The extraction of cooccurrences between two events, A and B, is a central learning mechanism shared by all species capable of associative learning. Formally, the cooccurrence of events A and B appearing in a sequence is measured by the transitional probability (TP) between these events, and it corresponds to the probability of the second stimulus…

In a range of settings, human operators make decisions with the assistance of automation, the reliability of which can vary depending upon context. Currently, the processes by which humans track the level of reliability of automation are unclear. In the current study, we test cognitive models of learning that could potentially explain how humans…

Refined tracking allows students and teachers to more accurately understand students' learning growth. To provide refined learning tracking with longitudinal diagnostic assessment, this article proposed a new model by incorporating probabilistic logic into longitudinal diagnostic modeling. Specifically, probabilistic attributes were used instead…

The adaptive learning problem concerns how to create an individualized learning plan (also referred to as a learning policy) that chooses the most appropriate learning materials based on a learner's latent traits. In this article, we study an important yet less-addressed adaptive learning problem--one that assumes continuous latent traits.…

In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

Existing approaches in the literature on cognitive control in conflict tasks almost exclusively target the outcome of control (by comparing mean congruency effects) and not the processes that shape control. These approaches are limited in addressing a current theoretical issue--what contribution does learning make to adjustments in cognitive…

There is currently a consensus in mathematics education that favors constructivist instructional models, which are based on the inquiry of knowledge by students. There are, however, different views that consider objectivist models, based on knowledge transmission (direct or explicit teaching) more effective in the teaching of scientific…

Stimuli that capture the central tendency of presented exemplars are often preferred--a phenomenon also known as the classic beauty-in-averageness effect. However, recent studies have shown that this effect can reverse under certain conditions. We propose that a key variable for such ugliness-in-averageness effects is the category structure of the…

BKT and other classical student models are designed for binary environments where actions are either correct or incorrect. These models face limitations in open-ended and data-driven environments where actions may be correct but non-ideal or where there may even be degrees of error. In this paper we present BKT-SR and RKT-SR: extensions of the…

In adaptive learning systems, various models are employed to obtain the optimal learning schedule and review for a specific learner. Models of learning are used to estimate the learner's current recall probability by incorporating features or predictors proposed by psychological theory or empirically relevant to learners' performance. Logistic…

We evaluate here the performance of four models of cross-situational word learning: two global models, which extract and retain multiple referential alternatives from each word occurrence; and two local models, which extract just a single referent from each occurrence. One of these local models, dubbed "Pursuit," uses an associative…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

Phonotactics--constraints on the position and combination of speech sounds within syllables--are subject to statistical differences that gradiently affect speaker and listener behavior (e.g., Vitevitch & Luce, 1999). What statistical properties drive the acquisition of such constraints? Because they are naturally highly correlated, previous…

Bayesian Knowledge Tracing (BKT) is a commonly used approach for student modeling, and Long Short Term Memory (LSTM) is a versatile model that can be applied to a wide range of tasks, such as language translation. In this work, we directly compared three models: BKT, its variant Intervention-BKT (IBKT), and LSTM, on two types of student modeling…

We show that student learning can be accurately modeled using a mixture of learning curves, each of which specifies error probability as a function of time. This approach generalizes Knowledge Tracing [7], which can be viewed as a mixture model in which the learning curves are step functions. We show that this generality yields order-of-magnitude…