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Should College Students Be Inventors? A Case Study of a Mathematics Professor in India
Get PDFThis qualitative case study attempts to understand instructional roles and goals that a mathematics professor in India sets and envisions for engaging students around abstract mathematical concepts. We generated the data with the professor while he participated in professional development program sessions we provided on the active role of students in learning mathematics. Guided by two theoretical lenses of Realistic Mathematics Education and Rehumanizing Mathematics, our data analysis identified three main themes through the teaching practices that he employs or conceives: (1) Supporting students to avoid faulty foundations by developing proofs, (2) Offering opportunities for exploration by giving appropriate guidance, and (3) Increasing motivation by providing the history of mathematical concepts. We offer implications for how two theoretical lenses can interact as well as how mathematics instructors, professional developers, and researchers might consider the teaching of mathematics
A Dualistic Interpretation of Mathematical Creation Through Art and Argumentation
Get PDFCreativity, informal reasoning and dynamic exchange of ideas form the pulsating heart of mathematical creation. In this approach, the concept of a mathematical object surpasses conventional boundaries of formal presentation, as they also encompass the intention to prove, significant creative stages within the proving, and the overall experience of prover\u27s journey, which may involve arguments, debates, discovery insights, aesthetic visualizations, and narrative elements. In this paper we present two conceptual frameworks, namely Argumentation-based Proof-Events Calculus (APEC) and Mathematical RUPAs, in order to provide distinct yet interconnected perspectives on informal thinking, knowledge creation, and proving in mathematics. Following the two perspectives, we explore the nature of mathematical objects, the diverse roles of provers, and the influence of social and pluralistic factors in proving practices. Through this analysis, we aim to create a synthesis, named RUPAPEC, that elucidates how the creative and sociocultural dimensions presented in these two approaches can come together into a harmonious whole by mutually reinforcing each other. This theoretical synthesis embodies an ontological exploration delineating the essence and existence of mathematical objects as dynamic entities shaped by creative cognitive processes and interactive dialogues
Mathiverse - A Potpourri of Mathematical Stanzas
Get PDFA collection of very short verses, mathematical in nature
Project-Based Learning with ODEs: Modeling Straw Rocket Motion with Air Resistance
Get PDFThis paper presents a hands-on project that guides students through building and validating a mathematical model of projectile motion. The project starts with the idealized case of motion under gravity without air resistance and then introduces air drag : first as a linear force, and then as a nonlinear quadratic force, with the Reynolds number providing the justification for the quadratic model. Students perform experiments with vertical and angled launches, capturing and analyzing motion data using video analysis software. Vertical launch data allows parameter estimation via least squares fitting of the nonlinear drag model, yielding values for initial velocity and drag coefficient. These parameters are then used to predict the outcomes of angled launches, highlighting asymmetries in flight time and range caused by drag. The activity connects theoretical modeling with experimentation and provides students with hands-on experience in testing assumptions, fitting parameters, and validating models
Unveiling Career Aspirations: The Role of Human, Social, and Cultural Capital Among California Community College Classified Staff
No full textCalifornia community colleges serve as a critical access point to higher education for diverse student populations, but the career paths of the classified staff who support the colleges remain largely understudied. The professional development of classified staff and their motivation for administrative leadership roles remain a sparsely researched topic. An impending retirement wave among senior community college leadership raises an important question: Do classified staff aspire to move up? If so, what factors shape or hinder their progression? Using human, social, and cultural capital theories, this dissertation used quantitative methods to examine classified staff’s career aspirations. The research involved evaluating which factors from human, social, and cultural capital are associated with aspirations for career advancement within community colleges. Findings from 324 classified professional survey responses at 54 institutions show