Two wires exit a black box that has three exposed light bulbs connected together in an unknown configuration. The task for students is to determine the circuit configuration without opening the box. In the activity described in this paper, we navigate students through the process of making models, developing and conducting experiments that can…

The paper explores and clarifies the similarities and differences that exist between proof by contradiction and proof by contraposition. The paper also focuses on the concept of contradiction, and a general model for this method of proof is offered. The introduction of mathematical proof in the classroom remains a formidable challenge to students…

Research on human causal induction has shown that people have general prior assumptions about causal strength and about how causes interact with the background. We propose that these prior assumptions about the parameters of causal systems do not only manifest themselves in estimations of causal strength or the selection of causes but also when…

The significance of the role of creativity as an essential component of giftedness has long been assumed by most of the experts in the field. The most fertile creations will often be those formed of elements drawn from domains which are far apart. It is assumed that creativity is a personality variable, and not an ability, and thus it is believed…

Learning probabilistic classification and prediction models that generate accurate probabilities is essential in many prediction and decision-making tasks in machine learning and data mining. One way to achieve this goal is to post-process the output of classification models to obtain more accurate probabilities. These post-processing methods are…

This dissertation, titled "Investigating Music Information Objects," is a study of the nature, description, representations, and ideas related to music information objects (MIOs). This research study investigates how music practitioners from various traditions describe and conceptualize MIOs, using a theoretical framework to classify…

This paper presents an extension of the Additive Factors Model to predict learning for students by accounting for aspects of collaboration. The results indicate that student performance is predicted more accurately when the model includes parameters that capture influences of working collaboratively. [This paper was published in: "Proceedings…

One of the reasons for the popularity of meta-analysis is the notion that these analyses will possess more power to detect effects than individual studies. This is inevitably the case under a fixed-effect model. However, the inclusion of the between-study variance in the random-effects model, and the need to estimate this parameter, can have…

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Despite today's proclaimed open-mindedness, a certain uniformity of thought, followed by a flattening of practices, can be observed in the processes of quality improvement in higher education. This narrowing of thought, which I call "relevance rationality," is an offshoot of instrumental reason and represents a debased,…

Despite significant scholarly attention, the literature on the existence and direction of gender differences in creativity has produced inconsistent findings. In the present paper, we argue that this lack of consensus may be attributable, at least in part, to gender-specific inconsistencies in the measurement of creative problem-solving. To…

A key property of relational representations is their "generativity": From partial descriptions of relations between entities, additional inferences can be drawn about other entities. A major theoretical challenge is to demonstrate how the capacity to make generative inferences could arise as a result of learning relations from…

The concept of intrinsic complexity explains why different problems of the same type, tackled by the same problem solver, can require different times to solve and yield solutions of different quality. This paper proposes a general four-step approach that can be used to establish a model for the intrinsic complexity of a problem class in terms of…

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided "P" value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The…

Background: Both observed studies and experimental studies have identified programs, practices, and treatments that are considered effective, ineffective, or harmful for juvenile offenders. Objective: Identify which dispositions were best and worse for each offense in the La Porte County, Indiana, juvenile justice database of over 8500 juvenile…