In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the…

The objective of this study was to measure the contribution of the left frontopolar cortex (FPC) to analogical reasoning. Our measure of analogical reasoning derives from performance on the radiation problem, a creative problem-solving task first used in Gestalt psychology (Duncker, 1945). Success on this task is as low as 10 % without the…

Student problems (preconceptions, errors, and learner-specific approaches) that arise when planning and conducting experiments are relevant for lesson planning and the further development of teaching practice overall. student problems are understood as a learning opportunity. So far, little attention has been paid to the relationships between…

Problem solving has been regarded as one of the most important cognitive skills in everyday life. The complexity of problem solving in technical areas is a critical component to developing the problem solving abilities of agricultural education students. This study grounded in Kirton's AdaptationInnovation Theory (A-I Theory), sought to identify…

This case is designed to be used in business analytics courses; particularly those that emphasize predictive analytics. Students are given background information on money laundering and data from People's United Bank, a regional bank in the northeast United States. The students must develop their hypothesis, analyze the data, develop and optimize…

Purpose: The purpose of this article is to describe the similarities between abductive reasoning and entrepreneurial learning processes in order to contribute to the conceptual understanding of learning as an entrepreneurial process in itself. Design/methodology/approach: The research is theoretically rooted in a conceptual development of the…

The role theory plays in research work cannot be over-emphasized. A theory that is apt gives direction to research work in explaining, organizing, analyzing, and predicting phenomenon and showing their relationships in order to enhance understanding. Despite these roles played by theory, upcoming scholars and students many at times fail to use…

Problem solving is an essential skill for students to be successful in life and careers. Students need to use efficient strategies to solve problems effectively. In this basic interpretive qualitative study, we aimed to (a) explore children's problem-solving strategies in a game-based tool (i.e., puzzles), and (b) investigate the troubleshooting…

Spaced and interleaved practices have been identified as effective learning strategies which sometimes are conflated as a single strategy and at other times treated as distinct. Learning sessions in which studying information or practicing problems are spaced in time with rest-from-deliberate-learning periods between sessions generally result in…

This paper presents research into closed orbits parallel to quadrilaterals inscribed in various geometric shapes that can be represented by mathematical functions: straight lines, circles, ellipses, parabolas, and hyperbolas. Mathematical proofs have been given for the existence of an infinite number of parallel orbits for each of these shapes.…

This design case introduces a design and development process of theories from environmental psychology, humanities, and social sciences as heuristic thinking devices to measure human-centered design solutions. The pedagogical review of the traditional studio design process revealed obstacles as students translated their research and program to the…

Here, we present a strong test of the hypothesis that sacrificial moral dilemmas are solved using the same value-based decision mechanism that operates on decisions concerning economic goods. To test this hypothesis, we developed Psychological Value Theory. Psychological Value Theory is an expansion and generalization of Cohen and Ahn's (2016)…