Dissertations / Theses on the topic 'Mathematics education|Elementary education|Teacher education'

The purpose of this qualitative case study was to gain a better understanding of how induction programs might effectively support STEM K?8 teacher preparation. American schools are not producing competent STEM graduates prepared to meet employment demands. Over the next decade, STEM employment opportunities are expected to increase twice as fast as all other occupations combined. To meet the economic needs, the STEM pipeline must be expanded to educate and produce additional STEM graduates. The meeting of this objective begins with having the teachers working in American classrooms fully prepared and trained in STEM content, curriculum, and pedagogy. Research shows that the interest in STEM subjects starts in elementary school and, therefore, the preparation of elementary teachers to be proficient in teaching STEM to their students is vital. However, most induction programs do not focus on preparing their teachers in STEM. This study researched the Alternative Induction Pathway (AIP) program, which had STEM preparation as one of its core outcomes in the Long Beach Unified School District (LBUSD). It investigated the program?s effectiveness in preparing K?8 teachers with STEM content knowledge, curriculum, pedagogical instruction preparation, and the program elements that contributed the most to their experience in the program and overall STEM preparation as a result. This study was carried out over the course of approximately 6 months. Data included focused interviews with participants as well as analysis of existing documents in order to triangulate perspectives from multiple sources. The AIP program had varied levels of effectiveness in STEM content, curriculum, and pedagogy preparation. Relationships between the induction mentor, the administration, and the participating teacher, when strong and positive, were powerful contributions to the success of the acquisition and integration of the STEM content, curriculum, and pedagogy. The most effective components of the AIP program were the monthly support groups, the curricular resources, and the professional development nights facilitating the teaching and learning process for the participating teacher in STEM integration. The results of this training included examples of well-planned and executed STEM lessons with creative risk-taking, and enhanced confidence for teachers and administrators alike. At the same time, the AIP program had struggles in achieving the desired outcomes of STEM integration, due to lack of preliminary training for program administrators in STEM integration, varied needs between the MS and SS credential teachers, and state standard requirements that spoke to science and mathematics, but not engineering or technology. The main recommendation for policy from the results of this study is that STEM should be woven into preservice and continue through induction and professional development to become one of the main tenets of curriculum development and standards of effective teaching. This policy would affect colleges of education and district induction programs, requiring that STEM courses be added or embedded into the credential pathways. However, this approach would ensure that STEM integration is supported academically as an important and valued aspect of the teacher?s entrance to their career, and that pre-service teachers are ready to take advantage of induction offerings on STEM integration in the induction phase and throughout their careers in continuing professional development. The study also provides practice and research recommendations in regard to possible roles and supports for mentor teachers, including their relationships with resident teachers, as well as suggestions for and to maximize the benefits for effective teaching and learning during the induction process.

Elementary mathematics teachers in Maryland are required to teach according to the Maryland College and Career-Ready Standards (MCCRS). Implementation of these standards requires teachers to understand and implement instructional shifts that are unlike the way most of them were taught mathematics in elementary school. Consequently, educator preparation programs in Maryland must ensure candidates are adequately prepared to teach elementary mathematics according to the Maryland standards and the necessary instructional shifts.

This study describes the preparedness of teacher candidates and first-year teachers from Maryland educator preparation programs to teach according to the elementary mathematics MCCRS. Preparedness is described from the perspective of mentor teachers who work with interns and mathematics instructional leaders (MILs) who work with first year teachers from Maryland preparation programs. The descriptions of the preparedness of these interns and first-year teachers provide multiple perspectives on both the strengths and needs of preservice teachers and recent graduates.

Mentors from five different school systems in Maryland and MILs from four school systems in Maryland completed a survey with both quantitative and qualitative questions. Nineteen mentors and 22 MILs participated in the survey. Ten of the participants volunteered for and participated in a follow-up interview. The participants reported on the interns or first-year teachers they worked with during the 2016–2017 school year.

Mentors and MILs described the teachers they work with as having strengths in implementing technology into instruction and described the teachers as willing to use manipulatives during instruction. Additionally, they perceived educator preparation programs as being well-aligned to their school system goals and priorities. Participants described needs of the teachers they work with, including the following: understanding the standards, understanding mathematics on a conceptual level, differentiating instruction, promoting mathematical discourse, and problem solving into instruction. These recommendations provide a basis for educator preparation programs when examining the preparedness of their candidates and graduates to teach according to the MCCRS for elementary mathematics.

