Prompted reflective thinking and implications for mathematics teacher efficacy in an elementary mathematics methods course

Although student-centered mathematics instruction, rooted in constructivism (NCTM, 2014), enhances students’ deep understanding of mathematics, many teachers fail to implement this approach, continuing to use more traditional, procedural instruction (Paolucci, 2015). One reason for these difficulties may be related to their teaching selfefficacy, or a person’s beliefs about their ability to complete a task. Wyatt’s (2016) expanded teacher self-efficacy model incorporates the reflective cycle and emphasizes the importance of reflection in the development of teacher self-efficacy. This study explored whether encouraging reflection in pre-service teachers may indirectly increase their use of student-centered methods in mathematics by increasing their self-efficacy. The purpose of this qualitative research study is to investigate the effects of an intervention involving extended reflective activities about mathematics instruction, with the goal of enhancing preservice teachers’ mathematics teaching self-efficacy and use of student-centered mathematics instruction as demonstrated in lesson plans. Over an 8- week period, preservice teachers were asked to engage in reflection through the use of reflective prompts after watching videos of teachers implementing student-centered mathematics instruction. These prompts focus on student understanding and the role the teacher plays in this development. Video reflections, lesson plans, lesson plan reflections, open-ended mathematics teaching efficacy responses, and course reflections were analyzed qualitatively using thematic analysis. Following the intervention, four themes were central across data sources: 1). Greater focus on students, specifically student understanding and student strategies; 2). shift in focus teachers to their role in developing student understanding; 3). change in understanding of mathematics instruction and what it means to teach and develop mathematical understanding, and; 4). expressed confidence in their ability to use studentcentered instruction and develop students’ mathematical understanding. A shift in mathematics teaching self-efficacy and expressed confidence in course reflections following the intervention may provide insight on the development and possible sources for PSTs’ mathematics teaching efficacy; increasing mathematics teaching efficacy is important as it may increase teachers’ willingness to try new instructional strategies, such as student-centered mathematics (Chatzistamatiou et al., 2014; Ross & Bruce, 2007; Zee & Koomen, 2016). The shifts observed in this study add to the literature in the mathematics education community as it can inform educators about how to develop preservice teachers’ thinking and shift their reflection to focus on their students which is key to student-centered mathematics instruction

STUDENT CENTERED MATHEMATICS INSTRUCTION: DEVELOPING A TEACHER AND STUDENT SURVEY AND UNDERSTANDING STUDENTS’ EXPERIENCES

Over the past thirty years, policies have been enacted at the local and state levels to reform mathematics instruction to be student-centered (see Cohen & Ball, 1990; Resnick, Stein, & Coon, 2008). Despite the wave of instructional reforms, several critical gaps remain in our understanding of student-centered mathematics instruction. First, the field lacks a conceptual framework that relates the underlying theories with student-centered instructional practice in mathematics. Second, there has been very little systematic and large-scale research on the implementation and effects of student-centered mathematics instruction. Third, we know very little about how students experience and respond to the implementation of student-centered instructional reform. The dissertation studies aimed to bridge these gaps with two mixed methods studies. Study 1 proposes a conceptual framework of student-centered mathematics instruction and uses a combination of literature review, feedback from experts, and data from a large sample of urban and suburban youth (n= 2,536 students) and their mathematics teachers (n = 34) to validate a student and teacher survey of student-centered mathematics instruction. Study 2 investigates seventh grade adolescents’ experiences of their mathematics teachers implementing a reform to student-centered instruction. Specifically, the study examines the emotional experience of getting stuck in their algebra coursework and how the frequency and nature of these emotions vary by student characteristics and how students’ emotional experiences influence their sense of competence in math. The studies have important implications for our understanding of student-centered mathematics instruction. In particular, the studies suggest that students’ perspective and experiences could be important to both the implementation and effects of student-centered mathematics instruction. The studies also suggest mechanisms for differential experiences and effects of student-centered instruction for minority, low-income, and female students. Study findings are discussed in terms of implications for education research, practice, and theory

Student-centered instruction and its effects on mathematics engagement by race

This study aimed to improve knowledge about the efficacy of student-centered instruction in mathematics and specifically examine relevant racial differences in its efficacy. In particular, the study tested student-centered instruction’s effects on four dimensions of mathematics engagement: behavioral, cognitive, emotional, and social. This was done using a multilevel path analysis that included a racial interaction variables as well as other control variables. The sample of the study was taken from Western Pennsylvania and is made up of 3883 6th through 12th graders. The study determined there was a positive relationship between student-centered instruction for all four measures of mathematics engagement. Black students appeared to benefit less from student-centered instruction than white students on all four measures of engagement, but those of low socioeconomic status seemed to benefit more from student-centered instruction on three of the dimensions. The implication that there is a racial difference in the effect of student-centered instruction should be investigated further

