Mathematics education reform has led to more conceptually focused instruction in the classroom. Yet, students with disabilities are receiving fewer chances than other students to engage in meaningful mathematics. Furthermore, a research divide between mathematics education and special education in mathematics has led to significant gaps in research on the individual and conceptual understanding of students with disabilities. Through task-based interviews and classroom observations, this study begins the process of closing this research gap through an examination of students' understanding of variational and covariational reasoning. Data suggest that the participants, two students with disabilities, increased their conceptual understanding in a reformed learning environment with support from teacher presence and questions. The students were able to increase their understanding of the difference between discrete and continuous functions, demonstrated an ability to self-correct, and improved their ability to choose appropriate levels of reasoning. The results suggest that conceptually oriented instruction with the presence and questioning of a teacher can support students with disabilities in developing a deep and rich understanding of complex mathematics.

Student achievement and motivation to learn physics is highly valued in many industrialized countries including the United States and Japan. Science education curricula in these countries emphasize the importance and encourage classroom teachers to use an inquiry approach. This dissertation investigated high school students? motivational orientations and their understanding of physics concepts in a context of inquiry-based instruction. The goals were to explore the patterns of instructional effects on motivation and learning in each country and to examine cultural differences and similarities. Participants consisted of 108 students (55 females, 53 males) and 9 physics teachers in the United States and 616 students (203 females and 413 males) and 11 physics teachers in Japan. Students were administered (a) Force Concept Inventory measuring physics conceptual understanding and (b) Attitudes about Science Questionnaire measuring student motivational orientations. Teachers were given a survey regarding their use of inquiry teaching practices and background information. Additionally, three teachers in each country were interviewed and observed in their classrooms. For the data analysis, two-level hierarchical linear modeling (HLM) methods were used to examine individual student differences (i.e., learning, motivation, and gender) within each classroom (i.e., inquiry-based teaching, teaching experience, and class size) in the U.S. and Japan, separately. Descriptive statistical analyses were also conducted. The results indicated that there was a cultural similarity in that current teaching practices had minimal influence on conceptual understanding as well as motivation of high school students between the U.S. and Japan. In contrast, cultural differences were observed in classroom structures and instructional approaches. Furthermore, this study revealed gender inequity in Japanese students? conceptual understanding and self-efficacy. Limitations of the study, as well as implications for high school physics teachers are discussed. Future research in this line could explore students? use of cognitive strategies to overcome misconceptions in Western and Eastern cultures. Also, exploring the best practices in changing student misconceptions and promoting motivation across cultures would enrich our understanding and current teaching practices.

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The topic of heat transfer is traditionally taught as an upper level, lecture-style course to mechanical engineering students. Such courses do not provide students with ways to see and feel the important heat transfer concepts at hand. As a way to overcome this, novel, hands-on workshops have been designed and implemented into a heat transfer class taught to junior level mechanical engineering students. Two types of experimental workshops were created and used in two different years of a section of a heat transfer class. In the first year, twelve workshops were designed which included live demos so that the students could see and feel different modes of heat transfer while taking data and seeing real-time plots of temperature and heat flux in different experiments. The workshop introduced each topic the students would be learning in the lecture and was performed the week before the actual lecture on the topic. Each workshop included easily available materials, thermocouples, heat flux sensors, and data acquisition instruments for the students to use. The workshops also served replacements for what would be the third lecture of the week. Results from a concept inventory test given at the end of the first year showed a significant difference on certain question between an experimental group of students who had the workshops and a control group who took the traditional class lecture. However, there were still concepts and topics that the experimental group did not show improvement. They also showed a lack of improvement in their problem solving skills for quiz and test problems. For the second year of the experiment, the workshops were restructured quite a bit. The original 12 workshop format was cut down to only six in order to focus on the ones the students seemed to have benefited from the most. The workshops were also changed into a video-enhanced format where the students would watch a video of the experiment being done while also having the materials in front of them to place their hands on themselves. The students could therefore see and feel what was physically happening and still perform the experiment while watching real-time, pre-recorded plots of heat flux and temperature without worrying about making sure their setup was right and acquiring good results. The new video-enhanced workshops also included control volume and resistance diagrams for each experiment in order to help the students relate the workshops and concepts back to problems on their quizzes and tests. Results from these workshops seemed to show some statistical significance between the experimental and control groups on concept questions given on quizzes throughout the semester, but there was no difference on any questions from the ten concept questions given on the final exam. However, surveys taken by the students indicate that they believed the workshops did help them to understand the concepts in a real-world sense and that they helped them understand the class material better overall. Aside from the results of the workshops on the students learning, this study concludes with an analysis of important heat transfer concepts and how to test them. There is much debate about the underlying concepts in the topic of heat transfer and a thorough analysis on what specific concepts are important for students to know must be addressed. Many heat transfer concept questions on current concept inventories have more to do with thermodynamics and the mixing of the two topics is itself a misconception. / Master of Science