linkages between various forms of capital and career aspirations in terms of leadership, educational, and achievement aspirations, net of individual and institutional backgrounds, and some of the observed relationships vary by gender and race/ethnicity. The path to leadership roles becomes difficult for many classified staff since structural barriers, limited mentorship access, and an institutional slow pace block their development. The probability that someone will aspire to leadership roles depends heavily on their educational attainment, workplace relationships, and chances for emerging leadership positions. However, systemic inequities—particularly along the lines of race, gender, and job classification— highlight the uneven landscape of career advancement. Research findings expand workforce development knowledge in higher education and create strategies that institutional leaders, policymakers, and professional membership groups use to create equal promotion routes for classified personnel. Communities can develop an expanded pool of higher-level administrators by overcoming leadership advancement challenges at community colleges, thus preparing tomorrow’s leadership group to tackle future sectoral changes
Unlocking Organizational Potential for GIS Collaboration in Higher Education
Get PDFHardware, performance, and complex interface issues are just a few barriers that Geographic Information Systems (GIS) instructors must overcome when collaborative efforts extend beyond their classrooms. As GIS technologies evolve, instructors must adapt quickly to new tools and methods to maintain effective collaboration and ensure students achieve positive learning outcomes. Successful cooperation between departments, institutions, and other organizations requires preparation and sustainability throughout the semester to foster meaningful partnerships and support institutional goals. This dissertation applies the Resource Dependency Theory (RDT) to identify and define the challenges faced by GIS instructors, examining how they navigate these barriers by leveraging internal and external resources necessary to support student learning. The study aims to pinpoint the primary obstacles GIS instructors encounter and the strategies to overcome them when collaborating beyond their academic department. This research seeks to enhance the understanding of effective GIS education and collaboration practices by addressing these challenges. The research methodology includes qualitative data collection through focus groups, semi-structured interviews, and surveys, providing in-depth insights into the experiences of GIS instructors. The findings will offer valuable insights into how GIS instructors can improve resource utilization and establish successful partnerships. Additionally, this study will provide recommendations for to support GIS instructors in overcoming collaboration barriers. This dissertation aims to contribute to the broader discussion on the issues surrounding GIS education and collaboration. By addressing these challenges, instructors can improve partnerships across academic and professional settings in GIS education, leading to more integrated and effective teaching practices
Analytical and Numerical Approaches to Parameter Estimation in Damped Oscillatory Systems
Get PDFWe investigate the inverse problem of identifying damping and stiffness parameters in one-dimensional damped oscillatory systems governed by second-order differential equations. Focusing on mass–spring–damper models, we analyze the qualitative behavior of solutions across underdamped, critically damped, and overdamped regimes, and derive explicit conditions for parameter recovery based on time-domain observations such as equilibrium crossings and turnaround points. Two numerical estimation methods are developed and compared: a finite-difference least-squares approach based on central difference approximations, and a finite element formulation derived from a variational framework using piecewise linear basis functions. Computational experiments using synthetic data assess the accuracy, stability, and noise sensitivity of both methods. Our results demonstrate that while both approaches perform well in noise-free settings, the finite element method offers greater robustness in the presence of measurement noise or coarse sampling. In addition to its theoretical and numerical contributions, this study serves as a pedagogical resource for integrating differential equations, numerical methods, and inverse modeling in undergraduate mathematics or engineering curricula
The 3D Double Spherical Pendulum: Modeling, Analysis, and Simulations
