# Student Research Showcase

**1:15 - 2:30 p.m.****LBJSC Ballroom**

## Sarah Kilgard

### Genetic Risk Via Observed Best Prediction

In 2015, President Barack Obama launched the Precision Medicine Initiative, which increased federal funding for genetic risk analysis research, and in the past decade, the field has advanced dramatically. While Empirical Best Linear Unbiased Prediction (EBLUP) is currently the standard methodology used to construct linear mixed models of genetic risk, it has its disadvantages. EBLUP uses Restricted Maximum Likelihood (REML), an optimal estimator, to estimate the variance components which sacrifice the accuracy of prediction. In our research, we used Observed Best Prediction (OBP) to increase the accuracy of our predictions. OBP calculates variance components by minimizing the mean-squared prediction error (MSPE) using Newton's Method with log barrier method. In our preliminary simulations, we've found the methods to have similar performance when the underlying model is linear and for OBP to have better performance when the underlying model is nonlinear. In the future, we will apply the methods to the Minnesota Twin Study.

## Elizabeth Wrightsman

### My Dissertation Story (so far)

Once upon a time, before graduate school and before I knew what math education was, I was in undergraduate Analysis II. Although I was unaware at the time, this is where my dissertation story begins. It might be challenging to imagine the massive undertaking of a dissertation, but I have learned that its inception is a culmination of interactions, course assignments, and experiences. I had to trust the process. I am far from the “happily ever after” ending, but in my research presentation, I will share the evolution of my dissertation story thus far.

## Brandon Watson

### Investigating How Students Try to Solve Real Analysis Problems

This study observed real analysis students attempting the homework assigned by their instructor to identify how they used resources, specifically example proofs, to complete their homework. The data consisted of seven students in total over three instructors. Overall, the study found that students tended to adopt a recurrent style of how they used their notes, or did not use their notes, to advance their solutions. However, there were some instances where the students would deviate from their style which could be linked to the type of problem as well as how the instructor taught that topic. This study contributes insight into how real analysis students may use their resources for the tasks assigned by the instructor.

## Elizabeth Hewer

### The good, the bad, and the ugly: Developmental mathematics students' perspectives on the paired courses

For the last several years, enrollment in the developmental mathematics paired courses has grown here at Texas State. We are serving more and more of these students who face several obstacles to getting a college degree. As a result of the increased enrollment, more instructors are teaching this population who tend to need more support from their instructors to be successful. As part of a larger study, I conducted focus groups throughout the semester with students enrolled in one of the paired courses, the lower-level developmental mathematics course paired with a college-credit baring course. During my presentation, I will discuss what these students reported as helping them and what they struggled with while enrolled in both courses.

## Blake Dvarishkis

### Combinatorial Determinants Via Contributor Duality

This presentation gives sentiments to integer determinant calculations by providing an avenue of understanding through vertex-permutations of an oriented hypergraph known as contributors. All coefficients of characteristic polynomials are characterized. The diagonal entries of the Laplacian give a duality theorem that allows us to reclaim the Matrix Tree Theorem for graphs and explain isospectrality for any Laplacian and its dual.

## Elizabeth Roan

### Reasoning Students Employed When Mathematizing During a Disease Transmission Modeling

Previous research on differential equations notes that students tend to conflate rate of change and amounts of change. In this study, we create a local causal explanation (Maxwell, 2004) for why one participant did distinguish between the rate of change in a population and change in a population, while the other did not. We conjecture that students may only be able to construct (or talk about) rates of change if they have the appropriate quantities available to them in which to coordinate.

## Jialong Li

### Logistic Regression 101

In this presentation, we'll begin by introducing supervised learning. Next, we'll then delve into the mathematical understanding of logistic regression and apply the multinomial logistic regression algorithm to classify the MNIST dataset—a renowned benchmark in the field. If time allows, we'll also discuss our current and upcoming research plans. This work was conducted in collaboration with Prof. Young-Ju Lee from the Department of Mathematics at Texas State University.

## Zafer Buber

### Slow Down to Speed Up

Despite all the efforts, the problem of low levels of success in precalculus courses in the US has not improved significantly over the last four decades. The research identifies poor instructional practices as one of the main factors contributing to this issue and finds them to be associated with overloaded curricula and fast-paced instruction in precalculus classes. Given that the primary instructional method in most college mathematics courses is direct instruction, this quasi-experimental study aims to investigate the impact of a low-time commitment active learning strategy on students’ achievement and participation in college precalculus classes. The planned intervention aims to slow down the instructional pace, especially for the students who need more time for conceptual advancement and create more opportunities to provide students with more time to reason and think. Preliminary results indicate that this intervention has the potential to improve student achievement and increase.