Analysis of multiple data sources revealed a prevalent gap between high school and middle school African American students and their White counterparts in mathematics. Based on these data and a gap in the literature, further research was needed regarding how the mathematics performance of African American students is influenced by culturally responsive leadership and culturally responsive teaching. The purpose of this study was to determine if culturally responsive behaviors of high school and middle school principals influence the behaviors of mathematics teachers resulting in building conceptual understanding of their students; and, how teachers' culturally responsive actions impact the mathematics performance of African American students. The research questions guiding this qualitative study were (1) To what extent, if any, do principals at the high school and middle school levels that exemplify culturally responsive leadership influence mathematics teachers' use of culturally responsive teaching that results in building conceptual understanding in mathematics? and, (2) To what extent, if any, do culturally responsive teaching practices impact the mathematics performance of African American students at the high school and middle levels? The results indicated that the purposive sample of high school and middle school principals (n = 7) exhibited critical consciousness (self-awareness) and interrelationships amongst teachers and students; communication and being present; and, data- driven decision-making. The purposive sample of high school and middle school mathematics teachers (n = 23) exhibited content knowledge that allowed for differentiated instruction inclusive of building conceptual understanding through multiple mathematical representations; and, engaged their students in mathematical discourse requiring students to reason and justify their solutions. Thus, such actions created a familial-like atmosphere inherent in optimal learning environments for African American students. Students with culturally responsive teachers performed better on division-wide assessments, with the effect of reducing the achievement gap between African American and White students compared to teachers not self-identified as having high levels of cultural responsiveness with results statistically significant at the 0.01 level after conducting a two-proportions z-test. / Doctor of Education / The purpose of this study was to determine if culturally responsive behaviors of high school and middle school principals influence the behaviors of mathematics teachers resulting in building conceptual understanding of their students; and, how teachers' culturally responsive actions impact the mathematics performance of African American students. The synthesis of the literature review and the results of this study could provide information that would assist school leaders and teachers in not only understanding their respective roles impacting and influencing the mathematics performance of African American students at the high school and middle school levels, but also understanding the pedagogical, conceptual understanding, and leadership practices and factors that can lead to this improvement. A qualitative study design was used in one urban Virginia school division encompassing a preliminary screening of high school and middle school principals and mathematics teachers; observations of high school and middle school principals and mathematics teachers; and, a culminating culturally responsive leadership practices survey. The researcher sought to examine (1) To what extent, if any, do principals at the high school and middle school levels that exemplify culturally responsive leadership influence mathematics teachers' use of culturally responsive teaching that results in building conceptual understanding in mathematics? and, (2) To what extent, if any, do culturally responsive teaching practices impact the mathematics performance of African American students at the high school and middle levels? Data from division-wide assessments demonstrated that the students of culturally responsive teachers performed better and with a reduced achievement gap between African American and White students compared to teachers not having self-identified with high levels of cultural responsiveness. Observations from the high school and middle school principals and mathematics teachers revealed specific behaviors and strategies used consistently across the sample. From the findings, implications for practices and recommendations for future studies were rendered.

