The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event "A" after learning "B" should equal the conditional probability of "A" given "B" prior to learning "B". We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial…

Within the theoretical framework of knowledge space theory, a probabilistic skill multimap model for assessing learning processes is proposed. The learning process of a student is modeled as a function of the student's knowledge and of an educational intervention on the attainment of specific skills required to solve problems in a knowledge…

The field of the learning sciences appears to favor cognitive and social approaches to the study of human learning. In this article, the author proposes that a deep cognizance of cultural influences on learning is vital if formal and informal learning are to make vital connections to learners' lives and their personal need for meaning making in…

Research has documented two effects of interfeature causal knowledge on classification. A "causal status effect" occurs when features that are causes are more important to category membership than their effects. A "coherence effect" occurs when combinations of features that are consistent with causal laws provide additional…

In a recent study, G. Kuhn and Z. Dienes (2005) reported that participants previously exposed to a set of musical tunes generated by a biconditional grammar subsequently preferred new tunes that respected the grammar over new ungrammatical tunes. Because the study and test tunes did not share any chunks of adjacent intervals, this result may be…

The most important thing for learners in Programming Language subject is problem solving. During the practical programming project, various problems may occur and learners usually need consultation from the senior programmers (i.e. the experts) to assist them in solving the problems. Thus, the inquiry-based learning with learning forum is applied…

A. Redish et al. (2007) proposed a reinforcement learning model of context-dependent learning and extinction in conditioning experiments, using the idea of "state classification" to categorize new observations into states. In the current article, the authors propose an interpretation of this idea in terms of normative statistical inference. They…

Acquisition of interactive skills involves the use of internal and external cues. Experiment 1 showed that when actions were interdependent, learning was effective with and without external cues in the single-task condition but was effective only with the presence of external cues in the dual-task condition. In the dual-task condition, actions…

Dealing with alternative causes is necessary to avoid making inaccurate causal inferences from covariation data. However, information about alternative causes is frequently unavailable, rendering them unobserved. The current article reviews the way in which current learning models deal, or could deal, with unobserved causes. A new model of causal…

The study focused on the interaction between two secondary school students while they were working on computerized mathematical investigation tasks related to probability theory. The aim was to establish how such interaction helped the students to learn from one another, and how it may have hindered their learning process. The assumption was that…

Tobacco use is a major health problem that is estimated to cause 4 million deaths a year worldwide. Nicotine is the main addictive component of tobacco. It acts as an agonist to activate and desensitize nicotinic acetylcholine receptors (nAChRs). A component of nicotine's addictive power is attributable to actions on the mesolimbic dopaminergic…

The authors explore the division of labor between the basal ganglia-dopamine (BG-DA) system and the orbitofrontal cortex (OFC) in decision making. They show that a primitive neural network model of the BG-DA system slowly learns to make decisions on the basis of the relative probability of rewards but is not as sensitive to (a) recency or (b) the…

This essay introduces a series of studies developing a statistical theory of elementary learning processes. An attempt is made to derive relations among commonly used measures of behavior and quantitative expressions describing simple learning phenomena. Laws of the theory state probability relations between momentary changes in behavioral and…