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…

This study by Lio Moscardini of the University of Strathclyde shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in…

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…

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…

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…

Undergraduate students today often enroll in introductory religious studies or theology classes because they want the time and space to reflect on their personal spiritual questions. Such a motivation can clash with the faculty's desire to introduce students to rigorous academic study of their field. Barbara Walvoord has proposed four "voices"…

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…

For learners to communicate efficiently in the L2, they must avoid pragmatic failure. In many cases, teachers' praxis centres on the learner's performance in the L2 or his role as a speaker, which neglects the importance of his role as interpreter of utterances. Assuming that, as hearers, learners also have a responsibility to avoid…

“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…

Balancing content and students' participation in the mathematics classroom is an area of both practical and theoretical interest. In this article we relate and contribute to these two interests by analyzing classroom data from an intervention project aiming at teaching mathematics through problem solving. The study shows that several aspects such…