Related papers: Simplifying and Refactoring Introductory Calculus
Intelligent Tutoring Systems often grant learners shared control over skill and problem selection. This choice brings motivational and metacognitive benefits. At the same time, past literature suggests that learners exhibit diverse…
This article presents the findings of a case study which introduced online quizzes as a form of assessment in pure mathematics. Rather than being designed as an assessment of learning, these quizzes were designed to be an assessment for…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Since 2010, the Yale physics department has offered a novel calculus-based introductory physics for the life science (IPLS) sequence, that re-imagines the IPLS syllabus to include a selection of biologically and medically relevant topics,…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
The paper reports on first preliminary results and insights gained in a project aiming at implementing the fluent calculus using methods and techniques based on binary decision diagrams. After reporting on an initial experiment showing…
Reinforcement learning (RL) can elicit strong reasoning in large language models (LLMs), yet most open efforts focus on math and code. We propose Reasoning Curriculum, a simple two-stage curriculum that first elicits reasoning skills in…
This paper investigates how high school students approach computing through an introductory computer science course situated in the Logic Programming (LP) paradigm. This study shows how novice students operate within the LP paradigm while…
Context: Students often misunderstand programming problem descriptions. This can lead them to solve the wrong problem, which creates frustration, obstructs learning, and imperils grades. Researchers have found that students can be made to…
Complex software can be hard to read, adapt, and maintain. Refactoring it can create cleaner and self-explanatory code. Refactoring tools try to guide developers towards better code, with more quality. However, most of them take too long to…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
An important goal of graduate physics core courses is to help students develop expertise in problem solving and improve their reasoning and meta-cognitive skills. We explore the conceptual difficulties of physics graduate students by…
Motivated by children inventing creatively laws on how to add or multiply fractions, we introduce four fraction operations and discover some of their properties.
Theory of computing (ToC) courses are a staple in many undergraduate CS curricula as they lay the foundation of why CS is important to students. Although not a stated goal, an inevitable outcome of the course is enhancing the students'…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department. The main lesson is that model building and the process of modelling must be placed at the centre stage of logic…
Much effort and research has been invested into understanding and bridging the gaps which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in…