Students often make errors when trying to solve qualitative or conceptual physics problems, and while many successful instructional interventions have been generated to prevent such errors, the process of deduction that students use when solving physics problems has not been thoroughly studied. In an effort to better understand that reasoning…

This paper reports on a component of a large yearlong study in three Year 7 classes in three different schools. The aim of this research component was to determine the relationship between students' number sense and their problem-solving ability by means of paper-and-pencil tests, classroom observations, and interviews of students and teachers.…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

Psychophysical reverse-correlation methods such as the "classification image" technique provide a unique tool to uncover the internal representations and decision strategies of individual participants in perceptual tasks. Over the past 30 years, these techniques have gained increasing popularity among both visual and auditory psychophysicists.…

When subjects are given the balls-and-boxes problem-solving task (Kotovsky & Simon, 1990), they move rapidly towards the goal after an extended exploratory phase, despite having no awareness of how to solve the task. We investigated possible non-conscious learning mechanisms by giving subjects three runs of the task while recording ERPs. Subjects…

Establishing caring communities in child care centers is one of the most important, yet challenging undertakings for early childhood professionals. Lessons in accomplishing this goal can be learned from the inhabitants of the island communities of coastal Maine who work together to overcome the challenges of living in remote locations. In this…

Using different representations and having flexibility of transition between representations throughout the definite integral problem-solving process are thought to be effective on the development of conceptual understanding and students' performance. The study aims at considering the effects of representations used in the definite integral on…

This project served as a capstone event for the United States Military Academy sophomore Calculus II course. This multi-disciplinary problem-solving exercise motivated the link between math and biology and many other fields of study. The seven-lesson block of instruction was developed to show students how mathematics play a role in every…

This paper is concerned with the relationship between authenticity and adult learning and prompted by some studies in which adult "authentic learning" is a central concept. The implication revealed by them is that real-worldness of learning contexts, learning content and learning tasks is perceived as conferring authenticity on learning. Here,…

This article describes a design problem that not only takes students through the technological design process, but it also provides them with real-world problem-solving experience as it relates to the manufacturing and engineering fields. It begins with a scenario placing the student as a custom wheel designer for an automotive manufacturing…

This paper outlines the solution that the Team of Austria found to problem number 7, "skateboarder", presented in the finals of the 22nd International Young Physicists' Tournament (IYPT) in Tianjin, China. We investigated how a skateboarder can accelerate from rest on a horizontal surface without touching an external support. The focus was laid on…

We conducted a series of experiments to investigate the extent to which prompting the construction of a force diagram affects student solutions to simple mechanics problems. A total of 891 university introductory physics students were given typical force and motion problems under one of the two conditions: when a force diagram was or was not…

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…