The Value of Why for Student and Teacher Learning

We believe teaching for understanding begins with the development of a few essential orientations. Teachers must have an appreciation for student-centered mathematics teaching, valuing an approach that builds on student thinking. In addition, teachers must appreciate the complexity of students’ mathematical thinking and ideas. Once these orientations are in place we can attend to student thinking in ways that draw inferences about their understanding (Carpenter, Fennema, Peterson & Carey, 1988; Ma, 1999) and use those inferences to further probe, uncover and extend the complexities of student thinking. We contend this is possible through the value of “why.” Asking “why?” when teaching mathematics has benefits for both students and teachers

The Development and Validation of the Emporium Model Motivation Scale (EMMS)

The purpose of this research study was to begin the development and validation of a new survey instrument; the Emporium Model Motivation Scale (EMMS). The instrument is designed to be used as part of a more holistic evaluation of non-traditional student-centered mathematics courses or programs redesigned using the Emporium Model (E-Model). EdResearch suggested that the design of the E-Model environment was better suited to help students become more autonomy-natured (Williams, 2016). The present research was rooted in Self-determination Theory (SDT), which asserted that all individuals had a natural desire to strive for autonomy, competence, and relatedness in their social environments (Ryan & Deci, 2000; 2017). The research study consisted of a random sample of n = 463 respondents from both a U.S. community college and 4-year public university. Results of an Exploratory Factor Analysis (EFA) produced four parsimonious factor solutions that showed potential to be valid, highly reliable with (ω ≥ .89) and replicable across other samples or populations. The factors were analyzed using Polychoric correlations, with Unweighted Least Squares (ULS) extraction and Promax rotation. Correlational analysis, MANOVA, ANOVA, and Standard Multiple Regression were performed with accurate and reliable standardized factor score estimates. Overall results revealed statistically significant differences between the two institutions of higher learning across levels of the EMMS factors. Further analyses revealed that age was a statistically significant predictor of the EMMS factors and that older respondents were more autonomous and receptive of the E-Model design for course instruction

An Up-Close Look at Student-Centered Math Teaching: A Study of Highly Regarded High School Teachers and Their Students - Executive Summary

Today, far too many students see mathematics as a subject to be endured, rather than a subject of real-world importance and personal value. That doesn't have to be the case. When teachers use student-centered techniques to engage studentsin more active and authentic ways, they can transform math classrooms into lively learning environments in which studentstake charge of their own learning, collaborate with others, persist in solving complex problems, and make meaningfulconnections to the world around them. Through such experiences, students may come to appreciate mathematics as adiscipline that enriches their lives and their understanding of the world.While a growing body of research supports many of the principles of student-centered instruction, there is still a great dealto learn about how such approaches enhance student learning in mathematics. Recent calls for strengthening the STEMworkforce and for more rigorous K-12 standards via the Common Core State Standards have placed increased emphasison developing higher-order thinking and problem-solving skills in high school mathematics, heightening the need for moreinformation about how teachers can effectively engage students with math content.The American Institutes of Research (AIR), with support from the Nellie Mae Education Foundation, conducted a study ofhighly regarded high school math teachers to expand the research base in two important ways. First, rather than assumingstudent-centered instruction is a monolithic construct, the team used a case study approach to provide rich descriptions ofhow the approach plays out in several classrooms, taking into account how teachers' personal philosophy and the school'sinstructional context might influence their practice. The case study also provided insights into students' perspectives on different approaches to mathematics instruction. Second, the researchers look across a larger sample of classrooms to determine the effects of varying degrees of student-centeredness on students' engagement with learning and their problem-solving skills.This brief offers highlights from the study's design and findings. Readers are encouraged to access the full paper for more details

Emirati Pre-service Teacher Behaviors in Mathematics Classrooms

The purpose of this study was to investigate the teaching behaviors of Emirati pre-service teachers in mathematics classrooms. Using a validated ecobehavioral assessment tool, the Mainstream Code for Instructional Structure for Instructional Software (MS-CISSAR), the current study examined the teaching behaviors of nine pre-service teachers in general education Cycle 1 (elementary) public schools in Abu Dhabi. Results revealed the pre-service teachers taught mathematics using instructional groupings of whole class for 62% of the time and small group sessions for 22% of the time. Independent work time was assigned for only 8% of the mathematics class. The participants engaged students in discussion for 32% of the time and used other media such as a mathematics video and/or manipulatives for 31% of the time. Worksheets were assigned for only 16% of the time. The pre-service teachers spent 45% of class time talking or asking questions about academics and 15% of the time engaged in talk related to managing the classroom. Implications for teacher education and directions for future research are discussed. Keywords: Pre-service teachers, Mathematics, Ecobehavioral assessment, MS-CISSAR, Middle Eas