The subjects of science, technology, engineering, and math (STEM) have grown in importance because they are fundamental to the future quality of life and the ability to compete in today’s global society. The demand for STEM careers is increasing; however, the United States is having difficulty meeting this demand. Society needs students who can research and think critically, so they can be proficient in STEM education and become the next generation of mathematicians, scientists, technologists, and engineers. Mathematical proficiency is of particular concern because while it is required for STEM education success, individuals find it challenging.

Both adults and children have apprehension about mathematics, and their negative attitudes toward math develop a barrier to STEM education and careers. This negative math phobia, or math anxiety, causes a decrease in math achievement. This study explored the perceptions of elementary teachers in establishing a classroom environment free of math anxiety. Specifically, this study focused on best practices that teachers incorporate in order to reduce math anxiety.

The purpose of the study was to (a) determine the strategies and practices teachers employ to reduce math anxiety, (b) determine the challenges teachers face in reducing math anxiety, (c) determine how teachers measure the success of their practices in reducing math anxiety, and (d) determine the recommendations teachers would make for future implementation of strategies in reducing math anxiety.

The purpose of this study was to examine the effects of virtual manipulative on children’s algebraic thinking in their early math education. The virtual manipulative is considered as a means of intervention, and its effects is proven to be an effective way through the action research working with the third-grade elementary students. In doing so, this study evaluated the effectiveness of e-based virtual manipulative to support children’s algebraic thinking development in their early math education. Data collected for this study included pre-disposition and post-disposition surveys, pretest and posttest for algebraic thinking, and intervention assignments utilizing online math content materials regarding algebraic thinking. Data was analyzed using a statistical method using SPSS 24.0, including descriptive statistics, Pearson correlation analysis, effective size, and paired t-test. This study found that students’ test scores improved significantly in overall math scores, showing that there was a statistically significant difference between the pretest and the posttest through the intervention using e-based virtual manipulative. This study also found that student’s test scores increased in three algebra thinking content areas such as unknown variables, properties of operations, and arithmetic pattern with a significant difference. This study also found that students’ disposition scores increased in all three areas of attitude, confidence, and belief. This study will benefit students in early-grade levels with positive impact on usage of e-based virtual manipulative intervention activities for better understanding algebraic thinking and effective pedagogy.

The purpose of this study was to examine the differences between mathematics preparation and teachers' perception of self-efficacy for teaching mathematics at low- and high-performing schools. Bandura's theory of self-efficacy was the guiding theoretical framework. The study used a descriptive comparative method to obtain quantitative data regarding teacher backgrounds and teacher efficacy level. Self-reported data from the Mathematics Teacher Efficacy Belief Instrument was used to calculate two dimensions of teaching efficacy, personal mathematics teaching efficacy (PMTE) and mathematics teaching outcome expectancy (MTOE). Preparation was determined by individual calculations for successful completion of preservice mathematics coursework, completion of mathematics methodologies coursework as well as hours and types of teacher professional development completed. An analysis of 69 teachers, 33 from low-performing schools and 36 from high-performing schools, revealed statistically homogenous mathematics preparation and self-reported self-efficacy levels. Elementary mathematics teachers from high-performing schools demonstrated slightly higher level of preparation, PMTE and MTOE; however, differences were not statistically significant. Results were incongruent with prior research and indicate the need for future research supported by data collected from external sources, beyond self-reported data.

Throughout the history of teacher education, the final fieldwork experience has often been called the single most influential experience in teacher preparation programs (Burns, Jacobs, & Yendol-Hoppey, 2016; Feiman-Nemser & Buchmann, 1986; Parker-Katz & Bay, 2008). Though this experience has been expanded to include fieldwork experiences throughout many teacher education programs (Guyton & McIntyre, 1990), the final fieldwork experience remains the closing activity and the lasting image of teacher preparation (Feiman-Nemser & Buchmann, 1986; Rosaen & Florio-Ruane, 2008). Given its importance, though, researchers know relatively little about it. “The knowledge thus produced is akin to the quantum theory of physics; we know what goes in . . . and what comes out . . . but not what occurs in the interim” (Guyton & McIntyre, 1990, p. 524). Given the current reforms in mathematics education and mathematics teacher education (National Council for the Accreditation of Teacher Education, 2010; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), Guyton and McIntyre’s observation is still relevant today.

