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Tasks for Learning Trigonometry
Get PDFMany studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing sine and cosine functions, the sum and difference identities, and vectors. The four tasks were implemented in trigonometry courses and then student work was collected and analyzed for the following research questions: (1) What approaches did the student use to complete the task given; (2) How can student responses to the tasks help to improve the tasks (i.e., are there errors in the students’ logic, did they answer the questions fully, how can the task be improved to allow student critical thinking, etc.). Along with the four lessons, a formative assessment was given to assess students as related to the objectives of the task. Using student data, the lessons were revised to allow for student critical thinking and engagement. The implementation of the tasks was observed using the observation tool known as the Mathematics Classroom Observation Protocol for Practice (MCOP2). The MCOP2 was used to measure student engagement for each task. Reflections were completed using the Thinking Through a Lesson Protocol (TTLP) to allow the instructor to reflect on the implementation of the tasks and how they can continue to be improved with these observations. Finally, students were asked to complete an end-of-semester survey to reflect on all four tasks. The results of the study are four tasks with formative assessments in trigonometry that are mathematically rich and allow critical thinking from students
Oxider to Fuel Ratio Shift Compensation Via Vortex Strength Control in Hybrid Rocket Motors
Get PDFHybrid motors have existed as a hypothetical propulsion system for decades in a wide range of upper stage rocket motors due to their simple, robust, non-toxic, and versatile nature. However, inherent to hybrids is Oxidizer to Fuel ratio (O/F) shift over time, which results in performance losses for the majority of the rocket’s lifetime. The purpose of this study is to develop a hybrid rocket motor capable of manipulating O/F at will, resulting in an engine which eliminates the undesirable effects of O/F shift. By developing and refining a numerical simulation, a novel injector system, and an open-loop control scheme, this thesis demonstrates programmable O/F manipulation in an experimental hybrid engine
A Content Analysis on Emotions Presented in Preschool Children\u27s Television
Get PDFLearning about emotions is an essential aspect of early childhood. Because of the increasing access to screen time during the COVID-19 pandemic, children have more resources in their environment to learn from. However, before more can be known about whether children are learning about emotions during their screen time, it is important to know how emotions are being presented to them in their online content. Therefore, this study sought to gather data regarding how four emotions (happiness, sadness, anger, fear) are portrayed verbally and nonverbally among three types of preschool television shows (entertainment, balanced, educational). A sample of 60 preschool television shows available in the United States from 2019-2021 were analyzed in this study.
Overall, there were no differences found between educational, balanced, or entertainment shows in how emotions were portrayed. This means that it did not matter whether a show had a high or low educational value; emotions were presented very similarly across all shows. It was further found that happiness emotion expressions were presented significantly greater than sadness, anger, and fear emotions expressions, regardless of the type of television show. Nonverbal positive emotions, therefore tend to appear more often than other nonverbal negative emotions in preschool television shows. Likewise, emotion expression for all four emotions was presented significantly greater than emotion language for all four emotions, regardless of the type of television show. This shows that emotions are more likely to be presented nonverbally than verbally in preschool television shows.
From these findings, it can be concluded that preschool television programs, regardless of their educational status, are not great resources for teaching children about emotions. This is because emotions are not being identified verbally nearly as much as they are portrayed nonverbally, and exposure to emotion language is a key aspect of developing emotion identification capabilities in early childhood. There is also little variation in the types of emotions portrayed in preschool television shows. This leads to a misrepresentation of the typical emotional experience of children in their television content
On the Existence of Periodic Traveling-Wave Solutions to Certain Systems of Nonlinear, Dispersive Wave Equations
Get PDFA variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields of mathematics known as partial differential equations and nonlinear waves, and has potential applications in the study of fluid dynamics
Assessing Extant Methods for Generating \u3ci\u3eG\u3c/i\u3e-Optimal Designs and a Novel Methodology to Compute the \u3ci\u3eG\u3c/i\u3e-Score of a Candidate Design
Get PDFExperimental designs are used by scientists to allocate treatments such that statistical inference is appropriate. Most traditional experimental designs have mathematical properties that make them desirable under certain conditions. Optimal experimental designs are those where the researcher can exercise total control over the treatment levels to maximize a chosen mathematical property. As is common in literature, the experimental design is represented as a matrix where each column represents a variable, and each row represents a trial. We define a function that takes as input the design matrix and outputs its score. We then algorithmically adjust each entry until a design is found that minimizes or maximizes the function of interest.
