相关论文: Students' Comparison of Their Trigonometric Answer…
AI-augmented classrooms generate rich teacher and student feedback before graded outcomes become available, yet these signals can be difficult to translate into timely instructional decisions. We propose an interpretable decision layer: a…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…
Recommendation, information retrieval, and other information access systems pose unique challenges for investigating and applying the fairness and non-discrimination concepts that have been developed for studying other machine learning…
Equity of educational outcome and fairness of AI with respect to race have been topics of increasing importance in education. In this work, we address both with empirical evaluations of grade prediction in higher education, an important…
This study investigated potential scoring biases and disparities toward English Language Learners (ELLs) when using automatic scoring systems for middle school students' written responses to science assessments. We specifically focus on…
Research shows that expert-like approaches to problem-solving can be promoted by encouraging students to explicate their thought processes and follow a prescribed problem-solving strategy. Since grading communicates instructors'…
Was it fair that Harry was hired but not Barry? Was it fair that Pam was fired instead of Sam? How can one ensure fairness when an intelligent algorithm takes these decisions instead of a human? How can one ensure that the decisions were…
Flipped classroom pedagogy is widely used in undergraduate mathematics to promote active learning, yet it remains unclear whether students experience it in systematically different ways. In this study, we analyze student perceptions from an…
Computer-aided decision making--where a human decision-maker is aided by a computational classifier in making a decision--is becoming increasingly prevalent. For instance, judges in at least nine states make use of algorithmic tools meant…
As design thinking education grows in secondary and tertiary contexts, educators face the challenge of evaluating creative artefacts that combine visual and textual elements. Traditional rubric-based assessment is laborious, time-consuming,…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
Students sometimes produce code that works but that its author does not comprehend. For example, a student may apply a poorly-understood code template, stumble upon a working solution through trial and error, or plagiarize. Similarly,…
Dual-submission homework, where students submit work, receive feedback and then revise has gained attention as a way to foster reflection and discourage reliance on online answer repositories. This study analyzes 13 years of exam data from…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…
In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…
Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical…
Is analogical reasoning a task that must be learned to solve from scratch by applying deep learning models to massive numbers of reasoning problems? Or are analogies solved by computing similarities between structured representations of…