During the final fieldwork experience, university-based and school-based mathematics educators must work together on behalf of the novice to marry university-promoted theory (especially reform-oriented theory) with the practical classroom expectations of day-to-day teaching life. Though there is much research on how this kind of work should be done and the dilemmas that have arisen during fieldwork (e.g., Knight, 2009; Loughran, 2006; Nolan & Hoover, 2004; Sergiovanni & Starratt, 2006; Sullivan & Glanz, 2013), we have little information about the experiences of the mathematics educators who collaborate during final fieldwork. Furthermore, we have very little information on how these educators navigate mathematics reforms to prepare teachers of mathematics.

This multi-case study was designed to investigate three novices, their school-based mentors, and their university-based mentor (me) who collaborated during a year-long final fieldwork experience at the close of a middle school mathematics teacher preparation program. To write single case reports that illuminated our collaborative experiences, I wrote the “stories” of each triad. To collect these stories, I used individual and group interviews, paired conversations, asynchronous text interviews, conference observations, collaborative fieldwork artifacts, my own practitioner-researcher journal, and three cycles of participant member checks. After verifying the veracity of the stories of each triad, I engaged in cross-case analysis to make assertions about the commonalities and unique circumstances that defined these fieldwork cases. This study adds to teacher preparation fieldwork literature by evoking a response from educators working in the field and providing them with examples of open dialogue that created more empathetic collaborative experiences. The study also provides evidence that the empathy generated by sharing stories can create more productive and effective learning experiences for the novices involved. In particular, open dialogue provided the collaborators in these cases with a platform for acknowledging pedagogical differences, negotiating fieldwork expectations, and setting and meeting novices’ professional goals. For future investigations of teacher preparation fieldwork collaboration, this study provides evidence that a practitioner approach to research affords the researcher exceptional access to the stories of novices and mentors and establishes empathetic bonds that can make the telling of those stories both illuminating and respectful of the voices they represent.

Educators are now charged with instructing students who are growing up in a digital environment (Hsin, Li & Tsai, 2014). Students need access to 21st century learning environments that incorporates technology use, especially in mathematics (Darling-Hammond, Wilhoit & Pittenger, 2014). Unfortunately studies show that technology integration is happening least in mathematics compared to other subject areas (Howard, Chan, & Caputi, 2015a; Howard, Chan, Mozejko & Caputi, 2015b; Howard, Chan, and Caputi, 2014). Moeller and Reitzes (2011) found that according to a National Center for Education Statistics study, only 23% of K-12 teachers feel prepared to integrate technology into instruction.

The purpose of this sequential explanatory mixed methods study was to investigate and explore teacher perceptions regarding technology knowledge, content knowledge, pedagogy, and preparedness to implement technology integration in mathematics instruction in elementary teachers in an urban ring district in a northeast state.

This study addressed the following research questions: 1. How do elementary teachers rate their perceived knowledge of teaching and technology in mathematics on the following components of the Technological Pedagogical and Content Knowledge (TPACK) framework: technological knowledge (TK), content knowledge (CK), pedagogical knowledge (PK), pedagogical content knowledge (PCK), technological content knowledge (TCK), technological pedagogical knowledge (TPK), technological pedagogical content knowledge (TPACK), and models of TPACK related to preparedness? 2. Is there a significant difference in how elementary teachers rate their perceived knowledge of teaching and technology in mathematics on the components of the Technological Pedagogical and Content Knowledge (TPACK) framework by the following demographics: gender, age and years of teaching experience? 3. How do elementary teachers describe their perceived technology knowledge, content knowledge, pedagogical knowledge, and preparedness to implement technology integration as they relate to mathematics instruction?

The major themes that emerged from this study included limited teacher mathematics knowledge because mathematics instruction and expectations for understanding are different today than in the past; and teachers did not feel like they were supported or prepared well to integrate technology into mathematics instruction. Administration and teacher educators may benefit from knowing teachers feel a need to be supported in mathematics conceptual knowledge, problem solving and technology integration.

With the new goal of K-12 education being to prepare students to be college and career ready at the end of high school, education needs to start changing at the elementary school level. The literature suggests that teachers need reflective professional development (PD) to effectively teach to the new standards and to demonstrate change to their current instructional practices. This mixed-method multiple-case study investigated the impacts of a reflective professional development (PD) in changing elementary school teachers' instructional practices.

Teachers Instructional Portfolios (TIPs) were scored with a TIP rubric based on best practices in teaching mathematics problem-solving and science inquiry. The TIPs were also analyzed with a qualitative coding scheme. Case descriptions were written and all the collected data were used to explain the impacts of the reflective PD on changes in teachers' instructional practices.

