The research shows a lack of representation of Black women in mathematics education. The purpose of this study was to explore Black women’s perspectives on how their mathematical experiences influenced their decisions to pursue a doctoral degree in mathematics education. To address this issue the following research questions were explored: What perspectives do Black women who are in pursuit of a doctorate of philosophy degree in mathematics education have about their mathematical experiences? How have those perspectives of their experiences influenced their pursuit of a doctorate of philosophy in mathematics education? For this study purposeful sampling was used to select seven participants, that classify themselves as Black women and are currently in a doctoral program in mathematics education. Individual and group interviews conducted with the participants were analyzed using a grounded theory approach to gain an understanding of their mathematical experiences as learners with respect to their trajectories in becoming doctoral students in mathematics education. The Black women that participated in this study had positive feelings about their mathematical abilities. This resulted in confident mathematical identities. The mathematical environment included classrooms with supportive teachers, classmates that were mainly Black, and an even split between the genders. Once this environment was challenged a crisis occurred which caused them to lose confidence in themselves. All of the participants began teaching secondary mathematics as a career change from their initial undergraduate degree. Their initial graduate degrees were in conjunction with their decision to pursue a career as a mathematics educator. The decision to pursue a doctoral degree was out of a personal desire to advance academically as well as desire to effect change within their community. The findings of this study support an achievement motivation framework. This research presents an initial understanding of how perspectives of mathematical experiences influence their decision to pursue doctoral degrees in mathematics education.

<p> Esta investigaci&oacute;n estudi&oacute; las estrategias de soluci&oacute;n de problemas y estrategias sociales que utilizan estudiantes de nivel elemental cuando resuelven problemas matem&aacute;ticos. Adem&aacute;s, se analiz&oacute; el proceso que siguen los estudiantes al resolver problemas de matem&aacute;ticas. En el estudio participaron seis estudiantes de la Escuela Elemental de la Universidad de Puerto Rico. Cada estudiante resolvi&oacute; cuatro problemas; dos de manera individual y dos en pareja. Se utilizaron tres diferentes fuentes de recopilaci&oacute;n de informaci&oacute;n: los trabajos escritos por los estudiantes, las observaciones directas del investigador y entrevistas a los estudiantes inmediatamente despu&eacute;s de la soluci&oacute;n de los problemas. Algunos de los hallazgos m&aacute;s importantes son: (1) los ni&ntilde;os vieron diferentes estrategias de soluci&oacute;n de problemas y al no encontrar soluci&oacute;n con una cambiaban r&aacute;pidamente a otra, en esto muestran diferencia con los adultos, quienes insiste en la estrategia seleccionada. (2) Las estrategias que m&aacute;s utilizaron los estudiantes al resolver los problemas fueron el uso de operaciones b&aacute;sicas y la asociaci&oacute;n con problemas previos. Se observ&oacute; que frecuentemente los estudiantes integran ambas estrategias para desarrollar un proceso de soluci&oacute;n que le permita obtener la respuesta. La operaci&oacute;n b&aacute;sica que m&aacute;s utilizaron fue la suma, en la modalidad de sumas repetidas. Otras estrategias que utilizaron los estudiantes para resolver problemas fueron: an&aacute;lisis, c&oacute;mputo mental, tanteo y error, representaciones ic&oacute;nicas, patrones, uso de modelos concretos y uso de representaciones visuales. Otros hallazgos fueron: (3) Los estudiantes tienen la capacidad de establecer asociaciones de estrategias que les permiten resolver problemas at&iacute;picos de diferentes formas. (4) Los estudiantes utilizan diversas estrategias sociales al resolver en pareja problemas de matem&aacute;ticas. (5) El proceso t&iacute;pico que sigue el estudiante al resolver problemas es el siguiente: (a) lee y comprende el problema formulado, (b) pone a prueba alguna de las estrategias de soluci&oacute;n que conoce, (c) verifica si el resultado obtenido concuerda con el contexto del problema, (d) si le parece razonable, acepta su resultado, de lo contrario lo rechaza y pone a prueba otra de las estrategias que conoce. A la luz de estos hallazgos se sugiere invertir el proceso de ense&ntilde;anza de forma que el maestro comience la clase con la presentaci&oacute;n de un problema que contenga subyacente los contenidos que se pretenden estudiar. De esta manera el ni&ntilde;o tiene la posibilidad de reflexionar sobre su propio conocimiento y cuando descubra la soluci&oacute;n podr&aacute; hacer, de una manera m&aacute;s sencilla, las conexiones esperadas.</p>