This thesis explores a conceptual understanding of dialogue within a community of practice. It argues that meaningful conversations are at the core of critical, reflective, and analytical praxis, and that a critical understanding holds transformative possibilities for teaching and learning. Aspects of western and ethnic paradigms and their theoretical constructs, which may either enhance or hinder current practices, are identified, as are elements that arise from several case studies drawn from a large banking organisation operating out of South Africa. It is hoped that an evaluation of the research findings will provide a basis for an understanding of dialogue within a local context and that, further, it will provide a platform for extended dialogical exploration and research.

<p>As pedagogical innovations continue to be developed and adopted in engineering education, it is important to understand how these innovations affect the students’ experiences and achievements. A common data analysis practice when evaluating educational innovations is to aggregate the data from all of the students together. However, this data aggregation inherently biases the results toward the characteristics of the dominant student group, leaving the experiences of minority groups largely unexplored. In this dissertation, I investigate the students’ experiences and achievements in an undergraduate dynamics course, and I intentionally use analysis methods that disaggregate the data to better understand the behaviors and performance of smaller subgroups of students, not just the majority.</p> <p> This dissertation presents three studies that examine: 1) the validity, reliability, and fairness of a standardized set of conceptual questions on the final exam, with a focus on gender fairness, 2) how and why the students use the available resources, and 3) how the students’ holistic resource usage patterns relate to their academic achievement. My motivation for choosing these studies was that conceptual assessments and customized resources are two key components of the learning environment for the dynamics course. However, the quality of the conceptual exam questions used for the course had yet to be evaluated. Similarly, the learning environment for the course incorporates many customized resources, including a custom-written “lecturebook” (a hybrid of a textbook and a workbook) and an extensive online library of videos, but little was known about how the students used these resources, or how the students’ pattern of resource usage related to their performance in the course. </p> <p> The first study in this dissertation used multiple-group confirmatory factor analysis to investigate item-level gender bias in a 12-item Abbreviated Dynamics Concept Inventory (aDCI), which was a set of standardized conceptual questions included on the final exam. The results suggested that two items were slightly biased against women, with stereotypically-masculine contexts and content as possible sources of the bias. The bias in the aDCI items likely unfairly lowered some women’s final exam scores, highlighting the need for engineering educators to consider the fairness of their assessments.</p> <p> The second study used a cluster analysis of survey responses to identify nine archetypical patterns of resource usage, all of which differed from the average resource-usage pattern of the aggregated sample. An analysis of forty-four student interviews, organized by resource-usage cluster, determined that students exhibited their resource-usage behaviors largely because of how they perceived the resource’s availability, accessibility, and quality. The results illustrate that there is no “typical” way in which the students used the resources, so it is important for instructors to consider a wide array of usage behaviors when designing a course’s learning environment and resources.</p> <p> The third study utilized a multiple regression analysis to find that <i>on average</i> a student’s resource-usage pattern is not related to their achievement when controlling for many other demographic, cognitive, and non-cognitive factors that can affect resource usage and performance. However, two individual resource-usage patterns were significantly related to achievement. Students who primarily used their lecturebook and their peers for support performed better than their similar peers in other resource-usage clusters. Conversely, students who rarely used their lecturebook had lower course grades than their peers. Drawing from the results of the second study, general study-habit suggestions for the students in the course were extracted from the qualitative themes found in the interviews of the students in these two clusters.</p> <p> Overall, the results of these three studies highlight how the experiences and achievements of smaller groups of students would go unnoticed if analytical methods that only utilized aggregated data were used. While the setting of this research is specific to the assessments and resources of a given dynamics course, the methods used to disaggregate the data to gain insights about different subgroups of students are applicable to many engineering education contexts. My hope is that this work inspires more researchers to consider the experiences of all students, not just those of the majority.</p>

