A typical textbook problem in rotational dynamics involves calculating the angular acceleration of a massive pulley due to a string, such as in the example shown in Fig. 1. The string is assumed to be massless and to move without slipping over the pulley, which is mounted on a frictionless axle. If T[subscript L] and T[subscript R] are the…

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students' flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent…

The standard approach to the general rules for differentiation is to first derive the power, product, and quotient rules and then derive the chain rule. In this short article we give an approach to these rules which uses the chain rule as the main tool in deriving the power, product, and quotient rules in a manner which is more student-friendly…

The full promise of class room learning is dependent on its ability to incorporate 21st century skills in its instructional design, delivery and implementation. In this increasingly competitive global economy, it is not enough for students to acquire subject-level mastery alone. Skills like creative thinking, problem-solving, communication and…

This study investigated the relationship between problem familiarity and students' learning in a problem-based course. Problem familiarity in this study refers to the extent to which a problem fits with students' prior knowledge and experiences. As part of regular course work, 172 students were given two problems on different occasions.…

Problem-Based Learning (PBL) has been one of the popular pedagogical strategies these years. PBL is about students connecting disciplinary knowledge to real-world problems--the motivation to solve a problem. To recognize general elements and typological differences of language in translation is the motivation to solve real problems such as…

The purpose of this study was to identify the extent to which multidiscipline early intervention providers identified and demonstrated caregiver-teaching strategies. A total of 78 providers submitted 205 videotaped segments to illustrate 1 of 5 caregiver-teaching strategies (i.e., demonstration; caregiver practice with feedback; guided practice;…

This article describes the use of a progressive paper in a capstone course to develop students' writing skills. A progressive paper is one that students write one section at a time: as they add each new section, they go back and revise the previous parts based on actionable feedback from the instructor. In this course, the progressive paper takes…

Problem solving is a necessary component of developing a strong mathematics curriculum that will help all students achieve their life goals, regardless of their specific academic plans. What day-to-day instructional decisions do teachers need to make if they believe that problem solving is a vehicle for learning mathematical content? In this…

We assessed the learning approaches and learning styles of a sample of 148 excellent students selected from 11 degrees from nine centers of the Polytechnic University of Valencia (Spain), and we compared the results with those of a sample of 133 average students from the same centers. We found that excellent students took deeper approach than…

While the value of "schematic representations" in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of "schematic…

A homework assignment is outlined in which students learn Computational Fluid Dynamics (CFD) concepts of discretization, numerical stability and accuracy, and verification in a hands-on manner by solving physically realistic problems of practical interest to engineers. The students solve a transient-diffusion problem numerically using the common…

Democratic problem-solving necessitates an active and informed citizenry, but existing research on service-learning has shed little light on the relationship between pedagogical practices and civic competence outcomes. This study developed and tested a model to represent that relationship and identified pedagogical catalysts of civic competence…

We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of…

“Let’s do it again,” shout the children as they complete an activity in music class. A casual observer would be aware that the children are fully engaged but may not be sure of the lesson focus. Is it to help children learn a new orchestra piece? To teach about the beat? To teach form? To teach rhythm? To teach children to read a music score? To…