Exploring Teachers’ Beliefs and Practices on Mathematical Discourse for Diverse Students in Inclusive Classrooms

The recent implementation of rigorous standards in mathematics education has required shifts in classroom practices. Standards-based instruction places large emphasis on students’ conceptual understanding, requiring them to demonstrate high cognitive levels of mastery of the content through communication of their mathematical reasoning. Teachers and students’ mathematical discursive practices in the classroom can lead to meaningful discussions that integrate students’ explanation, justification, and arguments of ideas or claims and understanding of the content. Research on teachers’ discursive practices has shown that (a) teacher talk tends to dominate classroom instruction and (b) classroom discourse lacks frequent opportunities for teacher-student and peer interactions. The purpose of this exploratory sequential mixed methods study was to increase understanding regarding teachers’ beliefs and practices related to the planning and implementation of mathematical discourse in inclusive general education elementary mathematics settings. Specifically, this research study centered on the development of a valid and reliable instrument on teachers’ beliefs and practices related to mathematical discourse that could be used by teachers and researchers interested in the implementation of equitable mathematical discursive practices in the classroom that promote students’ conceptual understanding. The development of the survey occurred over a multiphase process: content development (qualitative data collection and analysis), survey development and pretesting (survey validity measures), and pilot testing (survey reliability measures). Six general and three special education teachers participated in Phase 1 and 2, and 18 teachers (i.e., 13 general and 5 special education teachers) participated in Phase 3. Data sources included individual interviews, a focus group, classroom observations, teachers’ lesson plans, and the Teachers’ Beliefs and Practices on Mathematical Discourse Survey. Qualitative and quantitative findings showed that teachers believe mathematical discourse is intuitively implemented during instruction without much planning, all students should participate in the classroom discourse, and mathematical discourse should be explicitly taught and modeled to students. Findings on teachers’ perceived practices showed that teachers mainly utilize discourse to assess understanding by soliciting students’ mathematical reasoning, generally use the curriculum to guide their mathematical discourse practices and implement varied grouping strategies to facilitate discourse. Findings on teachers’ observed practices indicated that (a) teacher-led, authoritative discourse dominated discursive practices during mathematics instruction, (b) discursive practices were mostly focused on assessing understanding and addressing misconceptions, (c) participation and engagement generally involved all students in the classroom, and (d) planning for mathematical discourse was solely based on activities explicitly included in the curriculum. Based on these findings a 50-item Teachers’ Beliefs and Practices on Mathematical Discourse Survey was created, pretested, and pilot tested for validity and reliability purposes. The alpha coefficient for each of the two survey constructs suggested that overall measures of validity and reliability were sufficient by showing relatively high internal consistency to support the survey use in future research and program and professional development planning

Microscopy of elongated superfluids

This thesis covers three experiments with cold and ultracold (Bose-Einstein condensate based) alkali Rb-87 gases for quantum simulation. In the first experiment, we quantum simulate Abelian and non-Abelian gauge fields in the parameter space of a four-level quantum system. Then, we describe the experimental framework to perform optimal in-situ microscopy of elongated quantum gases. We then study the thermodynamics of individual one-dimensional Bose gases using in-situ resonant absorption imaging. Finally, we combine holographic microscopy and impulse correlations to digitally enhance our absorption images

Teacher Leadership in Systemic Reform: Opportunities for Graduate Education Programs

Nevada has recently taken considerable steps to reform English learner (EL) education across the state with teacher development as a primary focus. Educational reform agendas necessitate that teachers not only rethink their practices but teach in novel ways. It has been argued that teacher development through graduate education and other professional development (PD) avenues are ineffective in shifting instructional practices, highlighting a theory-to-practice gap. Further, it has been postulated that without teachers’ participation and leadership in reform, such efforts will fail. This article details a graduate PD model designed specifically to prepare teachers as teacher leaders and address the theory-to-practice gap. Our university enhanced our graduate educator preparation program in English Language Learning (ELL) to build statewide collaborative cohorts of urban and rural teacher leaders prepared to implement and facilitate educational improvements for ELs within their varied educational contexts

Effects of mirror birefringence and its fluctuations to laser interferometric gravitational wave detectors