Den här studien undersöker gymnasieelevers begreppsförståelse inom trigonometri. Eleverna, som samtliga läser Ma 4, besvarade anonymt två frågeformulär där det ena bestod av en öppen fråga, medan det andra var upplagt som ett test med uppgifter att lösa. Den kvalitativa analysen baseras på Tall och Vinners (1981) teori om begreppsbild och Sfards (1991) uppdelning av begreppsförståelse i de tre processerna interiorisering, kondensering och reifiering. Resultatet indikerar att elever tenderar att använda cirkeltrigonometri före triangeltrigonometri för att lösa uppgifter, men att majoriteten av deras begreppsbilder består av både och. Det visade sig att radianer var det trigonometriska begrepp eleverna hade svårast för. Detta stämmer överens med tidigare forskning på området. Tre elever analyseras djupare med avseende på hur långt de har kommit i sin utveckling av begreppsförståelse inom trigonometri. Det ges även exempel på hur utvecklingsfaserna kan ge sig till uttryck hos enskilda elever. Såväl begreppsbild som vilka stadier eleverna befinner sig på i sin begreppsförståelse varierar stort. / This study investigates the conceptual understanding of high school students in a trigonometry context. The students, all of them taking the Swedish math course Ma 4, anonymously answered two questionnaires, one of them containing an open question, while the other was constructed like a test with problems to solve. The qualitative analysis is based on Tall &amp; Vinner’s (1981) theory of concept image and Sfard’s (1991) division of conceptual understanding into the three processes interiorization, condensation and reification. The result indicates that students tend to use circle trigonometry over triangle trigonometry for problem solving, however the majority of their concept images consist of both. Radians seemed to be the trigonometrical concept that the students had most trouble understanding. This corresponds with earlier research of trigonometry. In the analysis three students are more deeply analysed, based on how far they have come in their development of trigonometric conceptual understanding. Furthermore there are concrete examples of how the phases of development can be presented among individual students. The concept image as well as the levels of the students’ conceptual understanding vary considerably.

Research on conceptual change provides strong evidence that not only children but also many adults have incorrect or incomplete understanding of science concepts. This mixed methods study was concerned with preservice and inservice teachers’ understanding of six earth and space science concepts commonly taught in elementary school: reasons for seasons, phases of the moon, reasons for the wind, the rock cycle, soil formation, and earthquakes. The first part of the study determined and compared the level of conceptual understanding held by both groups on topics they will need to teach in the Georgia Performance Standards [GPS]. The second part focused on whether readings or hands-on learning stations, in some cases combined with concept mapping, improves preservice teachers’ understanding of these concepts. The third part described the application of conceptual change strategies of one group of preservice teachers during their field placements. The overall sample was two cohorts of preservice teachers, one cohort of preservice teachers from an alternative initial certification program, and two masters’ cohorts consisting of inservice teachers. Four data sources were: a six item open-ended survey, concept maps, the field assignments, and the researcher’s field notes. Rubrics were used to score answers to each survey question. Concept map scores were calculated based on the criteria developed by Novak and Gowin (1984). The first part of the study shows that both preservice and inservice teachers have low conceptual understanding of the earth science concepts taught in elementary school. Independent samples t-tests results indicate that both groups have similar understanding about these concepts. A two way ANOVA with repeated measures analysis demonstrated that readings and learning stations are both successful in building preservice teacher’s understanding and that benefits from the hands-on learning stations approached statistical significance. A paired samples t-test shows that concept mapping added to the participants’ conceptual understanding whether the participants learned the concepts through readings or stations. Finally, field assignments allowed the participants to apply knowledge that they learned in their science methods course in their classroom placements. This study has implications for teacher preparation programs, staff development, and conceptual change practices in field placements.