Related papers: Learning Mathematics through incorrect Problems
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
This study explores the impact of class outliers on the effectiveness of example-based explainability methods for black-box machine learning models. We reformulate existing explainability evaluation metrics, such as correctness and…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
If spreadsheets are not erroneous then who, or what, is? Research has found that end-users are. If end-users are erroneous then why are they? Research has found that responsibility lies with human beings' fast and slow thinking modes and…
Modeling plausible student misconceptions is critical for AI in education. In this work, we examine how large language models (LLMs) reason about misconceptions when generating multiple-choice distractors, a task that requires modeling…
A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically these exams are prepared several days in advance, and generic question scores are used based on rough…
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
When deploying online homework in physics courses, an important consideration is how many attempts should be allowed in order to solve numerical free-response problems. While on the one hand, the maximum number of attempts should be large…
Students entering engineering in universities of applied sciences were tested to see whether they understood easy Science problems within the first week of the first semester. The test comprised of mathematics and physics questions in both…
The process of constructing knowledge is typically taught to students by having them reproduce established results (e.g., homework problems). An alternative pedagogical strategy is to illustrate this process using an open problem, such as…
Adversarial examples are inputs for machine learning models that have been designed by attackers to cause the model to make mistakes. In this paper, we demonstrate that adversarial examples can also be utilized for good to improve the…
Parsons problems are a type of programming activity that present learners with blocks of existing code and requiring them to arrange those blocks to form a program rather than write the code from scratch. Micro Parsons problems extend this…
Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a…
Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of…
The resources compiled in this document provide an approach to embed and teach Ethics in Mathematics at the undergraduate level. We provide mathematical exercises and homework problems that teach students ethical awareness and transferable…