Scholarship
Current:
- Discovery Learning Assessments:
Overview:
Discovery Learning Assessments are a way of re-claiming assessment time as learning time during which students are assessed on skills that are most relevant for success in today's world. They take the place of traditional quizzes and exams to make assessment time more relevant for students and instructors alike. DLAs do this by requiring students to investigate a real-world scenario before coming to class to participate in a three-part assessment flowing from an individual component to a team component to an individual reflection component which is followed up with constructive instructor feedback soon thereafter. More information, samples, and resources can be found here.
Relevant Publications:
- Creativity in Problem Solving:
Overview:
As we face new problems every day, it becomes more and more clear that the solutions and even the methods of the past and present are not going to sufice for the future. Therefore, developing creative problem-solving skills in our students is imperitive for our future. We work to establish our courses in ways that will grow these skills and to create methods to evaluate our successes and failures along the way. More information about our work can be found here.
Relevant Publications:
- Classroom Teaching Ideas
Overview:
I love trying new things in the classroom to make material more approachable and engaging. Sometimes those new things work amazingly well and are original ideas. When that happens, I do my best to share them.
Relevant Publications:
- Chapter 13: Matheamtical Communication Games: Telestrations in the Mathematics Classroom in Teaching Mathematics Through Games (2021)
- Guiding Students to Discover Counting Formulas - With a Modeling Twist (The UMAP Journal 2022)
- A paper about physically exploring prime factorizations is in progress.
- A paper about having students read modeling papers at varying levels as a part of a modeling class is in progress.
- Meaningful Peer Assessments:
Since Discovery Learning Assessments result in student grades being based in part on team work, we introduced peer assessments to Mathematical Modeling and Introduction to Calculus course at the United States Military Academy. In doing so, we are attempting to motivate students to be good teammates. However, we have found that the quantitative scores that students assign to one another often do not match the qualitative feedback that they provide. The quantitative scores often seem inflated. This observation led to a desire to figure out how to make student peer assessment grades more meaningful.
Our current goal is to build a model that will utilize sentiment analysis of qualitative feedback that students provide on peer assessments to generate a quantitative score that more accurately reflects their contributions to a team.
Past:
- Undergraduate Combinatorics Education:
- Influences of Probability Instruction on Undergraduates' Understanding of Counting Processes (Dissertation)
Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of my dissertation study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, the study provides insights that inform future instruction in courses that include counting and probability. Consequently, the study lays the groundwork for future inquiries in the field of undergraduate combinatorics education that will further improve student learning and resulting performance in counting and probability.
- Finite Matematics Students' Use of Counting Techniques in Proabbiltiy Applications (2018 RUME Proceedings)
In this study we seek to better understand how students are using counting techniques within the context of the probability application. To do so we investigate three semesters of finite mathematics students’ use of enumeration, Venn diagrams, and counting formulas on probability free-response exam questions at a large public university in the mid-south. The study found that appropriate use of enumeration techniques and Venn diagrams both statistically significantly increased a student’s likelihood of arriving at a correct answer, while there is statistically significant evidence that the use of counting formulas decreased a student’s likelihood of arriving at a correct answer. We conclude with a discussion of the implications of this study for the practice
- Discrete Geometry:
- In 2012 I participated in the Discrete and Computational Geometry Mathematics Research Community. During my time there I worked on a few open problems and was exposed to many more. The following problem from the Open Problems Project is one that I particularly enjoyed working on during my week at Snowbird.
- "Is it possible to trap all the light from one point source by a finite collection of two-sided disjoint segment mirrors? A light ray is trapped if it includes no point strictly exterior to the convex hull of the mirrors. The source point is disjoint from the mirrors. Although several versions of the problem are possible, it seems to make the most sense to treat the mirrors as open segments (i.e., not including their endpoints), but demand that they are disjoint as closed segments."
- Additionally, before moving from the Mathematics PhD program to the STEM Education PhD program, I began and made some progress researching in Discrete Geometry with Carl Lee. In this research, I was working on finding new relations between polytopes by studying the effects of combinations of pyramid and prism operations on their respective Ehrhart series. As a result, I hoped to develop analogs to and relations with their cd-indices.
- Research Assistant Experience: