Rural high school graduates in the United States lag behind in college math preparedness, therefore prompting researchers to identify instructional practices that would advance student math performance. This quantitative research study investigated specific teacher practices and their correlation with student gains in college math preparedness on the American College Test (ACT). Data were collected using a teacher questionnaire to quantify the level of reform practices among a sample of six math teachers and used ACT pre and posttests to assess 312 11th grade students' gains in college math readiness in a public rural high school in Southeast Tennessee. Correlation analysis of reform indicators from the teacher questionnaire compared the interrelatedness of six predictor variables on student math gains. The level of reform practices of the teacher was insignificant when correlated with student gains on the ACT Math subtest, r < .1, yet yielded important insights into rural teaching practices at the sample school. Teacher questionnaire responses indicated consistently low scores in teacher conceptual beliefs and rural connectedness, suggesting room for reform in those areas. The average Math ACT gain was 1.97 points with an average math score of 19.3. This suggests the 2016 school average will exceed the 2015 school average of 19.1 since students in the study have another year of math instruction prior to graduation. Extending the current study through college may reveal a correlation between specific teacher practices and rural student math gains.

Research suggests that student success in mathematics is positively correlated to math self-efficacy and negatively correlated to math anxiety. At a Hispanic serving community college in the Midwest, developmental math students had a lower pass rate than did college-level math students, but the role of math self-efficacy and math anxiety on these students' learning was unknown. This causal comparative, correlational study, guided by social cognitive theory and math anxiety research, hypothesized that students in developmental math would have lower levels of math self-efficacy and higher levels of math anxiety, and that significant correlations would exist between course level, self-efficacy, and anxiety. All math students at this setting (N = 1,019) were contacted to complete the self-report Mathematics Self-Efficacy and Anxiety Questionnaire; 32 developmental math and 103 college-level math students returned the survey. A random sample of 32 college-level students was selected to create equal group sizes for the data analyses. Independent samples t-tests revealed no significant differences in self-efficacy and anxiety between the groups. Significant correlations were found for course level, self-efficacy, and anxiety. Lower course level math students reported on average significantly lower levels of self-efficacy and significantly higher levels of anxiety than did upper course level students. A professional development program was created to educate faculty about math self-efficacy and math anxiety and to implement strategies that may increase math self-efficacy and decrease math anxiety over time. This doctoral study has the potential to create social change by offering educators new insight into the role of math self-efficacy and math anxiety in student learning.

Previous literature leaves us unanswered questions about whether teaching behaviors mediate the relationship between teacher education level and experience with student science achievement. This study examined this question with 655 students from sixth to eighth grade and their 12 science teachers. Student science achievements were measured at the beginning and end of 2006-2007 school year. Given the cluster sampling of students nested in classrooms, which are nested in teachers, a two-level multilevel model was employed to disentangle the effects from teacher-level and student-level factors. Several findings were discovered in this study. Science teachers possessing of advanced degrees in science or education significantly and positively influenced student science achievement. However, years of teaching experience in science did not directly influence student science achievement. A significant interaction was detected between teachers possessing an advanced degree in science or education and years of teaching science, which was inversely associated to student science achievement. Better teaching behaviors were also positively related to student achievement in science directly, as well as mediated the relationship between student science achievement and both teacher education and experience. Additionally, when examined separately, each teaching behavior variable (teacher engagement, classroom management, and teaching strategies) served as a significant intermediary between both teacher education and experience and student science achievement. The findings of this study are intended to provide insights into the importance of hiring and developing qualified teachers who are better able to help students achieve in science, as well as to direct the emphases of ongoing teacher inservice training.

The subject of this study grew out of a desire to estimate the value of high school chemistry and its relation to college chemistry. The purpose is to bring about a better understanding of the necessity of a closer tie-up between different levels of our educational system. Life and growth are continuous processes, and, if education if life, we must make it a continuous experience. While limited because of incomplete records and changing classifications of our high schools, it is hoped that this study will lead to a further and more scientific study of related problems in this field.

The purpose of this study was threefold: (1) to ascertain what is being done in elementary science on the fourth grade level in the states included in this study; (2) to determine whether the work being done is in keeping with the thinking of the modern authorities on the teaching of elementary science; and (3) to formulate a program of elementary science on the fourth grade level based on the materials considered most practical and organized around the "center of interest" currently accepted as basic for the teaching of science in the fourth grade.

This thesis has been written to emphasize the differences in two methods of teaching arithmetic - mechanical drill and meaningful drill - and attempts to present a psychologically and theoretically sound proposal for instruction in number skills in the primary grades of the elementary school.

This study involves the following divisions: To build a course of study in plane geometry consisting of six units developed. To suggest some ways of evaluating a course of study.

Secondary school science consists of biology, chemistry, physics, or a combination course known as general science. General science deals only with the practical side of the laws of physics. It fails to go into detail and very often omits the law entirely. Physics in high school requires a special room in the building which is not easily adapted to other use. A large amount of expensive equipment is need to teach it efficiently. Can all of this expense be justified? Is the student who ends his school career with high school graduation sent out into life with a large amount of useful information? Is the student who goes on into college given a clearer conception of the subject? Is he able to go farther in his college science because of his high school background? This study will try to answer these last two questions.

Two groups of Title I Math teachers, one representing school systems which reported second and third grade student achievement gains of one year or more on the Comprehensive Test of Basic Skills for 1978-79, and one group which reported gains of less than eight months, were surveyed in an effort to identify which methods of presentation and types of materials apparently contributed to the most successful Title I Math programs, in terms of student achievement gains. A study of survey results indicated that a Title I Math pull-out program served by a teacher in groups of less than ten students was the most common method of presentation in both survey groups. Results suggested that small-group settings, contact with a teacher and an aide in a pull-out situation, and a low student-teacher ratio were among the factors which influenced the achievement of Title I Math students. In regard to program planning. school systems which reported higher CTBS test scores achieved a more even balance of time spent between teaching from commercial materials/programs and teaching from teacher-made units or packets of work. with a limited amount of time utilized for games and other approaches; school systems which reported lower test scores devoted over half their teaching time to the use of teacher-made materials. Teachers from both groups indicated that their students, who represented several age groups from more than one grade level, necessitated a wide range of Math materials; because of the ages and individual differences in students, no one program or approach to teaching Title I Math was preferred or felt to be more effective than any other. An approach to teaching Title I Math suggested paying heed to the abilities and needs of the students, utilizing resources from a variety of commercial materials, permitting the teacher flexibility in developing work packets as needed, and infusing any other methods in planning a Title I Math curriculum.

The purpose of this thesis is to compile and discuss some of the methods of solution of both ordinary and partial differential equations, whose solutions are expressible in the form of a series. An exhaustive study is not attempted. A few of the methods of most common occurrence for finding solutions in series are discussed and examples illustrating these methods are presented.