The Nature of Science (NOS) and traditional ecological knowledge (TEK) have commonalities in the knowledge bases: they are both ways of explaining the natural world; founded on a set of practices and the historical accumulation of knowledge; and part of the education is learning practices and developing knowledge of the concepts that are foundational to the disciplines. Throughout the United States, schools are attempting to strengthen students' understanding of NOS through various approaches, although few have adopted the integration of TEK into curriculum. This research assesses two summer camps for middle school students that are science focused, one with TEK integration and one with minimal TEK integration. Pre- and post- surveys and student work samples were analyzed to determine the impact of TEK integration on students' understanding of some of the NOS concepts. A significant increase was observed in the camp that integrated TEK, while no change was observed in students' understanding of NOS in the camp that had minimal TEK integration.

The purpose of this case study was to examine the experience of one secondary mathematics teacher during his efforts to facilitate mathematical discussions in a secondary algebra class. Class discussions and interviews were documented and analyzed to investigate the patterns of discussion, the teacher's role in facilitating discussion, and the struggles encountered by the teacher through his attempts to enact reform-oriented strategies. The investigation focused on the teacher's vision for and actual practice in utilizing reform-oriented strategies for discussion in his Algebra class. The teacher's vision of reform was largely based on NCTM Standards recommendations for reforming the teaching and learning of mathematics. Data was collected through various sources and was analyzed using qualitative methods in the spirit of naturalistic inquiry. Data was generated through classroom observations, teacher interviews, audiotapes of whole-class discussions, and personal log notes written by the researcher. Although the teacher expressed intentions to reform discussion in his classroom, he continued to experience struggles in realizing his intentions. Class discussions that were largely teacher-directed and followed traditional patterns of interaction. The teacher struggled with three main issues: classroom challenges, perceptions of student resistance, and teacher authority. The findings of this study suggest that mathematics teachers, even those with extensive experience and grounded knowledge in current reform initiatives, will need to further develop strategies for facilitating a Standards-like environment in their classrooms. Pre-service and in-service educators should also examine the development of programs that can better reflect actual practice and build on classroom teachers' prior experiences and practice. / Ph. D.

Eighth grade students at a middle school in a southern state were required a mathematics pass rate of 67.6% to meet annual yearly progress (AYP). Black and Hispanic students performed below the required pass rate on state assessments; thus, the school did not make AYP from 2007-2010. In an attempt to address low test scores in mathematics, the principal assigned 1 teacher to implement multiple intelligences (MI) instructional strategies, while the other teachers (n = 3) would use traditional strategies. The purpose of this qualitative bounded, descriptive case study was to identify students' MI preferences through an MI inventory, to observe which MI strategies students used to solve problems, and to compare unit pre- and posttest scores of students who received MI strategies instruction with students who received a traditional approach. Gardner's MI theory served as the framework. Students' chosen MI included logical-mathematical, visual, and bodily kinesthetic as evidenced by students' tallied MI preferences and lesson observations. Classroom observations were analyzed with thematic analysis using open coding. Observation data revealed that students used MI techniques that aligned with their preferred intelligences to solve mathematics problems. According to unit test scores, Black and Hispanic students in the MI classes scored higher on the unit test than Black and Hispanic students in the more traditional classrooms. Based on the findings of this study, a mathematics professional development project was designed to help teachers improve instruction. These endeavors may contribute to positive social change for Black and Hispanic students when teachers design mathematics lessons using students' preferred MI to improve student achievement.

