Most teachers agree that if a student understands a particular mathematical topic well, he/she will probably be able to do problems correctly. The converse, however, frequently fails: students who do problems correctly sometimes do not actually have robust understandings of the topic in question. In this paper we explore this phenomenon in the…

The work described here represents an effort to understand and influence visual attention while solving physics problems containing a diagram. Our visual system is guided by two types of processes--top-down and bottom-up. The top-down processes are internal and determined by ones prior knowledge and goals. The bottom-up processes are external and…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

The traditional approach to teach problem solving usually consists in showing students the solutions of some example-problems and then in asking students to practice individually on solving a certain number of related problems. This approach does not ensure that students learn to solve problems and above all to think about the solution process in…

Individual differences in working memory capacity (WMC) increase the ability and tendency to devote greater attentional control to a task--improving performance on a wide range of skills. In addition, recent research on enclothed cognition demonstrates that the situational influence of wearing a white lab coat increases controlled attention, due…

The Traveling Salesperson Problem (TSP) is a computationally difficult combinatorial optimization problem. In spite of its relative difficulty, human solvers are able to generate close-to-optimal solutions in a close-to-linear time frame, and it has been suggested that this is due to the visual system's inherent sensitivity to certain geometric…

The goal of this study is to identify the characteristics of pre-service primary teachers' configural reasoning, understood as the relationships between concepts and figures set to solve geometrical proof problems. Ninety-seven primary teachers were asked to solve two geometrical proof problems in which a geometrical figure was provided. The…

Base-rate neglect refers to the tendency for people to underweight base-rate probabilities in favor of diagnostic information. It is commonly held that base-rate neglect occurs because effortful (Type 2) reasoning is required to process base-rate information, whereas diagnostic information is accessible to fast, intuitive (Type 1) processing…

The current study examines the performance and achievement of students in the Systematic Qualitative Analyses of Cations (SQACs). We sought answers to questions such as, "What are the students' levels of performance?" and "What is the relation between the average scores for performance and achievement?." This was done by using…

Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

In recent years, a number of models concerning problem solving systems have been put forward. However, many of them stress on technology and neglect the research of problem solving itself, especially the learning mechanism related to problem solving. In this paper, we analyze the learning mechanism of problem solving, and propose that when…

The concept of intentional learning is well established in the educational community. Intentional learning implies that there is a recognized learning goal and that those involved are rational agents who can make choices with regard to achieving that goal. There are typically two different kinds of people involved in a learning situation--learners…

By 3 years of age, children can solve tasks involving physical principles such as locating a ball that rolled down a ramp behind an occluder by the position of a partially visible solid wall (Berthier, DeBlois, Poirer, Novak, & Clifton, 2000; Hood, Carey, & Prasada, 2000). However, the extent to which children use physical information (the…

Computer-based assessment can provide new insights into behavioral processes of task completion that cannot be uncovered by paper-based instruments. Time presents a major characteristic of the task completion process. Psychologically, time on task has 2 different interpretations, suggesting opposing associations with task outcome: Spending more…

This multiple-case study examined how advanced learners solved a complex problem, focusing on how their frequency and application of cognitive processes contributed to differences in performance outcomes, and developing a mental model of a problem. Fifteen graduate students with backgrounds related to the problem context participated in the study.…