While contemplating ways to extend the author's ninth-grade honors geometry students' thinking and knowledge about area and perimeter, he discovered an interesting type of problem based on Erickson's (2001) rectangle problem, which he had been using for ten years. Erickson's original problem involves creating random rectangles with lengths and…

The present study investigates the statistical consequences of attribute misspecification in the rule space method for cognitively diagnostic measurement. The two types of attribute misspecifications examined in the present study are exclusion of an essential attribute (which affects problem-solving performance) and inclusion of a superfluous…

Adolescent identity and parent-adolescent conflict have each attracted considerable research interest. However, few studies have examined the important link between the two constructs. The present study examined the associations between adolescent identity processing styles and adolescent conflict resolution styles in the mother-adolescent dyad.…

In this study we explored the relation between private speech and task mastery by using the microgenetic method to examine the language and performance of 13 children aged 4 and 5 as they gained expertise with a spatial, multi-step planning task across 6 sessions. Seven of the 13 children's performances across these sessions were characterized by…

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

During creative problem-solving, designers frequently come across a variety of rich visual displays. While browsing for different sources of information, pictorial representations of existing concepts take prominence. However, once designers start generating new solution ideas to design problems, they often become too attached to some of the…

It is important to let students see the value of mathematics in design--and how mathematics lends perspective to problem solving. In this article, the author describes a water-service challenge which enables students to design a water utility system that uses surface runoff into an open reservoir as the potable water source. This challenge…

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

This paper presents a theoretical basis for cultivating engineering education as a complex system that will prepare students to think critically and make decisions with regard to poorly understood, ill-structured issues. Integral to this theoretical basis is a solution space construct developed and presented as a benchmark for evaluating…

Novice problem solvers are rather sensitive to surface problem features, and they often resort to trial and error formula matching rather than identifying an appropriate solution approach. These observations have been interpreted to imply that novices structure their knowledge according to surface features rather than according to problem type…

This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.

Action research in China during late 1970s and 1980s was influenced by positivist scientific research, believing the purpose of doing action research is to explore the general law of education. It was carried out through educational experimentations emphasizing the control of the experimental conditions. Starting from 1990s, action research in…

The focus of this special section is on the processes involved when solving information-based problems. Solving these problems requires from people that they are able to define the information problem, search and select usable and reliable sources and information and synthesise information into a coherent body of knowledge. An important aspect…

From the 1990s until 2017 the High Ability and Inquiry Research Group (HAIR) at McGill University in Montreal, received C$1.3M in research funds from Canadian, Quebec, and US agencies to support its research and graduate training in education and educational psychology. Their research encompassed two principal areas, Inquiry in Education and…

"The Complete Learning Disabilities Resource Guide" (formerly "The Complete Learning Disabilities Directory") has been a comprehensive and sought-after resource for professionals, families and individuals with learning disabilities since 1992. This twenty-first edition is the most comprehensive and current source of resources…