In this thesis we study how to best minimize a prediction-variance criteria called the G-criteria, which is the maximum scaled-prediction-variance (SPV) over the entire design-space. Researchers may choose to implement this type of optimal experimental design when they need make accurate predictions on untested regions of their design space. In this thesis we apply various algorithms to the G-optimal problem, identifying and scoring candidate G-optimal designs with a combination of novel and legacy algorithms. We find that combining a novel scoring method called Gloptipoly with the best-known searching method (particle swarm optimization) produces the best-known G-optimal designs to-date
Special Study: Vulnerability
Get PDFSpecial Study: Vulnerability is a collection of creative nonfiction essays engaged in recovering the stories of homeless individuals living in Salt Lake City, Utah. The recovery project is focused on the years 2017-2023, with special attention to the events of Operation Rio Grande (2017-2020). The essays seek to, among other things, provide a critique of public policy, increase public awareness of the issues facing the homeless population, and elicit empathy from readers
Creating Sustainable School and Home Gardens: Raised Bed Gardening
Get PDFThis fact sheet is part of a series about creating sustainable school and home gardens. It provides information and resources on raised bed gardening, which can help gardeners maximize space and increase food or flower production, all with fewer weeds
Two-Station Height Measurements of Mesospheric Bores at Equatorial Latitudes
No full textSince their discovery over the Hawaii Islands in the early 1990\u27s (Taylor et al., 1995), prominent bore-like waves (initially termed mesospheric frontal events), have now been observed by a number of researchers at equatorial (e.g., Medeiros et al., 2001; Smith et al., 2005), mid (Smith et al., 2003; She et al., 2004), and most recently high latitudes (Nielsen et al., 2006; Stockwell et all., 2006). These unusual gravity wave events are characterized in the nightglow emissions by a sharp leading front usually followed by a coherent train of waves that grow in number with time. Often times, the front exhibits a reversal in contrast when images in two emission layer separated by several km (see figure above). Dewan and Picard (2001) have shown that these features are consistent with a ducted perturbation (akin to a river bore) propagating horizontally at mesospheric heights. Subsequent lidar, imager and TIMED satellite measurements have demonstrated the existence of a temperature inversion layer supporting the ducted wave hypothesis (smith et al., 2003, 2005; She et al., 2004). However, to date there have been no direct height measurements of such bore events. This poster presents novel two-station measurements of mesospheric bores imaged near simultaneously in the OH emission at equatorial latitudes during 2006. Several bore events have been identified in both data sets. Their signatures are faint but sufficient to permit an initial investigation of their height and structure using tomographic reconstruction techniques
Imaging Mesospheric Gravity Waves Under Adverse Lighting Conditions
No full textDigital (CCD) imaging systems are regularly used to study gravity wave properties in the Mesosphere and Lower Thermosphere (MLT) region (~80-100 km) using well-defined nighttime airglow emission layers (e.g. Bear Lake Observatory [BLO, UT]) to maximize data quality. Moonlight and other sources of light pollution (e.g. aurora, street lights, etc.) can significantly limit the use of CCD imagers which are sensitive to light in the visible and near-infrared spectral range (\u3c 1 µm). Here we investigate the use of new infrared imaging systems to mitigate problems with background lighting conditions.
All-sky observations of the OH emission (87 km) were made from Utah State University (USU) campus using an infrared (0.9-1.7 µm) cooled InGaAs camera. Test data were obtained in 2012 under a wide range of background lighting conditions to assess the potential for producing high-quality data under adverse conditions thereby enhancing future capability for continuous nighttime measurements at various sites
Establishing the Temporal Relationship Between Religious Commitment, Sexual Identity Struggles, and Religious Struggles Among Sexual Minorities
Get PDFObjective: Conclusions about the temporal relationship between religiousness and both religious and sexual identity struggles are frequently made in the absence of longitudinal data. The present study examines the temporal relationship between religious identification, sexual identity struggles, and religious struggles.
Methods: Participants were 132 Latter-day Saint sexual minorities who provided data at two timepoints, two years apart. We employed two cross-lagged panel models, one focusing on religious struggles and religious commitment and the other focusing on sexual identity struggles and religious commitment, to understand the temporal relationships between these variables.
Results: Cross-lagged panel models suggested that interpersonal religious struggles and sexual identity uncertainty at time 1 were negatively related to religious commitment at time 2. Similarly, religious commitment at time 1 was related to decreased sexual identity affirmation and increased religious doubt at time 2.
Conclusions: Although there is some degree of reciprocity to the relationship between religious/sexual identity struggles and religious commitment, certain struggles (interpersonal religious struggles, identity uncertainty) predicted later decreases in religious commitment, and religious commitment predicted an increase in certain types of struggles (religious doubt, lack of sexual identity affirmation)