While we found no predictive patterns in relation to teachers changing their classroom practices based on the reflective PD, we claim that teachers' desire to change might contribute to improvements in instruction. We also observed that teachers' self-assessment scores tend to be higher than the actual TIP scores corroborating with the literature on the usage of self-assessment to evaluate teachers' instructional practices.

This mixed-methods study sought to explore the impact the role a mathematics curriculum coach has on teacher efficacy and instructional practice.

School systems across the country are being asked to do more with less money. At the same time, districts are faced with mathematics standards that require a new approach to instruction. In response to these issues, school districts are choosing to implement the role of a mathematics curriculum coach. As a result, the question is raised, “are the funds utilized for math coaches being used effectively?” This mixed-methods study compared two schools of similar makeup. School A employs a math curriculum coach, while School B employs a general curriculum coach. Through the use of a survey (MTEBI), curriculum coach journaling, focus groups, and one-on-one interviews, this study sought to answer three research questions: (a) What is the impact of the use of a math curriculum coach on teacher instructional practices in the area of math; (b) What is the impact of the use of a math curriculum coach on teacher perceptions of their instructional practice; and (c) What is the impact of the use of a math curriculum coach on teacher sense of self-efficacy? The survey was administered to all teachers at both schools with an overall response rate of 63.6%. The focus groups and interviews were a small random sample of teachers at each school who provided an in-depth view of their perceptions regarding the impact of the coaches on their instructional practice and self-efficacy as related to mathematics. The teachers had high levels of self-efficacy when teaching math and high outcome expectancy. These measures did not change over the period of the study. This study found that the math curriculum coach did have an impact on teacher instructional practices.

The purpose of this research study is to describe and analyze the self-reported experiences of exemplary high school mathematics teachers who underwent personal and professional transformations in order to develop and use a standards-based, constructivist (SBC) teaching paradigm in their classrooms. These teachers were all past recipients of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST), an award that required them to demonstrate that their mathematics instruction was rigorous in the manner described by the NCTM standards.

The following research questions are addressed: (a) What are the paths SBC secondary mathematics teachers who received the PAEMST pursued to become highly effective?, (b) What obstacles and challenges did they encounter and how were these obstacles overcome?, and (c) What sustained them on their journeys? The research methodology used to be a narrative inquiry. Following a wide survey of PAEMST recipients, five volunteer participants were chosen for the study. Data were collected from each participant using a one-to-one interview and the written section of each participant's PAEMST application. A narrative was written for each participant describing the path they had followed to become a highly effective high school mathematics teacher. The narrative was sent to each participant, and a follow-up interview was conducted via telephone amending the narrative to reflect the participant's additions and deletions. From the five amended narratives, eight themes were identified: (a) influences; (b) education; (c) professional development; (d) NCTM standards; (e) teaching style: beginning, current, or end of a career; (f) obstacles; (g) personality traits and personal beliefs; and (h) student influence.

Several of the themes were supported by previous research. However, this research study discovered two new findings. First, the five participants had common characteristics and beliefs: (a) belief in their students, (b) persistence, (c) belief that professional development is vital for teacher growth, and (d) passion about mathematics and about conveying that passion to their students. The second research finding pertained to the influence that their own students had on all of the five participants. All the participants purposely sought out their students' thoughts about the classroom curriculum and about the instruction they received. The teachers considered their students part of the classroom learning community, and they honored and acted on their input.

Finally, in addition to describing the trajectory of five PAEMST winning teachers, this study offers recommendations for students studying to become high school mathematics teachers, teacher educators, and educational researchers. For these students, their teaching preparation courses need to be taught adhering to the four principles of learning: activity, reflection, collaboration and community. According to this research, the model of teacher preparation courses that emphasize the teaching of the above four principles using a traditional teacher-directed method does not prepare future mathematics teachers for the use of SBC teaching in their classrooms. Suggestions about further research are addressed.

