Related papers: Mathematical Proofs 101: How Proofs Should Be Read…
Experimental activities are an essential part of physics education. In addition to conveying scientific knowledge, they play a significant role in developing scientific literacy, inquiry skills, and critical thinking. In today's world,…
We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students…
The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand…
We discuss first experiences with a new variant of self-assessment in higher mathematics education. In our setting, the students of the course have to mark a part of their homework assignments themselves and they receive the corresponding…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
While many methods purport to explain predictions by highlighting salient features, what aims these explanations serve and how they ought to be evaluated often go unstated. In this work, we introduce a framework to quantify the value of…
Most work on scholarly document processing assumes that the information processed is trustworthy and factually correct. However, this is not always the case. There are two core challenges, which should be addressed: 1) ensuring that…
This article deals with peer-assessment in the context of higher education teaching in mathematics, and examines the nature of student activity when assessing work produced by peers. After an overview of research on peer assessment, we…
Grading of examination papers is a hectic, time-labor intensive task and is often subjected to inefficiency and bias in checking. This research project is a primitive experiment in the automation of grading of theoretical answers written in…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
Studying for physics exams can be difficult and stressful, especially during a student's introductory year in physics. For students who do not plan to major in physics, the desire to do well is based less on understanding concepts and more…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Optimizing the phrasing of argumentative text is crucial in higher education and professional development. However, assessing whether and how the different claims in a text should be revised is a hard task, especially for novice writers. In…
Information Retrieval evaluation has traditionally focused on defining principled ways of assessing the relevance of a ranked list of documents with respect to a query. Several methods extend this type of evaluation beyond relevance, making…
Testing is a vital part of software development, and spreadsheets are like any other software in this respect. This paper discusses the testing of spreadsheets in the light of one practitioner's experience. It considers the concept of…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
With an investigation into how students in a physics Master of science program make sense of their whole first year study experience in one of the years following a programme reform, we try to offer insights and advice to consider when…