How well students perform in mathematics and sciences continues to be a measure of a country's worth (Conference Board of the Mathematical Sciences [CBMS], 2012). Nations that want an educated citizenry have consistently studied ways in which to improve performance in mathematics (Claessens and Engel, 2013; Dearing et al., 2012; Draper and Siebert, 2004). More and more researchers have examined the relationship reading has on mathematics performance (Grimm, 2008; Halaar, Kovas, Dale, Petrill, and Plomin, 2012). This study was an effort to contribute to this growing body of knowledge. Therefore the purpose of this study was to examine what relationship exists between reading and mathematics and whether early reading performance could predict subsequent mathematics performance as measured by the Virginia Standards of Learning Assessments. Using a sample of students from a Virginia high school, this quantitative study utilized Virginia Standards of Learning (SOL) tests as instruments and Chi-square Test of Association as the analysis to address the research questions: 1. What is the relationship between Virginia Standards of Learning (SOL) reading performance and SOL mathematics performance at each grade level in Grade 3 through Grade 8? 2. What is the relationship between SOL reading performance in Grade 3 and subsequent performance on Virginia SOL End-of-Course Algebra I assessment? 3. To what extent does SOL reading performance in Grade 3 predict subsequent performance on Virginia SOL End-of-Course Algebra I assessment? Virginia SOL reading performance was found to be associated with mathematics performance at each grade level. Reading performance at Grade 3 was not found to be associated with Algebra I EOC performance. Grade 5, Grade 6, Grade 7, and Grade 8 reading performance were all found to be associated with Algebra I EOC performance. As a limitation, this study utilized data from assessments designed to assess the 2001 Virginia SOL standards, which have since been updated. Therefore should be replicated using the current standards. The results of this study could be used to assist teacher leaders, principals, division leaders, and teacher preparation program leaders with working with teachers to address reading and mathematics deficiencies in a different way. / Ed. D.

abstract: The focus of the study was to identify secondary school students' difficulties with aspects of linearity and linear functions, and to assess their teachers' understanding of the nature of the difficulties experienced by their students. A cross-sectional study with 1561 Grades 8-10 students enrolled in mathematics courses from Pre-Algebra to Algebra II, and their 26 mathematics teachers was employed. All participants completed the Mini-Diagnostic Test (MDT) on aspects of linearity and linear functions, ranked the MDT problems by perceived difficulty, and commented on the nature of the difficulties. Interviews were conducted with 40 students and 20 teachers. A cluster analysis revealed the existence of two groups of students, Group 0 enrolled in courses below or at their grade level, and Group 1 enrolled in courses above their grade level. A factor analysis confirmed the importance of slope and the Cartesian connection for student understanding of linearity and linear functions. There was little variation in student performance on the MDT across grades. Student performance on the MDT increased with more advanced courses, mainly due to Group 1 student performance. The most difficult problems were those requiring identification of slope from the graph of a line. That difficulty persisted across grades, mathematics courses, and performance groups (Group 0, and 1). A comparison of student ranking of MDT problems by difficulty and their performance on the MDT, showed that students correctly identified the problems with the highest MDT mean scores as being least difficult for them. Only Group 1 students could identify some of the problems with lower MDT mean scores as being difficult. Teachers did not identify MDT problems that posed the greatest difficulty for their students. Student interviews confirmed difficulties with slope and the Cartesian connection. Teachers' descriptions of problem difficulty identified factors such as lack of familiarity with problem content or context, problem format and length. Teachers did not identify student difficulties with slope in a geometric context. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2011

The purpose of the current study was to discern the effects of three latent constructs – self-efficacy, academic engagement, and student-teacher relationships on Algebra I achievement among ninth-grade African American male students. A nationally representative sample from the High School Longitudinal Study of 2009 (HSLS09) was used in the study. Study participants were 697 African American males enrolled in ninth grade in the fall of 2009 across the United States. Structural Equation Modeling (SEM) analytical procedures were performed to test the hypothesized relationships of Bandura’s social cognitive theory (SCT) theoretical assumptions. The results indicate that the three latent variables directly or indirectly were related to Algebra I achievement among ninth grade African American male students. Moreover, the results revealed that self-efficacy and student-teacher relationships constructs had direct significant impact on Algebra I academic performance; nonetheless, the relationships were not strong. These two latent variables had small effect sizes of 5% and 1%, respectively. Combined, self-efficacy, academic engagement, and student-teacher relationships explained only 8% of the variance in the Algebra I achievement among African American males across the United States (R2=.08). The magnitude effect of these factors on Algebra I achievement was minimal. Overall, these findings suggest that the self-efficacy and student-teacher relationships latent variables had a negligible effect as predictors of Algebra I academic success among ninth grade African American male students. A summary of the results are presented and future research is recommended.

Students with specific learning disabilities (SLD) are educated in general education classrooms. As a result, these students are faced with more challenging instructional curricula. Although some students with SLD perform as well in mathematics as students without disabilities, most perform below state standards despite being provided instructional and testing accommodations. Policy makers have envisioned the implementation of instructional accommodations as a primary means of ensuring an appropriate education (Mcleskey, Hoppey, Williamson & Rentz, 2004; Scalon & Baker, 2012) for students with disabilities in general education classrooms (Mc Guire, Scott, & Shaw, 2006). The researcher implemented a non-experimental ex post facto research design to investigate the research hypothesis to determine the relationship between the five most frequently used accommodations by general education teachers who teach students with SLD and student achievement in Algebra 1. At the beginning of the 2016 – 2017 school year, the collection of data began by emailing the Qualtrics Survey Software (V.23) to 185 general education mathematics teachers in Miami-Dade County Public Schools. Four main instructional accommodation constructs were assessed using a 15-item questionnaire. From the responses to the survey, the five of the most frequently used accommodations were determined. Nine general education Algebra 1 teachers from six high schools across the county who reported using similar accommodations and taught three or more students with SLD in mathematics participated in the study. The researcher and two peer researchers conducted in-class observations on the participants’ fidelity of implementation of accommodations (FOI) using a checklist during the period in which they taught students with SLD. An Algebra I test was used for pre- and post-testing to determine student mathematics achievement. The results of the survey indicated that teachers most frequently provided: (a) sample problems of varying levels, (b) guides or prompts or personal (teacher/peer) assistance, (c) extended access to instructional resources and equipment, (d) provided preferential seating and (e) additional time to complete assignment or class projects. Linear regression analysis revealed a significant positive relationship between teacher FOI of accommodations and student achievement (p < .05).