Justification and argumentation have been identified as important mathematical practices; however, little work has been done to understand the knowledge and pedagogy teachers need to support students in these ambitious practices. Data for this research was drawn from the Justification and Argumentation: Growing Understanding in Algebraic Reasoning (JAGUAR) project. JAGUAR was a multi-year research and professional development project in which 12 middle school math teachers and a group of researchers explored the knowledge and pedagogy needed to support student justifications. This dissertation consists of three case study analyses. The first paper describes the development of teacher conceptions of justification, including their proficiency with justification and purpose of justification in the middle school classroom. The second paper examines the relationship between teacher understanding of empirical reasoning and their use of examples in their classrooms. The final paper describes the relationship between task scaffolding and student forms of reasoning in the context of a justification task. Collectively, this body of work identifies important relationships between teacher knowledge, practice, and student justification activity.

Too often teachers see mathematics as a culturally neutral subject. Teacher educators need to be aware of their own practice and how it impacts the facilitation of preservice teacher learning, in particular in relation to elementary mathematics and culturally responsive teaching. This qualitative self-study focused on understanding a teacher educator’s enactment of an espoused platform in an integrated instructional third space of an elementary field experience and an elementary mathematics methods course in relation to culturally responsive teaching and mathematics. The research questions guiding this self-study were: (1) In the context of the selfstudy, to what extent do I enact my espoused teacher education platform in the integrated instructional third space that exists at the intersection of an undergraduate elementary field experience and an undergraduate elementary mathematics methods course in relation to culturally responsive teaching and mathematics?; with one sub question (a) What facilitators and challenges do I face as I try to navigate living out my espoused platform within this third space?; (2) In the context of the self-study, how do I transform as a teacher educator while engaging in the process of framing and reframing my platform within this integrated instructional third space? The study took place in the unique context of an integrated instructional third space with the same person who served as the instructor of the mathematics methods course and field supervisor. Data collection included the researcher’s teacher education platform, field notes from observations, and field notes from pre and post conferences with preservice teachers, documents and artifacts from teaching, and a researcher’s journal. The findings pointed to a set of routines of practice for teacher educators to engage in while facilitating preservice teacher learning about culturally responsive teaching and mathematics knowledge for teaching. The routines of practice included: probing questions, utilizing personal connections, offering suggestions, modeling, and targeted activities. The findings also included facilitators and barriers to the process of working with preservice teachers in the integrated instructional third space in relation to their learning of culturally responsive teaching and mathematics; they include: relationships with preservice teachers, relationships with collaborating teachers, and critical conversations. This study has implications for teacher education program design, mathematics course development, field experience course development, and teacher educator professional development.

This study investigated the teaching experiences of six elementary preservice teachers (EPTs), three with high mathematics anxiety and three with low mathematics anxiety, during their student teaching semester. The EPTs were selected from an initial pool of 121 EPTs who took the Abbreviated Mathematics Anxiety Scale. The cases were compared in a cross case analysis to highlight mathematics teaching experiences among EPTs. Data sources included EPT and researcher journal entries, interview transcripts, pre-lesson surveys, field notes, lesson plans, and artifacts of observed lessons. Data were coded using Shulman’s content knowledge, Graeber’s mathematics pedagogical content knowledge, and mathematics anxiety characteristics. Findings revealed both similarities and differences across EPTs as related to four major categories: (a) planning and resources used, (b) role of the cooperating teacher, (c) content knowledge, and (d) pedagogical content knowledge. All EPTs used mostly direct instruction and relied on the course textbook and their respective cooperating teacher as their primary resources for planning. Additionally, across participants, the cooperating teacher influenced EPTs’ perceptions of students and teaching. Also, EPTs with high mathematics anxiety were weaker with respect to content knowledge and pedagogical content knowledge. Findings suggest a need to re-design methods courses to address improving the pedagogical content knowledge of EPTs with mathematics anxiety. Findings also suggest a need to develop content specific mathematics courses for EPTs to improve their content knowledge. Future studies could include a longitudinal study to follow highly anxious EPTs who take content specific elementary mathematics courses to observe their content knowledge and mathematics anxiety.

Energy resource conservation.

Sixth grade students at a Mid-Atlantic, urban, PreK-8 public school have shown weak mathematical performance. In accordance with the No Child Left Behind (NCLB) Act of 2001, the local district has implemented numerous policy changes to improve performance, but no substantial improvements in test scores have been seen so far. This project study focused on the development of automaticity and fluency of math facts to address this problem. The theoretical framework of the study was based on Haring and Eaton's instructional competency hierarchy framework, which claims that students who master basic mathematics skills are better able to progress to more general and abstract skills. A modified, quasi-experimental, nonequivalent control-group design was used with 2 groups of 20 sixth grade students who were neither randomly selected nor assigned to either group. Data analysis using one-way analysis of variance revealed that computer aided instruction--specifically, Fluency and Automaticity through Systematic Teaching and Technology (FASTT) Math--was more effective than the other classroom's mathematics instruction in developing multiplication fluency. In response, a curriculum policy recommendation was drafted as a project and will be presented to the board of education to conduct additional evaluations of FASTT Math as a supplemental tool in third through eighth grades in the district. This project is expected to contribute to social change by improving mathematics achievement which will create a mathematically literate cadre of students to meet the needs of 21st century employers, thus improving the quality of life in the broader community.

