Why is hope such an important concept for schools to consider? Research has clearly demonstrated that more hopeful students perform better in school and in life than less hopeful students. Hopeful thought reflects the belief that one can find pathways to desired goals and become motivated to use those pathways. As a result, hope drives the…

Our 1997 article in "IJAIED" reported on a study that showed that a new algebra curriculum with an embedded intelligent tutoring system (the Algebra Cognitive Tutor) dramatically enhanced high-school students' learning. The main motivation for the study was to demonstrate that intelligent tutors that have cognitive science research…

This paper develops a theoretical framework that could facilitate the application of the Autovalutazione, Valutazione periodica, Accreditamento (AVA) method in Italian universities, trying to simplify the use of this approach, and to cover the existing gap between Italy and others European academic institutions. The new competitive environment in…

Raising expectations is nothing new. Every iteration of standards elevates the expectations for what students should know and be able to do. The Common Core State Standards for Mathematics (CCSSM) is no exception, with standards for content and practice that move beyond memorization of traditional algorithms to "make sense of problems and…

In this article, we propose a family of second derivative Adams-type methods (SDAMs) of order up to 2k + 2 ("k" is the step number) for initial value problems. The methods are constructed through a continuous approximation of the SDAM which is obtained by multistep collocation. The continuous approximation is used to obtain initial value methods,…

The purpose of this article is to describe a couple of challenging mathematical problems that involve paper folding. These problem-solving tasks can be used to foster geometric and algebraic thinking among students. The context of paper folding makes some of the abstract mathematical ideas involved relatively concrete. When implemented…

This article describes the implementation of high-altitude balloon (HAB) research into a variety of undergraduate atmospheric science classes as a means of increasing active student engagement in real-world, problem-solving events. Because high-altitude balloons are capable of reaching heights of 80,000-100,000 ft (24-30 km), they provide a…

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 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…