Teacher Efficacy in Secondary Mathematics: Fostering Confidence and Fluency
This research focused on understanding what factors affected the perception of efficacy in the teaching and learning of mathematics in several progressive secondary schools. Efficacy is the belief in one’s ability to produce the desired or intended results. For teachers, this is the belief the practices and structures they use and work in contribute to student success. For students, this is the belief they can use mathematics and are prepared for college level work. The conclusion of this study to improve perceived efficacy can be specifically attributed to two areas: 1) Unclear expectations or vision of the mathematics program, and 2) A need for more effective strategies for reaching all learners in a classroom. Vision in this context is defined as having a plan to define clear goals and the methods to reach those goals. I believe there are two main areas which may develop this vision: 1) Defining the institution’s goals for secondary mathematics, and 2) Teacher preparedness and support.
Dewey and Defining Vision
Literature (Harel, 2008, Hauk et al., 2010, Polya, 1954) stresses in order to learn and use mathematics one needs to provide both ways of thinking and applying mathematics along with knowing and practicing the procedures and formulas. The majority of current mathematics teachers were taught with traditional methods and in transition to teaching in a more progressive setting, it may be necessary for teachers and directors to reflect on the questions Dewey (1938) posed to progressive educators:
The problem for progressive education is: What is the place and meaning of subject-matter and of organization within experience? How does subject-matter function? Is there anything inherent in experience, which tends towards progressive organization of its contents? What results follow when the materials of experience are not progressively organized? A philosophy which proceeds on the basis of rejection, of sheer opposition, will neglect these questions.
Dewey was trying to stress the importance of having a plan or vision for student learning. The setting schools possess a design principle of the teacher being the primary designer of their curriculum and assessments. This design principle allows for teacher passion to infuse the learning arena; if teachers are excited about their lessons, the students will also be excited. This is a valid premise, however it does not preclude the necessary standards or progression of learning which needs to take place in order for students to successfully gain mathematical fluency.
In answering Dewey’s questions regarding subject-matter functions, organization and progression, the CCSSM have been developed to guide educators to what topics and practices a student needs to understand and use to meet the goals of secondary mathematics, but not how to teach them. The setting schools have adopted the framework of the CCSSM, but there are still questions in how to incorporate them with the model of project-based learning. Teacher efficacy is being affected by the pull of the school model, parent and student desire (and their own) to have the students perform well on gatekeeping exams, and their own backgrounds in traditional mathematics instruction.
Mathematics teachers in this research setting have been gathered from various industries and discipline majors. As Jim Lewis, a professor of mathematics at the University of Nebraska-Lincoln and researcher with the Mathematics Teacher Education Partnership (MTEP) states, "One of the ideas is that what you need to know in order to teach well is different from what you need to know to be a young engineer or economist," and, "In mathematics, you are often trying to synthesize knowledge. As a teacher, you're trying to pull apart knowledge and understand why people have difficulty learning" (Sawchuk, 2014). The varied backgrounds of teachers in this research may contribute to a lack of common understanding and/or how to foster the development of mathematical practices for students. Teachers and directors within a school need to define what those practices mean to them and develop a common language to facilitate their successful acquisition by students. As shown by my experiences within one setting school, having the desire and time to define these practices developed teacher efficacy; if there is a plan, there is a way to know if one is being effective. The process we employed was similar to the design thinking process developed by Stanford’s d.school (see Figure 8); a suggested model for the process can be found in Appendix E.
However, the process would have benefited from more frequent meetings and the use of an instructional coach or mentor to guide the process (Behrstock-Sherratt et al. 2014; Lemov, 2012). Additional areas for research and dialogue would be to extend this conversation and process to middle school and elementary teachers to align the vision and practices of the K-12 student experience in mathematics.
