Educational systems use models of student skill to inform decision-making processes. Defining such models manually is challenging due to the large number of relevant factors. We propose learning multidimensional representations (embeddings) from student activity data -- these are fixed-length real vectors with three desirable characteristics:…

Discussion forums in learning management systems (LMS) have been shown to promote student interaction and contribute to the collaborative practice in the teaching-learning process. By evaluating the postings, teachers can identify students with learning difficulties. However, due to the large volume of posts that are generated on a daily basis in…

Although providing open learner models to teachers and learners has proven effective, building accurate learner models remains a very complex task, partly due to the large amount of data that must be analyzed. We propose a method for specifying an open learner model at the conceptual level. This model re-uses constraints or indicators already…

This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead…

Answer Set Programming (ASP) is one of the most prominent and successful knowledge representation paradigms. The success of ASP is due to its expressive non-monotonic modeling language and its efficient computational methods originating from building propositional satisfiability solvers. The wide adoption of ASP has motivated several extensions to…

Humans can learn to organize many kinds of domains into categories, including real-world domains such as kinsfolk and synthetic domains such as sets of geometric figures that vary along several dimensions. Psychologists have studied many individual domains in detail, but there have been few attempts to characterize or explore the full space of…

The advantages of Gaussian-type orbitals (GTO) over Slater-type orbitals (STO) in quantum chemistry calculations are clarified here by means of a holistic approach. The popular Microsoft Office Excel program was used to create an interactive application with which students are able to explore the features of GTO, including automatic calculations…

The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…

This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr's Level Theory: the computational…

Research in the field of Automated Planning is largely focused on the problem of constructing plans or sequences of actions for going from a specific initial state to a goal state. The complexity of this task makes it desirable to find "generalized" plans which can solve multiple problem instances from a class of similar problems. Most approaches…

The goal of this article is to contribute fragments of concrete understanding to the on-going search for meaning in ideas associated with the learning sciences (Sawyer, 2006b) by adding to the repertoire of domain specific studies pertaining to this relatively new field. The learning sciences are first characterized as a system of learning…

It has been proposed that causal power (defined as the probability with which a candidate cause would produce an effect in the absence of any other background causes) can be intuitively computed from cause-effect covariation information. Estimation of power is assumed to require a special type of counterfactual probe question, worded to remove…

We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

The Latent Semantic Indexing and MatchPlus systems examine similar contexts in which words appear and create representational models that capture the similarity of meaning of terms and then use the representation for retrieval. Text Retrieval Conference experiments using these systems demonstrate the computational feasibility of using…

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed…