Breakout Sessions: Graduate Students (Sat. Mar. 23rd)

Moderator names listed below table.
(You may sort by room or by time of presentation.)

TIme	Location	Title and Presenter(s)	Abstract
10:00	ENCINO 104	Unlearn to Learn Intervention: To Promote Positive Attitudes Towards Mathematics Among Developmental Mathematics Students Dharmanie Gamage Texas State University	Many students enrolled in developmental mathematics exhibit negative attitudes towards the subject and perform inadequately. For many years, researchers have examined the association between students' attitudes towards mathematics and their academic performance. However, the research aimed at enhancing students' attitudes towards the subject is deficient in empirical evidence. The main purpose of the Unlearn to Learn intervention is to foster unlearning through purposefully designed writing tasks assigned as homework to the treatment group students. This study will be conducted at a large university in the Southwestern United States and will use quasi-experimental repeated measure design to measure the effect of the intervention. The sample will be comprised of two sections of developmental mathematics classes, both taught by the same instructor. The study will utilize Fennema-Sherman's (1976) 4 subscales to measure the attitude change from pre-survey to post-survey. This study will provide practical recommendations for educators in developmental mathematics, with a focus on the significance of creating homework tasks that foster student achievements by facilitating a change in attitude.
10:30	ENCINO 104	Exploring how preservice teachers learn to notice student measurement thinking Mai Bui Texas State University	Teacher noticing of students’ mathematical thinking plays a pivotal role in reform-oriented instruction. Hence, it is crucial to support preservice teachers, who do not generally possess well-developed noticing skills, in learning to notice student thinking. However, this line of research is scarce in the domain of measurement, an important topic in mathematics curricula. In this paper, I report the learning path to notice student thinking about length measurement of a preservice teacher when given various learning opportunities to develop her noticing. Findings suggest that with the support of a framework on student measurement thinking, the preservice teacher’s attention and interpretation become broader, deeper, and better aligned with research-based knowledge. However, her learning path does not consistently follow an upward trend.
11:00	ENCINO 104	How Fractions are Introduced Around the Globe: A Comparative Textbook Analysis of Seven Countries Stephanie Tarigan Texas State University	An international cohort of doctoral and master’s students at Texas State University investigate how the concept of fractions is introduced and developed in elementary school textbooks worldwide. Fractions represent a pivotal foundation in a students’ mathematical journey, demanding a subtle grasp of abstract concepts and symbolic notations from an early age. Departing from standard viewpoints that textbooks are merely a compilation of basic mathematical concepts and corresponding problem sets. Rather, our research views textbooks as a bridge between the theory and practice of mathematics education, and the curriculum. According to empirical research, for many teachers, the methods of teaching mathematical concepts presented in the textbook are the most effective. Utilizing a two-dimensional approach, firstly, we compare how mathematics textbooks from Ghana, Indonesia, Singapore, Trinidad & Tobago, Türkiye, Uganda, and the United States introduce the idea of fractions. Secondly, a two-dimensional analysis was used: (i) horizontal dimension which consists of the scope and sequence, number of pages, etc. (ii) vertical dimension which explores the cognitive demands, contextual features, and problem-solving activities. Lastly, we compared the methodologies used in the textbooks for teaching fractions, based on the literature recommendations.
11:30	ENCINO 104	Prediction Of College Students Academic Risk Level Using Machine Learning Models Richard Kyei Stephen F. Austin University	In today's changing education landscape, there's a growing interest in helping students succeed academically. When college students fall short of their potential, it has significant societal, economic, and personal consequences. Detecting and supporting disengaged students early on is crucial to addressing this issue and preventing academic setbacks. This study aims to find the most effective machine learning model for predicting a college student's academic risk in a semester. Four models, Multiple Linear Regression (MLR), K-Nearest Neighbours (KNN), Decision Trees (DT), and Random Forest (RF), were tested to identify the best one. The R software and Microsoft Excel spreadsheet were the tools that aided in the data analysis. The focus was on early detection and intervention for disengaged students before their academic performance suffers. The results show that, assuming students have missing data not at random, MLR is the top-performing model with a precision rate of 60%, which is 6% higher than models that performed best when assumed that students have missing data at random. Regardless of whether data is assumed to be missing at random or not, all models performed similarly across different risk levels. Further investigation was conducted to determine which model is most effective for specific subpopulations, taking into account the type of missing data. Based on our findings, we recommend specific model that is best for college student advisors to use to detect students in subpopulations who stand a high risk of poor academic outcomes. This approach can significantly contribute to monitoring and providing necessary support to students who may be at risk of falling behind academically.
10:00	ENCINO 216	Modeling of disease dissemination with heat image equation M.D. Ahiduzzaman Texas A&M University – Commerce	Modeling the way diseases disseminate in human organs is an important and useful area of research. The main goal is to facilitate medical practitioners to detect and diagnose any disease inside the human organs. In the present study we model this process of disease dissemination by using the heat equation with right side function of the image of the organ. We considered two such functions. The first one includes the gradient of the image, while the second one uses the Laplace operator of the image. We found the approximate solutions, for the two cases, using finite difference method. To validate the theoretical approach, we programmed it in python and validated the method with several 2D scenarios. The obtained results from these experiments would be shown during the presentation.
10:30	ENCINO 216	Existence of two Infinite families of Solutions to a Singular Superlinear Equation on Exterior Domains. Narayan Aryal University of North Texas	We are concerned with the radial solutions of the Dirichlet problem -∆u=K(|x|)f(u) on the exterior of the ball of radius R>0 centered at the origin in ℝN with N ≥ 3 where f is superlinear at infinity and has a singularity at 0 with f(u) ~ 1/{|u|{q-1}u} and 0 < q < 1 for small u. We prove that if K(|x|) ~ |x|-α with α<2(N-1) then there exist two infinite families of sign-changing radial solutions.
11:00	ENCINO 216	Is the Mandelbrot Set Connected? James Shirley Stephen F. Austin University	Since its conception in 1978 under the context of Kleinian Groups, the Mandelbrot set and its respective Julia sets have been the subject of research - not only due to its applications in mathematics, but to its surge in popularity as computer graphics became increasingly better at rendering images of this strange fractal. Among its most interesting and difficult results is the question of this set’s connectedness (shown by the collaborators, Drs. Adrien Douady and John Hubbard). This presentation aims to introduce the audience to the realm of simple complex dynamics theory and demonstrate intuitively the connectedness of this strange set.
11:30	ENCINO 216	Nested Snakes and Ladders Yujin Yoshimura University of North Texas	The game of 'nested snakes and ladders' is defined as follows: When the game starts, the player's piece is positioned on the start square. On each turn, the player rolls a fair 6-sided die and moves the piece according to the number rolled. The player wins once the piece reaches the goal square (even if it moves beyond it). If the player's piece lands on a nest square, a mini-game 'nested snakes and ladders' begins. Upon winning the mini-game, the player can continue from the nest square they landed on. The board is arranged as follows: [start] [nest] [nest] [nest] [nest] [nest] [goal] What is the probability of the player winning this game?
10:00	ENCINO 213	The Impact of Adaptive Designs When Performing Survival Analysis Quentin Eloise Stephen F. Austin University	Survival analysis is a critical statistical method in healthcare to assess patient treatment effects and disease progression. Another critical area of statistical methodology in health care is the practice of adaptive designs. Adaptive designs allow for interim analyses to take place during a study and various decisions and actions can take place more ethically. This is beneficial for studies that take multiple years to complete and allows administrators and healthcare providers to make sound decisions as early as possible. A challenging aspect to adaptive designs is that the number of interim analyses is known in advance which is applicable in controlled experiments such as randomized clinical trials. Motivated and highlighted by our collaborations with Fresenius Medical Care, many clinical studies are observational in nature and have no clear endpoint making it difficult to determine the number of interim analyses that will be conducted. This research considers the application of survival analysis using adaptive designs within observational studies. To do so, we developed a collection of statistical programs to simulate these types of interim analyses while accounting for the additional complexity that survival data exhibits. Simulation’s summaries were performed and we will summarize some of the key results including investigations of statistical power, type-I error control, and parameter estimation performance. Additionally, this work aims to assess the necessary conditions to achieve reasonable power at early looks and/or establishing general rules of thumb when designing the study. In conclusion, this abstract underscore the impact of adaptive designs in survival analysis, unlocking new avenues for innovation and efficiency in clinical research. Using adaptive methodologies, researchers can navigate the complexities of survival endpoints and improve patient outcomes.
10:30	ENCINO 213	A Uniform Most Powerful (Ump) Test For The Mean Of A Beta Distribution Richard Kyei Stephen F. Austin	The Beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is Beta distributed. Many analysts will conduct traditional analyses using a t-test or nonparametric approach, try transformations, or use standard maximum likelihood-based approaches. We will show via simulations that these tools cannot appropriately control type-I error rates for various situations. Additionally, this research has set out to construct a uniformly most powerful test using saddle point approximations. These approximations tend to have better accuracy than traditional likelihood-based methods, even when sample sizes are quite low. We provide the necessary methodology development to perform the test. Further simulation studies on power of test are conducted to compare our new method to traditional approaches and illustrate the superiority of our test in many situations. We'll also provide recommendations on the best way to use this new approach as well.
11:00	ENCINO 213	A Simulation Study on Some Confidence Intervals for the Population Standard Deviation Theophilus Oppong Kyeremeh Stephen F. Austin University	This work investigates alternative methods for constructing confidence intervals for the population standard deviation (σ), especially when dealing with non-normal data. While the sample standard deviation (S) is commonly used, it can be unreliable for skewed or heavy-tailed distributions and sensitive to outliers. This work explores alternative confidence interval estimation methods that are less susceptible to these limitations. Through a simulation study, the performance of these methods will be evaluated using data from various distributions, including normal, heavy-tailed, and skewed. The results will be compared to existing work and potentially lead to modifications of existing approaches. This research aims to identify more reliable and robust methods for obtaining interval estimates of σ, especially in situations where normality assumptions are not met.
11:30	ENCINO 213	Approximating Solutions to the Two-Dimensional Euler System Using Rational Exponential Functions Julio Paez UT Rio Grande Valley	In the study of shallow water waves, the Euler system describes the relationship between how the water looks like on the surface and how the particles within the fluid domain move. Using Rational Exponential Functions, we can obtain approximate solutions to the system that exhibit fission and fusion behavior on the surface.
10:00	ENCINO 214	Congruence properties of consecutive coefficients in arithmetic progression of Gaussian polynomials Joselyne Aniceto University of Texas – Rio Grande Valley	A 2023 result of Eichhorn, Engle, and Kronholm describes an interval of consecutive congruences for p(n,m,N), the function that enumerates the partitions of n into at most m parts, none of which are larger than N, in arithmetic progression. This function is the partition theoretic interpretation of the coefficient on qn of the Gaussian polynomial, ${{N+m \brack m}}$ , otherwise known as the q-binomial coefficient. In this talk we will considerably expand their result to capture a much larger family of congruences. We will consider known infinite families of congruences for p(n,m), the function that enumerates the partitions of n into at most m parts, and introduce a related infinite family of congruences for a two-colored partition function. The result Eichhorn, Engle, and Kronholm becomes a special case of our expanded theorem.
10:30	ENCINO 214	Ramanujan Type Congruences for quotients of the Rogers Ramanujan function Jeffery Opoku University of Texas – Rio Grande Valley	In this work, Ramanujan type congruences modulo primes $p\le 29$ are derived for a general class of products that are modular forms of level 5. The vectors of exponents corresponding to these products that are modular forms for $\Gamma_{1} (5)$ are subsets of bounded polytopes with explicit parameterizations. This allows for the derivation of a complete list of products in $\Bbb Z^{2}$ that are modular forms for $\Gamma_{1} (5)$ of weights $kK for that satisfy Ramanujan type congruences for primes p ≤ 29.
11:00	ENCINO 214	Ramanujan's Partition Congruences and Dyson's Rank: How is the Division to be Made? Jena Gregory University of Texas – Rio Grande Valley	A partition of a positive integer $n$ is a finite nonincreasing sequence of positive integers $\lambda_1, \dots, \lambda_m$ such that $\sum^m_{i=1} \lambda_i =n$. For example, the partitions of 4 are: 4, 3+1, 2+2, 2+1+1, 1+1+1+1. The sequence of partitions numbers is $$\{p(n)\}_{n=0}^{\infty}=1,1,2,3,5,7,11,15,22,30,...$$ Mathematicians are interested in the patterns in this sequence. In 1919, Ramanujan proved the following congruences with $q$-series: For all nonnegative integers $k$, \begin{align} %\begin{split} p(5k+4)&\equiv 0\pmod 5\label{Ramanujan19195} \\ p(7k+5)&\equiv 0\pmod 7 \label{Ramanujan19197}\\ p(11k+6)&\equiv 0\pmod{11}. \label{Ramanujan191911} %\end{split} \end{align} In 1944, Dyson requested proofs of Ramanujan's congruences that ``will not appeal to generating functions but will demonstrate by cross-examination of the partitions themselves." Dyson proposed a statistic called the rank that would do just that. In this talk, we discuss Ramanujan’s partition congruences and Dyson’s rank. We extend these ideas to a certain restricted partition function and consider Dyson style witnesses for congruences.\\ Candy will be served!