To Test or Not To Test
An additional area affecting teacher efficacy is standardized testing. High school students wishing to pursue a college degree are directly affected by the outcomes of college entrance exams. The setting schools are performing in line with state averages. However, given the advantages of smaller classes and more personalized instruction, shouldn’t the results reflect those benefits? The CRESST center at UCLA stated the new SBAC and PARCC tests reflect a shift towards measuring deeper learning (Hermann & Linn, 2013), with similar revisions to the college entrance exams also forthcoming. If these tests are geared towards assessing deeper learning and the CCSSM and those are the frameworks for the mathematics program at the setting and other progressive schools, will they be deemed as important benchmarks for student learning? There are conflicting messages being sent to the educators in this study regarding the importance of standardized tests.
Progressive school educators and leaders need to decide if the CCSSM and associated gate-keeping exams are important to them as an institution. If they value what gets measured, then the teaching will follow with whatever modifications this involves. This does not need to translate to “teaching to the test,” however it does mean aligning curriculum to the skills and knowledge required to be successful. Teachers can still use their individual passions to help students discover the math, but alignment of vision and practices is key across grade levels and schools. If school leaders don’t value what they measure, then they have to be clear to their stakeholders (teachers, students, parents and the community) about that idea, and let the stakeholders make an informed judgement regarding their decision to be involved with the institution. Having an aligned and public vision will foster efficacy, and it does not have to trump teacher as designer. It solely provides a framework of understanding and purpose to the work.
New, and some experienced, teachers could benefit from professional development to assist them in their transition to the pedagogical aspects of deeper learning and strategies for differentiating instruction. Multiple conversations with teachers, even those with masters in mathematics, admitted to being unaware of the “ways of thinking” (Harel, 2008) behind certain mathematical knowledge they possess. As stated earlier, being “good at math” or even using math in the workplace is different from understanding what strategies will help student learn. In order to further develop a sense of efficacy, additional content, discourse and anticipatory knowledge (Hauk et al., 2010) is needed. The use of mentors was deemed the most effective method of support for new teachers from this research and others (Behrstock-Sherratt et al, 2014, Lemov, 2012). The use of instructional coaches as a professional development strategy also provides “a mentor that is readily available.”
The inclusive environment provides a layer of complexity for educators. The majority of educators in this setting expressed concern over reaching all students. Researchers Powell et al. (2013) found students with mathematics learning disabilities (MD) need “explicit instruction” which involves teacher demonstration of detailed step-by-step instructions along with independent practice. The methods needed to help MD students may be in conflict with the model of project-based learning or they may need additional strategies to reach competency. In recent interviews with students regarding YouthTruth survey results, those who find mathematics “easy” expressed concerns regarding teachers focusing instruction on the students who need more support thereby impeding their ability to move deeper and/or faster through the material.
A strategy that may increase teacher and student efficacy is increased dialogue and cooperation with inclusion specialists or special educators. Hobbs & Westling (2002) and Monsen et al. (2014) found teacher efficacy improved when special educators and teachers worked together to form a support system for themselves and students. Jointly reviewing case studies helped them develop best practices and led to “an emphasis on cooperative learning and team decision making” (Hobbs & Westling, 2002, p. 188).
Research Surrounding Project-Based Learning
An area for additional research could focus on the complexities of trying to teach mathematics through the use of projects. Teachers may benefit from specific teaching strategies to improve the balance of instruction between thinking, understanding and practicing mathematics when attempting instruction through projects. Questions surrounding time allocation and the ability for students to effectively gain the adopted standards through project work could be key considerations. Also, research regarding the definition and structure of “mathematics projects” could help educators more effectively plan and coordinate instruction. Again, these future research considerations are in line with defining the vision of a mathematics program.
I believe the ultimate goal of mathematics education is to create learning environments to increase student efficacy. Student efficacy will hopefully result in the successful attainment of the language of mathematics and its associated college and career readiness. Efficacy appears to be a cyclical event. Student efficacy can facilitate teacher efficacy and vice versa. Teacher and student efficacy can be facilitated by defining the goals of a mathematics program and making them transparent to stakeholders. Providing educators with continued professional development in their own transitions from traditional methodologies to a more progressive or constructivist approach to mathematics is key to improving their efficacy. If students and teachers share common vision, practices and language of mathematics across the K-12 spectrum, who knows where we could rank as a nation.