Doctor of Philosophy / Curriculum and Instruction Programs / Margaret G. Shroyer / This study was designed to investigate teaching practices of mathematics teachers in rural high schools in Kansas in the context of the NCTM Principles and Standards. National reports advocate for change in the mathematics classroom while state assessments force teachers to focus on test scores. This study investigated the extent to which teachers whose students experienced repeated success on state assessments integrated the NCTM Process and Content Standards into the mathematics classroom. Those data were then compared with the teaching practices in schools whose students repeatedly did poorly on state assessments. This two-phase study used both quantitative and qualitative data from four main sources: survey, interview, observation, and collection of artifacts. Phase I surveyed all mathematics teachers in high performing and low performing rural high schools throughout the state of Kansas. Data collected in Phase I were used to examine differences and similarities in teaching practices of teachers from high and low performing schools. During Phase II qualitative data were collected and analyzed to further explore any existing patterns among high performing and low performing schools. Results from teachers in high and low performing schools were compared and contrasted to determine if there were differences between the teaching practices that were demonstrated by each group of teachers. Results of surveys, interviews, observations, and artifacts revealed teachers in high performing schools used a variety of different representations to teach and assess a topic while those teachers from low performing schools used one or two representations. Students from high performing schools had more frequent opportunities to communicate with the teacher to gain additional assistance in learning the mathematics content. Teachers in high performing schools also used formal assessment strategies as part of the learning process more consistently than their counterparts from low performing schools. Results from interviews, observations, and artifacts reveal that teachers in high and low performing schools implement teaching practices aligned with the algebra content standards in a very similar manner.

As of 1999, high school teachers without majors in their subject areas number 37% of biology teachers, 59% of physical science teachers, and 60% of mathematics teachers. These discouraging statistics grow more extreme in middle schools and high poverty public high schools, especially regarding mathematics and physical sciences instruction. The statistics are especially worrisome given the strong correlation between thorough teacher subject matter preparation and higher student performance. Unfortunately, the literature is limited in terms of a direct comparison between mathematics and science majors and individuals who become mathematics and science teachers. This study was undertaken to add to the body of literature in hopes of informing universities and school districts of the characteristics of individuals who enter the mathematics and science teacher pipeline. The purpose of this study was to determine whether predictive relationships exist among the independent variables and the dependent variable, and whether certain attributes account for significant differences between mathematics and science degree earners who choose to enter the mathematics and science teacher pipeline and those who show no interest in mathematics and science teaching. This study provided a snapshot of the characteristics of both groups of individuals. The sample for this investigation came from the Baccalaureate and Beyond Longitudinal Study (B&B: 08/09) cohort of approximately 19,000. B&B:08/09 examined information on students’ educational and work experiences after they completed a bachelor’s degree, with a special emphasis on the experiences of new elementary and secondary teachers. In the present study, the sample consisted of 2,400 individuals majoring in mathematics and science fields including mathematics and science education. The research design that was used is the analytical cross sectional design. The analytical cross sectional design investigates associations and measures differences between groups. In this study, deep descriptions were used to describe the sample. A logistic regression analysis was used to assess the degree to which the dependent (outcome) variable, teacher pipeline status, is related to the independent (predictor) variables (persistence, academic performance, selected demographics).

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<div>Previous studies indicated that calculus courses are considered `weed-out' courses as a lot of students in STEM majors struggle to pass. Instructors and researchers explored various instructional methods to facilitate calculus learning, however, more tailored instructional strategies are still needed. Inventing Contrasting Case is a strategy that has been proven effective in transfer, yet, its effect when combined with the motivational factor and across various content areas should be investigated further. Therefore, this study investigated the relationship between participants' motivation, instruction condition, and the performance on the direct application and transfer problems using Calculus 1 content. The data was collected from undergraduate students in STEM majors at a Midwestern university who were required to complete a Calculus 1 course to attain their degree. Eighty-one students participated for the study. Participants were assigned to either the iCalCulus (iCC) group or the Tell and Practice (TP) group. The study consisted of two separate sessions. In Session 1, participants were provided with a motivation survey, calculus course experience survey, pre-requisite knowledge check test, ICC task or TP task, and post-test. Seven days later, participants took a delayed post-test (Sesson 2). Google Forms was used to create study materials. The results from Bayesian independent sample t-test analyses indicated that the iCC group did not outperform the TP group in direct application problems. In addition, the iCC group did not outperform the TP group in PFL problems in either test. However, the ICC group outperformed the TP group in the further PFL problems from the delayed post-test (BF01 = .096, p = .003). The results from Bayesian one-way ANCOVA analyses indicated that there was the moderate idence that supports the effect of group condition on direct application, Preparation for Future Learning (PFL) performance from the post-test, while controlling for the average pre-requisite knowledge check test score and motivational level. The results also indicated that there was from moderate to strong evidence to support that group condition had an eect on PFL performance from the delayed post-test (Session 2), and the further PFL performance from both post-test and delayed post-test while controlling for the average pre-requisite knowledge check test score. In addition, motivational level was shown to not be an effective moderator between instructional condition and performance in PFL problems. The results from GLM repeated measure analyses showed the ICC strategy had a more significant effect on the participants regarding PFL performance and further PFL performance over time as there was a significant cross-over interaction effect between the time and the instruction condition (p = .012, <b>η_p²= .</b>08 for PFL performance and p = .003, <b>η_p²</b> = .11 for further PFL performance). The direction for potential future studies is addressed in the conclusion section including the importance of developing curriculum to train students' transfer ability; and a new type of assessment to measure transfer is offered for consideration.</div>

