondents. This sentiment was echoed in interview responses gathered from a teacher support specialist or instructional “coach” at one of the school sites. When asked what the coach interpreted as challenges math teachers faced, one response focused on the lack of vision or clarity. Questions such as “

In correlation to the vision and purpose of mathematics questions, the idea of efficacy, or the belief one is effective, is a factor in the success of teaching and learning in any subject area (Hoy & Spero, 2005; Shaughnessy, 2004). One of the survey questions posed to teachers was whether they believed the school’s structure for math was adequately challenging all math students.

*Vision and Efficacy - Teachers*In trying to understand the mindsets of teachers, questions surrounding the purpose of mathematics were posed. As per the indicated research (Harel, 2008; Polya, 1954), teachers understood the importance of thinking critically and providing a foundation of math skills. However the teacher responses to the purpose of these skills varied; with eight of the ten responses focused more on college and exam preparation, “

*...because of the traditional exams and courses in their near future...it is to prepare them for those things.*” However, a few responses focused more on the exploration of math as demonstrated by this response:*I think math education should be allowing students to find their identity, empowering them, allowing them to be autonomous with each other, free from some (mathematical) authority through an inquiry based system where they are collaborating, critically thinking and making sense out of math (reality) with each other. I also feel like they can meet ‘standards’ and develop processes through this system.*While teacher passion and commitment to their students was evident in their responses, there was confusion, and sometimes disagreement, as to what the purpose of mathematics education is across the respondents. This sentiment was echoed in interview responses gathered from a teacher support specialist or instructional “coach” at one of the school sites. When asked what the coach interpreted as challenges math teachers faced, one response focused on the lack of vision or clarity. Questions such as “

*What are the expectations of us as math educators in a PBL school?*” and “*How does it look?*” were two themes which emerged. This was echoed by another instructional coach’s reflection on the question of vision. “*People in math education are having trouble progressing as quickly as the other disciplines are for some reason, because we all learned math this way, and we like math this way, and math worked for us this way…but people aren’t walking around loving math*.”In correlation to the vision and purpose of mathematics questions, the idea of efficacy, or the belief one is effective, is a factor in the success of teaching and learning in any subject area (Hoy & Spero, 2005; Shaughnessy, 2004). One of the survey questions posed to teachers was whether they believed the school’s structure for math was adequately challenging all math students.

*Figure 4*shows the results; 72.7% of the respondents either disagreed or were neutral with the statement indicating a high level of dissatisfaction with the current structure.*Vision and Efficacy - Students*

This variety of expectations and dissatisfaction with the mathematics program was also evident in the student YouthTruth open-ended responses. Students were asked to comment on areas of strengths and improvements about their schools. Students selected areas where they interpreted the school needed improvement from various categories, including the option of “Nothing.” Of the 479 responses, 32% of the responses indicated there were no areas for improvement. Of the 68%, or 325 respondents, indicating an area for improvement, 20% of those comments included the keyword of math.

*Figure 5*displays the comparison to other discipline specific comments using the keywords “humanities” and “science” showing of the three disciplines, “math” received 87% of the responses.

There were many responses regarding the math program not adequately preparing students for exams and future math courses, but some students appreciated the emphasis on thinking about math. An 11th grade student shared, “

*For example, in math class, I learn and practice learning HOW to think like a mathematician and HOW to think out of the box to solve problems by myself rather than being told how to solve a problem and memorizing the steps.”*However, the majority of comments focused on a desire for more foundation work which is reflected by this 10th grade student response, “

*My school's math curriculum works with conceptual math, which is important, but learning can be very confusing when a teacher starts with the conceptual math and teaches solely with it. One really needs procedural math as well.”*This comment is corroborated by students who have supplemented their learning through outside resources, “

*As a result of our inept math program, I've had to work very hard at Community College to make up for lost ground just to be prepared for a four year college.*” Student perception of the program affects all the stakeholders, including parents, teachers and directors.

Though the majority of comments focused on students feeling unprepared or wanting additional challenges, it could also be perceived as a misunderstanding regarding what the institution values. Students (and parents) may be unclear of the design principles of deeper learning and/or project-based learning, specifically in terms of math as evidenced by the following student comment and others like it; “

*I want to learn high school math from public schools where they give you a lecture on how to do this math and giving examples with the class.*” This shared lack of clarity by teachers and students as to the purpose and methods to teach and learn mathematics is a contributing factor in the efficacy of the program.

*Inclusion and Efficacy*

Another question posed to teachers dealt with the subject of whether an all-inclusive model affected their teaching, and if so, how. Of the eleven respondents, ten of them, or 91%, said the model affected their teaching; eight respondents felt it was a difficult challenge while three of them were either neutral or felt it challenged them to be better teachers. Figure 6 provides some sample responses.