The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed teachers' perceptions of how they teach underachieving students' word problem-solving skills, how prepared they feel, the challenges they experience when teaching word problem-solving skills, and the resources for instructing underachieving students on mathematical word problem-solving. Semi-structured interviews were conducted with 8 certified elementary classroom teachers. Data from the teacher interviews were analyzed using pattern coding and thematic analysis. The findings indicated that teachers are not fully prepared to teach the CCSSM, teachers need assistance in creating standards-based detailed lesson plans, and teachers need help with the development of pedagogical strategies that enhance students' math vocabulary. Findings may lead to positive social change by informing the design of professional development and increasing the number of students who achieve proficiency in mathematical word problem-solving.

Common Core State Standards (CCSS) for writing have created a challenge for teachers at an urban elementary school as they struggled to provide effective writing instruction to support the rigorous expectations of the standards. The purpose of this study was to explore elementary teachers' lived experiences of instruction and better understand instructional writing procedures and strategies. The conceptual framework of this study was based on Dennick's work for incorporating educational theory into teaching practices, which combined elements of constructivist, experiential, and humanist learning theories. Research questions investigated how teachers perceived the impact of the CCSS writing standards on their practice and what kinds of support they needed in order to effectively support writing instruction. A phenomenological design was selected to capture the lived experiences of participants directly associated with CCSS writing instruction. The study included 6 individual teacher interviews and a focus group session of 6 teachers who met the criteria for experience in Grades 3-5 at the elementary school. Data were coded and then analyzed to determine common themes that surfaced from the lived experiences of teachers including the need for training in writing instruction, the impact of common core standards on the increased rigor of current writing instruction, a lack of PD at the local school, and instructor challenges with differentiated writing instruction. A job-embedded professional development model was designed to support teachers with effective writing instruction and improve teacher practice at the local school, the district, and beyond. When fully implemented, this professional development may provide elementary teachers with research-based writing strategies that will support the rigor of CCSS standards and college and career readiness.

In an urban Title 1 school district, the average number of Grade 3-5 students who scored proficient or advanced on the state standardized assessment was 37.3% below Grade 3-5 students countywide and 19.4% below Grade 3-5 students statewide. Low mathematics scores may indicate a gap in practice that affects student achievement. The purpose of this descriptive case study was to examine teachers' descriptions of instructional strategies implemented to mediate instruction for students who struggle in mathematics. This study was based on the conceptual framework of Tomlinson's differentiated instruction (DI), a means of accommodating the varied ways that students learn. The research questions guided an inquiry into how teachers of students in Grades 3-5 in the school district described DI in practice and explained their professional development on DI strategies. Data were collected from individual interviews with 8 elementary school teachers of students in Grades 3-5 and an instructional coach in the local school district with 3 or more years of experience who considered themselves knowledgeable of DI. I coded the meaningful data collected from the interviews and subsequently formed themes. Themes that emerged from the interviews included defining DI, tools for instruction, classroom set-up and transitioning, assessments, professional development, and grouping strategies. Results revealed that interviewees were confident in defining and facilitating DI grouping strategies for English and language arts but felt the need for more professional development to implement and understand DI in relation to mathematics. The study outcome may impact social change by affecting the gap in practice through professional development that helps teachers implement DI strategies in the classroom to improve student achievement in mathematics.

Standardized test data indicate that student achievement in science is a problem both nationally and locally. At the study site, only a small percentage of fifth-grade students score at the advanced level on the Maryland state science assessment (MSA). In addition, the performance of African American, economically disadvantaged, and special education students is well below that of the general student population. Some studies have shown that teacher self-efficacy affects student achievement. Therefore, the purpose of this study was to explore the relationship between fifth-grade teacher inquiry science instruction self-efficacy scores and the scores of their students on the MSA. Bandura's work on the effect of self-efficacy on human behavior provided the theoretical basis for this study. The research questions examined the relationship between teacher inquiry science instructional self-efficacy scores and students' science MSA scores as well as the relationship by student subgroups. A correlational research design was used. The Teaching Science as Inquiry survey instrument was used to quantify teacher self-efficacy, and archival MSA data were the source for student scores. The study included data from 22 teachers and 1,625 of their students. A 2-tailed Pearson coefficient analysis revealed significant, positive relationships with regard to overall student achievement (r20 = .724, p < .01) and the achievement of each of the subgroups (African American: r20 = .549, p < .01; economically disadvantaged: r20 = .655, p < .01; and special education: r18 = .532, p < .05). The results of this study present an opportunity for positive social change because the local school system can provide professional development that may increase teacher inquiry science instruction self-efficacy as a possible means to improve overall science achievement and to reduce achievement gaps.

According to the National Assessment of Educational Progress, a significant percent of 4th grade students read below the basic level. In one elementary school students participated in additional reading instruction as intervention for students scoring basic and below basic on the state standardized test. The purpose of this ex post facto non-experimental quantitative study was to determine the effectiveness of direct instruction versus fluency (repeated reading) instruction on the reading achievement of 4th grade students. This study is based on the theory of automatic information processing in reading and the theory of prosody. The overarching research question for this study examined if the reading achievement scores of 4th grade students improved with fluency instruction or direct instruction. Two separate years of archived data from the 2011-2012 (Group A) and 2012-2013 (Group B) school years were used to examine student reading levels using the Developmental Reading Assessment (DRA) test. Sample size for both Group A and Group B equaled 76 participants respectively. Use of an independent samples t test indicated there was a significant mean difference of reading achievement scores between student groups as measured by the DRA. Students who received fluency instruction achieved greater comprehension scores than students who did not receive fluency instruction . Findings from this study give indication of improvement in reading achievement with the implementation of fluency instruction. Implications for social change include changing the behavior, perceptions, and customs of teachers towards students in and urban public school and district through professional development and professional learning community sessions.