Purpose. A multivariate approach was used to investigate sex differences and socioeconomic status (SES) in high school mathematics achievement and attitude. These variables were also examined to see if they had an effect on the student's intention to continue in mathematics. Procedures. A random sample (N = 364) of students was drawn from the mathematics classes of a large California school district. This sample was compared with certain trace variables of two larger samples drawn from the district. The sample was found to be representative along these variables. The Fennema-Sherman and Sandman attitude tests were used to measure attitude toward mathematics. Achievement was measured by the student's grade. The reliability of the attitude tests was calculated. The attitude scales were checked for content validity using factor analysis. The descriptive statics were reported. The hypotheses were tested using chi-square, analysis of variance and analysis of covariance. Findings. (1) There was no significant difference in the number of males and females enrolled in the high school mathematics classes. (2) The intention to continue in mathematics was equally distributed with respect to males and females except for those enrolled in the highest level of high school mathematics. Enrollment rates dropped sharply irregardless of the sex of the student. (3) The females consistently achieved higher than males in all the math class levels. However, this difference was not significant. But, when achievement was covaried with attitude and SES, this difference was significant. (4) Achievement was found to differ significantly between those that intend to continue in mathematics and those that do not. But, again, there were no sex differences within these categories. (5) The mean achievement of the students became higher as the math class level also became more difficult. The mean achievement differences became smaller for the students who intended to continue in mathematics and those that did not as the mathematics level became more difficult. (6) The SES quarter of the student was significantly related to achievement in mathematics. (7) There was no significant difference in attitude between male and female students. Attitude toward mathematics became more positive with the higher mathematics class. (8) SES quarter was not related to attitude toward mathematics. (9) The mean SES was found to differ between mathematics class levels. The students of higher SES continue to be enrolled in mathematics. The lower SES student often does not continue past geometry. Recommendations. (1) An ex-post facto study of contemporary female mathematics and scientists should be undertaken to determine variables which are related to their decision to enter their profession. (2) A study to determine what ethnic or cultural differences may affect mathematics achievement and continuing in mathematics is recommended. (3) A longitudinal study should examine mathematics achievement, mathematics attitude, and continuing in mathematics. The sample should be followed from high school mathematics through college. (4) The effect of the number of required mathematics courses on the student's decision to continue further in mathematics should be examined.

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The purpose of this study was to investigate Saudi mathematics teachers’ understanding and practices of formative assessment as well as determine the factors affecting the practice of formative assessment in mathematics education. The sample included 202 in-service mathematics teachers at both rural and urban public elementary schools in Al Baha district, Saudi Arabia. A concurrent mixed methods design was used. Quantitative data were collected through the questionnaire and data analysis consisted of descriptive statistics, ANOVA, and t-test. Qualitative data were gathered through open-ended questions on the questionnaire and the semi-structured interview. A thematic analysis approach was utilized to analyze the qualitative data. The major findings of this study are that the participants have a high level of understanding of formative assessment. However, the results revealed the participants do not always practice formative assessment during their instruction. In regard to the factors hindering the practice of formative assessment, the participants reported three major factors which are the workload of the mathematics curriculum, the lack of time, and the large number of students in the class respectively. In addition, the results showed that the level of education and teaching experience have an impact on mathematics teachers using formative assessment. Recommendations to policymakers, mathematics teachers, and future research to incorporate formative assessment within a balanced assessment system and ongoing professional development for mathematics teachers.

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Graduate teaching assistants (GTAs) play an integral role at large, research-intensive universities. GTAs have become increasingly important for instruction particularly in laboratory and discussion sections. This dissertation focuses on the use of a mixed reality teaching simulator, TeachLivE™, alongside existing Science, Technology, Engineering, and Mathematics (STEM) GTA training. In Chapter 1 we focus on an introduction to chemistry education research (CER) and the background of the study presented. In Chapter 2 the focus shifts to discussing the theoretical and conceptual frameworks as well as the relevant study instruments. In Chapter 3, we introduce the simulator as a training method for GTAs through the development of content rich concept modules. We discuss their development from selecting the relevant pedagogical skills, integrating student conceptions, and testing the modules with experienced GTAs. We found that the modules provided the GTAs a low-risk environment to practice cold calling and normalizing error skills. In Chapter 4 we analyze GTA conceptualization and use of error framing and cold calling in the simulator as well as their use of the two skills in the classroom. We found that while GTAs were able to use error framing in the simulator, they used the skill less frequently in the classroom. We found that cold calling was used frequently in the simulator and the GTAs were able to integrate the skill into their training practice and classroom. In Chapter 5 we focus on the impact of the teaching simulator on GTA instruction. We identified three GTA instructional styles and found that the method of training had an impact on the instructional styles GTAs used when they taught. Finally, in Chapter 6 we discuss the overall outcomes of the work and future works associated with the project. The result from this dissertation shows the impact of a mixed reality teaching simulator on chemistry GTAs' instructional styles and the ability of this simulator to be integrated into existing training to help prepare GTAs for their roles as instructors.