11:30	ENCINO 214	Scripting Tasks for Assessing Learning in Calculus II Eduardo Torres Manzanarez UT Arlington	Scripting tasks have been used in various studies to investigate preservice and inservice mathematics teachers' mathematical or pedagogical knowledge. While the use of such tasks has largely focused on these groups, scripting tasks have also been used in undergraduate mathematics courses to explore students' mathematical understandings. In this presentation, I will discuss and present examples of such tasks from the mathematics education research literature. In addition, I will discuss a set of scripting tasks I created for my research that align with the Calculus II curriculum topics of infinite series and Taylor’s remainder theorem. For these calculus-based scripting tasks, I will discuss the inspiration behind their creation, the mathematical understandings the scripts aim to assess, and further motivation for creating similar tasks to be leveraged in undergraduate mathematics education research and educational settings.
10:00	ENCINO 230	Instilling Mathematical Autonomy in Undergraduate Mathematics Teaching Te'a Riley UT Arlington	This talk will discuss findings from my dissertation study that suggests instilling autonomous practices in our undergraduate mathematics classes. My study explored the experiences of Ph.D. women mathematicians from groups historically disenfranchised in mathematics in their undergraduate and graduate real analysis courses. Using Self-Determination Theory (Deci & Ryan, 1985) to analyze my data, which suggests that humans have three basic needs: competence, autonomy, and relatedness, I found that participants were more controlled than autonomous. On the contrary, the participants needs of competency and relatedness were fulfilled more than they were threatened. Without autonomy, students are controlled learners which shifts their motivation from intrinsic to extrinsic. Being a controlled learner can still lead to success, as my study shows, but my study suggests that negative experiences can change the mathematical identity, self-efficacy, and motivation of the learner.
10:30	ENCINO 230	Using Machine Learning To Identify The Initial Planting Date of Crops Abstract Angela Avila University of Texas at Arlington	This study focuses on training a neural network to accurately predict the planting date of any given field by leveraging time series leaf area index (LAI) data. Specifically, we utilize LAI data collected in Bushland, TX over a span of 35 years as the basis for our model. Through a third-degree polynomial regression, the LAI time series growth of different crops is fitted, and the resulting coefficients are utilized to train a neural network, enabling estimation of the field's initial planting date. To enhance the effectiveness of the neural network training, our dataset is augmented by creating various third-degree polynomials that mimic the LAI growth patterns of crops. The preliminary data indicated the predictive Machine Learning Model is able to predict the planting dates of various crops. Continuing the project requires linking LAI to satellite imagery. This entails utilizing normalized difference vegetation index (NDVI) data to establish a correlation with LAI. Achieving this involves using multiview learning techniques to correlate the growth curves of LAI and NDVI.
11:00	ENCINO 230	Bayesian Inference for Deep Learning Ricardo Reyna University of Texas – Rio Grande Valley	Convolutional neural networks [CNN] have been used widely for image classification. However, CNN usually needs large amounts of data. Small amounts make CNNs prone to over fitting [Blei D. M., Kucukelbir A., and McAuliffe J. D. (2018)]. This makes it unable to properly weigh what inputs properly correspond to the outputs of a data analysis. Bayesian Inference studies has been a popular topic in machine learning, where it helps to reduce the problem network overfitting associated with neural networks. We have seen several integrations of Bayesian ideas into several types of neural networks [Yu, H., et al. (2021)][Rodrigo, H. and Tsokos, C. (2020)]. By incorporating Bayesian analysis in to CNN, we could possibly make them more efficient, even with a small amount of data. In this project, we will introduce three different Bayesian Inference methods, particularly the evidence approach [MacKay, D. J. C. (1992)], Hybrid Monte Carlo, and the combination of both [Rodrigo, H. and Tsokos, C. (2020)]. Specifically the Hybrid Monte Carlo has with the intention increasing the efficacy of the convolutional neural networks with the Bayesian approaches with the image analysis.
11:30	ENCINO 230	Using the K-Nearest Neighbor Algorithm to Predict Precipitation Based on Historical Data Sean Guidry Stanteen University of Texas at Arlington	This study explores the application of the K-Nearest Neighbor (KNN) algorithm for predicting precipitation patterns using historical data. The KNN algorithm is employed to analyze past weather data and identify similar patterns to forecast future precipitation events. The research aims to assess the effectiveness of the KNN approach in predicting precipitation, thereby providing valuable insights for meteorological forecasting, and improving our understanding of weather patterns. Results indicate promising potential for accurate and efficient precipitation prediction using the KNN algorithm.

Moderators