This article explores to what extent a problem-based learning unit in combination with cooperative learning and affectively oriented teaching methods facilitates intercultural learning. As part of the study, students reflected on critical incidents, which display misunderstandings or conflicts that arise as a result of cultural differences. In…

Language may ordinarily account for difficulties in solving word problems and this is particularly true if mathematical word problems are taught in a language other than one's native language. Research into cognitive load may offer a clear theoretical framework when investigating word problems because memory, specifically working memory, plays a…

Fox, Ericsson, and Best's (2011) thoughtful justification of the use of think-aloud protocols for revealing the stream of consciousness comes on the centennial of the death of William James, history's greatest practitioner and advocate of introspection. This confluence naturally invites speculation about how James might have responded to the…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

Complex problem solving is often an integration of perceptual processing and deliberate planning. But what balances these two processes, and how do novices differ from experts? We investigate the interplay between these two in the game of SET. This article investigates how people combine bottom-up visual processes and top-down planning to succeed…

Previous studies found that performance on the remote associates test (RAT) improves after a period of incubation and that increased alpha brain waves over the right posterior brain predict the emergence of RAT insight solutions. We report an experiment that tested whether increased alpha brain waves during incubation improve RAT performance.…

The title is that of a course with the same name, designed for teachers of mathematics. The rational for a course specifically on geometry was that "many of those currently teaching mathematics in school had little geometrical education". Teachers on the course experience geometry through problem solving, and learning to pose geometrical problems.…

We investigated examinees' cognitive processes while they solved selected items from the Multistate Bar Exam (MBE), a high-stakes professional certification examination. We focused on ascertaining those mental processes most frequently used by examinees, and the most common types of errors in their thinking. We compared the relationships between…

The purpose of this study was to explore effective ways to design guided practices within a web-based mathematics problem solving tutorial. Specifically, this study examined student learning outcome differences between two support designs (e.g. adaptively faded and fixed). In the adaptively faded design, students were presented with problems in…

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

Critical thinking, problem solving, the use of tools, and the ability to consume and analyze information are important skills for the 21st century workforce. This article presents a qualitative case study that follows five undergraduate biology majors in a computer science course (CS0). This CS0 course teaches programming within a data-driven…

Students start to memorize arithmetic facts from early elementary school mathematics activities. Their fluency or lack of fluency with these facts could affect their efforts as they carry out mental calculations as adults. This study investigated participants' levels of brain activation and possible reasons for these levels as they solved…

Given the growing popularity of digital games as a form of entertainment, educators are interested in exploring using digital games as a tool to facilitate learning. In this study, we examine game-based learning by describing a learning environment that combines game elements, play, and authenticity in the real world for the purpose of engaging…

Students in this post-industrial technological age require opportunities for the acquisition of new skills, especially in the marketplace of innovation. A pedagogical strategy that is becoming more and more popular within social studies classrooms is the use of computer and video games as enhancements to everyday lesson plans. Computer/video games…

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…