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…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…

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,…

This article deals with a theory-based investigation of the diagnostic problem-solving process in professional contexts. To begin with, a theory of the diagnostic problem-solving process was developed drawing on findings from different professional contexts. The theory distinguishes between four sub-processes of the diagnostic problem-solving…

Collaborative learning is well-established as a method to improve student learning and retention in engineering classrooms. One problem with collaborative learning is difficulty maximizing engagement of all students during group activities. We tested a change in implementation of collaborative problem solving sessions (Workshops) in a first-year…

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…

Teaching introductory statistics using curricula focused on modeling and simulation is becoming increasingly common in introductory statistics courses and touted as a more beneficial approach for fostering students' statistical thinking. Yet, surprisingly little research has been conducted to study the impact of modeling and simulation curricula…

A growing body of scholarly work indicates that student performance on physics problems stems from many factors, including relevant conceptual understanding. However, in contexts in which significant conceptual difficulties have been documented via research, it can be difficult to pinpoint and isolate such factors because students' written and…

We sought to test a hypothesis that systemic blind spots in active learning are a barrier both for instructors--who cannot see what every student is actually thinking on each concept in each class--and for students--who often cannot tell precisely whether their thinking is right or wrong, let alone exactly how to fix it. We tested a strategy for…