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…

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…

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.…

The impact of retrieval practice on analogical-problem-solving performance was investigated using a complex, educationally relevant task. Participants studied a statistical hypothesis testing scenario and practiced recalling the material or repeatedly studied it. Participants then completed a final test either 5 minutes or 1 week later involving a…

Hypothesis testing involves a complex stepwise procedure that is challenging for many students in introductory university statistics courses. In this paper we assess how feedback from an Intelligent Tutoring System can address the logic of hypothesis testing and whether such feedback contributes to first-year social sciences students' proficiency…

Insightful problem solving is a vital part of human thinking, yet very difficult to grasp. Traditionally, insight has been investigated by using a set of established "insight tasks," assuming that insight has taken place if these problems are solved. Instead of assuming that insight takes place during every solution of the 9 Dot, 8 Coin,…

Collaborative problem-solving is often not a sequential process; instead, it can involve tasking switching or dual tasking (i.e., multitasking) activities in that the collaborators need to shift their attention between the targeted problems and the conversations they carry on with their collaborators. It is not known to what extent the…

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

In this paper we report the results of an experiment designed to test the hypothesis that when faced with a question involving the inverse direction of a reversible mathematical process, students solve a multiple-choice version by verifying the answers presented to them by the direct method, not by undertaking the actual inverse calculation.…

In this paper, the author reports the results of an empirical study on the relationship between a student's programming experience and their success in a traditional Systems Analysis and Design (SA&D) class where technical skills such as dataflow analysis and entity relationship data modeling are covered. While it is possible to teach these…

The results of qualitative and quantitative investigations conducted with individuals who learned algorithms in school are presented in this article. In these investigations, eye-tracking technology was used to follow the process of solving algorithmic problems. The algorithmic problems were presented in two comparable variants: in a pseudocode…

Research on incidence of and changes in confusion during complex learning and problem-solving calls for advanced methods of confusion detection in digital learning environments (DLEs). In this study we attempt to address this issue by investigating the use of multiple measures, including psychophysiological indicators and self-ratings, to detect…

In the context of higher education, a competence may be understood as the combination of skills, knowledge, attitudes, values, and abilities that underpin effective and/or superior performance in a professional area. The aim of the work reported here was to design a set of procedures to assess a transferable competence, i.e., problem solving, that…