The authors present a Web application they designed in the R programming language as an experiential learning tool for teaching production theory. The app simulates production decisions where a manager is tasked to find the optimal mixture of inputs through experimentation. Users of the application are instructed to use calculations and intuitions…

In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the…

Computational thinking (CT) has the potential to enhance learning when integrated into mathematical classroom activities. Teachers are being asked to include CT concepts in their core disciplines; however, there is an open question as to how best to equip teachers to integrate CT into their practice. Oftentimes teacher candidates enter math and…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

Intuition is the first way humans get knowledge. A worker in making a traditional West Java house works using his experience to be able to determine how many building materials are needed to become a house. The roof of the house is one part that is quite complicated to determine the amount of wood needed. Workers using intuition based on…

The integration of visual programming in early formal education has been found to promote computational thinking of students. Teachers' intuitive perspectives about optimal learning processes -- "folk psychology" -- impact their perspectives about teaching "folk pedagogy" and play a significant role in integrating educational…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form--where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach…

In human problem solving, there is a wide variation between individuals in problem solution time and success rate, regardless of whether or not this problem solving involves insight. In this paper, we apply computational and parameterized analysis to a plausible formalization of extended representation change theory (eRCT), an integration of…

This emerging technology report describes virtual environment interactions an approach for blending movement and computer programming as an embodied way to support girls in building computational thinking skills. The authors seek to understand how body syntonicity might enable young learners to bootstrap their intuitive knowledge in order to…

This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…

Chess is a game of minds, bodies, and emotions. Most players recognize each of these as essential to playful competition, and all three are embedded in social relations. Thus chess, despite its reputation as a game of the mind, is not only a deeply thoughtful exercise, but also a test of physical endurance and strong emotions in its joys and…

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an…

The paper presents findings of a small scale study of a few items related to problem solving with squares and roots, for different teacher groups (pre-service and in-service mathematics teachers: elementary and junior high school). The research participants were asked to explain what would be the units digit of a natural number to be squared in…

On the basis of earlier findings, we (Fiedler & Kareev, 2006) presented a statistical decision model that explains the conditions under which small samples of information about choice alternatives inform more correct choices than large samples. Such a small-sample advantage (SSA) is predicted for choices, not estimations. It is contingent on high…

This paper provides a critical examination of the current state and future possibility of formal cognitive theory for insight problem solving and its associated "aha!" experience. Insight problems are contrasted with move problems, which have been formally defined and studied extensively by cognitive psychologists since the pioneering…