Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

Programming skills are increasingly important to the current digital economy, yet these skills have long been regarded as challenging to acquire. A central challenge in learning programming skills involves the simultaneous use of multiple component skills. This article investigates why students struggle with integrating component skills--a…

Prior programming knowledge of students has a major impact on introductory programming courses. Those with prior experience often seem to breeze through the course. Those without prior experience see others breeze through the course and disengage from the material or drop out. The purpose of this study is to demonstrate that novice student…

Background: Learning analytics (LA) research often aggregates learning process data to extract measurements indicating constructs of interest. However, the warranty that such aggregation will produce reliable measurements has not been explicitly examined. The reliability evidence of aggregate measurements has rarely been reported, leaving an…

Knowledge tracing (KT) models are a popular approach for predicting students' future performance at practice problems using their prior attempts. Though many innovations have been made in KT, most models including the state-of-the-art Deep KT (DKT) mainly leverage each student's response either as correct or incorrect, ignoring its content. In…

We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of…

Introductory programming courses (CS1) are difficult for novices. Inspired by "Problem solving followed by instruction" and "Productive Failure" approaches, we define an original "necessity-driven" learning design. Students are put in an apparently well-known situation, but this time they miss an essential ingredient…

Background and Context: Productive failure (PF) is a learning paradigm that flips the order of instruction: students work on a problem, then receive a lesson. PF increases learning, but less is known about student emotions and collaboration during PF, particularly in a computer science context. Objective: To provide insight on students' emotions…

Understanding students' learning of knowledge components (KCs) is an important educational data mining task and enables many educational applications. However, in the domain of computing education, where program exercises require students to practice many KCs simultaneously, it is a challenge to attribute their errors to specific KCs and,…

Pair programming (PP), as a mode of collaborative problem solving (CPS) in computer programming education, asks two students work in a pair to co-construct knowledge and solve problems. Considering the complex multimodality of pair programming caused by students' discourses, behaviors, and socio-emotions, it is of critical importance to examine…

Background and Context: Research in programming education seems to show that hands-on writing at the keyboard is beneficial for learning, but we lack an explanation of why that is and an underlying theory to anchor that explanation. Objective: The first objective is to lay out a theoretical foundation for understanding the learning situation when…

The ability to properly evaluate one's own academic progress has long been considered a predictor of academic success. However, its distinctive role in the context of computational mathematics remains underexplored. Grounded in social cognitive theory, this study investigates the critical role of self-regulated learning (SRL) strategies in…

The purpose of this study was to investigate the collaborative dialogue patterns of pair programming and their impact on programming self-efficacy and coding performance for both slow- and fast-paced students. Forty-six postgraduate students participated in the study. The students were asked to solve programming problems in pairs; those pairs'…

Background: This study posits that scaffolded team-based computational modeling and simulation projects can support model-based learning that can result in evidence of representational competence and regulatory skills. The study involved 116 students from a second-year thermodynamics undergraduate course organized into 24 teams, who worked on…