<p> This qualitative case study examined the connection between experienced teachers' pedagogical beliefs and their learning of mathematics content. The beliefs of eight experienced elementary (K-8) mathematics teachers were examined before, during, and after the teachers participated in a professional development training exclusively teaching elementary mathematics content. Teachers' beliefs about quality mathematics lessons were solicited through lesson plans, journals, and interviews. Research questions discussed are: (1) What do experienced K-8 teachers believe constitutes a "quality mathematics lesson?" (2) How does the experience of learning mathematics content through inquiry change teachers' beliefs about what constitutes a "quality mathematics lesson?" This study found that teachers changed their beliefs about quality lessons with regard to mathematics content, to pedagogical strategies, and to students as learners through their experience learning mathematics. Teacher beliefs became more focused on mathematical reasoning, more focused on inquiry, and more student-centered. These new beliefs better align with definitions of quality instruction from the literature. Teachers incorporated their beliefs about mathematics, pedagogical strategies, and students as learners into a vision of quality mathematics lessons and the teacher's role in creating those lessons. Teachers' vision of their role changed from that of provider of knowledge to a guide of student discovery of mathematical understandings. The data indicated that these changes in beliefs, including changes in beliefs about pedagogy, were driven by the act of learning mathematics content via methods of inquiry. The results of this study have implications for understanding current and future research on teacher beliefs, for in-service professional development training in mathematics teaching, and for improving teacher effectiveness and student achievement in mathematics.</p>

No description available.

<p> The purpose of this phenomenological study was to gain a better understanding of third grade math teachers' beliefs and practices regarding homework, to explain how teachers' beliefs and practices regarding homework aligned to the framework of the Revised Bloom's Taxonomy Cognitive Domain, and to determine the administrative influences on homework practices. The data were collected during October and November 2013. Six third grade math teachers (primary unit of analysis) and four principals (secondary unit of analysis) were interviewed from Dell School District. Each participant (teacher and principal) was interviewed for approximately one hour. A second meeting was set at a later time with the teachers. This second meeting was arranged in order to ask additional questions based on the interviewees' responses from the initial interview and also to collect homework samples. The follow-up meetings varied between 10 to 15 minutes. The interview transcripts were then transcribed. The data were analyzed to determine the themes: teachers' beliefs and practices of homework, alignment of homework items to the Revised Bloom's Taxonomy, and administrative influences on homework.</p><p> Three major themes emerged regarding teachers' beliefs about homework&mdash;extra repetition of practice, connection between home and school, and building responsibility. Four major themes related to teachers' homework practices were found&mdash; quantity of homework, type of homework, source of homework, and differentiation of homework. Overall, the majority of homework items, across all cognitive domain levels, were aligned to a low category (<i>remembering</i>, 68%); however, there were some variations among the distributions of homework. In comparing what teachers espoused about homework practices and what was actually assigned, the majority were aligned. Four major themes emerged from the principals' comments&mdash;school-wide expectations for homework, complaints about homework, principals' beliefs and value about homework, and cognitive domain of homework. The four major findings of the study included: homework was used primarily for low-level practice, more so than high-level thinking; teachers' homework practices were not part of the principals' leadership agenda, because principals took a &ldquo;hands-off approach&rdquo; to homework; teachers assigned low-level homework with little attention to Bloom's Taxonomy cognitive domain, because this allowed students to be successful and responsible for completing their homework and; homework was a lost art, because principals did not utilize the opportunity to talk with teachers about using homework more effectively to promote students' learning; therefore, teachers continued implementing their same homework practices from the past.</p>

<p> Mathematics, in general, and algebra courses, in particular, have been categorized as "gatekeepers" for higher education, better jobs, and even citizenship. For many low-income and working adults, community college is the institution where they choose to develop their mathematics understanding so they can pursue their dreams. Unfortunately many fail in their attempts. In an effort to better understand their plight so that the community colleges can better meet their needs, I studied community college students' foundational fraction understanding. Specifically, I examined students' procedural skills and problem-solving strategies to determine evidence of fragmented knowledge and fragile learning. I investigated a sample of 373 adult students in four tiers of community college developmental education mathematics courses: Computational Arithmetic, Pre-Algebra, Beginning Algebra, and Intermediate Algebra. In Phase 1, I quantitatively examined students' performance on a written assessment of foundational fraction problems. I compared groups of students to determine if differences might be due to factors of course level, age, and number of years out of school. In Phase 2, I interviewed 33 of the lowest performing students and examined their explanations and categorized students' problem-solving strategies and levels of procedures and explanations while using the strategies. My analysis revealed five major findings. 1. Students' average score on an 11-item foundational fraction assessment was 74%, below what I considered mastery level on the assessment. 2. The assessment scores differed based on course level rather than other demographic factors. 3. On specific NAEP items, Algebra and Intermediate Algebra students scored similarly to United States eighth-graders, whereas Arithmetic and Pre-Algebra students scored higher than 4th graders yet lower than eighth-graders. 4. The foundational fraction items related to magnitude tended to be the most difficult for the students. 5. The major characteristics of students' conceptual understanding were fragmented, fragile, non-fluent and only rarely, sophisticated. While community college developmental education students know something about fractions, my research indicated that their knowledge was held as multiple unconnected knowledge chunks, bits and pieces of prior knowledge mixed with inaccurate, imprecise and partial notions and procedures making students' resulting "fraction sense" tenuous. Although they sometimes successfully solved problems, occasionally with sophisticated self-generated strategies, students were not fluent in their fraction knowledge. The dissertation ends with some recommendations for instructors to address students' limited fraction understanding along with some suggestions for the system as a whole to make fraction instruction a greater priority in developmental courses so that more students can achieve their goals.</p>

No description available.

