Organic chemistry problems that interrelate and integrate synthesis with spectroscopy are presented. These synthesis-spectroscopy roadmap (SSR) problems uniquely engage second-year undergraduate organic chemistry students in the personal discovery of organic chemistry. SSR problems counter the memorize-or-bust strategy that many students tend to…

Multiple-choice questions are an important part of large-scale summative assessments, such as the advanced placement (AP) chemistry exam. However, past AP chemistry exam items often lacked the ability to test conceptual understanding and higher-order cognitive skills. The redesigned AP chemistry exam shows a distinctive shift in item types toward…

Technology alone won't be enough to improve teaching and learning to where it needs to be for 21st century skills. Where it is being done successfully, teachers collectively share a vision of promoting deeper learning in all their students, and have collaboratively redesigned the role of the teacher to that of facilitator who uses technology as a…

The How Far Do You Think You Can Jump? activity (see EJ1174770) was completed in three different contexts: an after-school mathematics enrichment program at Woodland and Country Schools in Weston, Massachusetts; a small-group pull-out of second graders at Wren Elementary in Piedmont, South Carolina; and a family math night in Lafayette, Indiana.…

This guide is a revised and updated edition of "Making It Count." This version contains much of the information from the earlier publication but also includes strategies for using project-based learning and Web-based instructional programs to support the development of mathematics proficiency for youth in short-term juvenile correctional…

This paper is, essentially, the transcription of my conference at the conference CIEAEM 63, promoted by the CIEAEM/Commission for the Study and Improvement of Mathematics Teaching, held in Barcelona, Spain, from 24 to 29 July 2011. The main objective of the CIEAEM, since its foundation, in the fifties, has been to analyze the actual conditions and…

The recent push for more problem solving in elementary school mathematics classrooms intimidates many teachers. Anyone can look at the arguments--that problem solving deepens knowledge, provides real-world context, allows for multiple entry points, and so on--and see their logic and potential (Lester and Charles 2003). But teachers tend to think…

The purpose of this essay is to draw out key insights from Dewey's important text "Logic: The Theory of Inquiry" to provide theoretical and practical support for the emergent field of teacher research. The specific focal point is the argument in Cochran-Smith and Lytle's "Inside/Outside: Teacher Research and Knowledge" on the significance of…

The problem of optimizing the number of circular sprinklers watering large fields is used to introduce, from a purely elementary geometrical perspective, some basic concepts in crystallography and comment on a few size effects in condensed matter physics. We examine square and hexagonal lattices to build a function describing the, so-called, dry…

This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

Just as students need plenty of time to practice skills such as solving fraction problems, they also need time to practice the skills of discourse to become better communicators and stronger mathematicians. Embedded within discourse strategies are specific ways to maximize communication. When repeatedly practiced, students learn to listen to one…

This note explains how Emil Artin's proof that row rank equals column rank for a matrix with entries in a field leads naturally to the formula for the nullity of a matrix and also to an algorithm for solving any system of linear equations in any number of variables. This material could be used in any course on matrix theory or linear algebra.

This article describes a grading approach that encourages students to employ particular problem-solving skills. Some strengths of this method, called "process-based grading," are that it is easy to implement, requires minimal time to grade, and can be used in conjunction with either an online homework delivery system or paper-based homework.

In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and…

The problem of charge motion governed by image force attraction near a plane metal surface is considered and solved self-consistently. The temporal dispersion of metal dielectric permittivity makes the image forces dynamic and, hence, finite, contrary to the results of the conventional approach. Therefore, the maximal attainable velocity turns out…