Flow is a human psychological state positively correlated to self-efficacy, motivation, engagement, and academic achievement, all of which positively affect learning. However, automatic, real-time flow detection is extremely difficult, a challenge particularly exacerbated in a Massively Online Open Course (MOOC) context, where the distant, and asynchronous components rejoin the educational and online context. We approach this issue by training a Machine Learning (ML) model to detect flow transparent and automatically in a MOOC. We pair the results of the EduFlow2 and Flow-Q questionnaires (n = 1 553, two years data collection), and their MOOC log data (French MOOC "Gestion de Projet" [Project Management]) to a ML pipeline to create a ML model that detects flow (ROC = 0.68 and PRC = 0.87) in a MOOC context. This ML model detects flow (0.85) with a greater Precision than its absence (0.34).

Flow is a human psychological state positively correlated to self-efficacy, motivation, engagement, and academic achievement. In a MOOC, flow detection and prediction would potentially allow for learners’ content personalization, fostering engagement and increasing already-low completion rates. In this study, we propose a Machine Learning flow-predicting model by pairing the results of the EduFlow-2 and Flow-Q measure instruments issued to participants of a MOOC (n = 1589, 2-year data collection). The resulting flow-predicting-model detects flow in an automatic, asynchronous fashion by applying only the EduFlow-2 measurement instrument. Our model proposal predicts flow presence with greater precision than it detects flow absence.

Nowadays, Machine Learning (ML) techniques play an increasingly important role in educational settings such as behavioral academic pattern recognition, educational resources suggestion, competences and skills prediction, or clustering students with similar learning characteristics, among others. Knowledge Tracing (KT) allows modelling the learner’s mastery of skills and to predict student’s performance by tracking within the Learner Model (LM) the students’ knowledge. Based on the PRISMA method, we survey and describe commonly used ML techniques employed for KT shown in 51 articles on the topic, among 628 publications from 5 renowned academic sources. We identify and review relevant aspects of ML for KT in LM that contribute to a more accurate panorama of the topic and hence, help to choose an appropriate ML technique for KT in LM. This work is dedicated to MOOC designers/providers, pedagogical engineers and researchers who need an overview of existing ML techniques for KT in LM.

Flow is a human psychological state positively correlated to self-efficacy, motivation, engagement, and academic achievement, all of which positively affect learning. However, automatic, real-time flow prediction is quite difficult, particularly in a Massively Online Open Course context, because of its online, distant, asynchronous, and educational components. In such context, flow prediction would allow for personalization of activities, content, and learning-paths. By pairing the results of the EduFlow2 and Flow-Q questionnaires (n = 1589, two years data collection) from the French MOOC "Gestion de Projet" (Project Management) to Machine Learning techniques (Logistic Regression), we create a Machine Learning model that successfully predicts flow (combined Accuracy & Precision similar to 0.8, AUC = 0.85) in an automatic, asynchronous fashion, in a MOOC context. The resulting Machine Learning model predicts the presence of flow (0.82) with a greater Precision than it predicts its absence (0.74).

Let $L$ be a finite lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of given $L$ and $f,g \in \mathcal{E}(L)$, finding the greatest lower bound $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ in the lattice $\mathcal{E}(L)$. (1) We show that if $L$ is distributive, the problem can be solved in time $O(n)$ where $n=| L |$. The previous upper bound was $O(n^2)$. (2) We provide new algorithms for arbitrary lattices and give experimental evidence that they are significantly faster than the existing algorithm. (3) We characterize the standard notion of distributed knowledge of a group as the greatest lower bound of the join-endomorphisms representing the knowledge of each member of the group. (4) We show that deciding whether an agent has the distributed knowledge of two other agents can be computed in time $O(n^2)$ where $n$ is the size of the underlying set of states. (5) For the special case of $S5$ knowledge, we show that it can be decided in time $O(n\alpha_{n})$ where $\alpha_{n}$ is the inverse of the Ackermann function.

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that the distributed information of c amongst a group is the greatest lower bound of all possible combinations of information in the spaces of the agents in the group that derive c. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application to mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs. (C) 2021 Elsevier Inc. All rights reserved.

While setting up a Massive Open Online Course for Lifelong Learners, the choice of the most adequate Learner Model for this most current context is paramount: not all Learner Models are created equal, despite their overall added value to facilitate the learner's follow-up, course content personalization and trainers/teachers' practices in various Learning Environments. This systematic review of literature defines, compares, and highlights eight features of interest of Learner Models for Massive Open Online Courses from a Lifelong Learning perspective. It discerns 17 of the most-current, existing Learner Models out of 442 search results. It concludes on the four most adequate, and current Learner Models in this context. In addition, we study how they handle the learning experience personalization. This work is primarily dedicated to MOOC designers/providers, pedagogical engineers and researchers who meet difficulties to model and evaluate MOOC's learners using Learning Analytics.

Machine Learning (ML) techniques are being intensively applied in educational settings. They are employed to predict competences and skills, grade exams, recognize behavioural academic patterns, evaluate open answers, suggest appropriate educational resources, and group or associate students with similar learning characteristics or academic interests. Knowledge Tracing (KT) allows modelling the learner's mastery of skill and to meaningfully predict student's performance, as it tracks within the Learner Model (LM) the knowledge state of students based on observed outcomes from their previous educational practices, such as answers, grades and/or behaviours. In this study, we survey commonly used ML techniques for KT figuring in 51 papers on the topic, out of an original search pool of 628 articles from 5 renowned academic sources, encompassing the latest research, based on the PRISMA method. We identify and review relevant aspects of ML for KT in LM that help paint a more accurate panorama on the topic and hence, contribute to alleviate the difficulty of choosing an appropriate ML technique for KT in LM. This work is dedicated to MOOC designers/providers, pedagogical engineers and researchers who need an overview of existing ML techniques for KT in LM.

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that distributed information of a group is the greatest information below all possible combinations of information in the spaces of the agents in the group that derive a given piece of information. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application on mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs.

Nowadays, Learning Analytics is an emerging topic in the Technology Enhanced Learning and the Lifelong Learning fields. Learner Models also have an essential role on the use and exploitation of learner-generated data in a variety of Learning Environments. Many research studies focus on the added value of Learner Models and their importance to facilitate the learner's follow-up, the course content personalization and the trainers/teachers' practices in different Learning Environments. Among these environments, we choose Massive Open Online Courses because they represent a reliable and considerable amount of data generated by Lifelong Learners. In this paper we focus on Learner Modelling in Massive Open Online Courses in an Lifelong Learning context. To our knowledge, currently there is no research work that addresses the literature review of existing Learner Models for Massive Open Online Courses in this context in the last five years. This study will allow us to compare and highlight features in existing Learner Models for a Massive Open Online Course from a Lifelong Learning perspective. This work is dedicated to MOOC designers/providers, pedagogical engineers and researchers who meet difficulties to model and evaluate MOOCs' learners based on Learning Analytics.

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set $\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. In particular, we show for $\mathbf{M}_n$, the discrete order of $n$ elements extended with top and bottom, $| \mathcal{E}(\mathbf{M}_n) | =n!\mathcal{L}_n(-1)+(n+1)^2$ where $\mathcal{L}_n(x)$ is the Laguerre polynomial of degree $n$. We also study the following problem: Given a lattice $L$ of size $n$ and a set $S\subseteq \mathcal{E}(L)$ of size $m$, find the greatest lower bound ${\large\sqcap}_{\mathcal{E}(L)} S$. The join-endomorphism ${\large\sqcap}_{\mathcal{E}(L)} S$ has meaningful interpretations in epistemic logic, distributed systems, and Aumann structures. We show that this problem can be solved with worst-case time complexity in $O(mn)$ for distributive lattices and $O(mn + n^3)$ for arbitrary lattices. In the particular case of modular lattices, we present an adaptation of the latter algorithm that reduces its average time complexity. We provide theoretical and experimental results to support this enhancement. The complexity is expressed in terms of the basic binary lattice operations performed by the algorithm.

Lifelong Learning encompasses vast learning opportunities and MOOCs are a learning environment that can be up to the challenge if current modeling challenges are addressed. Studies have shown the importance of modeling the learner for a more personal and tailored learning experience in MOOC. Furthermore, Open Learner Models have proven their added value in facilitating learner's follow-up and course content personalization. However, while modeling the learner's knowledge is a common practice, modeling the learner's psychological state is a relegated concern within the community. This is despite the myriad of scientific evidence backing up the importance and repercussion of the learner's psychological state during and on the learning process. Flow is a psychological state characterized by total immersion in a task and a state of optimal performance. Programmers often refer to it as "being in the zone". It reliably correlates favorable learning metrics, such as motivation and engagement, among others. The aim of this paper is to propose a functional and technical architecture (comprising a Domain Model, a Flow Model, and an Open Learner Model for MOOC in a Lifelong Learning context) accounting for the learner's Flow state. This work is dedicated to MOOC designers/providers, pedagogical engineers, psychology, and education researchers who meet difficulties to incorporate and account for the Flow psychological state in a MOOC.

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide algorithms that compute the distributive group information of finite groups.

La multitude de travaux sur les pratiques numeriques des jeunes temoignent de la place importante occupee par le numerique dans leur quotidien. Espace d’experimentation identitaire et d'autonomie comportementale , le numerique est percu comme emancipateur du monde adulte , voire « le symbole de {leurs} activites privatives » . Et, dans un contexte d’integration du numerique en milieu scolaire, des questions d’enchevetrement et de porosite des espaces-temps scolaires (normes et normatifs) et non scolaires (supposement plus libres) se posent. Notre proposition vise a presenter une etude en cours sur les interstices qui apparaissent alors et designent des usages qui relevent a la fois d’un espace-temps scolaire et non scolaire. Ces espaces-temps qui ne sont ni exclusivement scolaires ni exclusivement prives sont identifies par l’analyse des representations de lyceens et par l’analyse de leurs pratiques numeriques, apprehendees par leurs traces d’activite.

This paper addresses the issue of specifying, simulating, and verifying reactive systems in rewriting logic. It presents an executable semantics for probabilistic, timed, and spatial concurrent constraint programming —here called stochastic and spatial concurrent constraint systems (sscc)— in the rewriting logic semantic framework. The approach is based on an enhanced and generalized model of concurrent constraint programming (CCP) where computational hierarchical spaces can be assigned to belong to agents. The executable semantics faithfully represents and operationally captures the highly concurrent nature, uncertain behavior, and spatial and epistemic characteristics of reactive systems with flow of information. In sscc, timing attributes —represented by stochastic duration— can be associated to processes, and exclusive and independent probabilistic choice is also supported. SMT solving technology, available from the Maude system, is used to realize the underlying constraint system of sscc with quantifier-free formulas over integers and reals. This results in a fully executable real-time symbolic specification that can be used for quantitative analysis in the form of statistical model checking. The main features and capabilities of sscc are illustrated with examples throughout the paper. This contribution is part of a larger research effort aimed at making available formal analysis techniques and tools, mathematically founded on the CCP approach, to the research community.