The problem with which this investigation was concerned was that of determining the effect of teaching freshman mathematics with the Spitz Student Response System upon a student's anxiety level, attitude and achievement.

The problem of this study was to determine the predictive validities, as measured by multiple correlation, of certain mathematics course grades and the American College Test (ACT) battery when various achievement criteria were used. This study had a two-fold purpose: (1) to determine measures which could be used effectively to predict academic achievement in college mathematics, and (2) to determine whether the multiple correlation between selected predictors and each criterion were significant.

The purpose of this study was to examine the effects of professional development (PD) on the infusion of engineering design into high school curricula. Four inservice teachers with backgrounds in physics, chemistry, industrial education, math, and electrical engineering participated in the 2006 National Center of Engineering and Technology Education (NCETE)-sponsored PD workshops at California State University, Los Angeles (CSULA) and provided three sources of data that were used to answer the research question, "What are the effects of PD on infusing engineering design into high school science, technology, engineering, and math (STEM) curricula"? Three major themes emerged from the data. They were (a) incorporation of PD content, (b) challenges with incorporating PD content, and (c) benefits of incorporating PD content. It was shown that the effect that the NCETE PD had on the infusion of engineering design into high school curricula varied among each of the four teachers due to their subject area, educational backgrounds, and experiential knowledge. Implications of these findings may be used to inform the design and delivery of future STEM PD efforts.

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The problem of this study was a comparison of two techniques of teaching general education mathematics: a transpersonal psychology technique and a lecture-oriented technique. The purposes of the study were to determine the relative effectiveness of a transpersonal psychology technique and a lecture-oriented technique in promoting an understanding of the structure of the real number system, in the development of students' attitudes toward mathematics, and in the retention of knowledge of the real number system. The results of this study were generally inconclusive. It seems necessary that more research be done in the application of relaxation procedures and guided fantasy journeys to the teaching of mathematics before definite conclusions are drawn concerning the effectiveness of the techniques. The paper describing the experimental study consists of five chapters, five appendixes, and a general bibliography. The first chapter is introductory and presents the problem, purposes, hypotheses, and other introductory materials. The second chapter consists of a synthesis of research done in the area of man's two-hemisphere brain and a synthesis of material on the informal applications of the transpersonal teaching technique. Chapters four and five describe the collection of data and the analysis of the data. The fifth chapter presents findings, conclusions, and recommendations.

Prior researchers (Anderson et al. 1994; Ballard & Johnson 2004; Hoag & Benedict 2010) have shown that different math abilities do not equally correlate with success in economics, yet no research has specifically compared algebra and geometry skills as predictors of economics success. In the first essay, I find that students’ standardized geometry scores are a much greater predictor of success in economics than standardized algebra test scores. The study uses a rich data set that includes all Georgia public high school students who took a mandatory economics course in 2006, 2007, or 2008. Results from this study provide supporting evidence that utilizing a generic math proxy is probably unwise for researchers modeling economics success. These findings can also be used to strengthen recruitment efforts since geometry scores seem to be a strong predictor of economics aptitude. Although causality cannot be inferred from my findings, it is plausible that a mandatory geometry course prior to economics would improve student outcomes in economics. In the second essay, I analyze the relationship between economics education and macroeconomic policy attitudes of the general public following the financial crisis of 2008. Using survey data of all 50 states, I find that economics literacy is correlated with preferences for three of the six policies preferences studied. Specifically, economics literacy is positively correlated with support for decreased taxes and a smaller government, and negatively correlated with supporting a ceiling on CEO salaries. Additionally, the completion of college and high school economics is positively associated with supporting a decreased role of government. While prior researchers (Roos 2007; Walstad 1997) found that economics literacy can influence policy preferences, there have been no prior studies, to my knowledge, that analyzed the effects of economics knowledge and economics course-taking on policy preferences within the same dataset. My results show that economics literacy and course-taking exert independent effects on macroeconomic preferences for some policies. Thus, any researcher predicting economic preferences should consider controlling for these economics literacy and economics course-taking variables. Furthermore, my findings suggest that the advancing prevalence of economics education could lead to a shift in public preferences.