Crystalline materials are promising candidates as substrates or high-reflective coatings of mirrors to reduce thermal noises in future laser interferometric gravitational wave detectors. However, birefringence of such materials could degrade the sensitivity of gravitational wave detectors, not only because it can introduce optical losses, but also because its fluctuations create extra phase noise in the arm cavity reflected beam. In this paper, we analytically estimate the effects of birefringence and its fluctuations in the mirror substrate and coating for gravitational wave detectors. Our calculations show that the requirements for the birefringence fluctuations in silicon substrate and AlGaAs coating will be on the order of $10^{-8}$ and $10^{-10}$ rad/$\sqrt{\rm Hz}$ at 100~Hz, respectively, for future gravitational wave detectors. We also point out that optical cavity response needs to be carefully taken into account to estimate optical losses from depolarization.Comment: 11 pages, 4 figure

Health-Related Conditions and Depression in Elderly Mexican American and Non-Hispanic White Residents of a United States-Mexico Border County: Moderating Effects of Educational Attainment

We investigated the prevalence of “high” levels of depressive symptomatology and 13 health-related medical conditions in elderly Mexican American (MA) and non-Hispanic white (NHW) residents of El Paso County, Texas. We analyzed the extent to which depressive symptoms in this population are associated with these conditions. Elderly MA residents possessed a higher prevalence of current depression, a relatively unique health-related condition profile, and were more likely to experience a set of conditions that impede participation in daily life—conditions that we found to be strongly associated with high depressive symptomatology in the elderly. After adjusting for educational attainment, using multiple regression analyses, depression was not associated with ethnicity and only six of the health related conditions showed significant differences between MA and NHW subjects. We believe these results provide an important insight into the mechanism of health-related conditions and depressive symptomatology in a large sample of elderly MAs; and how conditions typically attributed to MA ethnicity may in actuality be an artifact of socioeconomic status variables such as educational-attainment

Social networks and COVID-19 vaccination hesitancy in Mexican older adults

Introduction: The importance of social networks is growing, impacting everyday life. At this stage of global COVID-19 vaccination roll-out, hesitancy to get immunized is slowing this process; it is thought that this decision could be impacted by information shared on social networks. Objective: Determine whether the use of social networks is associated with the willingness to get the COVID-19 vaccine. Methods: This is a secondary analysis of the ENSANUT COVID-19 study, that measures the impact of the pandemic on the Mexican population. Only older adults, aged 65 years or older, were included in this work. Face to face interviews were performed to determine social network utilization, willingness to get vaccinated, and socio-demographic information on health and COVID-19. Bivariate analysis and logistic regression were performed. Results: From a total of 1,490 older adults, 59.3 % were women whose mean age was 73.5 (SD 6.8), and 53.3% (n = 795) were willing to get a COVID-19 vaccine when available. In an adjusted multivariate logistic regression model, WhatsApp was found to be a significant variable related to lower risk of vaccine hesitancy (OR 0.43, 95% CI, 0.2–0.85; p = 0.016). Other variables related to vaccine hesitancy were being a woman (OR 1.58, 95% CI, 2–1.23; p < 0.001) and COVID-19 literacy (OR 1.32, 95% CI, 1.01–1.74; p = 0.047). Conclusion: The use of social networks such as WhatsApp is a factor that can influence older adult vaccination against COVID-19. Social networks, among other variables, should be taken into account when analyzing factors that lead to vaccination hesitancy in older adults.Introduction: The importance of social networks is growing, impacting everyday life. At this stage of global COVID-19 vaccination roll-out, hesitancy to get immunized is slowing this process; it is thought that this decision could be impacted by information shared on social networks. Objective: Determine whether the use of social networks is associated with the willingness to get the COVID-19 vaccine. Methods: This is a secondary analysis of the ENSANUT COVID-19 study, that measures the impact of the pandemic on the Mexican population. Only older adults, aged 65 years or older, were included in this work. Face to face interviews were performed to determine social network utilization, willingness to get vaccinated, and socio-demographic information on health and COVID-19. Bivariate analysis and logistic regression were performed. Results: From a total of 1,490 older adults, 59.3 % were women whose mean age was 73.5 (SD 6.8), and 53.3% (n = 795) were willing to get a COVID-19 vaccine when available. In an adjusted multivariate logistic regression model, WhatsApp was found to be a significant variable related to lower risk of vaccine hesitancy (OR 0.43, 95% CI, 0.2–0.85; p = 0.016). Other variables related to vaccine hesitancy were being a woman (OR 1.58, 95% CI, 2–1.23; p < 0.001) and COVID-19 literacy (OR 1.32, 95% CI, 1.01–1.74; p = 0.047). Conclusion: The use of social networks such as WhatsApp is a factor that can influence older adult vaccination against COVID-19. Social networks, among other variables, should be taken into account when analyzing factors that lead to vaccination hesitancy in older adults