*Figure 6: Responses from teacher survey question - "Does having an all-inclusive model affect your teaching, and if so, how?"*

*Comments on Challenges*

*I find it incredibly challenging to assist all students at their current level of mathematics.**Yes, I have to make sure to plan both interventions and extensions for my units. It can be very difficult to balance and make sure all needs are being met all the time.**Absolutely. Theoretically it is a great idea. In practice, I am not equipped with enough time or manpower to service all students as well as they deserve.**I do not feel that I have enough time to modify, scaffold and accommodate all learners in this setting.*

Comments on Benefits

Comments on Benefits

*Yes, you have to be an even better teacher. You have to find the right problems and strategies to provide a rigorous class for all constituents.**Yes, it makes the classroom richer and pushes me/us to a more open ended approach and values all types of thinking and approaches to problems.*

While a few teachers expressed optimism with the current school structures and the all-inclusive nature of the classrooms, the majority of teachers did not. The teachers’ comments regarding challenges were also substantiated by interview responses from one of the instructional coaches. Responses to the question of teacher challenges included “having mixed classrooms” and “meeting the needs of all of our learners.” If a teacher doesn’t feel they are helping all the students in their classroom, combined with the student perception of dissatisfaction with the math program and individual teacher performance, than their degree of confidence in the ability to do their job has been compromised.

The research conducted found these two main factors, misunderstanding the goals of the program and the ability to reach all learners in a classroom, contribute to the perceived and documented challenges of teachers and students. These problems, though not officially stated as such, are not new to the organization and there have been attempts to lessen the effect on teaching and learning by the various school sites. The following section will attempt to provide a sampling of the strategies employed.

*Strategies Which Lead to the Formation of Vision*

During the course of my research I also embedded myself within the mathematics discipline group at one of the school sites. The group consisted of seven teachers with three of them being first year hires. Discipline meetings occurred approximately every other week for forty-five minutes before classes began. Facilitation of the meetings was on a rotational basis to follow the design principle of teacher-as-designer without imposed hierarchical structures. However, this structure was not initially conducive to teacher learning as there was no defined vision or arc to the meetings. It was perceived no one teacher wanted to step forward to define this vision lest it be perceived they were somehow superior to their peers.

After dealing with parent complaints on the effectiveness of teachers and the math program, the school director and I brainstormed with the group on what practices they believed should be evident in all classrooms (see Appendix D for a listing of those practices). This event was followed by several meetings where the group individually defined and defended the meanings of these practices to reach a common definition for each of them. This was then followed by three-meeting arcs covering the various practices. This processes of collectively agreeing on what was important was a unifying factor for the group. In an exit card response after one of the meetings to “

*What worked well for you today?*” the response was “

*I think the structure and positive dialogue with a purpose”*(Exit Card).

Other school sites are taking advantage of additional professional development meeting times to self-select into action groups to continue their discussions and support of math learning. This creates a weekly check-in with discipline members, as opposed to a two to three week cycle, which allows them to “gain traction” in advancing their vision and improved practices. Some practices, including the use of improvement science or rapid cycles of measurable change initiatives, have focused on improving lessons and classroom management. I did not directly observe these practices but learned of them through interviews.

*Using Instructional Coaches*

Other school sites are employing the use of the aforementioned teacher support specialists or instructional coaches. These positions tend to be temporary from year to year depending upon available funding. Of the five secondary sites, two of them have either a full or part-time math instructional coaches with another site utilizing a graduate student in the role. As per one of the instructional coach’s reflection, having a dedicated resource to assist in planning has been very helpful to teachers. “Staff meetings are more big picture, the coach relationship is like having a mentor that is readily available.” On a related note, during follow-up interviews with three teachers, all three mentioned mentors during their first year was one of the most helpful support structures they experienced.

In delving deeper to understand how and why the school settings are structured the way they are, I interviewed the directors of four out of the five secondary schools. Their leadership experiences with the setting schools ranged from first year to eight plus years, and in addition they were all experienced educators. All the directors stated mathematics instruction and learning was an area for growth. In support of having instructional coaches, one director stated “Teachers are really excited to have that consistent, ongoing support” and it is “

*An amazing luxury … having a structure for dialogue as to what we want our math to look like.*” Another director, who uses two part-time teacher/coaches as “

*management designees*” for math does so in response to not having a background in math and having a larger staff than other sites. When directors were asked whether other discipline groups have had a similar structure of coaches, the answer was no. This revelation seems seminal in understanding teacher efficacy and will be discussed further in the conclusion. Also, one director tied in the need for “

*students to develop a growth mindset and overcome a lack of self-efficacy.*” Finally, multiple directors spoke about the need to prepare teachers for the transition from traditional teaching methods to a more progressive approach and the Common Core standards. A major source of funding for the instructional coaches are paid from Common Core transition grants. A further area for research may be to examine the perceived effectiveness of the coaching based on their qualifications and/or training in implementing common core methods and standards.

There were many practices occurring across the school sites to improve the instruction and learning of mathematics. It is an area of ongoing contemplation and research surrounding the practices, methods and support structures to increase efficacy. Whether it is student or teachers, the idea of efficacy and having a mindset which allows for growth and a positive experience appears to be an important factor in affecting math instruction and learning.