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We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and…
While the positive outcomes of undergraduate research experiences (UREs) have been extensively categorized, the mechanisms for those outcomes are less understood. Through lightly structured focus group interviews, we have extracted the…
This innovative practice category paper presents an innovative framework for teaching Reinforcement Learning (RL) at the undergraduate level. Recognizing the challenges posed by the complex theoretical foundations of the subject and the…
The objectives of physics laboratory courses include fostering conceptual understanding and development of several important cognitive, psycho-motor, attitudinal and affective abilities. In most of the Indian colleges and universities (and…
Being aware of the motivation problems observed in many scientific oriented careers, we present two experiences to expose to college students to environments, methodologies and discovery techniques addressing contemporary problems. This…
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
The notion of an equational shell is studied to involve the objects and their environment. Appropriate methods are studied as valid embeddings of refined objects. The refinement process determines the linkages between the variety of…
To be successful, junior faculty must properly manage their time in the face of expanding responsibilities. One such responsibility is supervising undergraduate research projects. Student research projects (either single or multi-student)…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
As artificial intelligence systems become increasingly prevalent in education, a fundamental challenge emerges: how can we verify if an AI truly understands how students think and reason? Traditional evaluation methods like measuring…
Contributing to the literature on aptitude-treatment interactions between worked examples and problem-solving, this paper addresses differential learning from the two approaches when students are positioned as domain experts learning new…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
For the past five years advanced students have developed projects for our redesigned Calculus II classes to use. Our student project designers are often mathematically early in their careers, and so this provides them with an opportunity to…
The paper focuses on identifying the causes of student performance to provide personalized recommendations for improving pass rates. We introduce the need to move beyond predictive models and instead identify causal relationships. We…
Research has shown that both high school and university students' reasoning patterns regarding direct current resistive electric circuits often differ from the currently accepted explanations. At present, there are no standard diagnostic…
The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
Expert problem solvers are characterized by continuous evaluation of their progress towards a solution. One characteristic of expertise is self-diagnosis directed towards elaboration of the solvers' conceptual understanding, knowledge…
Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc (or runtime) anomaly detection techniques to detect (and discard) these anomalous…