<p> Research has demonstrated that well into their undergraduate and even graduate education, learners often struggle to understand basic statistical concepts, fail to see their relevance in their personal and professional lives, and often treat them as little more than mere mathematics exercises. Undergraduate learners often see statistical concepts as means to passing exams, completing required courses, and moving on with their degree, and not as <i>instruments of inquiry</i> that can illuminate their world in new and useful ways. </p><p> This study explored ways help learners in an undergraduate learning context to treat statistical inquiry as mattering in a practical research context, by inviting them to ask questions about and analyze large, real, messy datasets that they have collected about their own personal lives (i.e., <i>self </i>-data). This study examined the conditions under which such an intervention might (and might not) successfully lead to a greater sense of the relevance of statistics to undergraduate learners. The goal is to place learners in a context where their relationship with data analysis can more closely mimic that of disciplinary professionals than that of students with homework; that is, where they are illuminating something about their world that concerns them for reasons beyond the limited concerns of the classroom.</p><p> The study revealed five themes in the experiences of learners working with self-data that highlight contexts in which data-analysis can be made to matter to learners (and how self-data can make that more likely): learners must be able to form expectations of the data, whether based on their own experiences or external benchmarks; the data should have variation to account for; the learners should treat the ups and downs of the data as more or less preferable in some way; the data should address or related to ongoing projects or concerns of the learner; and finally, learners should be able to investigate quantitative or qualitative covariates of their data. In addition, narrative analysis revealed that learners using self-data treated data analysis as more than a mere classroom exercise, but as exercises in inquiry and with an invested engagement that mimicked (in some ways) that of a disciplinary professional. </p>

<p> This study sought to identify the instructional strategies used by developmental mathematics instructors in Missouri&rsquo;s public 2-year colleges to engage students in the learning process, determine the cognitive complexity of the instructional strategies, and find out the support needed by these instructors to engage their students in the learning process. A sequential mixed method design was employed in which quantitative and qualitative data was collected. Initial participants in this study included developmental mathematics instructors from all 13 of Missouri&rsquo;s 2-year public community colleges, making for a total of 494 instructors. Quantitative data statistical analysis was completed on the demographic data, as well as on the rating and implementation of recommended instructional strategies using the <i>Qualtrics</i> survey tool. Qualitative analysis was completed on the instructor descriptions of strategies for engaging students in the learning process. Additionally, three participants were chosen from the survey for case study analysis in which three observations, post-observation interviews, and artifact collections were used to obtain more extensive qualitative data.</p><p> Results indicate that developmental mathematics instructors describe the methods they use to engage students in the learning process comparably to those instructional strategies as recommended by the American Mathematical Association of Two-Year Colleges (AMATYC, 2006) to promote active learning, while also including additional strategies. How the instructors rated the instructional strategies as recommended by AMATYC (2006) are given in depth. An overview of the instructional strategies employed by three instructors who were observed, and the cognitive complexity of the tasks and questions used in these instructional strategies is given. Furthermore, recommendations are given for the support needed by developmental mathematics instructors to aid them in engaging their students in the learning process. Implications are offered for the (1) AMATYC (2006) Framework, (2) Professional development on discovery-based learning, (3) Professional development on cognitive complexity of tasks and questions, and (4) Support needed to implement instructional strategies.</p>

<p> The purpose of this study was to determine if there was a significant difference in total scores on the <i>Mathematical Self-Efficacy Scale, </i> the mathematics task self-efficacy portion of the scale, and the math-related school subjects self-efficacy portion of the scale for middle school students between students assigned to a homogeneously grouped accelerated math class and students assigned to a heterogeneously grouped math class. </p><p> The instrument used to gather information for thus study on student self-efficacy was the <i>Mathematics Self-Efficacy Scale</i> (MSES). The MSES measures 2 domains of mathematics-related behaviors and capabilities. The <i> Mathematics Task Self-Efficacy</i> scale is designed to measure the level of confidence the student would have when successfully completing the given task. The <i>Math-Related School Subjects Self-Efficacy</i> scale is designed to measure the level of confidence the student would have when successfully completing a college level course with a final grade of an A or B. The 2 parts of the MSES may be individually scored or holistically scored to obtain a total score representing overall mathematical self-efficacy.</p><p> Descriptive and inferential statistics were used to analyze the data for the 9 research questions. Participants in the study were randomly assigned to the heterogeneous or homogeneous groups by their schools and were not controlled by the researcher. Students within the groups were chosen as participants based on their math ability and scores on the seventh grade TCAP test. At the time of the survey these students attended either a K-8 elementary school or a middle school in Northeast Tennessee. The population consisted of 357 gifted or talented eighth grade math students in 6 school districts in Northeast Tennessee.</p><p> The results of this study does not support or discourage the practice of acceleration by retaining 7 of the 9 null hypotheses that there are no significant difference in self-efficacy scores between homogeneous grouped eighth grade math students who were placed in accelerated coursework by taking Algebra I and those students who were heterogeneously grouped in a regular eighth grade math class.</p>