This research explored the nuances of co-creating and implementing a co-constructed and reconceptualized Kindergarten mathematics curriculum including innovative teaching practices such as number talks, math baskets, and counting collections to examine their impact on a student's mathematical identity, mindset, and content knowledge. The goal of this research was to provide a counter-story on mathematics curriculum in an early elementary classroom setting with a focus on social justice and equity. The project employed qualitative methodologies using a bricolage approach. A critical theoretical framework and related postdiscourses guided my research design, data collection, and analysis. Data sources for this study included a reflective journal kept by myself as a teacher-researcher focused on mathematical curriculum experiences, semi-structured focus group discussions with students, and electronic student artifacts collected over a twelve-week period in the late fall and winter of a school year. Data was analyzed using open and thematic coding. The major themes that emerged were used to create a community autoethnographic narrative via a bricolage of vignettes. The large and overarching theme of social justice and equity permeated the research findings in connection with students establishing a mathematical identity and mathematical mindset. Other themes included: (a) "growing our math brains"; (b) culturally relevant pedagogy (CRP); (c) operating as a community of learners; (d) students taking ownership of their mathematical learning; (e) teacher as ethnographer, facilitator and co-creator of learning; (f) making math meaningful and tangible; (g) play, enjoyment, and fun during math learning; and (h) meeting or exceeding standards with a localized curriculum in lieu of following a standardized curriculum. The vignettes and subsequent analyses are not intended to be a replicable mathematics curriculum for Kindergarten students. Rather, the vignettes are intended to inspire teachers to reconceptualize mathematics curriculums that influence their young students' mathematical identities. It is suggested that a reconceptualized and co-constructed mathematics curriculum will have a lasting influence on the mathematical mindset and identities of young students.

Keywords: reconceptualized mathematics curriculum; mathematical identity; mathematical mindset; number talks; math baskets; criticalism; social justice and equity; bricolage; community autoethnography; Kindergarten; early childhood education

Progress monitoring has been shown to be effective for gauging student growth in the area of mathematics. Likewise, self-graphing has been shown to improve student achievement in education. The present study investigates the effectiveness of progress monitoring as an intervention with a self-graphing component for second-grade students in the area of mathematics. This research examines the impact of progress monitoring on increased math skills, accuracy, and generalization to universal screening assessments. While results were variable, students' accuracy improved upon implementation of progress monitoring. All-together, results suggest that progress monitoring with self-graphing can be an effective intervention.

The purpose of this study was to determine if positive teacher-to-student relationships impacted student academic performance. This case study involved examination of the results of data collected from 43 students who participated in a mentor adoption program initiated with the intent to enhance positive teacher-to-student relationships for the 2013-2014 school year. Archival data of students who participated in the mentor adoption program were compared to data from a stratified group of students who did not participate in the mentor adoption program. Data from English language arts (ELA) and mathematics (MA) Missouri Assessment Program (MAP) scale scores, attendance rate, and number of discipline referrals were compiled and analyzed using paired-samples t-tests. The results of the study showed students who participated in the mentor adoption program demonstrated a significant increase in MAP ELA scale scores, increase in MAP MA scale scores, and significant decrease in the number of discipline referrals. Students who did not participate in the mentor adoption program showed significant improvement only in MAP MA scale scores. Perceptual interview data were gathered and analyzed from 10 teachers who participated in the mentor adoption program to determine teacher perceptions and feelings about the program. The results indicated teachers believed the mentor adoption program had value and should be continued in Elementary School A. The analysis of these data showed student academic performance was significantly impacted by the use of a mentor adoption program in Elementary School A.

This study investigated secondary mathematics pre-service teachers’ (PSTs) knowledge of resources in terms of digital technologies, and explored the processes of both selection and integration of technology into their lesson plans. This study employed a case study design. Participants were six secondary mathematics PSTs who enrolled in a methods course. Data sources included technology portfolios submitted as a requirement in the methods course and semi-structured interviews. The types of digital technologies were classified either conveyance technologies which are used to convey information or cognitive technologies which enable users to perform mathematical actions and receive immediate feedback (Dick & Hollebrand, 2011). Each task in these lesson plans was evaluated by using the Task Analysis Guide (Stein, Smith, Henningsen, & Silver, 2009). Finally, the intended way of technology use was identified whether as amplifier which enables students to accomplish a task more efficiently and accurately or as recognizer which transforms students’ actions and enables them to reorganize their thinking (Pea, 1985).

The findings indicated that the PSTs’ technology knowledge was limited in terms of the content. It was clear that these PSTs’ technology knowledge, the capability of technology, ease of use, availability of technology in the context, students’ familiarity with technology, and appropriateness of technology to meet the learning objectives were the most important factors influencing their technology selection and integration. Furthermore, the findings exhibited that the PSTs preferred to build their lesson around with a high cognitive level tasks which were either doing mathematics or procedures with connections and their intended way of technology use in these tasks was identified as either an amplifier or a reorganizer. In general, the findings also revealed that when the level of cognitive demand of the selected task was doing mathematics, the intended way of the technology use in these tasks were as reorganizer.