Related papers: Transitioning to Proof
Libraries of formalized mathematics use a possibly broad range of different representations for a same mathematical concept. Yet light to major manual input from users remains most often required for obtaining the corresponding variants of…
This essay discusses the effectiveness of a graduate course for physics students, with a course goal to write a publishable article on a modern research topic (graphene). I analyze the tools used to this end, which included Web 2.0 methods,…
Formal methods yet advantageous, face challenges towards wide acceptance and adoption in software development practices. The major reason being presumed complexity. The issue can be addressed by academia with a thoughtful plan of teaching…
We present a computational exploration of argument critique writing by young students. Middle school students were asked to criticize an argument presented in the prompt, focusing on identifying and explaining the reasoning flaws. This task…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
Recently, there has been increased attention to improving laboratory instruction at all levels. At the introductory level, research results have shown differing levels of success based on the nature of the desired learning outcomes. In…
Experiments performed in the Physics Laboratory play a significant role in understanding the concepts taught in the theory. A good accompanying laboratory manual serves as a concise guideline which students can use to complete the…
Physics lab courses are integral parts of an undergraduate physics education, and offer a variety of opportunities for learning. Many of these opportunities center around a common learning goal in introductory physics lab courses:…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…
Formal work in linguistics has both produced and used important mathematical tools. Motivated by a survey of models for context and word meaning, syntactic categories, phrase structure rules and trees, an attempt is being made in the…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
Learning to transfer considers learning solutions to tasks in a such way that relevant knowledge can be transferred from known task solutions to new, related tasks. This is important for general learning, as well as for improving the…
Language transformations are algorithms that take a language specification in input, and return the language specification modified. Language transformations are useful for automatically adding features such as subtyping to programming…
There is a sharp disconnect between the programming and mathematical portions of the standard undergraduate computer science curriculum, leading to student misunderstanding about how the two are related. We propose connecting the subjects…
Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
Instructors of statistics who teach non-statistics majors possess varied academic backgrounds, and hence it is reasonable to expect variability in their content knowledge, and pedagogical approach. The aim of this study was to determine the…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…
In this paper we describe our experience in developing curriculum courses aimed at graduate students in emerging computational fields, including biology and medical science. We focus primarily on computational data analysis and statistical…