Get PDFThis paper presents an inquiry-based research project that develops and analyzes the system of ordinary differential equations governing the motion of the 3D double pendulum, blending computational experiments with applied and theoretical mathematics. We formulate the Lagrangian for the three-dimensional double spherical pendulum and use Maple to derive the four coupled ordinary differential equations (ODEs) in angular variables; for completeness, we also present an equivalent Cartesian formulation. We then compare and visualize the models using the Taylor Center high-order Taylor-series solver, which delivers high-accuracy trajectories and real-time animations in 2D and anaglyph 3D (red/blue). We place the system in context by comparing the spherical double pendulum with the planar double pendulum and the spherical single pendulum, highlighting structural similarities, differences, and special cases of uniform motion. The Taylor Center environment functions as a virtual laboratory, enabling students to vary parameters and initial conditions and to observe qualitative changes in the dynamics. Intended for undergraduates with solid backgrounds in ODEs and numerical analysis, the module shows how symbolic derivation and modern solvers make complex three-dimensional dynamics accessible and engaging for students
Optimization of a Vertical-Axis Wind Turbine Airfoils Using Machine Learning, Numerical and Experimental Methodologies
No full textThis study aimed to enhance the aerodynamic performance of a Vertical-Axis Wind Turbine (VAWT) airfoil through a multidisciplinary approach that combines Machine Learning (ML), Computational Fluid Dynamics (CFD), and experimental validation. The focus was on enhancing the lift-to-drag coefficients ratio (퐶 푙 /퐶 퐷 ), particularly at higher Angles of Attack (AoA ≥ 20°), a critical operational regime for VAWTs. A baseline airfoil of 12-inch chord length and 10-inch wingspan was analyzed using ANSYS Fluent across a range of AoA (0°–90°) at a constant freestream velocity of 10 m/s (Re ≈ 2.0 × 10 5 ). This served as a performance benchmark. Using ANSYS Design Explorer and Python-coded constraints, ML-based optimization—employing adjoint solvers and stochastic gradient descent—was applied to the baseline geometry at 20° AoA. The resulting AI-optimized airfoil was then evaluated across all AoAs, both with and without specially designed endplates. CFD simulations revealed substantial aerodynamic improvements, with the AI airfoil delivering markedly higher 퐶 푙 /퐶 퐷 across the full AoA range. In the critical 10°– 15° AoA zone, the AI airfoil with endplates achieved more than twice the 퐶 푙 /퐶 퐷 of the baseline without endplates, highlighting improvements in lift generation, drag reduction, and vortex control. Experimental validation using a 3D-printed scale model in an open circuit wind tunnel further substantiated the CFD findings. Across all AoAs, the AI-optimized airfoil—particularly with endplates—demonstrated superior aerodynamic performance, closely aligning with CFD predictions (within 2%–7.8% deviation). Experimental results confirmed a 퐶 푙 /퐶 퐷 gain of over 133% at 0° AoA and consistent improvements of 40–55% between 5° and 15° AoA when using endplates. At higher AoAs (25°–50°), the AI airfoil maintained elevated performance levels, benefitting from delayed stall and improved flow coherence enabled by the endplates. This investigation confirms the dominant role of airfoil geometry and endplate design in aerodynamic optimization. The study highlights the reliability of CFD-ML methods for airfoil design. Future research will implement these AI-optimized geometries in a full VAWT setup, evaluating torque, power coefficients with tip-speed ratio (TSR) through transient CFD and further experimental validation. These results lay a strong foundation for next-generation VAWT development driven by computational intelligence and aerodynamic refinement
The Way Work Should Be™ Fostering a Stigma-Free Workplace for Mainers
Get PDFThe proposed program, The Way Work Should Be ™, aims to enhance Mental Health & Illness education and establish a Stigma-Free Workplace. NAMI Maine, a leader in mental health advocacy, will partner with organizations throughout Maine to provide essential resources, including mental health toolkits, training for recognizing and addressing mental health issues, and strategies to create supportive work environments. The urgency for mental health training in Maine\u27s business community is clear. Employers and employees require resources to effectively manage mental health issues, which can lead to immediate and lasting positive outcomes. This project includes a comprehensive Program Evaluation to establish the effectiveness of The Way Work Should Be ™ in Maine. The Evaluation Proposal will provide an evidence-based foundation for success, allowing NAMI\u27s national branch to implement the program nationwide. Guided by the CDC evaluation framework, the data collected will demonstrate the program\u27s impact on workplaces, the return on community stakeholders\u27 investment, and identify which training and strategies are most effective