The Mathematical Association of America Maryland-District of Columbia-Virginia Section

Students in AP Calculus BC encounter these topics as applications of integration, and it is helpful pedagogically for them to see the connections between the calculus techniques and the ideas of measurement that they learned in geometry and algebra classes. But it is even more fascinating for them to revisit ruler measurement, the distance formula, and the Pythagorean theorem, adding the very old theorems of Pappus to make the surface areas in calculus make sense. Then the very contemporary ideas and skills of chaos theory and fractals with their new way of considering measurement of coastlines together with the technology methods of the Gaussian quadrature in the TI calculators (for fnInt) are added to create a rich blend of methods, history, and understanding of advanced calculus techniques. This is a very powerful couple of days in a high school classroom with eager young minds.

Every year the population for English Learner (EL) students increases in K-12 classrooms. This has raised questions about how teacher preparation programs can better equip future educators to support linguistically diverse learners in mathematics classrooms. This study examines whether education majors and non-education majors support requiring education majors to complete at least two Spanish courses as part of their teacher preparation. Spanish is the second largest language used in the United States, which means a large portion of EL students' primary language is Spanish. Using a cross sectional survey design, undergraduate students will be recruited, surveyed, and categorized as education majors and non-education majors. Participants will rate their level of support using a six point Likert scale. A two sample t-test will be conducted to determine whether a statistically significant difference exists between the mean levels of support reported by the two groups.

Testing water quality is critical to measuring environmental change and ensuring the health of an ecosystem. With the necessity of expensive equipment to measure water quality directly, environmental stewards implement citizen-led macroinvertebrate bioassessment programs, like Virginia Save-Our-Streams as a "canary in the coal mine" to identify environmental stressors in aquatic systems. The proportion of mayflies, caddisflies and stoneflies in a freshwater ecosystem has been shown to be an effective proxy for water quality. But the process of identifying these species requires extensive training and time investment. For this reason we have developed an image-based convolutional neural network (CNN) capable of classifying the three taxa from field photographs, eliminating the need for expert identification. Our initial results demonstrate promising classification accuracy across the three taxa, laying the groundwork for a deployable field tool.

Classical ciphers are a symmetric form of encryption, meaning they require the same key to be used for encryption and decryption. The Key-Sharing Problem is the challenge of securely sending and receiving these keys in a public channel. We consider methods of overcoming this problem for several ciphers by making use of Elliptic Curves (ECs). We then examine implementations of the resulting asymmetric key-exchange algorithms in python and discuss the trade-offs between traditional approaches and the EC key exchanges.

Math anxiety is a persistent issue among college students that can negatively impact performance, confidence, and motivation in math courses. The goal of this research study is to examine which academic support methods Shenandoah University college students use to help themselves with math anxiety and which methods students perceive as most effective in helping them succeed. Research was conducted using two surveys, one at the beginning and one at the end of a semester, with questions related to math anxiety, the three outlined support methods, and students' perceived effectiveness of those methods. The key findings of this research study are that low levels of confidence in math lead to more math anxiety, students feel their low math confidence stems from a lack of foundational skills, it doesn’t matter how effective students think a support method is if they still choose not to use it, if you have liked your past math teachers you’re more likely to be confident and less anxious in your current math class, and anxiety and confidence play a role in students deciding whether or not to make steps to help themselves in math. These findings helped inform the development of two proposed intervention programs for students to be more confident and less anxious when going into their math classes. The first proposed intervention is a structured review program at the beginning of every semester, which is focused on building and reviewing basic math skills so students feel prepared for their class. The second intervention program requires or gives an incentive to students to get tutoring so they are more proactive in their learning and less reactionary.

Modern AI development has two primary bottlenecks: hardware limitations and the architectures running on top of them. As transistor scaling slows, traditional silicon-based and von Neumann architectures struggle to meet growing computational and energy demands of large machine learning workloads. The widespread adoption of AI in business and consumer applications means that routine AI training and testing workflows have become a common business requirement. Data center energy consumption has risen as natural language processor and large language model implementation continues to grow. Resource consumption is projected to increase, with data center projects to be constructed nationwide within the next 10 years, specifically dedicated to AI training and research. To mitigate the computational and environmental impact of this growth, researchers have begun exploring biologically inspired alternatives that utilize properties of neural systems. Two methods have emerged from these experiments: synthetic biological semiconductors, and brain organoids derived from stem cells. Both methods utilize characteristics of neural networks, like parallel processing and nonlinear dynamics. Researchers have begun examining neural structures as dynamical systems using living neurons cultured from stem cells into small brain-like organoids. Organoids may provide parallel, dynamic, energy-efficient compute power suitable for machine learning applications. Early studies show that integrated neurons may be able to more efficiently support machine learning workloads using a fraction of the energy requirements of a traditional CPU/GPU architecture. This review synthesizes current research in neuromorphic and biological computing to evaluate their potential as a sustainable next generation in AI architecture.

Mathematical origami is a theoretical extension of paper origami where the complex plane can represent an infinitely large piece of paper, and the “folds” of this paper are represented by a set of allowed angles. We study the structure of the set of intersection points between all pairs of angles. This has been well described in 2 dimensions; however, little is known about them in multidimensional space. We determine how an origami set that generates a lattice in three-dimensional space is altered by introducing an additional allowed angle. We also implement an algorithm in SageMath that computes the intersections of pairs of allowed angles from given starting points. The algorithm then computes the projections from the new intersection points back onto the real number line.